Meaning Quotes (244 quotes)
Meanings Quotes
Meanings Quotes
...it is not to be taken in the sense of our day, which we reckon by the course of the sun; but it must have another meaning, applicable to the
three days mentioned before the creation of the heavenly bodies.
three days mentioned before the creation of the heavenly bodies.
“It's absolutely clear that the function of the world is to declare the glory of God.” I thought, what does that sentence mean?!
[Culture] denotes an historically transmitted pattern of meanings embodied in symbols, a system of inherited conceptions expressed in symbolic forms, by means of which men communicate, perpetuate, and develop their knowledge about and attitudes toward life.
[In] the realm of science, … what we have achieved will be obsolete in ten, twenty or fifty years. That is the fate, indeed, that is the very meaning of scientific work. … Every scientific “fulfillment” raises new “questions” and cries out to be surpassed and rendered obsolete. Everyone who wishes to serve science has to resign himself to this.
[Radius]: You will work. You will build ... You will serve them... Robots of the world... The power of man has fallen... A new world has arisen. The rule of the Robots... March!
The word 'robot' was coined in this play for a new working class of automatons (from the Czech word robota meaning compulsory labour)
The word 'robot' was coined in this play for a new working class of automatons (from the Czech word robota meaning compulsory labour)
[Scientists] define these [terms] in tight phrases which convey a meaning only to those who already understand it.
[Two college boys on the Flambeau River in a canoe]…their first…taste of freedom … The elemental simplicities of wilderness travel were thrills not only because of their novelty, but because they represented complete freedom to make mistakes. The wilderness gave them their first taste of those rewards and penalties for wise and foolish acts which every woodsman faces daily, but against which civilization has built a thousand buffers. These boys were “on their own” in this particular sense. Perhaps every youth needs an occasional wilderness trip, in order to learn the meaning of this particular freedom.
'Causation' has been popularly used to express the condition of association, when applied to natural phenomena. There is no philosophical basis for giving it a wider meaning than partial or absolute association. In no case has it been proved that there is an inherent necessity in the laws of nature. Causation is correlation... [P]erfect correlation, when based upon sufficient experience, is causation in the scientific sense.
Question: If you were to pour a pound of molten lead and a pound of molten iron, each at the temperature of its melting point, upon two blocks of ice, which would melt the most ice, and why?
Answer: This question relates to diathermancy. Iron is said to be a diathermanous body (from dia, through, and thermo, I heat), meaning that it gets heated through and through, and accordingly contains a large quantity of real heat. Lead is said to be an athermanous body (from a, privative, and thermo, I heat), meaning that it gets heated secretly or in a latent manner. Hence the answer to this question depends on which will get the best of it, the real heat of the iron or the latent heat of the lead. Probably the iron will smite furthest into the ice, as molten iron is white and glowing, while melted lead is dull.
Answer: This question relates to diathermancy. Iron is said to be a diathermanous body (from dia, through, and thermo, I heat), meaning that it gets heated through and through, and accordingly contains a large quantity of real heat. Lead is said to be an athermanous body (from a, privative, and thermo, I heat), meaning that it gets heated secretly or in a latent manner. Hence the answer to this question depends on which will get the best of it, the real heat of the iron or the latent heat of the lead. Probably the iron will smite furthest into the ice, as molten iron is white and glowing, while melted lead is dull.
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 chemical name should not be a phrase, it ought not to require circumlocutions to become definite; it should not be of the type “Glauber’s salt”, which conveys nothing about the composition of the substance; it should recall the constituents of a compound; it should be non-committal if nothing is known about the substance; the names should preferably be coined from Latin or Greek, so that their meaning can be more widely and easily understood; the form of the words should be such that they fit easily into the language into which they are to be incorporated.
A great surgeon performs operations for stone by a single method; later he makes a statistical summary of deaths and recoveries, and he concludes from these statistics that the mortality law for this operation is two out of five. Well, I say that this ratio means literally nothing scientifically and gives us no certainty in performing the next operation; for we do not know whether the next case will be among the recoveries or the deaths. What really should be done, instead of gathering facts empirically, is to study them more accurately, each in its special determinism. We must study cases of death with great care and try to discover in them the cause of mortal accidents so as to master the cause and avoid the accidents.
A number of years ago, when I was a freshly-appointed instructor, I met, for the first time, a certain eminent historian of science. At the time I could only regard him with tolerant condescension.
I was sorry of the man who, it seemed to me, was forced to hover about the edges of science. He was compelled to shiver endlessly in the outskirts, getting only feeble warmth from the distant sun of science- in-progress; while I, just beginning my research, was bathed in the heady liquid heat up at the very center of the glow.
In a lifetime of being wrong at many a point, I was never more wrong. It was I, not he, who was wandering in the periphery. It was he, not I, who lived in the blaze.
I had fallen victim to the fallacy of the “growing edge;” the belief that only the very frontier of scientific advance counted; that everything that had been left behind by that advance was faded and dead.
But is that true? Because a tree in spring buds and comes greenly into leaf, are those leaves therefore the tree? If the newborn twigs and their leaves were all that existed, they would form a vague halo of green suspended in mid-air, but surely that is not the tree. The leaves, by themselves, are no more than trivial fluttering decoration. It is the trunk and limbs that give the tree its grