Understanding Quotes (527 quotes)
...That day in the account of creation, or those days that are numbers according to its recurrence, are beyond the experience and knowledge of us mortal earthbound men. And if we are able to make any effort towards an understanding of those days, we ought not to rush forward with an ill considered opinion, as if no other reasonable and plausible interpretation could be offered.
…we are all inclined to ... direct our inquiry not by the matter itself, but by the views of our opponents; and, even when interrogating oneself, one pushes the inquiry only to the point at which one can no longer offer any opposition. Hence a good inquirer will be one who is ready in bringing forward the objections proper to the genus, and that he will be when he has gained an understanding of the differences.
‘I was reading an article about “Mathematics”. Perfectly pure mathematics. My own knowledge of mathematics stops at “twelve times twelve,” but I enjoyed that article immensely. I didn’t understand a word of it; but facts, or what a man believes to be facts, are always delightful. That mathematical fellow believed in his facts. So do I. Get your facts first, and’—the voice dies away to an almost inaudible drone—’then you can distort ‘em as much as you please.’
[About research with big particle accelerators such as the Large Hadron Collider.] I think the primary justification for this sort of science that we do is fundamental human curiosity. ... It's true, of course, that every previous generation that's made some breakthrough in understanding nature has seen those discoveries translated into new technologies, new possibilities for the human race. That may well happen with the Higgs boson. Quite frankly, at the moment I don't see how you can use the Higgs boson for anything useful.
[An appealing problem is] a combination of being fairly concrete—so one can understand concretely examples—and also connecting with a lot of other ideas. For example, you see the analysis in a minimal surface equation, but then you also realize it has connections with other geometric questions that are not just analysis. I am definitely very attracted to the idea that there are a lot of different facets in mathematics and seeing the connections.
[Boundless curiosity.] That’s what being alive is about. I mean, it’s the fun of it all, making sense of it, understanding it. There’s a great pleasure in knowing why trees shed their leaves in winter. Everybody knows they do, but why? If you lose that, then you’ve lost pleasure.
[Learning is] the actual process of broadening yourself, of knowing there’s a little extra facet of the universe you know about and can think about and can understand. It seems to me that when it’s time to die, and that will come to all of us, there’ll be a certain pleasure in thinking that you had utilized your life well, that you had learned as much as you could, gathered in as much as possible of the universe, and enjoyed it. I mean, there’s only this universe and only this one lifetime to try to grasp it. And, while it is inconceivable that anyone can grasp more than a tiny portion of it, at least do that much. What a tragedy to just pass through and get nothing out of it.
[Misquotation; not by Einstein.] You do not really understand something unless you can explain it to your grandmother.
[On the practical applications of particle physics research with the Large Hadron Collider.] Sometimes the public says, “What's in it for Numero Uno? Am I going to get better television reception? Am I going to get better Internet reception?” Well, in some sense, yeah. … All the wonders of quantum physics were learned basically from looking at atom-smasher technology. … But let me let you in on a secret: We physicists are not driven to do this because of better color television. … That's a spin-off. We do this because we want to understand our role and our place in the universe.
[Public cynicism towards professional expertise is] entirely wrong, and it’s the road back to the cave. The way we got out of the caves and into modern civilisation is through the process of understanding and thinking. Those things were not done by gut instinct. Being an expert does not mean that you are someone with a vested interest in something; it means you spend your life studying something. You’re not necessarily right–but you’re more likely to be right than someone who’s not spent their life studying it.
[Richard Feynman] would be standing in front of the hall smiling at us all as we came in, his fingers tapping out a complicated rhythm on the black top of the demonstration bench that crossed the front of the lecture hall. As latecomers took their seats, he picked up the chalk and began spinning it rapidly through his fingers in a manner of a professional gambler playing with a poker chip, still smiling happily as if at some secret joke. And then—still smiling—he talked to us about physics, his diagrams and equations helping us to share his understanding. It was no secret joke that brought the smile and the sparkle in his eye, it was physics. The joy of physics!
[Scientists] define these [terms] in tight phrases which convey a meaning only to those who already understand it.
[The error in the teaching of mathematics is that] mathematics is expected either to be immediately attractive to students on its own merits or to be accepted by students solely on the basis of the teacher’s assurance that it will be helpful in later life. [And yet,] mathematlcs is the key to understanding and mastering our physical, social and biological worlds.
[There] are cases where there is no dishonesty involved but where people are tricked into false results by a lack of understanding about what human beings can do to themselves in the way of being led astray by subjective effects, wishful thinking or threshold interactions. These are examples of pathological science. These are things that attracted a great deal of attention. Usually hundreds of papers have been published upon them. Sometimes they have lasted for fifteen or twenty years and then they gradually die away.
[Coining the term “pathological science” for the self-deceiving application of science to a phenomenon that doesn't exist.]
[Coining the term “pathological science” for the self-deceiving application of science to a phenomenon that doesn't exist.]
[Understanding] dispels superstition, and it gives you a feeling of mastery which you can’t have any other way.
[W]hen Galileo discovered he could use the tools of mathematics and mechanics to understand the motion of celestial bodies, he felt, in the words of one imminent researcher, that he had learned the language in which God recreated the universe. Today we are learning the language in which God created life. We are gaining ever more awe for the complexity, the beauty, the wonder of God's most devine and sacred gift.
δος μοι που στω και κινω την γην — Dos moi pou sto kai kino taen gaen (in epigram form, as given by Pappus, classical Greek).
δος μοι πα στω και τα γαν κινάσω — Dos moi pa sto kai tan gan kinaso (Doric Greek).
Give me a place to stand on and I can move the Earth.
About four centuries before Pappas, but about three centuries after Archimedes lived, Plutarch had written of Archimedes' understanding of the lever:
Archimedes, a kinsman and friend of King Hiero, wrote to him that with a given force, it was possible to move any given weight; and emboldened, as it is said, by the strength of the proof, he asserted that, if there were another world and he could go to it, he would move this one.
A commonly-seen expanded variation of the aphorism is:
Give me a lever long enough and a place to stand, and I can move the earth.
δος μοι πα στω και τα γαν κινάσω — Dos moi pa sto kai tan gan kinaso (Doric Greek).
Give me a place to stand on and I can move the Earth.
About four centuries before Pappas, but about three centuries after Archimedes lived, Plutarch had written of Archimedes' understanding of the lever:
Archimedes, a kinsman and friend of King Hiero, wrote to him that with a given force, it was possible to move any given weight; and emboldened, as it is said, by the strength of the proof, he asserted that, if there were another world and he could go to it, he would move this one.
A commonly-seen expanded variation of the aphorism is:
Give me a lever long enough and a place to stand, and I can move the earth.
Der Schlussel zur Erkenntnis vom Wesen des bewussten Seelenlebens liegt in der Region des Unbewusstseins.
The key to the understanding of the character of the conscious lies in the region of the unconscious.
The key to the understanding of the character of the conscious lies in the region of the unconscious.
Dicere enim bene nemo potest, nisi qui prudenter intelligit.
No one can speak well, unless he thoroughly understands his subject.
No one can speak well, unless he thoroughly understands his subject.
Enlightenment is man’s emergence from his self-incurred immaturity. Immaturity is the inability to use one's own understanding without the guidance of another. This immaturity is self-incurred if its cause is not lack of understanding, but lack of resolution and courage to use it without the guidance of another. The motto of enlightenment is therefore: Sapere aude! Have courage to use your own understanding!
Les hommes ne sont pas faits pour savoir; les hommes ne sont pas faits pour comprendre … et nos illusions croissent avec nos connaissances.
Men are not created to know, men are not created to understand … and our illusions increase with our knowledge.
Men are not created to know, men are not created to understand … and our illusions increase with our knowledge.
Neumann, to a physicist seeking help with a difficult problem: Simple. This can be solved by using the method of characteristics.
Physicist: I'm afraid I don’t understand the method of characteristics.
Neumann: In mathematics you don't understand things. You just get used to them.
Physicist: I'm afraid I don’t understand the method of characteristics.
Neumann: In mathematics you don't understand things. You just get used to them.
To Wheeler's comment, If you haven't found something strange during the day, it hasn't been much of a day, a student responded, I can't believe that space is that crummy. Wheeler replied: To disagree leads to study, to study leads to understanding, to understand is to appreciate, to appreciate is to love. So maybe I'll end up loving your theory.
~~[Misattributed]~~ If the human mind were simple enough to understand, we’d be too simple to understand it.
— Pat Bahn
A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement.
A central lesson of science is that to understand complex issues (or even simple ones), we must try to free our minds of dogma and to guarantee the freedom to publish, to contradict, and to experiment. Arguments from authority are unacceptable.
A designer must always think about the unfortunate production engineer who will have to manufacture what you have designed; try to understand his problems.
A troubling question for those of us committed to the widest application of intelligence in the study and solution of the problems of men is whether a general understanding of the social sciences will be possible much longer. Many significant areas of these disciplines have already been removed by the advances of the past two decades beyond the reach of anyone who does not know mathematics; and the man of letters is increasingly finding, to his dismay, that the study of mankind proper is passing from his hands to those of technicians and specialists. The aesthetic effect is admittedly bad: we have given up the belletristic “essay on man” for the barbarisms of a technical vocabulary, or at best the forbidding elegance of mathematical syntax.
A visitor to Niels Bohr's country cottage, noticing a horseshoe hanging on the wall, teasing the eminent scientist about this ancient superstition. “Can it be true that you, of all people, believe it will bring you luck?'
'Of course not,' replied Bohr, 'but I understand it brings you luck whether you believe it or not.'”
'Of course not,' replied Bohr, 'but I understand it brings you luck whether you believe it or not.'”
According to Democritus, atoms had lost the qualities like colour, taste, etc., they only occupied space, but geometrical assertions about atoms were admissible and required no further analysis. In modern physics, atoms lose this last property, they possess geometrical qualities in no higher degree than colour, taste, etc. The atom of modern physics can only be symbolized by a partial differential equation in an abstract multidimensional space. Only the experiment of an observer forces the atom to indicate a position, a colour and a quantity of heat. All the qualities of the atom of modern physics are derived, it has no immediate and direct physical properties at all, i.e. every type of visual conception we might wish to design is, eo ipso, faulty. An understanding of 'the first order' is, I would almost say by definition, impossible for the world of atoms.
After the discovery of spectral analysis no one trained in physics could doubt the problem of the atom would be solved when physicists had learned to understand the language of spectra. So manifold was the enormous amount of material that has been accumulated in sixty years of spectroscopic research that it seemed at first beyond the possibility of disentanglement. An almost greater enlightenment has resulted from the seven years of Röntgen spectroscopy, inasmuch as it has attacked the problem of the atom at its very root, and illuminates the interior. What we are nowadays hearing of the language of spectra is a true 'music of the spheres' in order and harmony that becomes ever more perfect in spite of the manifold variety. The theory of spectral lines will bear the name of Bohr for all time. But yet another name will be permanently associated with it, that of Planck. All integral laws of spectral lines and of atomic theory spring originally from the quantum theory. It is the mysterious organon on which Nature plays her music of the spectra, and according to the rhythm of which she regulates the structure of the atoms and nuclei.
Alcmaeon was the first to define the difference between man and animals, saying that man differs from the latter in the fact that he alone has the power of understanding.
All knowledge and understanding of the Universe was no more than playing with stones and shells on the seashore of the vast imponderable ocean of truth.
All knowledge resolves itself into probability. ... In every judgment, which we can form concerning probability, as well as concerning knowledge, we ought always to correct the first judgment deriv’d from the nature of the object, by another judgment, deriv’d from the nature of the understanding.
All living organisms are but leaves on the same tree of life. The various functions of plants and animals and their specialized organs are manifestations of the same living matter. This adapts itself to different jobs and circumstances, but operates on the same basic principles. Muscle contraction is only one of these adaptations. In principle it would not matter whether we studied nerve, kidney or muscle to understand the basic principles of life. In practice, however, it matters a great deal.
All Nature is but Art, unknown to thee;
All Chance, Direction, which thou canst not see;
All Discord, Harmony, not understood;
All partial Evil, universal Good:
And, spite of Pride, in erring Reason’s spite,
One truth is clear, “Whatever IS, is RIGHT.”
All Chance, Direction, which thou canst not see;
All Discord, Harmony, not understood;
All partial Evil, universal Good:
And, spite of Pride, in erring Reason’s spite,
One truth is clear, “Whatever IS, is RIGHT.”
All of our experience indicates that life can manifest itself only in a concrete form, and that it is bound to certain substantial loci. These loci are cells and cell formations. But we are far from seeking the last and highest level of understanding in the morphology of these loci of life. Anatomy does not exclude physiology, but physiology certainly presupposes anatomy. The phenomena that the physiologist investigates occur in special organs with quite characteristic anatomical arrangements; the various morphological parts disclosed by the anatomist are the bearers of properties or, if you will, of forces probed by the physiologist; when the physiologist has established a law, whether through physical or chemical investigation, the anatomist can still proudly state: This is the structure in which the law becomes manifest.
All that science can achieve is a perfect knowledge and a perfect understanding of the action of natural and moral forces.
All that stuff I was taught about evolution, embryology, Big Bang theory, all that is lies straight from the pit of hell. It’s lies to try to keep me and all the folks who are taught that from understanding that they need a savior.
[Revealing his anti-science views, contrary to the qualifications needed to make important public policy on matters of science.]
[Revealing his anti-science views, contrary to the qualifications needed to make important public policy on matters of science.]
All the modern higher mathematics is based on a calculus of operations, on laws of thought. All mathematics, from the first, was so in reality; but the evolvers of the modern higher calculus have known that it is so. Therefore elementary teachers who, at the present day, persist in thinking about algebra and arithmetic as dealing with laws of number, and about geometry as dealing with laws of surface and solid content, are doing the best that in them lies to put their pupils on the wrong track for reaching in the future any true understanding of the higher algebras. Algebras deal not with laws of number, but with such laws of the human thinking machinery as have been discovered in the course of investigations on numbers. Plane geometry deals with such laws of thought as were discovered by men intent on finding out how to measure surface; and solid geometry with such additional laws of thought as were discovered when men began to extend geometry into three dimensions.
All the real true knowledge we have of Nature is intirely experimental, insomuch that, how strange soever the assertion seems, we may lay this down as the first fundamental unerring rule in physics, That it is not within the compass of human understanding to assign a purely speculative reason for any one phaenomenon in nature.
All the scientist creates in a fact is the language in which he enunciates it. If he predicts a fact, he will employ this language, and for all those who can speak and understand it, his prediction is free from ambiguity. Moreover, this prediction once made, it evidently does not depend upon him whether it is fulfilled or not.
Almost all aspects of life are engineered at the molecular level, and without understanding molecules we can only have a very sketchy understanding of life itself.
Although a science fair can seem like a big “pain” it can help you understand important scientific principles, such as Newton’s First Law of Inertia, which states: “A body at rest will remain at rest until 8:45 p.m. the night before the science fair project is due, at which point the body will come rushing to the body’s parents, who are already in their pajamas, and shout, “I JUST REMEMBERED THE SCIENCE FAIR IS TOMORROW AND WE GOTTA GO TO THE STORE RIGHT NOW!”
An egg is a chemical process, but it is not a mere chemical process. It is one that is going places—even when, in our world of chance and contingency, it ends up in an omelet and not in a chicken. Though it surely be a chemical process, we cannot understand it adequately without knowing the kind of chicken it has the power to become.
An engineer [is] one of those people who make things work without even understanding how they function. … Today I would add: one of those people who are unable to make anything work,
but think they know why it doesn’t function!
An expert is a man who understands everything, and nothing else.
An informed appraisal of life absolutely require(s) a full understanding of life’s arena–the universe. … By deepening our understanding of the true nature of physical reality, we profoundly reconfigure our sense of ourselves and our experience of the universe.
An understanding of the natural world and what’s in it is a source of not only a great curiosity but great fulfilment.
And I believe there are many Species in Nature, which were never yet taken notice of by Man, and consequently of no use to him, which yet we are not to think were created in vain; but it’s likely … to partake of the overflowing Goodness of the Creator, and enjoy their own Beings. But though in this sense it be not true, that all things were made for Man; yet thus far it is, that all the Creatures in the World may be some way or other useful to us, at least to exercise our Wits and Understandings, in considering and contemplating of them, and so afford us Subject of Admiring and Glorifying their and our Maker. Seeing them, we do believe and assert that all things were in some sense made for us, we are thereby obliged to make use of them for those purposes for which they serve us, else we frustrate this End of their Creation.
— John Ray
And yet I think that the Full House model does teach us to treasure variety for its own sake–for tough reasons of evolutionary theory and nature’s ontology, and not from a lamentable failure of thought that accepts all beliefs on the absurd rationale that disagreement must imply disrespect. Excellence is a range of differences, not a spot. Each location on the range can be occupied by an excellent or an inadequate representative– and we must struggle for excellence at each of these varied locations. In a society driven, of ten unconsciously, to impose a uniform mediocrity upon a former richness of excellence–where McDonald’s drives out the local diner, and the mega-Stop & Shop eliminates the corner Mom and Pop–an understanding and defense of full ranges as natural reality might help to stem the tide and preserve the rich raw material of any evolving system: variation itself.
Any man who is intelligent must, on considering that health is of the utmost value to human beings, have the personal understanding necessary to help himself in diseases, and be able to understand and to judge what physicians say and what they administer to his body, being versed in each of these matters to a degree reasonable for a layman.
Anyone who is not shocked by the quantum theory has not understood it. [Attributed.]
Archaeology gives a sense of place. It grounds us within the landscape and every place is unique. … Archaeology can also give an understanding of where we come from.
Art and science work in quite different ways: agreed. But, bad as it may sound, I have to admit that I cannot get along as an artist without the use of one or two sciences. ... In my view, the great and complicated things that go on in the world cannot be adequately recognized by people who do not use every possible aid to understanding.
As children we all possess a natural, uninhibited curiosity, a hunger for explanation, which seems to die slowly as we age—suppressed, I suppose, by the high value we place on conformity and by the need not to appear ignorant.
It betokens a conviction that somehow science is innately incomprehensible. It precludes reaching deeper, thereby denying the profound truth that understanding enriches experience, that explanation vastly enhances the beauty of the natural world in the eye of the beholder.
It betokens a conviction that somehow science is innately incomprehensible. It precludes reaching deeper, thereby denying the profound truth that understanding enriches experience, that explanation vastly enhances the beauty of the natural world in the eye of the beholder.
As for the search for truth, I know from my own painful searching, with its many blind alleys, how hard it is to take a reliable step, be it ever so small, towards the understanding of that which is truly significant.
As we continue to improve our understanding of the basic science on which applications increasingly depend, material benefits of this and other kinds are secured for the future.
As, no matter what cunning system of checks we devise, we must in the end trust some one whom we do not check, but to whom we give unreserved confidence, so there is a point at which the understanding and mental processes must be taken as understood without further question or definition in words. And I should say that this point should be fixed pretty early in the discussion.
Asked in 1919 whether it was true that only three people in the world understood the theory of general relativity, [Eddington] allegedly replied: “Who's the third?”
Astronomy is older than physics. In fact, it got physics started by showing the beautiful simplicity of the motion of the stars and planets, the understanding of which was the beginning of physics. But the most remarkable discovery in all of astronomy is that the stars are made of atoms of the same kind as those on the earth.
Astronomy is perhaps the science whose discoveries owe least to chance, in which human understanding appears in its whole magnitude, and through which man can best learn how small he is.
At every major step physics has required, and frequently stimulated, the introduction of new mathematical tools and concepts. Our present understanding of the laws of physics, with their extreme precision and universality, is only possible in mathematical terms.
Before an experiment can be performed, it must be planned—the question to nature must be formulated before being posed. Before the result of a measurement can be used, it must be interpreted—nature's answer must be understood properly. These two tasks are those of the theorist, who finds himself always more and more dependent on the tools of abstract mathematics. Of course, this does not mean that the experimenter does not also engage in theoretical deliberations. The foremost classical example of a major achievement produced by such a division of labor is the creation of spectrum analysis by the joint efforts of Robert Bunsen, the experimenter, and Gustav Kirchoff, the theorist. Since then, spectrum analysis has been continually developing and bearing ever richer fruit.
Being well-informed about science is not the same thing as understanding science.
Bistromathics itself is simply a revolutionary new way of understanding the behavior of numbers. Just as Einstein observed that space was not an absolute but depended on the observer's movement in space, and that time was not an absolute, but depended on the observer's movement in time, so it is now realized that numbers are not absolute, but depend on the observer's movement in restaurants.
Books have always a secret influence on the understanding; we cannot at pleasure obliterate ideas; he that reads books of science, thogh without any fixed desire of improvement, will grow more knowing…
Both social and biosocial factors are necessary to interpret crosscultural studies, with the general proviso that one’s research interest determines which elements, in what combinations, are significant for the provision of understanding.
But by far the greatest hindrance and aberration of the human understanding proceeds from the dullness, incompetency, and deceptions of the senses; in that things which strike the sense outweigh things which do not immediately strike it, though they be more important. Hence it is that speculation commonly ceases where sight ceases; insomuch that of things invisible there is little or no observation.
But, but, but … if anybody says he can think about quantum theory without getting giddy it merely shows that he hasn’t understood the first thing about it!
By science, then, I understand the consideration of all subjects, whether of a pure or mixed nature, capable of being reduced to measurement and calculation. All things comprehended under the categories of space, time and number properly belong to our investigations; and all phenomena capable of being brought under the semblance of a law are legitimate objects of our inquiries.
By the year 2070 we cannot say, or it would be imbecile to do so, that any man alive could understand Shakespearean experience better than Shakespeare, whereas any decent eighteen-year-old student of physics will know more physics than Newton.
By this we may understand, there be two sorts of knowledge, whereof the one is nothing else but sense, or knowledge original (as I have said at the beginning of the second chapter), and remembrance of the same; the other is called science or knowledge of the truth of propositions, and how things are called, and is derived from understanding.
Chemical biodynamics, involving as it does, the fusion of many scientific disciplines, … [played a role] in the elucidation of the carbon cycle. It can be expected to take an increasingly important place in the understanding of the dynamics of living organisms on a molecular level.
Chemistry as a science is still in its infancy. I hold to my view because there is still so much beyond our understanding even in the simplest systems the chemist has cared to deal with.
Common sense … is to the judgment what genius is to the understanding.
Computers and rocket ships are examples of invention, not of understanding. … All that is needed to build machines is the knowledge that when one thing happens, another thing happens as a result. It’s an accumulation of simple patterns. A dog can learn patterns. There is no “why” in those examples. We don’t understand why electricity travels. We don’t know why light travels at a constant speed forever. All we can do is observe and record patterns.
Contrary to popular parlance, Darwin didn't discover evolution. He uncovered one (most would say the) essential mechanism by which it operates: natural selection. Even then, his brainstorm was incomplete until the Modern Synthesis of the early/mid-20th century when (among other things) the complementary role of genetic heredity was fully realized. Thousands upon thousands of studies have followed, providing millions of data points that support this understanding of how life on Earth has come to be as it is.
Cosmic evolution may teach us how the good and evil tendencies of man may have come about; but, in itself, it is incompetent to furnish any better reason why what we call good is preferable to what we call evil than we had before. Some day, I doubt not, we shall arrive at an understanding of the evolution of the aesthetic faculty; but all the understanding in the world will neither increase nor diminish the force of the intuition that this is beautiful and that is ugly.
Creation science has not entered the curriculum for a reason so simple and so basic that we often forget to mention it: because it is false, and because good teachers understand why it is false. What could be more destructive of that most fragile yet most precious commodity in our entire intellectual heritage—good teaching—than a bill forcing our honorable teachers to sully their sacred trust by granting equal treatment to a doctrine not only known to be false, but calculated to undermine any general understanding of science as an enterprise?.
Curiosity atrophies after childhood unless it is transferred to an intellectual plane. The research worker is usually a person whose curiosity is turned toward seeking explanations for phenomena that are not understood.
Data is not information, Information is not knowledge, Knowledge is not understanding, Understanding is not wisdom.
Data isn't information. ... Information, unlike data, is useful. While there’s a gulf between data and information, there’s a wide ocean between information and knowledge. What turns the gears in our brains isn't information, but ideas, inventions, and inspiration. Knowledge—not information—implies understanding. And beyond knowledge lies what we should be seeking: wisdom.
Despite its importance to navigation, fishing, oil and gas development, and maritime safety, our understanding of how the Gulf system works remains extremely limited.
During the half-century that has elapsed since the enunciation of the cell-theory by Schleiden and Schwann, in 1838-39, it has became ever more clearly apparent that the key to all ultimate biological problems must, in the last analysis, be sought in the cell. It was the cell-theory that first brought the structure of plants and animals under one point of view by revealing their common plan of organization. It was through the cell-theory that Kolliker and Remak opened the way to an understanding of the nature of embryological development, and the law of genetic continuity lying at the basis of inheritance. It was the cell-theory again which, in the hands of Virchaw and Max Schultze, inaugurated a new era in the history of physiology and pathology, by showing that all the various functions of the body, in health and in disease, are but the outward expression of cell-activities. And at a still later day it was through the cell-theory that Hertwig, Fol, Van Beneden, and Strasburger solved the long-standing riddle of the fertilization of the egg, and the mechanism of hereditary transmission. No other biological generalization, save only the theory of organic evolution, has brought so many apparently diverse phenomena under a common point of view or has accomplished more far the unification of knowledge. The cell-theory must therefore be placed beside the evolution-theory as one of the foundation stones of modern biology.
During the war years I worked on the development of radar and other radio systems for the R.A.F. and, though gaining much in engineering experience and in understanding people, rapidly forgot most of the physics I had learned.
Each thing in the world has names or unnamed relations to everything else. Relations are infinite in number and kind. To be is to be related. It is evident that the understanding of relations is a major concern of all men and women. Are relations a concern of mathematics? They are so much its concern that mathematics is sometimes defined to be the science of relations.
Early in my school career, I turned out to be an incorrigible disciplinary problem. I could understand what the teacher was saying as fast as she could say it, I found time hanging heavy, so I would occasionally talk to my neighbor. That was my great crime, I talked in school.
EDUCATION, n. That which discloses to the wise and disguises from the foolish their lack of understanding.
Error is often nourished by good sense. … The meaning is, that the powers of the understanding are frequently employed to defend favourite errors; and that a man of sense frequently fortifies himself in his prejudices, or in false opinions which he received without examination, by such arguments as would not have occurred to a fool.
Euclidean mathematics assumes the completeness and invariability of mathematical forms; these forms it describes with appropriate accuracy and enumerates their inherent and related properties with perfect clearness, order, and completeness, that is, Euclidean mathematics operates on forms after the manner that anatomy operates on the dead body and its members. On the other hand, the mathematics of variable magnitudes—function theory or analysis—considers mathematical forms in their genesis. By writing the equation of the parabola, we express its law of generation, the law according to which the variable point moves. The path, produced before the eyes of the student by a point moving in accordance to this law, is the parabola.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
If, then, Euclidean mathematics treats space and number forms after the manner in which anatomy treats the dead body, modern mathematics deals, as it were, with the living body, with growing and changing forms, and thus furnishes an insight, not only into nature as she is and appears, but also into nature as she generates and creates,—reveals her transition steps and in so doing creates a mind for and understanding of the laws of becoming. Thus modern mathematics bears the same relation to Euclidean mathematics that physiology or biology … bears to anatomy.
Even fairly good students, when they have obtained the solution of the problem and written down neatly the argument, shut their books and look for something else. Doing so, they miss an important and instructive phase of the work. ... A good teacher should understand and impress on his students the view that no problem whatever is completely exhausted.
Even for the physicist the description in plain language will be a criterion of the degree of understanding that has been reached.
Even those to whom Providence has allotted greater strength of understanding, can expect only to improve a single science. In every other part of learning, they must be content to follow opinions, which they are not able to examine; and, even in that which they claim as peculiarly their own, can seldom add more than some small particle of knowledge, to the hereditary stock devolved to them from ancient times, the collective labour of a thousand intellects.
Even though the realms of religion and science in themselves are clearly marked off from each other, nevertheless there exist between the two strong reciprocal relationships and dependencies. Though religion may be that which determines the goal, it has, nevertheless, learned from science, in the broadest sense, what means will contribute to the attainment of the goals it has set up. But science can only be created by those who are thoroughly imbued with the aspiration toward truth and understanding. This source of feeling, however, springs from the sphere of religion. To this there also belongs the faith in the possibility that the regulations valid for the world of existence are rational, that is, comprehensible to reason. I cannot conceive of a genuine scientist without that profound faith. The situation may be expressed by an image: science without religion is lame, religion without science is blind.
Even today a good many distinguished minds seem unable to accept or even to understand that from a source of noise natural selection alone and unaided could have drawn all the music of the biosphere. In effect natural selection operates upon the products of chance and can feed nowhere else; but it operates in a domain of very demanding conditions, and from this domain chance is barred. It is not to chance but to these conditions that eveloution owes its generally progressive cource, its successive conquests, and the impresssion it gives of a smooth and steady unfolding.
Every discovery, every enlargement of the understanding, begins as an imaginative preconception of what the truth might be. The imaginative preconception—a “hypothesis”—arises by a process as easy or as difficult to understand as any other creative act of mind; it is a brainwave, an inspired guess, a product of a blaze of insight. It comes anyway from within and cannot be achieved by the exercise of any known calculus of discovery.
Every natural scientist who thinks with any degree of consistency at all will, I think, come to the view that all those capacities that we understand by the phrase psychic activities (Seelenthiitigkeiten) are but functions of the brain substance; or, to express myself a bit crudely here, that thoughts stand in the same relation to the brain as gall does to the liver or urine to the kidneys. To assume a soul that makes use of the brain as an instrument with which it can work as it pleases is pure nonsense; we would then be forced to assume a special soul for every function of the body as well.
Every sentence I utter must be understood not as an affirmation but as a question.
[A caution he gives his students, to be wary of dogmatism.]
[A caution he gives his students, to be wary of dogmatism.]
Everywhere science is enriched by unscientific methods and unscientific results, ... the separation of science and non-science is not only artificial but also detrimental to the advancement of knowledge. If we want to understand nature, if we want to master our physical surroundings, then we must use all ideas, all methods, and not just a small selection of them.
Faced with a new mutation in an organism, or a fundamental change in its living conditions, the biologist is frequently in no position whatever to predict its future prospects. He has to wait and see. For instance, the hairy mammoth seems to have been an admirable animal, intelligent and well-accoutered. Now that it is extinct, we try to understand why it failed. I doubt that any biologist thinks he could have predicted that failure. Fitness and survival are by nature estimates of past performance.
Facts are to the mind the same thing as food to the body. On the due digestion of facts depends the strength and wisdom of the one, just as vigor and health depend on the other. The wisest in council, the ablest in debate, and the most agreeable in the commerce of life is that man who has assimilated to his understanding the greatest number of facts.
Failure is central to engineering. Every single calculation that an engineer makes is a failure calculation. Successful engineering is all about understanding how things break or fail.
Faraday, … by his untiring faithfulness in keeping his diary, contributes to our understanding the objects of his scientific research in magnetism, electricity and light, but he also makes us understand the scientist himself, as a living subject, the mind in action.
Fifty years from now if an understanding of man’s origins, his evolution, his history, his progress is not in the common place of the school books we shall not exist.
First, as concerns the success of teaching mathematics. No instruction in the high schools is as difficult as that of mathematics, since the large majority of students are at first decidedly disinclined to be harnessed into the rigid framework of logical conclusions. The interest of young people is won much more easily, if sense-objects are made the starting point and the transition to abstract formulation is brought about gradually. For this reason it is psychologically quite correct to follow this course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
Not less to be recommended is this course if we inquire into the essential purpose of mathematical instruction. Formerly it was too exclusively held that this purpose is to sharpen the understanding. Surely another important end is to implant in the student the conviction that correct thinking based on true premises secures mastery over the outer world. To accomplish this the outer world must receive its share of attention from the very beginning.
Doubtless this is true but there is a danger which needs pointing out. It is as in the case of language teaching where the modern tendency is to secure in addition to grammar also an understanding of the authors. The danger lies in grammar being completely set aside leaving the subject without its indispensable solid basis. Just so in Teaching of Mathematics it is possible to accumulate interesting applications to such an extent as to stunt the essential logical development. This should in no wise be permitted, for thus the kernel of the whole matter is lost. Therefore: We do want throughout a quickening of mathematical instruction by the introduction of applications, but we do not want that the pendulum, which in former decades may have inclined too much toward the abstract side, should now swing to the other extreme; we would rather pursue the proper middle course.
First, In showing in how to avoid attempting impossibilities. Second, In securing us from important mistakes in attempting what is, in itself possible, by means either inadequate or actually opposed to the end in view. Thirdly, In enabling us to accomplish our ends in the easiest, shortest, most economical, and most effectual manner. Fourth, In inducing us to attempt, and enabling us to accomplish, object which, but for such knowledge, we should never have thought of understanding.
On the ways that a knowledge of the order of nature can be of use.
On the ways that a knowledge of the order of nature can be of use.
Flower in the crannied wall,
I pluck you out of the crannies;—
I hold you here, root and all, in my hand,
Little flower—but if I could understand
What you are, root and all, and all in all,
I should know what God and man is.
I pluck you out of the crannies;—
I hold you here, root and all, in my hand,
Little flower—but if I could understand
What you are, root and all, and all in all,
I should know what God and man is.
For me and many scientists, the understanding of nature is based upon scientific investigations that add to humankind’s ever increasing fund of knowledge. The fund is ever changing as new generations of scientists add to, debate, and reinterpret the data.
For the holy Bible and the phenomena of nature proceed alike from the divine Word, the former as the dictate of the Holy Ghost and the latter as the observant executrix of God's commands. It is necessary for the Bible, in order to be accommodated to the understanding of every man, to speak many things which appear to differ from the absolute truth so far as the bare meaning of the words is concerned. But Nature, on the other hand, is inexorable and immutable; she never transgresses the laws imposed upon her, or cares a whit whether her abstruse reasons and methods of operation are understandable to men. For that reason it appears that nothing physical which sense-experience sets before our eyes, or which necessary demonstrations prove to us, ought to be called in question (much less condemned) upon the testimony of biblical passages which may have some different meaning beneath their words.
Formal thought, consciously recognized as such, is the means of all exact knowledge; and a correct understanding of the main formal sciences, Logic and Mathematics, is the proper and only safe foundation for a scientific education.
Fractal geometry will make you see everything differently. There is a danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpet, bricks, and much else besides. Never again will your interpretation of these things be quite the same.
Freeman’s gift? It’s cosmic. He is able to see more interconnections between more things than almost anybody. He sees the interrelationships, whether it’s in some microscopic physical process or in a big complicated machine like Orion. He has been, from the time he was in his teens, capable of understanding essentially anything that he’s interested in. He’s the most intelligent person I know.
Freudian psychoanalytical theory is a mythology that answers pretty well to Levi-Strauss's descriptions. It brings some kind of order into incoherence; it, too, hangs together, makes sense, leaves no loose ends, and is never (but never) at a loss for explanation. In a state of bewilderment it may therefore bring comfort and relief … give its subject a new and deeper understanding of his own condition and of the nature of his relationship to his fellow men. A mythical structure will be built up around him which makes sense and is believable-in, regardless of whether or not it is true.
From the point of view of the pure morphologist the recapitulation theory is an instrument of research enabling him to reconstruct probable lines of descent; from the standpoint of the student of development and heredity the fact of recapitulation is a difficult problem whose solution would perhaps give the key to a true understanding of the real nature of heredity.
Fullness of knowledge always means some understanding of the depths of our ignorance; and that is always conducive to humility and reverence.
Furious activity is no substitute for understanding.
Geography is … only a branch of statistics, a knowledge of which is necessary to the well-understanding of the history of nations, as well as their situations relative to each other.
Geometry may sometimes appear to take the lead of analysis, but in fact precedes it only as a servant goes before his master to clear the path and light him on his way. The interval between the two is as wide as between empiricism and science, as between the understanding and the reason, or as between the finite and the infinite.
God was always invented to explain mystery. God is always invented to explain those things that you do not understand. Now, when you finally discover how something works … you don't need him anymore. But … you leave him to create the universe because we haven't figured that out yet.
Good luck is science not yet classified; just as the supernatural is the natural not yet understood.
Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand… So Greek mathematics is ‘permanent’, more permanent even than Greek literature.
Guide to understanding a net.addict’s day:
Slow day: didn’t have much to do, so spent three hours on usenet.
Busy day: managed to work in three hours of usenet.
Bad day: barely squeezed in three hours of usenet.
Slow day: didn’t have much to do, so spent three hours on usenet.
Busy day: managed to work in three hours of usenet.
Bad day: barely squeezed in three hours of usenet.
He that borrows the aid of an equal understanding, doubles his own; he that uses that of a superior elevates his own to the stature of that he contemplates.
Heredity, to our understanding is not capable of giving to this illness (paraphilia) its characteristic form ... Heredity invents nothing, creates nothing anew; it has no imagination.
Historically, science has pursued a premise that Nature can be understood fully, its future predicted precisely, and its behavior controlled at will. However, emerging knowledge indicates that the nature of Earth and biological systems transcends the limits of science, questioning the premise of knowing, prediction, and control. This knowledge has led to the recognition that, for civilized human survival, technological society has to adapt to the constraints of these systems.
How indispensable to a correct study of Nature is a perception of her true meaning. The fact will one day flower out into a truth. The season will mature and fructify what the understanding had cultivated. Mere accumulators of facts—collectors of materials for the master-workmen—are like those plants growing in dark forests, which “put forth only leaves instead of blossoms.”
How is it that there are so many minds that are incapable of understanding mathematics? ... the skeleton of our understanding, ... and actually they are the majority. ... We have here a problem that is not easy of solution, but yet must engage the attention of all who wish to devote themselves to education.
I am never content until I have constructed a mechanical model of the subject I am studying. If I succeed in making one, I understand. Otherwise, I do not. [Attributed; source unverified.]
I am not a speed reader. I am a speed understander.
I am of the decided opinion, that mathematical instruction must have for its first aim a deep penetration and complete command of abstract mathematical theory together with a clear insight into the structure of the system, and doubt not that the instruction which accomplishes this is valuable and interesting even if it neglects practical applications. If the instruction sharpens the understanding, if it arouses the scientific interest, whether mathematical or philosophical, if finally it calls into life an esthetic feeling for the beauty of a scientific edifice, the instruction will take on an ethical value as well, provided that with the interest it awakens also the impulse toward scientific activity. I contend, therefore, that even without reference to its applications mathematics in the high schools has a value equal to that of the other subjects of instruction.
I believe scientists have a duty to share the excitement and pleasure of their work with the general public, and I enjoy the challenge of presenting difficult ideas in an understandable way.
I believe that only scientists can understand the universe. It is not so much that I have confidence in scientists being right, but that I have so much in nonscientists being wrong.
I can see him [Sylvester] now, with his white beard and few locks of gray hair, his forehead wrinkled o’er with thoughts, writing rapidly his figures and formulae on the board, sometimes explaining as he wrote, while we, his listeners, caught the reflected sounds from the board. But stop, something is not right, he pauses, his hand goes to his forehead to help his thought, he goes over the work again, emphasizes the leading points, and finally discovers his difficulty. Perhaps it is some error in his figures, perhaps an oversight in the reasoning. Sometimes, however, the difficulty is not elucidated, and then there is not much to the rest of the lecture. But at the next lecture we would hear of some new discovery that was the outcome of that difficulty, and of some article for the Journal, which he had begun. If a text-book had been taken up at the beginning, with the intention of following it, that text-book was most likely doomed to oblivion for the rest of the term, or until the class had been made listeners to every new thought and principle that had sprung from the laboratory of his mind, in consequence of that first difficulty. Other difficulties would soon appear, so that no text-book could last more than half of the term. In this way his class listened to almost all of the work that subsequently appeared in the Journal. It seemed to be the quality of his mind that he must adhere to one subject. He would think about it, talk about it to his class, and finally write about it for the Journal. The merest accident might start him, but once started, every moment, every thought was given to it, and, as much as possible, he read what others had done in the same direction; but this last seemed to be his real point; he could not read without finding difficulties in the way of understanding the author. Thus, often his own work reproduced what had been done by others, and he did not find it out until too late.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
A notable example of this is in his theory of cyclotomic functions, which he had reproduced in several foreign journals, only to find that he had been greatly anticipated by foreign authors. It was manifest, one of the critics said, that the learned professor had not read Rummer’s elementary results in the theory of ideal primes. Yet Professor Smith’s report on the theory of numbers, which contained a full synopsis of Kummer’s theory, was Professor Sylvester’s constant companion.
This weakness of Professor Sylvester, in not being able to read what others had done, is perhaps a concomitant of his peculiar genius. Other minds could pass over little difficulties and not be troubled by them, and so go on to a final understanding of the results of the author. But not so with him. A difficulty, however small, worried him, and he was sure to have difficulties until the subject had been worked over in his own way, to correspond with his own mode of thought. To read the work of others, meant therefore to him an almost independent development of it. Like the man whose pleasure in life is to pioneer the way for society into the forests, his rugged mind could derive satisfaction only in hewing out its own paths; and only when his efforts brought him into the uncleared fields of mathematics did he find his place in the Universe.
I cannot separate land and sea: to me they interfinger like a pattern in a moss agate, positive and negative shapes irrevocably interlocked. My knowledge of this peninsula depends on that understanding: of underwater canyons that are continuations of the land, of the shell fossils far inland that measure continuations of the sea in eons past.
I cannot think of a single field in biology or medicine in which we can claim genuine understanding, and it seems to me the more we learn about living creatures, especially ourselves, the stranger life becomes.
I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.
I consider then, that generally speaking, to render a reason of an effect or Phaenomenon, is to deduce It from something else in Nature more known than it self, and that consequently there may be divers kinds of Degrees of Explication of the same thing. For although such Explications be the most satisfactory to the Understanding, wherein ’tis shewn how the effect is produc’d by the more primitive and Catholick Affection of Matter, namely bulk, shape and motion, yet are not these Explications to be despis’d, wherein particular effects are deduc’d from the more obvious and familiar Qualities or States of Bodies, … For in the search after Natural Causes, every new measure of Discovery does both instinct and gratifie the Understanding.
I did some very technical work in partial differential equations, made an unsuccessful pass at shock waves, worked in scale invariant variational problems, made a poor stab at three manifold topology, learned gauge field theory and then some about applications to four manifolds, and have recently been working in equations with algebraic infinite symmetries. I find that I am bored with anything I understand. My excuse is that I am too poor an expositor to want to spend time on formal matters.
I didn’t arrive at my understanding of the fundamental laws of the universe through my rational mind.
I do believe that a scientist is a freelance personality. We’re driven by an impulse which is one of curiosity, which is one of the basic instincts that a man has. So we are … driven … not by success, but by a sort of passion, namely the desire of understanding better, to possess, if you like, a bigger part of the truth. I do believe that science, for me, is very close to art.
I do not believe that a real understanding of the nature of elementary particles can ever be achieved without a simultaneous deeper understanding of the nature of spacetime itself.
I do not think it is possible really to understand the successes of science without understanding how hard it is—how easy it is to be led astray, how difficult it is to know at any time what is the next thing to be done.
I do not understand modern physics at all, but my colleagues who know a lot about the physics of very small things, like the particles in atoms, or very large things, like the universe, seem to be running into one queerness after another, from puzzle to puzzle.
I esteem his understanding and subtlety highly, but I consider that they have been put to ill use in the greater part of his work, where the author studies things of little use or when he builds on the improbable principle of attraction.
Writing about Newton's Principia. Huygens had some time earlier indicated he did not believe the theory of universal gravitation, saying it 'appears to me absurd.'
Writing about Newton's Principia. Huygens had some time earlier indicated he did not believe the theory of universal gravitation, saying it 'appears to me absurd.'
I have always found small mammals enough like ourselves to feel that I could understand what their lives would be like, and yet different enough to make it a sort of adventure and exploration to see what they were doing.
I have always tried to fit knowledge that I acquired into my understanding of the world. … When something comes along that I don’t understand, that I can’t fit in, that bothers me, I think about it, mull over it, and perhaps ultimately do some work with it. That’s perhaps the reason that I’ve been able to make discoveries in molecular biology.
I have before mentioned mathematics, wherein algebra gives new helps and views to the understanding. If I propose these it is not to make every man a thorough mathematician or deep algebraist; but yet I think the study of them is of infinite use even to grown men; first by experimentally convincing them, that to make anyone reason well, it is not enough to have parts wherewith he is satisfied, and that serve him well enough in his ordinary course. A man in those studies will see, that however good he may think his understanding, yet in many things, and those very visible, it may fail him. This would take off that presumption that most men have of themselves in this part; and they would not be so apt to think their minds wanted no helps to enlarge them, that there could be nothing added to the acuteness and penetration of their understanding.
I have found you an argument: but I am not obliged to find you an understanding.
I have never really had dreams to fulfil…. You just want to go on looking at these ecosystems and trying to understand them and they are all fascinating. To achieve a dream suggests snatching a prize from the top of a tree and running off with it, and that’s the end of it. It isn’t like that. … What you are trying to achieve is understanding and you don’t do that just by chasing dreams.
I have tried to read philosophers of all ages and have found many illuminating ideas but no steady progress toward deeper knowledge and understanding. Science, however, gives me the feeling of steady progress: I am convinced that theoretical physics is actual philosophy. It has revolutionized fundamental concepts, e.g., about space and time (relativity), about causality (quantum theory), and about substance and matter (atomistics), and it has taught us new methods of thinking (complementarity) which are applicable far beyond physics.
— Max Born
I know Teddy Kennedy had fun at the Democratic convention when he said that I said that trees and vegetation caused 80 percent of the air pollution in this country. ... Well, now he was a little wrong about what I said. I didn't say 80 percent. I said 92 percent—93 percent, pardon me. And I didn’t say air pollution, I said oxides of nitrogen. Growing and decaying vegetation in this land are responsible for 93 percent of the oxides of nitrogen. ... If we are totally successful and can eliminate all the manmade oxides of nitrogen, we’ll still have 93 percent as much as we have in the air today.
[Reagan reconfirming his own pathetic lack of understanding of air pollutants.]
[Reagan reconfirming his own pathetic lack of understanding of air pollutants.]
I like to think that when Medawar and his colleagues showed that immunological tolerance could be produced experimentally the new immunology was born. This is a science which to me has far greater potentialities both for practical use in medicine and for the better understanding of living process than the classical immunochemistry which it is incorporating and superseding.
I never said a word against eminent men of science. What I complain of is a vague popular philosophy which supposes itself to be scientific when it is really nothing but a sort of new religion and an uncommonly nasty one. When people talked about the fall of man, they knew they were talking about a mystery, a thing they didn’t understand. Now they talk about the survival of the fittest: they think they do understand it, whereas they have not merely no notion, they have an elaborately false notion of what the words mean.
I often use the analogy of a chess game: one can learn all the rules of chess, but one doesn’t know how to play well…. The present situation in physics is as if we know chess, but we don’t know one or two rules. But in this part of the board where things are in operation, those one or two rules are not operating much and we can get along pretty well without understanding those rules. That’s the way it is, I would say, regarding the phenomena of life, consciousness and so forth.
I returned and saw under the sun that the race is not to the swift, nor the battle to the strong, neither yet bread to the wise, nor yet riches to men of understanding, nor yet favour to men of skill; but time and chance happeneth to them all.
— Bible
I shall explain a System of the World differing in many particulars from any yet known, answering in all things to the common Rules of Mechanical Motions: This depends upon three Suppositions. First, That all Cœlestial Bodies whatsoever, have an attraction or gravitating power towards their own Centers, whereby they attract not only their own parts, and keep them from flying from them, as we may observe the Earth to do, but that they do also attract all the other Cœlestial bodies that are within the sphere of their activity; and consequently that not only the Sun and Moon have an influence upon the body and motion the Earth, and the Earth upon them, but that Mercury also Venus, Mars, Saturn and Jupiter by their attractive powers, have a considerable influence upon its motion in the same manner the corresponding attractive power of the Earth hath a considerable influence upon every one of their motions also. The second supposition is this, That all bodies whatsoever that are put into a direct and simple motion, will continue to move forward in a streight line, till they are by some other effectual powers deflected and bent into a Motion, describing a Circle, Ellipse, or some other more compounded Curve Line. The third supposition is, That these attractive powers are so much the more powerful in operating, by how much the nearer the body wrought upon is to their own Centers. Now what these several degrees are I have not yet experimentally verified; but it is a notion, which if fully prosecuted as it ought to be, will mightily assist the Astronomer to reduce all the Cœlestial Motions to a certain rule, which I doubt will never be done true without it. He that understands the nature of the Circular Pendulum and Circular Motion, will easily understand the whole ground of this Principle, and will know where to find direction in Nature for the true stating thereof. This I only hint at present to such as have ability and opportunity of prosecuting this Inquiry, and are not wanting of Industry for observing and calculating, wishing heartily such may be found, having myself many other things in hand which I would first compleat and therefore cannot so well attend it. But this I durst promise the Undertaker, that he will find all the Great Motions of the World to be influenced by this Principle, and that the true understanding thereof will be the true perfection of Astronomy.
I suppose that I tend to be optimistic about the future of physics. And nothing makes me more optimistic than the discovery of broken symmetries. In the seventh book of the Republic, Plato describes prisoners who are chained in a cave and can see only shadows that things outside cast on the cave wall. When released from the cave at first their eyes hurt, and for a while they think that the shadows they saw in the cave are more real than the objects they now see. But eventually their vision clears, and they can understand how beautiful the real world is. We are in such a cave, imprisoned by the limitations on the sorts of experiments we can do. In particular, we can study matter only at relatively low temperatures, where symmetries are likely to be spontaneously broken, so that nature does not appear very simple or unified. We have not been able to get out of this cave, but by looking long and hard at the shadows on the cave wall, we can at least make out the shapes of symmetries, which though broken, are exact principles governing all phenomena, expressions of the beauty of the world outside.
I think that the unity we can seek lies really in two things. One is that the knowledge which comes to us at such a terrifyingly, inhumanly rapid rate has some order in it. We are allowed to forget a great deal, as well as to learn. This order is never adequate. The mass of ununderstood things, which cannot be summarized, or wholly ordered, always grows greater; but a great deal does get understood.
The second is simply this: we can have each other to dinner. We ourselves, and with each other by our converse, can create, not an architecture of global scope, but an immense, intricate network of intimacy, illumination, and understanding. Everything cannot be connected with everything in the world we live in. Everything can be connected with anything.
The second is simply this: we can have each other to dinner. We ourselves, and with each other by our converse, can create, not an architecture of global scope, but an immense, intricate network of intimacy, illumination, and understanding. Everything cannot be connected with everything in the world we live in. Everything can be connected with anything.
I think the next [21st] century will be the century of complexity. We have already discovered the basic laws that govern matter and understand all the normal situations. We don’t know how the laws fit together, and what happens under extreme conditions. But I expect we will find a complete unified theory sometime this century. The is no limit to the complexity that we can build using those basic laws.
[Answer to question: Some say that while the twentieth century was the century of physics, we are now entering the century of biology. What do you think of this?]
[Answer to question: Some say that while the twentieth century was the century of physics, we are now entering the century of biology. What do you think of this?]
I think we may picture those domains where understanding exists, whether in physics, chemistry, biology, psychology, economics or any other discipline as cultivated valleys in a formidably mountainous country. We may recognise in principle that we all inhabit the same world but in practice we do well to cultivate our own valleys, with an occasional assault on the more accessible foothills, rather than to build roads in a vain attempt at colonisation.
I wanted to be a scientist from my earliest school days. The crystallizing moment came when I first caught on that stars are mighty suns, and how staggeringly far away they must be to appear to us as mere points of light. I’m not sure I even knew the word science then, but I was gripped by the prospect of understanding how things work, of helping to uncover deep mysteries, of exploring new worlds.
I was fascinated by fractional distillation as a method while still a school-boy, and built in the cellar of my home, which was my combined workshop and laboratory, distillation columns, packed with coke of graded size, some five feet in height. They were made from coffee tins (obtained from the kitchen), with the bottoms removed and soldered together! Experience with them served me in good stead and by the time I graduated I had a good understanding of the problems of fractional distillation.
I was sitting writing at my textbook but the work did not progress; my thoughts were elsewhere. I turned my chair to the fire and dozed. Again the atoms were gambolling before my eyes. This time the smaller groups kept modestly in the background. My mental eye, rendered more acute by the repeated visions of the kind, could now distinguish larger structures of manifold confirmation: long rows, sometimes more closely fitted together all twining and twisting in snake like motion. But look! What was that? One of the snakes had seized hold of its own tail, and the form whirled mockingly before my eyes. As if by a flash of lightning I awoke; and this time also I spent the rest of the night in working out the rest of the hypothesis. Let us learn to dream, gentlemen, then perhaps we shall find the truth... But let us beware of publishing our dreams till they have been tested by waking understanding.
I would clarify that by ‘animal’ I understand a being that has feeling and that is capable of exercising life functions through a principle called soul; that the soul uses the body's organs, which are true machines, by virtue of its being the principal cause of the action of each of the machine's parts; and that although the placement that these parts have with respect to one another does scarcely anything else through the soul's mediation than what it does in pure machines, the entire machine nonetheless needs to be activated and guided by the soul in the same way as an organ, which, although capable of rendering different sounds through the placement of the parts of which it is composed, nonetheless never does so except through the guidance of the organist.
I would rather live in a world where my life is surrounded by mystery than live in a world so small that my mind could comprehend it.
I would teach the world that science is the best way to understand the world, and that for any set of observations, there is only one correct explanation. Also, science is value-free, as it explains the world as it is. Ethical issues arise only when science is applied to technology – from medicine to industry.
I've found out so much about electricity that I've reached the point where I understand nothing and can explain nothing.
[Describing his experiments with the Leyden jar.]
[Describing his experiments with the Leyden jar.]
If a lion could talk, we could not understand him.
If a single cell, under appropriate conditions, becomes a man in the space of a few years, there can surely be no difficulty in understanding how, under appropriate conditions, a cell may, in the course of untold millions of years, give origin to the human race.
If it were always necessary to reduce everything to intuitive knowledge, demonstration would often be insufferably prolix. This is why mathematicians have had the cleverness to divide the difficulties and to demonstrate separately the intervening propositions. And there is art also in this; for as the mediate truths (which are called lemmas, since they appear to be a digression) may be assigned in many ways, it is well, in order to aid the understanding and memory, to choose of them those which greatly shorten the process, and appear memorable and worthy in themselves of being demonstrated. But there is another obstacle, viz.: that it is not easy to demonstrate all the axioms, and to reduce demonstrations wholly to intuitive knowledge. And if we had chosen to wait for that, perhaps we should not yet have the science of geometry.
If Nicolaus Copernicus, the distinguished and incomparable master, in this work had not been deprived of exquisite and faultless instruments, he would have left us this science far more well-established. For he, if anybody, was outstanding and had the most perfect understanding of the geometrical and arithmetical requisites for building up this discipline. Nor was he in any respect inferior to Ptolemy; on the contrary, he surpassed him greatly in certain fields, particularly as far as the device of fitness and compendious harmony in hypotheses is concerned. And his apparently absurd opinion that the Earth revolves does not obstruct this estimate, because a circular motion designed to go on uniformly about another point than the very center of the circle, as actually found in the Ptolemaic hypotheses of all the planets except that of the Sun, offends against the very basic principles of our discipline in a far more absurd and intolerable way than does the attributing to the Earth one motion or another which, being a natural motion, turns out to be imperceptible. There does not at all arise from this assumption so many unsuitable consequences as most people think.
If one small and odd lineage of fishes had not evolved fins capable of bearing weight on land (though evolved for different reasons in lakes and seas,) terrestrial vertebrates would never have arisen. If a large extraterrestrial object—the ultimate random bolt from the blue—had not triggered the extinction of dinosaurs 65 million years ago, mammals would still be small creatures, confined to the nooks and crannies of a dinosaur's world, and incapable of evolving the larger size that brains big enough for self-consciousness require. If a small and tenuous population of protohumans had not survived a hundred slings and arrows of outrageous fortune (and potential extinction) on the savannas of Africa, then Homo sapiens would never have emerged to spread throughout the globe. We are glorious accidents of an unpredictable process with no drive to complexity, not the expected results of evolutionary principles that yearn to produce a creature capable of understanding the mode of its own necessary construction.
If physical science is dangerous, as I have said, it is dangerous because it necessarily ignores the idea of moral evil; but literature is open to the more grievous imputation of recognizing and understanding it too well.
If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.
If the brain were so simple
That we could understand it,
We would be so simple
That we couldn’t.
That we could understand it,
We would be so simple
That we couldn’t.
If the task of scientific methodology is to piece together an account of what scientists actually do, then the testimony of biologists should be heard with specially close attention. Biologists work very close to the frontier between bewilderment and understanding.
Biology is complex, messy and richly various, like real life; it travels faster nowadays than physics or chemistry (which is just as well, since it has so much farther to go), and it travels nearer to the ground. It should therefore give us a specially direct and immediate insight into science in the making.
Biology is complex, messy and richly various, like real life; it travels faster nowadays than physics or chemistry (which is just as well, since it has so much farther to go), and it travels nearer to the ground. It should therefore give us a specially direct and immediate insight into science in the making.
If the term education may be understood in so large a sense as to include all that belongs to the improvement of the mind, either by the acquisition of the knowledge of others or by increase of it through its own exertions, we learn by them what is the kind of education science offers to man. It teaches us to be neglectful of nothing — not to despise the small beginnings, for they precede of necessity all great things in the knowledge of science, either pure or applied.
If this seems complex, the reason is because Tao is both simple and complex. It is complex when we try to understand it, and simple when we allow ourselves to experience it.
If we are correct in understanding how evolution actually works, and provided we can survive the complications of war, environmental degradation, and possible contact with interstellar planetary travelers, we will look exactly the same as we do now. We won’t change at all. The species is now so widely dispersed that it is not going to evolve, except by gradualism.
If we do discover a complete unified theory, it should be in time understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists and just ordinary people, be able to take part in the discussion of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason—for then we would know the mind of God.
If we wish to imitate the physical sciences, we must not imitate them in their contemporary, most developed form; we must imitate them in their historical youth, when their state of development was comparable to our own at the present time. Otherwise we should behave like boys who try to copy the imposing manners of full-grown men without understanding their raison d’être, also without seeing that in development one cannot jump over intermediate and preliminary phases.
If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it.
If you want to understand human beings, there are plenty of people to go to besides psychologists.... Most of these people are incapable of communicating their knowledge, but those who can communicate it are novelists. They are good novelists precisely because they are good psychologists.
In 1906 I indulged my temper by hurling invectives at Neo-Darwinians in the following terms. “I really do not wish to be abusive [to Neo-Darwinians]; but when I think of these poor little dullards, with their precarious hold of just that corner of evolution that a blackbeetle can understand—with their retinue of twopenny-halfpenny Torquemadas wallowing in the infamies of the vivisector’s laboratory, and solemnly offering us as epoch-making discoveries their demonstrations that dogs get weaker and die if you give them no food; that intense pain makes mice sweat; and that if you cut off a dog’s leg the three-legged dog will have a four-legged puppy, I ask myself what spell has fallen on intelligent and humane men that they allow themselves to be imposed on by this rabble of dolts, blackguards, imposters, quacks, liars, and, worst of all, credulous conscientious fools.”
In a certain sense I made a living for five or six years out of that one star [υ Sagittarii] and it is still a fascinating, not understood, star. It’s the first star in which you could clearly demonstrate an enormous difference in chemical composition from the sun. It had almost no hydrogen. It was made largely of helium, and had much too much nitrogen and neon. It’s still a mystery in many ways … But it was the first star ever analysed that had a different composition, and I started that area of spectroscopy in the late thirties.
In a crystal we have the clear evidence of the existence of a formative life-principle, and though we cannot understand the life of a crystal, it is none the less a living being.
In every science certain things must be accepted as first principles if the subject matter is to be understood; and these first postulates rest upon faith.
In mathematics, … and in natural philosophy since mathematics was applied to it, we see the noblest instance of the force of the human mind, and of the sublime heights to which it may rise by cultivation. An acquaintance with such sciences naturally leads us to think well of our faculties, and to indulge sanguine expectations concerning the improvement of other parts of knowledge. To this I may add, that, as mathematical and physical truths are perfectly uninteresting in their consequences, the understanding readily yields its assent to the evidence which is presented to it; and in this way may be expected to acquire the habit of trusting to its own conclusions, which will contribute to fortify it against the weaknesses of scepticism, in the more interesting inquiries after moral truth in which it may afterwards engage.
In my understanding of God I start with certain firm beliefs. One is that the laws of nature are not broken. We do not, of course, know all these laws yet, but I believe that such laws exist. I do not, therefore, believe in the literal truth of some miracles which are featured in the Christian Scriptures, such as the Virgin Birth or water into wine. ... God works, I believe, within natural laws, and, according to natural laws, these things happen.
In my view, the proper attitude of a public-service broadcaster is that it should attempt to cover as broad as possible a spectrum of human interest and should measure success by the width of those views. There shouldn’t be all that large a number of gaps in the spectrum; and a major element in the spectrum is scientific understanding. The fact that it doesn’t necessarily get as big an audience as cookery is of no consequence.
In no subject is there a rule, compliance with which will lead to new knowledge or better understanding. Skilful observations, ingenious ideas, cunning tricks, daring suggestions, laborious calculations, all these may be required to advance a subject. Occasionally the conventional approach in a subject has to be studiously followed; on other occasions it has to be ruthlessly disregarded. Which of these methods, or in what order they should be employed is generally unpredictable. Analogies drawn from the history of science are frequently claimed to be a guide; but, as with forecasting the next game of roulette, the existence of the best analogy to the present is no guide whatever to the future. The most valuable lesson to be learnt from the history of scientific progress is how misleading and strangling such analogies have been, and how success has come to those who ignored them.
In order to translate a sentence from English into French two things are necessary. First, we must understand thoroughly the English sentence. Second, we must be familiar with the forms of expression peculiar to the French language. The situation is very similar when we attempt to express in mathematical symbols a condition proposed in words. First, we must understand thoroughly the condition. Second, we must be familiar with the forms of mathematical expression.
In our day grand generalizations have been reached. The theory of the origin of species is but one of them. Another, of still wider grasp and more radical significance, is the doctrine of the Conservation of Energy, the ultimate philosophical issues of which are as yet but dimly seem-that doctrine which “binds nature fast in fate” to an extent not hitherto recognized, exacting from every antecedent its equivalent consequent, and bringing vital as well as physical phenomena under the dominion of that law of causal connexion which, so far as the human understanding has yet pierced, asserts itself everywhere in nature.
In point of fact, no conclusive disproof of a theory can ever be produced; for it is always possible to say that the experimental results are not reliable or that the discrepancies which are asserted to exist between the experimental results and the theory are only apparent and that they will disappear with the advance of our understanding. If you insist on strict proof (or strict disproof) in the empirical sciences, you will never benefit from experience, and never learn from it how wrong you are.
In studying the fate of our forest king, we have thus far considered the action of purely natural causes only; but, unfortunately, man is in the woods, and waste and pure destruction are making rapid headway. If the importance of the forests were even vaguely understood, even from an economic standpoint, their preservation would call forth the most watchful attention of government
In the case of the Sun, we have a new understanding of the cosmological meaning of sacrifice. The Sun is, with each second, transforming four million tons of itself into light—giving itself over to become energy that we, with every meal, partake of. The Sun converts itself into a flow of energy that photosynthesis changes into plants that are consumed by animals. Humans have been feasting on the Sun’s energy stored in the form of wheat or maize or reindeer as each day the Sun dies as Sun and is reborn as the vitality of Earth. These solar flares are in fact the very power of the vast human enterprise. Every child of ours needs to learn the simple truth: she is the energy of the Sun. And we adults should organize things so her face shines with the same radiant joy.
In the company of friends, writers can discuss their books, economists the state of the economy, lawyers their latest cases, and businessmen their latest acquisitions, but mathematicians cannot discuss their mathematics at all. And the more profound their work, the less understandable it is.
In the first papers concerning the aetiology of tuberculosis I have already indicated the dangers arising from the spread of the bacilli-containing excretions of consumptives, and have urged moreover that prophylactic measures should be taken against the contagious disease. But my words have been unheeded. It was still too early, and because of this they still could not meet with full understanding. It shared the fate of so many similar cases in medicine, where a long time has also been necessary before old prejudices were overcome and the new facts were acknowledged to be correct by the physicians.
In the sick room, ten cents’ worth of human understanding equals ten dollars' worth of medical science.
In the summer after kindergarten, a friend introduced me to the joys of building plastic model airplanes and warships. By the fourth grade, I graduated to an erector set and spent many happy hours constructing devices of unknown purpose where the main design criterion was to maximize the number of moving parts and overall size. The living room rug was frequently littered with hundreds of metal “girders” and tiny nuts and bolts surrounding half-finished structures. An understanding mother allowed me to keep the projects going for days on end.
In this great celestial creation, the catastrophy of a world, such as ours, or even the total dissolution of a system of worlds, may possibly be no more to the great Author of Nature, than the most common accident in life with us, and in all probability such final and general Doomsdays may be as frequent there, as even Birthdays or mortality with us upon the earth. This idea has something so cheerful in it, that I know I can never look upon the stars without wondering why the whole world does not become astronomers; and that men endowed with sense and reason should neglect a science they are naturally so much interested in, and so capable of enlarging their understanding, as next to a demonstration must convince them of their immortality, and reconcile them to all those little difficulties incident to human nature, without the least anxiety. All this the vast apparent provision in the starry mansions seem to promise: What ought we then not to do, to preserve our natural birthright to it and to merit such inheritance, which alas we think created all to gratify alone a race of vain-glorious gigantic beings, while they are confined to this world, chained like so many atoms to a grain of sand.
Increased knowledge of heredity means increased power of control over the living thing, and as we come to understand more and more the architecture of the plant or animal we realize what can and what cannot be done towards modification or improvement.
Increasingly, our leaders must deal with dangers that threaten the entire world, where an understanding of those dangers and the possible solutions depend on a good grasp of science. The ozone layer, the greenhouse effect, acid rain, questions of diet and of heredity--all require scientific literacy. Can Americans choose the proper leaders and support the proper programs if they are scientifically illiterate?
Increasingly, our leaders must deal with dangers that threaten the entire world, where an understanding of those dangers and the possible solutions depends on a good grasp of science. The ozone layer, the greenhouse effect, acid rain, questions of diet and heredity. All require scientific literacy. Can Americans choose the proper leaders and support the proper programs if they themselves are scientifically illiterate? The whole premise of democracy is that it is safe to leave important questions to the court of public opinion—but is it safe to leave them to the court of public ignorance?
Infinities and indivisibles transcend our finite understanding, the former on account of their magnitude, the latter because of their smallness; Imagine what they are when combined.
Injustice or oppression in the next street...or any spot inhabited by men was a personal affront to Thomas Addis and his name, from its early alphabetical place, was conspicuous on lists of sponsors of scores of organizations fighting for democracy and against fascism. He worked on more committees than could reasonably have been expected of so busy a man... Tom Addis was happy to have a hand in bringing to the organization of society some of the logic of science and to further that understanding and to promote that democracy which are the only enduring foundations of human dignity.
Intelligence is an extremely subtle concept. It’s a kind of understanding that flourishes if it’s combined with a good memory, but exists anyway even in the absence of good memory. It’s the ability to draw consequences from causes, to make correct inferences, to foresee what might be the result, to work out logical problems, to be reasonable, rational, to have the ability to understand the solution from perhaps insufficient information. You know when a person is intelligent, but you can be easily fooled if you are not yourself intelligent.
Is it possible that a promiscuous Jumble of Printing Letters should often fall into a Method and Order, which should stamp on Paper a coherent Discourse; or that a blind fortuitous Concourse of Atoms, not guided by an Understanding Agent, should frequently constitute the Bodies of any Species of Animals.
Is what you are doing fun? Of course, physics is also fun—indeed it is an enjoyable way of life. One reason physics is fun is that each element of progress transforms an area of ignorance into knowledge, but it also creates, as a by-product, an amount of new and additional ignorance in excess of that which was reduced to understanding. Thus, the volume of delicious ignorance we produce is ever-expanding, like our exponentially exploding universe.
It appears unlikely that the role of the genes in development is to be understood so long as the genes are considered as dictatorial elements in the cellular economy. It is not enough to know what a gene does when it manifests itself. One must also know the mechanisms determining which of the many gene-controlled potentialities will be realized.
It feels unacceptable to many people even to think of having a cosmology based on science. … They see fanciful origin stories as spicing up the culture. … Aspects of many origin stories can enrich our understanding of the scientific picture, but they cannot take its place.
It follows from the supreme perfection of God, that in creating the universe has chosen the best possible plan, in which there is the greatest variety together with the greatest order; the best arranged ground, place, time; the most results produced in the most simple ways; the most of power, knowledge, happiness and goodness the creatures that the universe could permit. For since all the possibles in I understanding of God laid claim to existence in proportion to their perfections, the actual world, as the resultant of all these claims, must be the most perfect possible. And without this it would not be possible to give a reason why things have turned out so rather than otherwise.
It is easier to understand mankind in general than any individual man.
It is exceptional that one should be able to acquire the understanding of a process without having previously acquired a deep familiarity with running it, with using it, before one has assimilated it in an instinctive and empirical way. Thus any discussion of the nature of intellectual effort in any field is difficult, unless it presupposes an easy, routine familiarity with that field. In mathematics this limitation becomes very severe.
It is from this absolute indifference and tranquility of the mind, that mathematical speculations derive some of their most considerable advantages; because there is nothing to interest the imagination; because the judgment sits free and unbiased to examine the point. All proportions, every arrangement of quantity, is alike to the understanding, because the same truths result to it from all; from greater from lesser, from equality and inequality.
It is hard to think of fissionable materials when fashioned into bombs as being a source of happiness. However this may be, if with such destructive weapons men are to survive, they must grow rapidly in human greatness. A new level of human understanding is needed. The reward for using the atom’s power towards man’s welfare is great and sure. The punishment for its misuse would seem to be death and the destruction of the civilization that has been growing for a thousand years. These are the alternatives that atomic power, as the steel of Daedalus, presents to mankind. We are forced to grow to greater manhood.
It is imperative in the design process to have a full and complete understanding of how failure is being obviated in order to achieve success. Without fully appreciating how close to failing a new design is, its own designer may not fully understand how and why a design works. A new design may prove to be successful because it has a sufficiently large factor of safety (which, of course, has often rightly been called a “factor of ignorance”), but a design's true factor of safety can never be known if the ultimate failure mode is unknown. Thus the design that succeeds (ie, does not fail) can actually provide less reliable information about how or how not to extrapolate from that design than one that fails. It is this observation that has long motivated reflective designers to study failures even more assiduously than successes.
It is in moments of illness that we are compelled to recognize that we live not alone but chained to a creature of a different kingdom, whole worlds apart, who has no knowledge of us, and by whom it is impossible to make ourselves understood: our body.
It is in our genes to understand the universe if we can, to keep trying even if we cannot, and to be enchanted by the act of learning all the way.
It is indeed an Opinion strangely prevailing amongst Men, that Houses, Mountains, Rivers, and in a word all sensible Objects have an Existence Natural or Real, distinct from their being perceived by the Understanding. But with how great an Assurance and Acquiescence soever this Principle may be entertained in the World; yet whoever shall find in his Heart to call it in Question, may, if I mistake not, perceive it to involve a manifest Contradiction. For what are the forementioned Objects but the things we perceive by Sense, and what do we perceive besides our own Ideas or Sensations; and is it not plainly repugnant that anyone of these or any Combination of them should exist unperceived?
It is my intent to beget a good understanding between the chymists and the mechanical philosophers who have hitherto been too little acquainted with one another's learning.
It is my object, in the following work, to travel over ground which has as yet been little explored and to make my reader acquainted with a species of Remains, which, though absolutely necessary for understanding the history of the globe, have been hitherto almost uniformly neglected.
It is not an easy paper to follow, for the items that require retention throughout the analysis are many, and it is fatal to one's understanding to lose track of any of them. Mastery of this paper, however, can give one the strong feeling of being ableto master anything else [one] might have to wrestle within biology.
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931).
Describing the paper 'A Correlation of Cytological and Genetic Crossings-over in Zea mays' published by Barbara McClintock and her student Harriet Creighton in the Proceedings of the National Academy of Sciences (1931).
It is not enough to say that we cannot know or judge because all the information is not in. The process of gathering knowledge does not lead to knowing. A child's world spreads only a little beyond his understanding while that of a great scientist thrusts outward immeasurably. An answer is invariably the parent of a great family of new questions. So we draw worlds and fit them like tracings against the world about us, and crumple them when we find they do not fit and draw new ones.
It is not enough to teach man a specialty. Through it he may become a kind of useful machine, but not a harmoniously developed personality. It is essential that the student acquire an understanding of and a lively feeling for values. He must acquire a vivid sense of the beautiful and of the morally good. Otherwise he—with his specialized knowledge—more closely resembles a well-trained dog than a harmoniously developed person.
It is often claimed that knowledge multiplies so rapidly that nobody can follow it. I believe this is incorrect. At least in science it is not true. The main purpose of science is simplicity and as we understand more things, everything is becoming simpler. This, of course, goes contrary to what everyone accepts.
It is popular to believe that the age of the individual and, above all, of the free individual, is past in science. There are many administrators of science and a large component of the general population who believe that mass attacks can do anything, and even that ideas are obsolete. Behind this drive to the mass attack there are a number of strong psychological motives. Neither the public or the big administrator has too good an understanding of the inner continuity of science, but they both have seen its world-shaking consequences, and they are afraid of it. Both of them wish to decerebrate the scientist, even as the Byzantine State emasculated its civil servants. Moreover, the great administrator who is not sure of his own intellectual level can aggrandize himself only by cutting his scientific employees down to size.
It is structure that we look for whenever we try to understand anything. All science is built upon this search; we investigate how the cell is built of reticular material, cytoplasm, chromosomes; how crystals aggregate; how atoms are fastened together; how electrons constitute a chemical bond between atoms. We like to understand, and to explain, observed facts in terms of structure. A chemist who understands why a diamond has certain properties, or why nylon or hemoglobin have other properties, because of the different ways their atoms are arranged, may ask questions that a geologist would not think of formulating, unless he had been similarly trained in this way of thinking about the world.
It is the individual only who is timeless. Societies, cultures, and civilizations - past and present - are often incomprehensible to outsiders, but the individual’s hunger, anxieties, dreams, and preoccupations have remained unchanged through the millennia. Thus, we are up against the paradox that the individual who is more complex, unpredictable, and mysterious than any communal entity is the one nearest to our understanding; so near that even the interval of millennia cannot weaken our feeling of kinshiIf in some manner the voice of an individual reaches us from the remotest distance of time, it is a timeless voice speaking about ourselves.
It is the intact and functioning organism on which natural selection operates. Organisms are therefore the central element of concern to the biologist who aspires to a broad and integrated understanding of biology.
It is the nature of an hypothesis, when once a man has conceived it, that it assimilates every thing to itself, as proper nourishment; and, from the first moment of your begetting it, it generally grows the stronger by every thing you see, hear, read, or understand.
It is unsafe to talk mathematics. Folks don’t understand.
It is when physicians are bogged down … when they lack a clear understanding of disease mechanisms, that the deficiencies of the health-care system are most conspicuous. If I were a policy-maker, interested in saving money for health care over the long haul, I would regard it as an act of high prudence to give high priority to a lot more basic research in biologic science.
It may be unpopular and out-of-date to say—but I do not think that a scientific result which gives us a better understanding of the world and makes it more harmonious in our eyes should be held in lower esteem than, say, an invention which reduces the cost of paving roads, or improves household plumbing.
It might interest you that when we made the experiments that we did not read the literature well enough—and you know how that happens. On the other hand, one would think that other people would have told us about it. For instance, we had a colloquium at the time in Berlin at which all the important papers were discussed. Nobody discussed Bohr’s paper. Why not? The reason is that fifty years ago one was so convinced that nobody would, with the state of knowledge we had at that time, understand spectral line emission, so that if somebody published a paper about it, one assumed “probably it is not right.” So we did not know it.
It often happens that men, even of the best understandings and greatest circumspection, are guilty of that fault in reasoning which the writers on logick call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that the art which affords a cure to this weakness, or defect, of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted anyone arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations ... It proceeds indeed upon mathematical principles in calculating the number of the combinations of the things proposed: but by the conclusions that are obtained by it, the sagacity of the natural philosopher, the exactness of the historian, the skill and judgement of the physician, and the prudence and foresight of the politician, may be assisted; because the business of all these important professions is but to form reasonable conjectures concerning the several objects which engage their attention, and all wise conjectures are the results of a just and careful examination of the several different effects that may possibly arise from the causes that are capable of producing them.
It seems to me, he says, that the test of “Do we or not understand a particular subject in physics?” is, “Can we make a mechanical model of it?” I have an immense admiration for Maxwell’s model of electromagnetic induction. He makes a model that does all the wonderful things that electricity docs in inducing currents, etc., and there can be no doubt that a mechanical model of that kind is immensely instructive and is a step towards a definite mechanical theory of electromagnetism.
It took Freud 38 years to understand it. You have one night. The psych exam is in 12 hours. And your id wants to party. Your ego wants to conk out. But your superego knows you need to stay awake tonight to cram. Fortunately, you've got Vivarin [caffeine tablets]. It helps keep you awake and mentally alert… So all your brainpower can focus on understanding the brain. If Freud had used Vivarin, maybe he could have understood the brain faster, too.
It usually develops that after much laborious and frustrating effort the investigator of environmental physiology succeeds in proving that the animal in question can actually exist where it lives. It is always somewhat discouraging for an investigator to realize that his efforts can be made to appear so trite, but this statement does not belittle the ecological physiologist. If his data assist the understanding of the ways in which an animal manages to live where it does, he makes an important contribution to the study of distribution, for the present is necessarily a key to the past.”
It was a great step in science when men became convinced that, in order to understand the nature of things, they must begin by asking, not whether a thing is good or bad, noxious or beneficial, but of what kind it is? And how much is there of it? Quality and Quantity were then first recognised as the primary features to be observed in scientific inquiry.
It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.
It was my science that drove me to the conclusion that the world is much more complicated than can be explained by science. It is only through the supernatural that I can understand the mystery of existence.
It’s important to always bear in mind that life occurs in historical time. Everyone in every culture lives in some sort of historical time, though it might not be perceived in the same way an outside observer sees it. It’s an interesting question, “When is now?” “Now” can be drawn from some point like this hour, this day, this month, this lifetime, or this generation. “Now” can also have occurred centuries ago; things like unfair treaties, the Trail of Tears, and the Black Hawk War, for instance, remain part of the “Now” from which many Native Americans view their place in time today. Human beings respond today to people and events that actually occurred hundreds or even thousands of years ago. Ethnohistorians have played a major role in showing how now is a social concept of time, and that time is part of all social life. I can only hope that their work will further the understanding that the study of social life is a study of change over time.
It’s only through honesty and courage that science can work at all. The Ptolemaic understanding of the solar system was undermined and corrected by the constant pressure of more and more honest reporting.
Judging from our experience upon this planet, such a history, that begins with elementary particles, leads perhaps inevitably toward a strange and moving end: a creature that knows, a science-making animal, that turns back upon the process that generated him and attempts to understand it. Without his like, the universe could be, but not be known, and this is a poor thing. Surely this is a great part of our dignity as men, that we can know, and that through us matter can know itself; that beginning with protons and electrons, out of the womb of time and the vastnesses of space, we can begin to understand; that organized as in us, the hydrogen, the carbon, the nitrogen, the oxygen, those 16-21 elements, the water, the sunlight—all having become us, can begin to understand what they are, and how they came to be.
Knowing how hard it is to collect a fact, you understand why most people want to have some fun analyzing it.
Knowing is not understanding. There is a great difference between knowing and understanding: you can know a lot about something and not really understand it.
Language is the principal tool with which we communicate; but when words are used carelessly or mistakenly, what was intended to advance mutual understanding may in fact hinder it; our instrument becomes our burden
Leaving aside genetic surgery applied humans, I foresee that the coming century will place in our hands two other forms of biological technology which are less dangerous but still revolutionary enough to transform the conditions of our existence. I count these new technologies as powerful allies in the attack on Bernal's three enemies. I give them the names “biological engineering” and “self-reproducing machinery.” Biological engineering means the artificial synthesis of living organisms designed to fulfil human purposes. Self-reproducing machinery means the imitation of the function and reproduction of a living organism with non-living materials, a computer-program imitating the function of DNA and a miniature factory imitating the functions of protein molecules. After we have attained a complete understanding of the principles of organization and development of a simple multicellular organism, both of these avenues of technological exploitation should be open to us.
Let us now declare the means whereby our understanding can rise to knowledge without fear of error. There are two such means: intuition and deduction. By intuition I mean not the varying testimony of the senses, nor the deductive judgment of imagination naturally extravagant, but the conception of an attentive mind so distinct and so clear that no doubt remains to it with regard to that which it comprehends; or, what amounts to the same thing, the self-evidencing conception of a sound and attentive mind, a conception which springs from the light of reason alone, and is more certain, because more simple, than deduction itself. …
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
It may perhaps be asked why to intuition we add this other mode of knowing, by deduction, that is to say, the process which, from something of which we have certain knowledge, draws consequences which necessarily follow therefrom. But we are obliged to admit this second step; for there are a great many things which, without being evident of themselves, nevertheless bear the marks of certainty if only they are deduced from true and incontestable principles by a continuous and uninterrupted movement of thought, with distinct intuition of each thing; just as we know that the last link of a long chain holds to the first, although we can not take in with one glance of the eye the intermediate links, provided that, after having run over them in succession, we can recall them all, each as being joined to its fellows, from the first up to the last. Thus we distinguish intuition from deduction, inasmuch as in the latter case there is conceived a certain progress or succession, while it is not so in the former; … whence it follows that primary propositions, derived immediately from principles, may be said to be known, according to the way we view them, now by intuition, now by deduction; although the principles themselves can be known only by intuition, the remote consequences only by deduction.
Let us then suppose the Mind to be, as we say, white Paper, void of all Characters, without any Ideas; How comes it to be furnished? Whence comes it by that vast store, which the busy and boundless Fancy of Man has painted on it, with an almost endless variety? Whence has it all the materials of Reason and Knowledge? To this I answer, in one word, from Experience: In that, all our Knowledge is founded; and from that it ultimately derives it self. Our Observation employ’d either about external, sensible Objects; or about the internal Operations of our Minds, perceived and reflected on by our selves, is that, which supplies our Understandings with all the materials of thinking.
Life is too complicated to permit a complete understanding through the study of whole organisms. Only by simplifying a biological problem—breaking it down into a multitude of individual problems—can you get the answers.
Linnaeus had it constantly in mind:“The closer we get to know the creatures around us, the clearer is the understanding we obtain of the chain of nature, and its harmony and system, according to which all things appear to have been created.”
Logic has borrowed the rules of geometry without understanding its power. … I am far from placing logicians by the side of geometers who teach the true way to guide the reason. … The method of avoiding error is sought by every one. The logicians profess to lead the way, the geometers alone reach it, and aside from their science there is no true demonstration.
Macaulay somewhere says, that it is extraordinary that, whereas the laws of the motions of the heavenly bodies, far removed as they are from us, are perfectly well understood, the laws of the human mind, which are under our observation all day and every day, are no better understood than they were two thousand years ago.
Magic and all that is ascribed to it is a deep presentiment of the powers of science. The shoes of swiftness, the sword of sharpness, the power of subduing the elements, of using the secret virtues of minerals, of understanding the voices of birds, are the obscure efforts of the mind in a right direction.
MAGNITUDE, n. Size. Magnitude being purely relative, nothing is large and nothing small. If everything in the universe were increased in bulk one thousand diameters nothing would be any larger than it was before, but if one thing remained unchanged all the others would be larger than they had been. To an understanding familiar with the relativity of magnitude and distance the spaces and masses of the astronomer would be no more impressive than those of the microscopist. For anything we know to the contrary, the visible universe may be a small part of an atom, with its component ions, floating in the life-fluid (luminiferous ether) of some animal. Possibly the wee creatures peopling the corpuscles of our own blood are overcome with the proper emotion when contemplating the unthinkable distance from one of these to another.
Man masters nature not by force but by understanding. That is why science has succeeded where magic failed: because it has looked for no spell to cast on nature.
Man, as the minister and interpreter of nature, is limited in act and understanding by his observation of the order of nature; neither his understanding nor his power extends further.
Man’s law changes with his understanding of man. Only the laws of the spirit remain always the same.
— Crow
Many consider that the conflict of religion and science is a temporary phase, and that in due course the two mighty rivers of human understanding will merge into an even mightier Amazon of comprehension. I take the opposite view, that reconciliation is impossible. I consider that Science is mightier than the Word, and that the river of religion will (or, at least, should) atrophy and die.
Many errors, of a truth, consist merely in the application of the wrong names of things. For if a man says that the lines which are drawn from the centre of the circle to the circumference are not equal, he understands by the circle, at all events for the time, something else than mathematicians understand by it.
Marxist philosophy holds that the most important problem does not lie in understanding the laws of the objective world and thus being able to explain it, but in applying the knowledge of these laws actively to change the world.
Mathematicians are only dealing with the structure of reasoning, and they do not really care what they are talking about. They do not even need to know what they are talking about … But the physicist has meaning to all his phrases. … In physics, you have to have an understanding of the connection of words with the real world.
Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
Mathematics make the mind attentive to the objects which it considers. This they do by entertaining it with a great variety of truths, which are delightful and evident, but not obvious. Truth is the same thing to the understanding as music to the ear and beauty to the eye. The pursuit of it does really as much gratify a natural faculty implanted in us by our wise Creator as the pleasing of our senses: only in the former case, as the object and faculty are more spiritual, the delight is more pure, free from regret, turpitude, lassitude, and intemperance that commonly attend sensual pleasures.
Mathematics, the science of the ideal, becomes the means of investigating, understanding and making known the world of the real. The complex is expressed in terms of the simple. From one point of view mathematics may be defined as the science of successive substitutions of simpler concepts for more complex.
Maybe we have to accept that after reaching the deepest possible level of understanding science can offer, there will nevertheless be aspects of the universe that remain unexplained. Maybe we will have to accept that certain features of the universe are the way they are because of happenstance, accident, or divine choice.
Medicine in its present state is, it seems to me, by now completely discovered, insofar as it teaches in each instance the particular details and the correct measures. For anyone who has an understanding of medicine in this way depends very little upon good luck, but is able to do good with or without luck. For the whole of medicine has been established, and the excellent principles discovered in it clearly have very little need of good luck.
Medicine rests upon four pillars—philosophy, astronomy, alchemy, and ethics. The first pillar is the philosophical knowledge of earth and water; the second, astronomy, supplies its full understanding of that which is of fiery and airy nature; the third is an adequate explanation of the properties of all the four elements—that is to say, of the whole cosmos—and an introduction into the art of their transformations; and finally, the fourth shows the physician those virtues which must stay with him up until his death, and it should support and complete the three other pillars.
Mediocre men often have the most acquired knowledge. It is in the darker. It is in the darker regions of science that great men are recognized; they are marked by ideas which light up phenomena hitherto obscure and carry science forward.
Men think epilepsy divine, mere because they do not understand it. But if they called everything divine which they do not understand, why, there would be no end of divine things.
More and more of out colleagues fail to understand our work because of the high specialization of research problems. We must not be discouraged if the products of our labor are not read or even known to exist. The joy of research must be found in doing since every other harvest is uncertain.
Most impediments to scientific understanding are conceptual locks, not factual lacks. Most difficult to dislodge are those biases that escape our scrutiny because they seem so obviously, even ineluctably, just. We know ourselves best and tend to view other creatures as mirrors of our own constitution and social arrangements. (Aristotle, and nearly two millennia of successors, designated the large bee that leads the swarm as a king.)
Much of the work we do as scientists involves filling in the details about matters that are basically understood already, or applying standard techniques to new specific cases. But occasionally there is a question that offers an opportunity for a really major discovery.
My child you may search forever the depths of this science [metaphysics] and you will never find a bottom. The secrets of eternal wisdom are not to be fathomed by our narrow understandings.
My goal is simple. It is a complete understanding of the universe, why it is as it is and why it exists at all.
My life as a surgeon-scientist, combining humanity and science, has been fantastically rewarding. In our daily patients we witness human nature in the raw–fear, despair, courage, understanding, hope, resignation, heroism. If alert, we can detect new problems to solve, new paths to investigate.
My scientific work is motivated by an irresistible longing to understand the secrets of nature and by no other feeling. My love for justice and striving to contribute towards the improvement of human conditions are quite independent from my scientific interests.
My view, the skeptical one, holds that we may be as far away from an understanding of elementary particles as Newton's successors were from quantum mechanics. Like them, we have two tremendous tasks ahead of us. One is to study and explore the mathematics of the existing theories. The existing quantum field-theories may or may not be correct, but they certainly conceal mathematical depths which will take the genius of an Euler or a Hamilton to plumb. Our second task is to press on with the exploration of the wide range of physical phenomena of which the existing theories take no account. This means pressing on with experiments in the fashionable area of particle physics. Outstanding among the areas of physics which have been left out of recent theories of elementary particles are gravitation and cosmology
Mystics understand the roots of the Tao but not its branches; scientists understand its branches but not its roots. Science does not need mysticism and mysticism does not need science; but man needs both.
Naturally, there is always a great diversity of opinion about a popular subject when it is not well understood. We all know how true this is of social, ethical and religious subjects, upon which no two persons ever really agree. The exact sciences, however, admit of no differences of opinion.
Nature is made in such a way as to be able to be understood. Or perhaps I should put it—more correctly—the other way around, and say that we are made in such a way as to be able to understand Nature.
Nature never “fails.” Nature complies with its own laws. Nature is the law. When Man lacks understanding of Nature’s laws and a Man-contrived structure buckles unexpectedly, it does not fail. It only demonstrates that Man did not understand Nature’s laws and behaviors. Nothing failed. Man’s knowledge or estimating was inadequate.
Nature never makes excellent things, for mean or no uses: and it is hardly to be conceived, that our infinitely wise Creator, should make so admirable a Faculty, as the power of Thinking, that Faculty which comes nearest the Excellency of his own incomprehensible Being, to be so idlely and uselesly employ’d, at least 1/4 part of its time here, as to think constantly, without remembering any of those Thoughts, without doing any good to it self or others, or being anyway useful to any other part of Creation.
Nearly every understanding is gained by a painful struggle in which belief and unbelief are dramatically interwoven.
Neither the naked hand nor the understanding left to itself can effect much. It is by instruments and helps that the work is done, which are as much wanted for the understanding as for the hand. And as the instruments of the hand either give motion or guide it, so the instruments of the mind supply either suggestions for the understanding or cautions.
No engineer can go upon a new work and not find something peculiar, that will demand his careful reflection, and the deliberate consideration of any advice that he may receive; and nothing so fully reveals his incapacity as a pretentious assumption of knowledge, claiming to understand everything.
No one has yet been found so firm of mind and purpose as resolutely to compel himself to sweep away all theories and common notions, and to apply the understanding, thus made fair and even, to a fresh examination of particulars. Thus it happens that human knowledge, as we have it, is a mere medley and ill-digested mass, made up of much credulity and much accident, and also of the childish notions which we at first imbibed.
No part of the world can be truly understood without a knowledge of its garment of vegetation, for this determines not only the nature of the animal inhabitants but also the occupations of the majority of human beings.
Not all is doom and gloom. We are beginning to understand the natural world and are gaining a reverence for life - all life.
Not enough of our society is trained how to understand and interpret quantitative information. This activity is a centerpiece of science literacy to which we should all strive—the future health, wealth, and security of our democracy depend on it. Until that is achieved, we are at risk of making under-informed decisions that affect ourselves, our communities, our country, and even the world.
Not one idiot in a thousand has been entirely refractory to treatment, not one in a hundred has not been made more happy and healthy; more than thirty per cent have been taught to conform to social and moral law, and rendered capable of order, of good feeling, and of working like the third of a man; more than forty per cent have become capable of the ordinary transactions of life under friendly control, of understanding moral and social abstractions, of working like two-thirds of a man.
Not only is science fiction an idea of tremendous import, but it is to be an important factor in making the world a better place to live in, through educating the public to the possibilities of science and the influence of science on life which, even today, are not appreciated byu the man on the street. ... If every man, woman, boy and girl, could be induced to read science fiction right along, there would certainly be a great resulting benefit to the community, in that the educational standards of its people would be raised tremendously. Science fiction would make people happier, give them a broader understanding of the world, make tham more tolerant.
Notable enough, however, are the controversies over the series 1 – 1 + 1 – 1 + 1 – … whose sum was given by Leibniz as 1/2, although others disagree. … Understanding of this question is to be sought in the word “sum”; this idea, if thus conceived—namely, the sum of a series is said to be that quantity to which it is brought closer as more terms of the series are taken—has relevance only for convergent series, and we should in general give up the idea of sum for divergent series.
Nothing could be more admirable than the manner in which for forty years he [Joseph Black] performed this useful and dignified office. His style of lecturing was as nearly perfect as can well be conceived; for it had all the simplicity which is so entirely suited to scientific discourse, while it partook largely of the elegance which characterized all he said or did … I have heard the greatest understandings of the age giving forth their efforts in its most eloquent tongues—have heard the commanding periods of Pitt’s majestic oratory—the vehemence of Fox’s burning declamation—have followed the close-compacted chain of Grant’s pure reasoning—been carried away by the mingled fancy, epigram, and argumentation of Plunket; but I should without hesitation prefer, for mere intellectual gratification (though aware how much of it is derived from association), to be once more allowed the privilege which I in those days enjoyed of being present while the first philosopher of his age was the historian of his own discoveries, and be an eyewitness of those experiments by which he had formerly made them, once more performed with his own hands.
Nothing is in the intellect that was not first in the senses.
Nihil est in intellectu quod non sit prius in sensu.
Nihil est in intellectu quod non sit prius in sensu.
Nothing without understanding would ever be more beauteous than with understanding.
— Plato
Now the word-symbols of conceptual ideas have passed so long from hand to hand in the service of the understanding, that they have gradually lost all such fanciful reference.
Observation, Reason, Human Understanding, Courage; these make the physician.
On the contrary, God was always invented to explain mystery. God is always invented to explain those things that you do not understand. Now when you finally discover how something works, you get some laws which you're taking away from God; you don't need him anymore. But you need him for the other mysteries. So therefore you leave him to create the universe because we haven't figured that out yet; you need him for understanding those things which you don't believe the laws will explain, such as consciousness, or why you only live to a certain length of time—life and death—stuff like that. God is always associated with those things that you do not understand. Therefore, I don't think that the laws can be considered to be like God because they have been figured out.
One cause of the error may be for want of a proper knowledge of the remote past. Here, as elsewhere, ’tis distance lends enchantment to the view. We fail to make due allowance for the refractive nature of the medium through which we are compelled to view the past. We naturally magnify the greatness of that which is remote. By this the imagination is addressed rather than the understanding. The dim and shadowing figures of the past are clothed in glorious light, and pigmies appear as giants.
One doesn’t really understand what mathematics is until at least halfway through college when one takes abstract math courses and learns about proofs.
One of the major goals when studying specific genetic diseases is to find the primary gene product, which in turn leads to a better understanding of the biochemical basis of the disorder. The bottom line often reads, 'This may lead to effective prenatal diagnosis and eventual eradication of the disease.' But we now have the ironic situation of being able to jump right to the bottom line without reading the rest of the page, that is, without needing to identify the primary gene product or the basic biochemical mechanism of the disease. The technical capability of doing this is now available. Since the degree of departure from our previous approaches and the potential of this procedure are so great, one will not be guilty of hyperbole in calling it the 'New Genetics'.
One of the ways the telegraph changed us as humans was it gave us a new sense of what time it is. It gave us an understanding of simultaneity. It gave us the ability to synchronize clocks from one place to another. It made it possible for the world to have standard time and time zones and then Daylight Savings Time and then after that jetlag. All of that is due to the telegraph because, before that, the time was whatever it was wherever you were.
One should not understand this compulsion to construct concepts, species, forms, purposes, laws ('a world of identical cases') as if they enabled us to fix the real world; but as a compulsion to arrange a world for ourselves in which our existence is made possible:—we thereby create a world which is calculable, simplified, comprehensible, etc., for us.
Only by following out the injunction of our great predecessor [William Harvey] to search out and study the secrets of Nature by way of experiment, can we hope to attain to a comprehension of 'the wisdom of the body and the understanding of the heart,' and thereby to the mastery of disease and pain, which will enable us to relieve the burden of mankind.
Our aim is not to make poets, but to allow people to express themselves in a meaningful and appropriate way. We try to get them to enjoy and open up to a point where they can relate—anything to reach the level of their feeling and understanding.
Our children will enjoy in their homes electrical energy too cheap to meter. … Transmutation of the elements, unlimited power, ability to investigate the working of living cells by tracer atoms, the secret of photosynthesis about to be uncovered, these and a host of other results, all in about fifteen short years. It is not too much to expect that our children will know of great periodic regional famines in the world only as matters of history, will travel effortlessly over the seas and under the and through the air with a minimum of danger and at great speeds, and will experience a life span far longer than ours, as disease yields and man comes to understand what causes him to age.
Our experience up to date justifies us in feeling sure that in Nature is actualized the ideal of mathematical simplicity. It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to understanding nature… In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
Our job in physics is to see things simply, to understand a great many complicated phenomena in a unified way, in terms of a few simple principles.
Our time is distinguished by wonderful achievements in the fields of scientific understanding and the technical application of those insights. Who would not be cheered by this? But let us not forget that human knowledge and skills alone cannot lead humanity to a happy and dignified life. Humanity has every reason to place the proclaimers of high moral standards and values above the discoverers of objective truth. What humanity owes to personalities like Buddha, Moses, and Jesus ranks for me higher than all the achievements of the inquiring constructive mind.
Our ultimate end must be precisely what Dr. Pauling says, peace based on agreement, upon understanding, on universally agreed and enforced law. I think this is a wonderful idea, but peace based on force buys us the necessary time, and in this time we can work for better understanding, for closer collaboration.
Our understanding of the causes of biological diversity is still crude. The science addressing it can be generously put at about the level of physics in the late nineteenth century.
Outside our consciousness there lies the cold and alien world of actual things. Between the two stretches the narrow borderland of the senses. No communication between the two worlds is possible excepting across the narrow strip. For a proper understanding of ourselves and of the world, it is of the highest importance that this borderland should be thoroughly explored.
Owing to his lack of knowledge, the ordinary man cannot attempt to resolve conflicting theories of conflicting advice into a single organized structure. He is likely to assume the information available to him is on the order of what we might think of as a few pieces of an enormous jigsaw puzzle. If a given piece fails to fit, it is not because it is fraudulent; more likely the contradictions and inconsistencies within his information are due to his lack of understanding and to the fact that he possesses only a few pieces of the puzzle. Differing statements about the nature of things, differing medical philosophies, different diagnoses and treatments—all of these are to be collected eagerly and be made a part of the individual's collection of puzzle pieces. Ultimately, after many lifetimes, the pieces will fit together and the individual will attain clear and certain knowledge.
Oxygen is the vital ingredient for the survival of every cell in our bodies. Too little–or too much–can spell disaster. Understanding how evolution has equipped cells to detect and respond to fluctuating oxygen levels helps answer fundamental questions.
Paris ... On this side of the ocean it is difficult to understand the susceptibility of American citizens on the subject and precisely why they should so stubbornly cling to the biblical version. It is said in Genesis the first man came from mud and mud is not anything very clean. In any case if the Darwinian hypothesis should irritate any one it should only be the monkey. The monkey is an innocent animal—a vegetarian by birth. He never placed God on a cross, knows nothing of the art of war, does not practice lynch law and never dreams of assassinating his fellow beings. The day when science definitely recognizes him as the father of the human race the monkey will have no occasion to be proud of his descendants. That is why it must be concluded that the American Association which is prosecuting the teacher of evolution can be no other than the Society for Prevention of Cruelty to Animals.
[A cynical article in the French press on the Scopes Monkey Trial, whether it will decide “a monkey or Adam was the grandfather of Uncle Sam.”]
[A cynical article in the French press on the Scopes Monkey Trial, whether it will decide “a monkey or Adam was the grandfather of Uncle Sam.”]
Peace cannot be achieved through violence, it can only be attained through understanding.
Peace cannot be kept by force. It can only be achieved by understanding.
People must understand that science is inherently neither a potential for good nor for evil. It is a potential to be harnessed by man to do his bidding.
Philosophy begins in wonder. And, at the end, when philosophic thought has done its best, the wonder remains. There have been added, however, some grasp of the immensity of things, some purification of emotion by understanding.
Physicists only talk to physicists, economists to economists—worse still, nuclear physicists only talk to nuclear physicists and econometricians to econometricians. One wonders sometimes if science will not grind to a stop in an assemblage of walled-in hermits, each mumbling to himself words in a private language that only he can understand.
Psychoanalysis has changed American psychiatry from a diagnostic to a therapeutic science, not because so many patients are cured by the psychoanalytic technique, but because of the new understanding of psychiatric patients it has given us and the new and different concepts of illness and health.
Psychology must not only strive to become a useful basis for the other mental sciences, but it must also turn again and again to the historical sciences, in order to obtain an understanding for the more highly developed metal processes.
Pure mathematics consists entirely of such asseverations as that, if such and such is a proposition is true of anything, then such and such another propositions is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is of which it is supposed to be true. Both these points would belong to applied mathematics. … If our hypothesis is about anything and not about some one or more particular things, then our deductions constitute mathematics. Thus mathematics may be defined as the the subject in which we never know what we are talking about, not whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.
Reading furnishes the mind only with materials of knowledge, it is thinking makes what we read ours.
Regardless of communication between man and man, speech is a necessary condition for the thinking of the individual in solitary seclusion. In appearance, however, language develops only socially, and man understands himself only once he has tested the intelligibility of his words by trial upon others.
Relativity was a highly technical new theory that gave new meanings to familiar concepts and even to the nature of the theory itself. The general public looked upon relativity as indicative of the seemingly incomprehensible modern era, educated scientists despaired of ever understanding what Einstein had done, and political ideologues used the new theory to exploit public fears and anxieties—all of which opened a rift between science and the broader culture that continues to expand today.
Religion, in contrast to science, deploys the repugnant view that the world is too big for our understanding. Science, in contrast to religion, opens up the great questions of being to rational discussion, to discussion with the prospect of resolution and elucidation.
Rules can seldom be safely applied without a clear understanding of the principles on which they rest.
Rules of Thumb
Thumb’s First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb’s Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Thumb’s First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb’s Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Science contributes to our culture in many ways, as a creative intellectual activity in its own right, as the light which has served to illuminate man's place in the universe, and as the source of understanding of man's own nature.
Science has a simple faith, which transcends utility. Nearly all men of science, all men of learning for that matter, and men of simple ways too, have it in some form and in some degree. It is the faith that it is the privilege of man to learn to understand, and that this is his mission. If we abandon that mission under stress we shall abandon it forever, for stress will not cease. Knowledge for the sake of understanding, not merely to prevail, that is the essence of our being. None can define its limits, or set its ultimate boundaries.
Science has to be understood in its broadest sense, as a method for apprehending all observable reality, and not merely as an instrument for acquiring specialized knowledge.
Science is a human activity, and the best way to understand it is to understand the individual human beings who practise it. Science is an art form and not a philosophical method. The great advances in science usually result from new tools rather than from new doctrines. ... Every time we introduce a new tool, it always leads to new and unexpected discoveries, because Nature's imagination is richer
than ours.
Science is the language of the temporal world; love is that of the spiritual world. Man, indeed, describes more than he explains; while the angelic spirit sees and understands. Science saddens man; love enraptures the angel; science is still seeking; love has found.
Science is the tool of the Western mind and with it more doors can be opened than with bare hands. It is part and parcel of our knowledge and obscures our insight only when it holds that the understanding given by it is the only kind there is.
Science not only purifies the religious impulse of the dross of its anthropomorphism but also contributes to a religious spiritualization of our understanding of life.
Science provides an understanding of a universal experience, and arts provides a universal understanding of a personal experience.
Science, then, is the attentive consideration of common experience; it is common knowledge extended and refined. Its validity is of the same order as that of ordinary perception; memory, and understanding. Its test is found, like theirs, in actual intuition, which sometimes consists in perception and sometimes in intent. The flight of science is merely longer from perception to perception, and its deduction more accurate of meaning from meaning and purpose from purpose. It generates in the mind, for each vulgar observation, a whole brood of suggestions, hypotheses, and inferences. The sciences bestow, as is right and fitting, infinite pains upon that experience which in their absence would drift by unchallenged or misunderstood. They take note, infer, and prophesy. They compare prophesy with event, and altogether they supply—so intent are they on reality—every imaginable background and extension for the present dream.
Scientific progress is the discovery of a more and more comprehensive simplicity... The previous successes give us confidence in the future of science: we become more and more conscious of the fact that the universe is cognizable.
Scientists are going to discover many subtle genetic factors in the makeup of human beings. Those discoveries will challenge the basic concepts of equality on which our society is based. Once we can say that there are differences between people that are easily demonstrable at the genetic level, then society will have to come to grips with understanding diversity—and we are not prepared for that.
Scientists often invent words to fill the holes in their understanding.These words are meant as conveniences until real understanding can be found. … Words such as dimension and field and infinity … are not descriptions of reality, yet we accept them as such because everyone is sure someone else knows what the words mean.
Scientists themselves readily admit that they do not fully understand the consequences of our many-faceted assault upon the interwoven fabric of atmosphere, water, land and life in all its biological diversity. But things could also turn out to be worse than the current scientific best guess. In military affairs, policy has long been based on the dictum that we should be prepared for the worst case. Why should it be so different when the security is that of the planet and our long-term future?
Since my logic aims to teach and instruct the understanding, not that it may with the slender tendrils of the mind snatch at and lay hold of abstract notions (as the common logic does), but that it may in very truth dissect nature, and discover the virtues and actions of bodies, with their laws as determined in matter; so that this science flows not merely from the nature of the mind, but also from the nature of things.
Since the beginning of physics, symmetry considerations have provided us with an extremely powerful and useful tool in our effort to understand nature. Gradually they have become the backbone of our theoretical formulation of physical laws.
So-called “common sense” is definitely detrimental to an understanding of the quantum realm!
Some of the scientists, I believe, haven’t they been changing their opinion a little bit on global warming? There’s a lot of differing opinions and before we react I think it’s best to have the full accounting, full understanding of what’s taking place.
Some people say they cannot understand a million million. Those people cannot understand that twice two makes four. That is the way I put it to people who talk to me about the incomprehensibility of such large numbers. I say finitude is incomprehensible, the infinite in the universe is comprehensible. Now apply a little logic to this. Is the negation of infinitude incomprehensible? What would you think of a universe in which you could travel one, ten, or a thousand miles, or even to California, and then find it comes to an end? Can you suppose an end of matter or an end of space? The idea is incomprehensible. Even if you were to go millions and millions of miles the idea of coming to an end is incomprehensible. You can understand one thousand per second as easily as you can understand one per second. You can go from one to ten, and then times ten and then to a thousand without taxing your understanding, and then you can go on to a thousand million and a million million. You can all understand it.
Someone with a fresh mind, one not conditioned by upbringing and environment, would doubtless look at science and the powerful reductionism that it inspires as overwhelmingly the better mode of understanding the world, and would doubtless scorn religion as sentimental wishful thinking.
String theory is revealing the deepest understanding of the Universe we have ever had.
Subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement.
Such propositions are therefore called Eternal Truths, not because they are Eternal Truths, not because they are External Propositions actually formed, and antecedent to the Understanding, that at any time makes them; nor because they are imprinted on the Mind from any patterns, that are any where out of the mind, and existed before: But because, being once made, about abstract Ideas, so as to be true, they will, whenever they can be supposed to be made again at any time, past or to come, by a Mind having those Ideas, always actually be true. For names being supposed to stand perpetually for the same ideas, and the same ideas having immutably the same habitudes one to another, Propositions concerning any abstract Ideas that are once true, must needs be eternal Verities.
Sufficient knowledge and a solid background in the basic sciences are essential for all medical students. But that is not enough. A physician is not only a scientist or a good technician. He must be more than that—he must have good human qualities. He has to have a personal understanding and sympathy for the suffering of human beings.
Suppose there is something which a person cannot understand. He happens to notice the similarity of this something to some other thing which he understands quite well. By comparing them he may come to understand the thing which he could not understand up to that moment. If his understanding turns out to be appropriate and nobody else has ever come to such an understanding, he can claim that his thinking was really creative.
Telescopes are in some ways like time machines. They reveal galaxies so far away that their light has taken billions of years to reach us. We in astronomy have an advantage in studying the universe, in that we can actually see the past.
We owe our existence to stars, because they make the atoms of which we are formed. So if you are romantic you can say we are literally starstuff. If you’re less romantic you can say we’re the nuclear waste from the fuel that makes stars shine.
We’ve made so many advances in our understanding. A few centuries ago, the pioneer navigators learnt the size and shape of our Earth, and the layout of the continents. We are now just learning the dimensions and ingredients of our entire cosmos, and can at last make some sense of our cosmic habitat.
We owe our existence to stars, because they make the atoms of which we are formed. So if you are romantic you can say we are literally starstuff. If you’re less romantic you can say we’re the nuclear waste from the fuel that makes stars shine.
We’ve made so many advances in our understanding. A few centuries ago, the pioneer navigators learnt the size and shape of our Earth, and the layout of the continents. We are now just learning the dimensions and ingredients of our entire cosmos, and can at last make some sense of our cosmic habitat.
That which today calls itself science gives us more and more information, an indigestible glut of information, and less and less understanding.
The Ideas of primary Qualities of Bodies, are Resemblances of them, and their Patterns do really exist in the Bodies themselves; but the Ideas, produced in us by these Secondary Qualities, have no resemblance of them at all. There is nothing like our Ideas, existing in the Bodies themselves. They are in Bodies, we denominate from them, only a Power to produce those Sensations in us: And what is Sweet, Blue or Warm in Idea, is but the certain Bulk, Figure, and Motion of the insensible parts in the Bodies themselves, which we call so.
The aims of pure basic science, unlike those of applied science, are neither fast-flowing nor pragmatic. The quick harvest of applied science is the useable process, the medicine, the machine. The shy fruit of pure science is understanding.
The astronomer may speak to you of his understanding of space, but he cannot give you his understanding. … And he who is versed in the science of numbers can tell of the regions of weight and measure, but he cannot conduct you thither.
The century of biology upon which we are now well embarked is no matter of trivialities. It is a movement of really heroic dimensions, one of the great episodes in man’s intellectual history. The scientists who are carrying the movement forward talk in terms of nucleo-proteins, of ultracentrifuges, of biochemical genetics, of electrophoresis, of the electron microscope, of molecular morphology, of radioactive isotopes. But do not be misled by these horrendous terms, and above all do not be fooled into thinking this is mere gadgetry. This is the dependable way to seek a solution of the cancer and polio problems, the problems of rheumatism and of the heart. This is the knowledge on which we must base our solution of the population and food problems. This is the understanding of life.
The chemical differences among various species and genera of animals and plants are certainly as significant for the history of their origins as the differences in form. If we could define clearly the differences in molecular constitution and functions of different kinds of organisms, there would be possible a more illuminating and deeper understanding of question of the evolutionary reactions of organisms than could ever be expected from morphological considerations.
The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.
The contributions of physiological knowledge to an understanding of distribution are necessarily inferential. Distribution is a historical phenomenon, and the data ordinarily obtained by students of physiology are essentially instantaneous. However, every organism has a line of ancestors which extends back to the beginning of life on earth and which, during this immensity of time, has invariably been able to avoid, to adapt to, or to compensate for environmental changes.
The effort to understand the universe is one of the very few things that lifts human life above the level of farce, and gives it some of the grace of tragedy.
The engineer is the key figure in the material progress of the world. It is his engineering that makes a reality of the potential value of science by translating scientific knowledge into tools, resources, energy and labor to bring them to the service of man ... To make contribution of this kind the engineer requires the imagination to visualize the needs of society and to appreciate what is possible as well as the technological and broad social age understanding to bring his vision to reality.
The equation of evolution with progress represents our strongest cultural impediment to a proper understanding of this greatest biological revolution in the history of human thought.
The existence of life must be considered as an elementary fact that can not be explained, but must be taken as a starting point in biology, in a similar way as the quantum of action, which appears as an irrational element from the point of view of classical mechanical physics, taken together with the existence of elementary particles, forms the foundation of atomic physics. The asserted impossibility of a physical or chemical explanation of the function peculiar to life would in this sense be analogous to the insufficiency of the mechanical analysis for the understanding of the stability of atoms.
The experimenter who does not know what he is looking for will never understand what he finds.
The eye, the window of the soul, is the chief means whereby the understanding can most fully and abundantly appreciate the infinite works of Nature; and the ear is second.
The eyes of the world now look into space, to the moon and to the planets beyond, and we have vowed that we shall not see it governed by a hostile flag of conquest, but by a banner of freedom and peace. We have vowed that we shall not see space filled with weapons of mass destruction, but with instruments of knowledge and understanding.
The fact that man produces a concept ‘I’ besides the totality of his mental and emotional experiences or perceptions does not prove that there must be any specific existence behind such a concept. We are succumbing to illusions produced by our self-created language, without reaching a better understanding of anything. Most of so-called philosophy is due to this kind of fallacy.
The feeling of understanding is as private as the feeling of pain. The act of understanding is at the heart of all scientific activity; without it any ostensibly scientific activity is as sterile as that of a high school student substituting numbers into a formula. For this reason, science, when I push the analysis back as far as I can, must be private.
The final results [of work on the theory of relativity] appear almost simple; any intelligent undergraduate can understand them without much trouble. But the years of searching in the dark for a truth that one feels, but cannot express; the intense effort and the alternations of confidence and misgiving, until one breaks through to clarity and understanding, are only known to him who has himself experienced them.
The function of Art is to imitate Nature in her manner of operation. Our understanding of “her manner of operation” changes according to advances in the sciences.
The function of Latin literature is its expression of Rome. When to England and France your imagination can add Rome in the background, you have laid firm the foundations of culture. The understanding of Rome leads back to the Mediterranean civilisation of which Rome was the last phase, and it automatically exhibits the geography of Europe, and the functions of seas and rivers and mountains and plains. The merit of this study in the education of youth is its concreteness, its inspiration to action, and the uniform greatness of persons, in their characters and their staging. Their aims were great, their virtues were great, and their vices were great. They had the saving merit of sinning with cart ropes.
The graceful minuet-dance of fancy must give place to the toilsome, thorny pilgrimage of understanding.
On the transition from the age of romance to that of science.
On the transition from the age of romance to that of science.
The great basic thought that the world is not to be comprehended as a complex of ready-made things, but as a complex of processes, in which the things apparently stable no less than their mind-images in our heads, the concepts, go through an uninterrupted change of coming into being and passing away, in which, in spite of all seeming accidents and of all temporary retrogression, a progressive development asserts itself in the end—this great fundamental thought has, especially since the time of Hegel, so thoroughly permeated ordinary consciousness that in this generality it is scarcely ever contradicted.
The great beauty of Darwin’s theory of evolution is that it explains how complex, difficult to understand things could have arisen step by plausible step, from simple, easy to understand beginnings. We start our explanation from almost infinitely simple beginnings: pure hydrogen and a huge amount of energy. Our scientific, Darwinian explanations carry us through a series of well-understood gradual steps to all the spectacular beauty and complexity of life.
The great enemy of communication, we find, is the illusion of it. We have talked enough; but we have not listened. And by not listening we have failed to concede the immense complexity of our society–and thus the great gaps between ourselves and those with whom we seek understanding.
The great object, in trying to understand history, political, religious, literary, or scientific, is to get behind men, and to grasp ideas.
The great truths with which it [mathematics] deals, are clothed with austere grandeur, far above all purposes of immediate convenience or profit. It is in them that our limited understandings approach nearest to the conception of that absolute and infinite, towards which in most other things they aspire in vain. In the pure mathematics we contemplate absolute truths, which existed in the divine mind before the morning stars sang together, and which will continue to exist there, when the last of their radiant host shall have fallen from heaven. They existed not merely in metaphysical possibility, but in the actual contemplation of the supreme reason. The pen of inspiration, ranging all nature and life for imagery to set forth the Creator’s power and wisdom, finds them best symbolized in the skill of the surveyor. "He meted out heaven as with a span;" and an ancient sage, neither falsely nor irreverently, ventured to say, that “God is a geometer”.
The greatest advantage to be derived from the study of geometry of more than three dimensions is a real understanding of the great science of geometry. Our plane and solid geometries are but the beginning of this science. The four-dimensional geometry is far more extensive than the three-dimensional, and all the higher geometries are more extensive than the lower.
The human understanding is moved by those things most which strike and enter the mind simultaneously and suddenly, and so fill the imagination; and then it feigns and supposes all other things to be somehow, though it cannot see how, similar to those few things by which it is surrounded.
The human understanding is of its own nature prone to suppose the existence of more order and regularity in the world than it finds. And though there be many things in nature which are singular and unmatched, yet it devises for them parallels and conjugates and relatives which do not exist. Hence the fiction that all celestial bodies move in perfect circles, spirals and dragons being (except in name) utterly rejected.
The human understanding is unquiet; it cannot stop or rest, and still presses onward, but in vain. Therefore it is that we cannot conceive of any end or limit to the world, but always as of necessity it occurs to us that there is something beyond... But he is no less an unskilled and shallow philosopher who seeks causes of that which is most general, than he who in things subordinate and subaltern omits to do so
The human understanding when it has once adopted an opinion (either as being the received opinion or as being agreeable to itself) draws all things else to support and agree with it. And though there be a greater number and weight of instances to be found on the other side, yet these it either neglects and despises, or else by some distinction sets aside and rejects, in order that by this great and pernicious predetermination the authority of its former conclusions may remain inviolate.
The hybridoma technology was a by-product of basic research. Its success in practical applications is to a large extent the result of unexpected and unpredictable properties of the method. It thus represents another clear-cut example of the enormous practical impact of an investment in research which might not have been considered commercially worthwhile, or of immediate medical relevance. It resulted from esoteric speculations, for curiosity’s sake, only motivated by a desire to understand nature.
The ill and unfit choice of words wonderfully obstructs the understanding.
The intellectual life of the whole of western society is increasingly being split into two polar groups… Literary intellectuals at one pole—at the other scientists, and as the most representative, the physical scientists. Between the two a gulf of mutual incomprehension—sometimes (particularly among the young) hostility and dislike, but most of all lack of understanding.
The interactions of man with his environment are so complex that only an ecological approach to nutrition permits an understanding of the whole spectrum of factors determining the nutritional problems that exist in human societies.
The invention of the scientific method and science is, I'm sure we'll all agree, the most powerful intellectual idea, the most powerful framework for thinking and investigating and understanding and challenging the world around us that there is, and it rests on the premise that any idea is there to be attacked. If it withstands the attack then it lives to fight another day and if it doesn't withstand the attack then down it goes. Religion doesn't seem to work like that.
The key to understanding overpopulation is not population density but the numbers of people in an area relative to its resources and the capacity of the environment to sustain human activities; that is, to the area’s carrying capacity. When is an area overpopulated? When its population can’t be maintained without rapidly depleting nonrenewable resources…. By this standard, the entire planet and virtually every nation is already vastly overpopulated.
The known is finite, the unknown infinite; intellectually we stand on an islet in the midst of an illimitable ocean of inexplicability. Our business in every generation is to reclaim a little more land, to add something to the extent and the solidity of our possessions. And even a cursory glance at the history of the biological sciences during the last quarter of a century is sufficient to justify the assertion, that the most potent instrument for the extension of the realm of natural knowledge which has come into men’s hands, since the publication of Newton's ‘Principia’, is Darwin's ‘Origin of Species.’
The largest land animal is the elephant, and it is the nearest to man in intelligence: it understands the language of its country and obeys orders, remembers duties that it has been taught, is pleased by affection and by marks of honour, nay more it possesses virtues rare even in man, honesty, wisdom, justice, also respect for the stars and reverence for the sun and moon.
The lives of scientists, considered as Lives, almost always make dull reading. For one thing, the careers of the famous and the merely ordinary fall into much the same pattern, give or take an honorary degree or two, or (in European countries) an honorific order. It could be hardly otherwise. Academics can only seldom lead lives that are spacious or exciting in a worldly sense. They need laboratories or libraries and the company of other academics. Their work is in no way made deeper or more cogent by privation, distress or worldly buffetings. Their private lives may be unhappy, strangely mixed up or comic, but not in ways that tell us anything special about the nature or direction of their work. Academics lie outside the devastation area of the literary convention according to which the lives of artists and men of letters are intrinsically interesting, a source of cultural insight in themselves. If a scientist were to cut his ear off, no one would take it as evidence of a heightened sensibility; if a historian were to fail (as Ruskin did) to consummate his marriage, we should not suppose that our understanding of historical scholarship had somehow been enriched.
The majority of mathematical truths now possessed by us presuppose the intellectual toil of many centuries. A mathematician, therefore, who wishes today to acquire a thorough understanding of modern research in this department, must think over again in quickened tempo the mathematical labors of several centuries. This constant dependence of new truths on old ones stamps mathematics as a science of uncommon exclusiveness and renders it generally impossible to lay open to uninitiated readers a speedy path to the apprehension of the higher mathematical truths. For this reason, too, the theories and results of mathematics are rarely adapted for popular presentation … This same inaccessibility of mathematics, although it secures for it a lofty and aristocratic place among the sciences, also renders it odious to those who have never learned it, and who dread the great labor involved in acquiring an understanding of the questions of modern mathematics. Neither in the languages nor in the natural sciences are the investigations and results so closely interdependent as to make it impossible to acquaint the uninitiated student with single branches or with particular results of these sciences, without causing him to go through a long course of preliminary study.
The meaning of human life and the destiny of man cannot be separable from the meaning and destiny of life in general. 'What is man?' is a special case of 'What is life?' Probably the human species is not intelligent enough to answer either question fully, but even such glimmerings as are within our powers must be precious to us. The extent to which we can hope to understand ourselves and to plan our future depends in some measure on our ability to read the riddles of the past. The present, for all its awesome importance to us who chance to dwell in it, is only a random point in the long flow of time. Terrestrial life is one and continuous in space and time. Any true comprehension of it requires the attempt to view it whole and not in the artificial limits of any one place or epoch. The processes of life can be adequately displayed only in the course of life throughout the long ages of its existence.
The mediocre mind is incapable of understanding the man who refuses to bow blindly to conventional prejudices and chooses instead to express his opinions courageously and honestly.
The method of arithmetical teaching is perhaps the best understood of any of the methods concerned with elementary studies.
The most important distinction between the two qualities [talent and genius] is this: one, in conception, follows mechanical processes; the other, vital. Talent feebly conceives objects with the senses and understanding; genius, fusing all its powers together in the alembic of an impassioned imagination, clutches every thing in the concrete, conceives objects as living realities, gives body to spiritual abstractions, and spirit to bodily appearances, and like
“A gate of steel
Fronting the sun, receives and renders back
His figure and his heat!”
“A gate of steel
Fronting the sun, receives and renders back
His figure and his heat!”
The most important thing for us to recall may be, that the crucial quality of science is to encourage, not discourage, the testing of assumptions. That is the only ethic that will eventually start us on our way to a new and much deeper level of understanding.
The most incomprehensible thing about the world is that it is comprehensible.
The most remarkable discovery made by scientists is science itself. The discovery must be compared in importance with the invention of cave-painting and of writing. Like these earlier human creations, science is an attempt to control our surroundings by entering into them and understanding them from inside. And like them, science has surely made a critical step in human development which cannot be reversed. We cannot conceive a future society without science.
The motive for the study of mathematics is insight into the nature of the universe. Stars and strata, heat and electricity, the laws and processes of becoming and being, incorporate mathematical truths. If language imitates the voice of the Creator, revealing His heart, mathematics discloses His intellect, repeating the story of how things came into being. And Value of Mathematics, appealing as it does to our energy and to our honor, to our desire to know the truth and thereby to live as of right in the household of God, is that it establishes us in larger and larger certainties. As literature develops emotion, understanding, and sympathy, so mathematics develops observation, imagination, and reason.
The Native writer and educator Greg Cajete has written that we humans have the gifts of using mind, body, emotion, and spirit to understand the world—and that we cannot claim to truly understand unless we learn to use all four.
The next care to be taken, in respect of the Senses, is a supplying of their infirmities with Instruments, and, as it were, the adding of artificial Organs to the natural; this in one of them has been of late years accomplisht with prodigious benefit to all sorts of useful knowledge, by the invention of Optical Glasses. By the means of Telescopes, there is nothing so far distant but may be represented to our view; and by the help of Microscopes, there is nothing so small, as to escape our inquiry; hence there is a new visible World discovered to the understanding. By this means the Heavens are open'd, and a vast number of new Stars, and new Motions, and new Productions appear in them, to which all the ancient Astronomers were utterly Strangers. By this the Earth it self, which lyes so neer us, under our feet, shews quite a new thing to us, and in every little particle of its matter, we now behold almost as great a variety of creatures as we were able before to reckon up on the whole Universe it self.
The nucleic acids, as constituents of living organisms, are comparable In importance to proteins. There is evidence that they are Involved In the processes of cell division and growth, that they participate In the transmission of hereditary characters, and that they are important constituents of viruses. An understanding of the molecular structure of the nucleic acids should be of value In the effort to understand the fundamental phenomena of life.
[Co-author with American chemist, B. Corey (1897-1971)]
[Co-author with American chemist, B. Corey (1897-1971)]
The only thing harder to understand than a law of statistical origin would be a law that is not of statistical origin, for then there would be no way for it—or its progenitor principles—to come into being. On the other hand, when we view each of the laws of physics—and no laws are more magnificent in scope or better tested—as at bottom statistical in character, then we are at last able to forego the idea of a law that endures from everlasting to everlasting.
The physicist is like someone who’s watching people playing chess and, after watching a few games, he may have worked out what the moves in the game are. But understanding the rules is just a trivial preliminary on the long route from being a novice to being a grand master. So even if we understand all the laws of physics, then exploring their consequences in the everyday world where complex structures can exist is a far more daunting task, and that’s an inexhaustible one I'm sure.
The process that I want to call scientific is a process that involves the continual apprehension of meaning, the constant appraisal of significance accompanied by a running act of checking to be sure that I am doing what I want to do, and of judging correctness or incorrectness. This checking and judging and accepting, that together constitute understanding, are done by me and can be done for me by no one else. They are as private as my toothache, and without them science is dead.
The quantum entered physics with a jolt. It didn’t fit anywhere; it made no sense; it contradicted everything we thought we knew about nature. Yet the data seemed to demand it. ... The story of Werner Heisenberg and his science is the story of the desperate failures and ultimate triumphs of the small band of brilliant physicists who—during an incredibly intense period of struggle with the data, the theories, and each other during the 1920s—brought about a revolutionary new understanding of the atomic world known as quantum mechanics.
The rainbow, “the bridge of the gods,” proved to be the bridge to our understanding of light—much more important.
The reason Dick's [Richard Feynman] physics was so hard for ordinary people to grasp was that he did not use equations. The usual theoretical physics was done since the time of Newton was to begin by writing down some equations and then to work hard calculating solutions of the equations. This was the way Hans [Bethe] and Oppy [Oppenheimer] and Julian Schwinger did physics. Dick just wrote down the solutions out of his head without ever writing down the equations. He had a physical picture of the way things happen, and the picture gave him the solutions directly with a minimum of calculation. It was no wonder that people who had spent their lives solving equations were baffled by him. Their minds were analytical; his was pictorial.
The reason of ordinary man is the reason of knowledge. The reason of normal man is the reason of understanding. Knowledge is temporary, can be changed. Understanding is permanent—unchangeable.
The scientific world-picture vouchsafes a very complete understanding of all that happens–it makes it just a little too understandable. It allows you to imagine the total display as that of a mechanical clockwork which, for all that science knows, could go on just the same as it does, without there being consciousness, will, endeavor, pain and delight and responsibility connected with it–though they actually are. And the reason for this disconcerting situation is just this: that for the purpose of constructing the picture of the external world, we have used the greatly simplifying device of cutting our own personality out, removing it; hence it is gone, it has evaporated, it is ostensibly not needed.
The scientist takes off from the manifold observations of predecessors, and shows his intelligence, if any, by his ability to discriminate between the important and the negligible, by selecting here and there the significant steppingstones that will lead across the difficulties to new understanding. The one who places the last stone and steps across to the terra firma of accomplished discovery gets all the credit.
The senses at first let in particular Ideas, and furnish the yet empty Cabinet: And the Mind by degrees growing familiar with some of them, they are lodged in the Memory, and Names got to them.
The size and age of the Cosmos are beyond ordinary human understanding. Lost somewhere between immensity and eternity is our tiny planetary home.
The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest.
The theoretical understanding of the world, which is the aim of philosophy, is not a matter of great practical importance to animals, or to savages, or even to most civilized men.
The theory of the earth is the science which describes and explains changes that the terrestrial globe has undergone from its beginning until today, and which allows the prediction of those it shall undergo in the future. The only way to understand these changes and their causes is to study the present-day state of the globe in order to gradually reconstruct its earlier stages, and to develop probable hypotheses on its future state. Therefore, the present state of the earth is the only solid base on which the theory can rely.
The understanding between a non-technical writer and his reader is that he shall talk more or less like a human being and not like an Act of Parliament. I take it that the aim of such books must be to convey exact thought in inexact language... he can never succeed without the co-operation of the reader.
The understanding must not however be allowed to jump and fly from particulars to axioms remote and of almost the highest generality (such as the first principles, as they are called, of arts and things), and taking stand upon them as truths that cannot be shaken, proceed to prove and frame the middle axioms by reference to them; which has been the practice hitherto, the understanding being not only carried that way by a natural impulse, but also by the use of syllogistic demonstration trained and inured to it. But then, and then only, may we hope well of the sciences when in a just scale of ascent, and by successive steps not interrupted or broken, we rise from particulars to lesser axioms; and then to middle axioms, one above the other; and last of all to the most general. For the lowest axioms differ but slightly from bare experience, while the highest and most general (which we now have) are notional and abstract and without solidity. But the middle are the true and solid and living axioms, on which depend the affairs and fortunes of men; and above them again, last of all, those which are indeed the most general; such, I mean, as are not abstract, but of which those intermediate axioms are really limitations.
The understanding must not therefore be supplied with wings, but rather hung with weights, to keep it from leaping and flying. Now this has never yet been done; when it is done, we may entertain better hopes of science.
The understanding must not therefore be supplied with wings, but rather hung with weights, to keep it from leaping and flying. Now this has never yet been done; when it is done, we may entertain better hopes of science.
The understanding of atomic physics is child’s play, compared with the understanding of child’s play.
The universality of parasitism as an offshoot of the predatory habit negatives the position taken by man that it is a pathological phenomenon or a deviation from the normal processes of nature. The pathological manifestations are only incidents in a developing parasitism. As human beings intent on maintaining man's domination over nature we may regard parasitism as pathological insofar as it becomes a drain upon human resources. In our efforts to protect ourselves we may make every kind of sacrifice to limit, reduce, and even eliminate parasitism as a factor in human life. Science attempts to define the terms on which this policy of elimination may or may not succeed. We must first of all thoroughly understand the problem, put ourselves in possession of all the facts in order to estimate the cost. Too often it has been assumed that parasitism was abnormal and that it needed only a slight force to reestablish what was believed to be a normal equilibrium without parasitism. On the contrary, biology teaches us that parasitism is a normal phenomenon and if we accept this view we shall be more ready to pay the price of freedom as a permanent and ever recurring levy of nature for immunity from a condition to which all life is subject. The greatest victory of man over nature in the physical realm would undoubtedly be his own delivery from the heavy encumbrance of parasitism with which all life is burdened.
The universe does not exist “out there,” independent of us. We are inescapably involved in bringing about that which appears to be happening. We are not only observers. We are participators. In some strange sense, this is a participatory universe. Physics is no longer satisfied with insights only into particles, fields of force, into geometry, or even into time and space. Today we demand of physics some understanding of existence itself.
The universe seems to me infinitely strange and foreign. At such a moment I gaze upon it with a mixture of anguish and euphoria; separate from the universe, as though placed at a certain distance outside it; I look and I see pictures, creatures that move in a kind of timeless time and spaceless space, emitting sounds that are a kind of language I no longer understand or ever register.
The way to solve the conflict between human values and technological needs is not to run away from technology, that’s impossible. The way to resolve the conflict is to break down the barriers of dualistic thought that prevent a real understanding of what technology is—not an exploitation of nature, but a fusion of nature and the human spirit into a new kind of creation that transcends both.
The wonderful structure of the animal system will probably never permit us to look upon it as a merely physical apparatus, yet the demands of science require that the evidently magnified principles of vitality should be reduced to their natural spheres, or if truth requires, wholly subverted in favor of those more cognizable by the human understanding. The spirit of the age will not tolerate in the devotee of science a quiet indifference. ...
The word “mathematics” is a Greek word and, by origin, it means “something that has been learned or understood,” or perhaps “acquired knowledge,” or perhaps even, somewhat against grammar, “acquirable knowledge,” that is, “learnable knowledge,” that is, “knowledge acquirable by learning.”
The work I have done has, already, been adequately rewarded and recognized. Imagination reaches out repeatedly trying to achieve some higher level of understanding, until suddenly I find myself momentarily alone before one new corner of nature’s pattern of beauty and true majesty revealed. That was my reward.
The world is very complicated and it is clearly impossible for the human mind to understand it completely. Man has therefore devised an artifice which permits the complicated nature of the world to be blamed on something which is called accidental and thus permits him to abstract a domain in which simple laws can be found.
There are four classes of Idols which beset men’s minds. To these for distinction’s sake I have assigned names,—calling the first class Idols of the Tribe; the second, Idols of the Cave; the third, Idols of the Market Place; the fourth, Idols of the Theatre …
The Idols of the Tribe have their foundation in human nature itself, and in the tribe or race of men. For it is a false assertion that the sense of man is the measure of things. On the contrary, all perceptions as well of the sense as of the mind are according to the measure of the individual and not according to the measure of the universe. And the human understanding is like a false mirror, which, receiving rays irregularly, distorts and discolours the nature of things by mingling its own nature with it.
The Idols of the Cave are the idols of the individual man. For every one (besides the errors common to human nature in general) has a cave or den of his own, which refracts and discolours the light of nature; owing either to his own proper and peculiar nature; or to his education and conversation with others; or to the reading of books, and the authority of those whom he esteems and admires; or to the differences of impressions, accordingly as they take place in a mind preoccupied and predisposed or in a mind indifferent and settled; or the like.
There are also Idols formed by the intercourse and association of men with each other, which I call Idols of the Market-place, on account of the commerce and consort of men there. For it is by discourse that men associate; and words are imposed according to the apprehension of the vulgar, and therefore the ill and unfit choice of words wonderfully obstructs the understanding. Nor do the definitions or explanations where with in some things learned men are wont to guard and defend themselves, by any means set the matter right. But words plainly force and overrule the understanding, and throw all into confusion, and lead men away into numberless empty controversies and idle fancies.
Lastly, there are Idols which have immigrated into men’s minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theatre; because in my judgment all the received systems are but so many stage-plays, representing worlds of their own creation after an unreal and scenic fashion.
The Idols of the Tribe have their foundation in human nature itself, and in the tribe or race of men. For it is a false assertion that the sense of man is the measure of things. On the contrary, all perceptions as well of the sense as of the mind are according to the measure of the individual and not according to the measure of the universe. And the human understanding is like a false mirror, which, receiving rays irregularly, distorts and discolours the nature of things by mingling its own nature with it.
The Idols of the Cave are the idols of the individual man. For every one (besides the errors common to human nature in general) has a cave or den of his own, which refracts and discolours the light of nature; owing either to his own proper and peculiar nature; or to his education and conversation with others; or to the reading of books, and the authority of those whom he esteems and admires; or to the differences of impressions, accordingly as they take place in a mind preoccupied and predisposed or in a mind indifferent and settled; or the like.
There are also Idols formed by the intercourse and association of men with each other, which I call Idols of the Market-place, on account of the commerce and consort of men there. For it is by discourse that men associate; and words are imposed according to the apprehension of the vulgar, and therefore the ill and unfit choice of words wonderfully obstructs the understanding. Nor do the definitions or explanations where with in some things learned men are wont to guard and defend themselves, by any means set the matter right. But words plainly force and overrule the understanding, and throw all into confusion, and lead men away into numberless empty controversies and idle fancies.
Lastly, there are Idols which have immigrated into men’s minds from the various dogmas of philosophies, and also from wrong laws of demonstration. These I call Idols of the Theatre; because in my judgment all the received systems are but so many stage-plays, representing worlds of their own creation after an unreal and scenic fashion.
There are no small problems. Problems that appear small are large problems that are not understood
There are two kinds of biologists, those who are looking to see if there is one thing that can be understood and those who keep saying it is very complicated and that nothing can be understood. ... You must study the simplest system you think has the properties you are interested in.
There is a story that once, not long after he came to Berlin, Planck forgot which room had been assigned to him for a lecture and stopped at the entrance office of the university to find out. Please tell me, he asked the elderly man in charge, “In which room does Professor Planck lecture today?” The old man patted him on the shoulder “Don't go there, young fellow,” he said “You are much too young to understand the lectures of our learned Professor Planck.”
There is a tendency to consider anything in human behavior that is unusual, not well known, or not well understood, as neurotic, psychopathic, immature, perverse, or the expression of some other sort of psychologic disturbance.
There is another form of temptation even more fraught with danger. This is the disease of curiosity. ... It is this which drives us on to try to discover the secrets of nature, those secrets which are beyond our understanding, which can avail us nothing and which men should not wish to learn.
There is another ground of hope that must not be omitted. Let men but think over their infinite expenditure of understanding, time, and means on matters and pursuits of far less use and value; whereof, if but a small part were directed to sound and solid studies, there is no difficulty that might not be overcome.
There is at least as much mystery in science for the modern man as there ever was in religion; in a sense there is more mystery, for the logic of science is still altogether beyond his understanding, whereas the logic of revelation is the logic of his own feelings.
There is no art or science that is too difficult for industry to attain to; it is the gift of tongues, and makes a man understood and valued in all countries, and by all nations; it is the philosopher's stone, that turns all metals, and even stones, into gold, and suffers not want to break into its dwelling; it is the northwest passage, that brings the merchant's ships as soon to him as he can desire: in a word, it conquers all enemies, and makes fortune itself pay contribution.
There is no art so difficult as the art of observation: it requires a skillful, sober spirit and a well-trained experience, which can only be acquired by practice; for he is not an observer who only sees the thing before him with his eyes, but he who sees of what parts the thing consists, and in what connexion the parts stand to the whole. One person overlooks half from inattention; another relates more than he sees while he confounds it with that which he figures to himself; another sees the parts of the whole, but he throws things together that ought to be separated. ... When the observer has ascertained the foundation of a phenomenon, and he is able to associate its conditions, he then proves while he endeavours to produce the phenomena at his will, the correctness of his observations by experiment. To make a series of experiments is often to decompose an opinion into its individual parts, and to prove it by a sensible phenomenon. The naturalist makes experiments in order to exhibit a phenomenon in all its different parts. When he is able to show of a series of phenomena, that they are all operations of the same cause, he arrives at a simple expression of their significance, which, in this case, is called a Law of Nature. We speak of a simple property as a Law of Nature when it serves for the explanation of one or more natural phenomena.
There is no doubt but men of genius and leisure may carry our method to greater perfection, but, having had long experience, we have found none equal to it for the commodiousness it affords in working with the Understanding.
There is no result in nature without a cause; understand the cause and you will have no need of the experiment.
There is not so contemptible a Plant or Animal that does not confound the most enlarged Understanding. Though the familiar use of Things, take off our Wonder; yet it cures not our Ignorance.
There is, then, one great purpose for man and for us today, and that is to try to discover man’s purpose by every means in our power. That is the ultimate relevance of science, and not only of science, but of every branch of learning which can improve our understanding. In the words of Tolstoy, “The highest wisdom has but one science, the science of the whole, the science explaining the Creation and man’s place in it.”
These Disciplines [mathematics] serve to inure and corroborate the Mind to a constant Diligence in Study; to undergo the Trouble of an attentive Meditation, and cheerfully contend with such Difficulties as lie in the Way. They wholly deliver us from a credulous Simplicity, most strongly fortify us against the Vanity of Scepticism, effectually restrain from a rash Presumption, most easily incline us to a due Assent, perfectly subject us to the Government of right Reason, and inspire us with Resolution to wrestle against the unjust Tyranny of false Prejudices. If the Fancy be unstable and fluctuating, it is to be poized by this Ballast, and steadied by this Anchor, if the Wit be blunt it is sharpened upon this Whetstone; if luxuriant it is pared by this Knife; if headstrong it is restrained by this Bridle; and if dull it is rouzed by this Spur. The Steps are guided by no Lamp more clearly through the dark Mazes of Nature, by no Thread more surely through the intricate Labyrinths of Philosophy, nor lastly is the Bottom of Truth sounded more happily by any other Line. I will not mention how plentiful a Stock of Knowledge the Mind is furnished from these, with what wholesome Food it is nourished, and what sincere Pleasure it enjoys. But if I speak farther, I shall neither be the only Person, nor the first, who affirms it; that while the Mind is abstracted and elevated from sensible Matter, distinctly views pure Forms, conceives the Beauty of Ideas, and investigates the Harmony of Proportions; the Manners themselves are sensibly corrected and improved, the Affections composed and rectified, the Fancy calmed and settled, and the Understanding raised and excited to more divine Contemplations. All which I might defend by Authority, and confirm by the Suffrages of the greatest Philosophers.
They [mathematicians] only take those things into consideration, of which they have clear and distinct ideas, designating them by proper, adequate, and invariable names, and premising only a few axioms which are most noted and certain to investigate their affections and draw conclusions from them, and agreeably laying down a very few hypotheses, such as are in the highest degree consonant with reason and not to be denied by anyone in his right mind. In like manner they assign generations or causes easy to be understood and readily admitted by all, they preserve a most accurate order, every proposition immediately following from what is supposed and proved before, and reject all things howsoever specious and probable which can not be inferred and deduced after the same manner.
This interpretation of the atomic number [as the number of orbital electrons] may be said to signify an important step toward the solution of the boldest dreams of natural science, namely to build up an understanding of the regularities of nature upon the consideration of pure number.
This is all very fine, but it won’t do—Anatomy—botany—Nonsense! Sir, I know an old woman in Covent Garden, who understands botany better, and as for anatomy, my butcher can dissect a joint full as well; no, young man, all that is stuff; you must go to the bedside, it is there alone you can learn disease!
Comment to Hans Sloane on Robert Boyle’s letter of introduction describing Sloane as a “ripe scholar, a good botanist, a skilful anatomist”.
Comment to Hans Sloane on Robert Boyle’s letter of introduction describing Sloane as a “ripe scholar, a good botanist, a skilful anatomist”.
This is an age of science. ... All important fields of activity from the breeding of bees to the administration of an empire, call for an understanding of the spirit and the technique of modern science. The nations that do not cultivate the sciences cannot hold their own.
This notion that “science” is something that belongs in a separate compartment of its own, apart from everyday life, is one that I should like to challenge. We live in a scientific age; yet we assume that knowledge of science is the prerogative of only a small number of human beings, isolated and priest-like in their laboratories. This is not true. It cannot be true. The materials of science are the materials of life itself. Science is part of the reality of living; it is the what, the how, and the why of everything in our experience. It is impossible to understand man without understanding his environment and the forces that have molded him physically and mentally.
Tho' there be no such Thing as Chance in the World; our Ignorance of the real Ccause of any Event has the same Influence on the Understanding, and begets a like Species of Belief or Opinion.
Those intervening ideas, which serve to show the agreement of any two others, are called proofs; and where the agreement or disagreement is by this means plainly and clearly perceived, it is called demonstration; it being shown to the understanding, and the mind made to see that it is so. A quickness in the mind to find out these intermediate ideas, (that shall discover the agreement or disagreement of any other) and to apply them right, is, I suppose, that which is called sagacity.
Those who are fruitful in useful inventions and discoveries, in the practical mechanical arts, are men, not only of the greatest utility, but possess an understanding, which should be most highly estimated.
Those who have handled sciences have been either men of experiment or men of dogmas. The men of experiment are like the ant; they only collect and use; the reasoners resemble spiders, who make cobwebs out of their own substance. But the bee takes a middle course; it gathers its material from the flowers of the garden and of the field, but transforms and digests it by a power of its own. Not unlike this is the true business of philosophy; for it neither relies solely or chiefly on the powers of the mind, nor does it take the matter which it gathers from natural history and mechanical experiments and lay it up in the memory whole, as it finds it; but lays it up in the understanding altered and digested. Therefore from a closer and purer league between these two faculties, the experimental and the rational (such as has never yet been made), much may be hoped.
Though Hippocrates understood not the Circulation of the Blood, yet by accurately observing the Effects of the Disease, which he looked upon as an unknown Entity, and by remarking the Endeavours of Nature, by which the Disease tended to either Health or Recovery, did from thence deduce a proper Method of Cure, namely by assisting the salutary Endeavours of Nature, and by resisting those of the Disease; and thus Hippocrates, ignorant of the Causes, cured Disease as well as ourselves, stocked with so many Discoveries.
Though the world does not change with a change of paradigm, the scientist afterward works in a different world... I am convinced that we must learn to make sense of statements that at least resemble these. What occurs during a scientific revolution is not fully reducible to a re-interpretation of individual and stable data. In the first place, the data are not unequivocally stable.
Thoughts without content are empty, intuitions without concepts are blind... The understanding can intuit nothing, the senses can think nothing. Only through their union can knowledge arise.
Through it [Science] we believe that man will be saved from misery and degradation, not merely acquiring new material powers, but learning to use and to guide his life with understanding. Through Science he will be freed from the fetters of superstition; through faith in Science he will acquire a new and enduring delight in the exercise of his capacities; he will gain a zest and interest in life such as the present phase of culture fails to supply.
To ask what qualities distinguish good from routine scientific research is to address a question that should be of central concern to every scientist. We can make the question more tractable by rephrasing it, “What attributes are shared by the scientific works which have contributed importantly to our understanding of the physical world—in this case the world of living things?” Two of the most widely accepted characteristics of good scientific work are generality of application and originality of conception. . These qualities are easy to point out in the works of others and, of course extremely difficult to achieve in one’s own research. At first hearing novelty and generality appear to be mutually exclusive, but they really are not. They just have different frames of reference. Novelty has a human frame of reference; generality has a biological frame of reference. Consider, for example, Darwinian Natural Selection. It offers a mechanism so widely applicable as to be almost coexistent with reproduction, so universal as to be almost axiomatic, and so innovative that it shook, and continues to shake, man’s perception of causality.
To be worthy of the name, an experimenter must be at once theorist and practitioner. While he must completely master the art of establishing experimental facts, which are the materials of science, he must also clearly understand the scientific principles which guide his reasoning through the varied experimental study of natural phenomena. We cannot separate these two things: head and hand. An able hand, without a head to direct it, is a blind tool; the head is powerless without its executive hand.
To make a discovery is not necessarily the same as to understand a discovery.
To me, science is an expression of the human spirit, which reaches every sphere of human culture. It gives an aim and meaning to existence as well as a knowledge, understanding, love, and admiration for the world. It gives a deeper meaning to morality and another dimension to esthetics.
To mean understandings, it is sufficient honour to be numbered amongst the lowest labourers of learning; but different abilities must find different tasks. To hew stone, would have been unworthy of Palladio; and to have rambled in search of shells and flowers, had but ill suited with the capacity of Newton.
To Monsieur Lavoisier by appointment. Madame Lavoisier, a lively, sensible, scientific lady, had prepared a dejuné Anglois of tea and coffee, but her conversation on Mr. Kirwan’s Essay on Phlogiston, which she is translating from the English, and on other subjects, which a woman of understanding, that works with her husband in his laboratory, knows how to adorn, was the best repast.
To suppose that so perfect a system as that of Euclid’s Elements was produced by one man, without any preceding model or materials, would be to suppose that Euclid was more than man. We ascribe to him as much as the weakness of human understanding will permit, if we suppose that the inventions in geometry, which had been made in a tract of preceding ages, were by him not only carried much further, but digested into so admirable a system, that his work obscured all that went before it, and made them be forgot and lost.
To understand God’s thoughts, one must study statistics, for these are the measure of His purpose.
To understand hydrogen is to understand all of physics.
Truth and falsity, indeed understanding, is not necessarily something purely intellectual, remote from feelings and attitudes. ... It is in the total conduct of men rather than in their statements that truth or falsehood lives, more in what a man does, in his real reaction to other men and to things, in his will to do them justice, to live at one with them. Here lies the inner connection between truth and justice. In the realm of behavior and action, the problem recurs as to the difference between piece and part.
Truth and understanding are not such wares as to be monopolized and traded in by tickets and statutes and standards. We must not think to make a staple commodity of all the knowledge in the land, to mark and license it like our broadcloth and our woolpacks.
Truth scarce ever yet carried it by Vote any where at its first appearance: New Opinions are always suspected, and usually opposed, without any other Reason, but because they are not already common.
Unconscious, perhaps, of the remote tendency of his own labours, he [Joseph Black] undermined that doctrine of material heat, which he seemed to support. For, by his advocacy of latent heat, he taught that its movements constantly battle, not only some of our senses, but all of them; and that, while our feelings make us believe that heat is lost, our intellect makes us believe that it is not lost. Here, we have apparent destructability, and real indestructibility. To assert that a body received heat without its temperature rising, was to make the understanding correct the touch, and defy its dictates. It was a bold and beautiful paradox, which required courage as well as insight to broach, and the reception of which marks an epoch in the human mind, because it was an immense step towards idealizing matter into force.
Understanding … must begin by saturating itself with facts and realities. … Besides, we only understand that which is already within us. To understand is to possess the thing understood, first by sympathy and then by intelligence. Instead of first dismembering and dissecting the object to be conceived, we should begin by laying hold of it in its ensemble. The procedure is the same, whether we study a watch or a plant, a work of art or a character.
Understanding a theory has, indeed, much in common with understanding a human personality. We may know or understand a man's system of dispositions pretty well; that is to say, we may be able to predict how he would act in a number of different situations. But since there are infinitely many possible situations, of infinite variety, a full understanding of a man's dispositions does not seem to be possible.
Understanding is the reward of faith. Therefore, do not seek to understand in order to believe, but believe that thou mayest understand; since “except ye believe ye shall not understand.”
Understanding the world for a man is reducing it to the human, stamping it with his seal.
Undeveloped though the science [of chemistry] is, it already has great power to bring benefits. Those accruing to physical welfare are readily recognized, as in providing cures, improving the materials needed for everyday living, moving to ameliorate the harm which mankind by its sheer numbers does to the environment, to say nothing of that which even today attends industrial development. And as we continue to improve our understanding of the basic science on which applications increasingly depend, material benefits of this and other kinds are secured for the future.
Unless you make yourself equal to God, you cannot understand God: for the like is not intelligible save to the like. Make yourself grow to a greatness beyond measure, by a bound free yourself from the body; raise yourself above all time, become Eternity; then you will understand God. Believe that nothing is impossible for you, think yourself immortal and capable of understanding all, all arts, all sciences, the nature of every living being. Mount higher than the highest height; descend lower than the lowest depth. Draw into yourself all sensations of everything created, fire and water, dry and moist, imagining that you are everywhere, on earth, in the sea, in the sky, that you are not yet born, in the maternal womb, adolescent, old, dead, beyond death. If you embrace in your thought all things at once, times, places, substances, qualities, quantities, you may understand God.
We achieve more than we know. We know more than we understand. We understand more than we can explain.
We are all travelers who are journeying … not knowing where the next day of our life is going to take us. We have no understanding of the surprises that are in store for us. Steadily we will know, understand and decipher and then it will all start to make sense. Until then keep travelling.
We are as remote from adequate explanation of the nature and causes of mechanical evolution of the hard parts of animals as we were when Aristotle first speculated on this subject … I think it is possible that we may never fathom all the causes of mechanical evolution or of the origin of new mechanical characters, but shall have to remain content with observing the modes of mechanical evolution, just as embryologists and geneticists are observing the modes of development, from the fertilized ovum to the mature individual, without in the least understanding either the cause or the nature of the process of development which goes on under their eyes every day
We are going through the body-snatching phase right now, and there are all these Burke and Hare attitudes towards geneticists-that they are playing God and that DNA is sacred. No, it’s not. It’s no more sacred than your toenails. Basically, we are not going to make long-term medical progress without understanding how the genes work.
[Referring to the similarity of fears and superstitions in genetics as once were associated with anatomy ]
[Referring to the similarity of fears and superstitions in genetics as once were associated with anatomy ]
We are just beginning to understand how molecular reaction systems have found a way to “organize themselves”. We know that processes of this nature ultimately led to the life cycle, and that (for the time being?) Man with his central nervous system, i.e. his memory, his mind, and his soul, stands at the end of this development and feels compelled to understand this development. For this purpose he must penetrate into the smallest units of time and space, which also requires new ideas to make these familiar concepts from physics of service in understanding what has, right into our century, appeared to be beyond the confines of space and time.
We believe that interest in nature leads to knowledge,
which is followed by understanding,
and later, appreciation.
Once respect is gained
it is a short step to responsibility,
and ultimately action
to preserve our Earth.
which is followed by understanding,
and later, appreciation.
Once respect is gained
it is a short step to responsibility,
and ultimately action
to preserve our Earth.
We cannot doubt the existence of an ultimate reality. It is the universe forever masked. We are a part of it, and the masks figured by us are the universe observing and understanding itself from a human point of view.
We cannot hope to either understand or to manage the carbon in the atmosphere unless we understand and manage the trees and the soil too.
We have to understand that the world can only be grasped by action, not by contemplation. The hand is more important than the eye ... The hand is the cutting edge of the mind.
We intend to say something about the structure of the atom but lack a language in which we can make ourselves understood. We are in much the same position as a sailor, marooned on a remote island where conditions differ radically from anything he has ever known and where, to make things worse, the natives speak a completely alien tongue.
We may best hope to understand the nature and conditions of real knowledge, by studying the nature and conditions of the most certain and stable portions of knowledge which we already possess: and we are most likely to learn the best methods of discovering truth, by examining how truths, now universally recognised, have really been discovered.
We may... have to relinquish the notion, explicit or implicit, that changes of paradigm carry scientists and those who learn from them closer and closer to the truth... The developmental process described in this essay has been a process of evolution from primitive beginnings—a process whose successive stages are characterized by an increasingly detailed and refined understanding of nature. But nothing that has been or will be said makes it a process of evolution toward anything.
We must not only prepare [students] in sciences, we must prepare them in other areas. For example, I teach Chemistry but on every test I give I have an English question. And I give a simple question. I say, “Discuss your understanding of this topic.”
We must painfully acknowledge that, precisely because of its great intellectual developments, the best of man's domesticated animals—the dog—most often becomes the victim of physiological experiments. Only dire necessity can lead one to experiment on cats—on such impatient, loud, malicious animals. During chronic experiments, when the animal, having recovered from its operation, is under lengthy observation, the dog is irreplaceable; moreover, it is extremely touching. It is almost a participant in the experiments conducted upon it, greatly facilitating the success of the research by its understanding and compliance.
We need science education to produce scientists, but we need it equally to create literacy in the public. Man has a fundamental urge to comprehend the world about him, and science gives today the only world picture which we can consider as valid. It gives an understanding of the inside of the atom and of the whole universe, or the peculiar properties of the chemical substances and of the manner in which genes duplicate in biology. An educated layman can, of course, not contribute to science, but can enjoy and participate in many scientific discoveries which as constantly made. Such participation was quite common in the 19th century, but has unhappily declined. Literacy in science will enrich a person’s life.
We often frame our understanding of what the [Hubble] space telescope will do in terms of what we expect to find, and actually it would be terribly anticlimactic if in fact we find what we expect to find. … The most important discoveries will provide answers to questions that we do not yet know how to ask and will concern objects we have not yet imagined.
We often observe in lawyers, who as Quicquid agunt homines is the matter of law suits, are sometimes obliged to pick up a temporary knowledge of an art or science, of which they understood nothing till their brief was delivered, and appear to be much masters of it.
We pass the word around; we ponder how the case is put by different people, we read the poetry; we meditate over the literature; we play the music; we change our minds; we reach an understanding. Society evolves this way. Not by shouting each other down, but by the unique capacity of unique, individual human beings to comprehend each other.
We think we understand the regular reflection of light and X rays - and we should understand the reflections of electrons as well if electrons were only waves instead of particles ... It is rather as if one were to see a rabbit climbing a tree, and were to say ‘Well, that is rather a strange thing for a rabbit to be doing, but after all there is really nothing to get excited about. Cats climb trees - so that if the rabbit were only a cat, we would understand its behavior perfectly.’ Of course, the explanation might be that what we took to be a rabbit was not a rabbit at all but was actually a cat. Is it possible that we are mistaken all this time in supposing they are particles, and that actually they are waves?
We want them to use the education to be leaders in their community with an understanding of ecology and conservation for the wild outdoors far beyond their legislators back home. We expect these people to he a grain of sand on the beach of future leadership.
We were very privileged to leave on the Moon a plaque ... saying, ‘For all Mankind’. Perhaps in the third millennium a wayward stranger will read the plaque at Tranquility Base. We’ll let history mark that this was the age in which that became a fact. I was struck this morning in New York by a proudly waved but uncarefully scribbled sign. It said, ‘Through you we touched the Moon.’ It was our privilege today to touch America. I suspect perhaps the most warm, genuine feeling that all of us could receive came through the cheers and shouts and, most of all, the smiles of our fellow Americans. We hope and think that those people shared our belief that this is the beginning of a new era—the beginning of an era when man understands the universe around him, and the beginning of the era when man understands himself.
What a splendid perspective contact with a profoundly different civilization might provide! In a cosmic setting vast and old beyond ordinary human understanding we are a little lonely, and we ponder the ultimate significance, if any, of our tiny but exquisite blue planet, the Earth… In the deepest sense the search for extraterrestrial intelligence is a search for ourselves.
What distinguishes the language of science from language as we ordinarily understand the word? … What science strives for is an utmost acuteness and clarity of concepts as regards their mutual relation and their correspondence to sensory data.
What has been learned in physics stays learned. People talk about scientific revolutions. The social and political connotations of revolution evoke a picture of a body of doctrine being rejected, to be replaced by another equally vulnerable to refutation. It is not like that at all. The history of physics has seen profound changes indeed in the way that physicists have thought about fundamental questions. But each change was a widening of vision, an accession of insight and understanding. The introduction, one might say the recognition, by man (led by Einstein) of relativity in the first decade of this century and the formulation of quantum mechanics in the third decade are such landmarks. The only intellectual casualty attending the discovery of quantum mechanics was the unmourned demise of the patchwork quantum theory with which certain experimental facts had been stubbornly refusing to agree. As a scientist, or as any thinking person with curiosity about the basic workings of nature, the reaction to quantum mechanics would have to be: “Ah! So that’s the way it really is!” There is no good analogy to the advent of quantum mechanics, but if a political-social analogy is to be made, it is not a revolution but the discovery of the New World.
What is a good definition? For the philosopher or the scientist, it is a definition which applies to all the objects to be defined, and applies only to them; it is that which satisfies the rules of logic. But in education it is not that; it is one that can be understood by the pupils.
What renders a problem definite, and what leaves it indefinite, may best be understood from mathematics. The very important idea of solving a problem within limits of error is an element of rational culture, coming from the same source. The art of totalizing fluctuations by curves is capable of being carried, in conception, far beyond the mathematical domain, where it is first learnt. The distinction between laws and co-efficients applies in every department of causation. The theory of Probable Evidence is the mathematical contribution to Logic, and is of paramount importance.
When he to whom a person speaks does not understand, and he who speaks does not understand himself, that is metaphysics.
When it comes to understanding the planet’s blue [ocean] frontier, one of the largest challenges we face can be encapsulated by a simple phrase: Out of sight, out of mind.
When scientific programs are judged by popular acclaim we inevitably have overemphasis on the spectacular. … The deeply important scientific advances moving today are not easy to understand. If they were they would have been accomplished long ago.
When understanding of the universe has become widespread, when the majority of men know that the stars are not sources of light but worlds, perhaps inhabited worlds like ours, then the Christian doctrine will be convicted of absurdity.
When we understand how animals are resistant to chemicals, the mechanisms are all independent of whether its natural or synthetic. And in fact, when you look at natural chemicals, half of those tested come out positive.
Where should I start? Start from the statement of the problem. ... What can I do? Visualize the problem as a whole as clearly and as vividly as you can. ... What can I gain by doing so? You should understand the problem, familiarize yourself with it, impress its purpose on your mind.
Wherever it was, I did not come to know it through the bodily senses; the only things we know through the bodily senses are material objects, which we have found are not truly and simply one. Moreover, if we do not perceive one by the bodily sense, then we do not perceive any number by that sense, at least of those numbers that we grasp by understanding.
Who then understands the reciprocal flux and reflux of the infinitely great and the infinitely small, the echoing of causes in the abysses of being, and the avalanches of creation?
Why does a man want to be a scientist? There are many goals: fame, position, a thirst for understanding. The first two can be attained without intellectual integrity; the third cannot. … The thirst for knowledge, what Thomas Huxley called the ‘Divine dipsomania’, can only be satisfied by complete intellectual integrity. It seems to me the only one of the three goals that continues to reward the pursuer. He presses on, “knowing that Nature never did betray the heart that loved her”. Here is another kind of love, that has so many faces. Love is neither passion, nor pride, nor pity, nor blind adoration, but it can be any or all of these if they are transfigured by deep and unbiased understanding.
Widespread intellectual and moral docility may be convenient for leaders in the short term, but it is suicidal for nations in the long term. One of the criteria for national leadership should therefore be a talent for understanding, encouraging, and making constructive use of vigorous criticism.
With the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out how thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which, at the same time, assist in understanding earlier theories and in casting aside some more complicated developments.
Without initiation into the scientific spirit one is not in possession of the best tools humanity has so far devised for effectively directed reflection. [Without these one] fails to understand the full meaning of knowledge.
Without my attempts in natural science, I should never have learned to know mankind such as it is. In nothing else can we so closely approach pure contemplation and thought, so closely observe the errors of the senses and of the understanding, the weak and strong points of character.
Without some idea of oxidation processes, of the chemical structure of food, and of the chemical reactions in digestion, visceral behavior is a blank. And without some understanding of visceral behavior, psychic behavior is up in the air.
Without the sensuous faculty no object would be given to us, without understanding no object would be thought. Thoughts without content are void, intuitions without conceptions, blind.
Wonder [admiratio astonishment, marvel] is a kind of desire for knowledge. The situation arises when one sees an effect and does not know its cause, or when the cause of the particular effect is one that exceeds his power of understanding. Hence, wonder is a cause of pleasure insofar as there is annexed the hope of attaining understanding of that which one wants to know. ... For desire is especially aroused by the awareness of ignorance, and consequently a man takes the greatest pleasure in those things which he discovers for himself or learns from the ground up.
Wonder [admiratio astonishment, marvel] is a kind of desire for knowledge. The situation arises when one sees an effect and does not know its cause, or when the cause of the particular effect is one that exceeds his power of understanding. Hence, wonder is a cause of pleasure insofar as there is annexed the hope of attaining understanding of that which one wants to know. ... For desire is especially aroused by the awareness of ignorance, and consequently a man takes the greatest pleasure in those things which he discovers for himself or learns from the ground up.
You don’t understand anything until you learn it more than one way.
You don't need a science degree to understand about science. You just need to think about it.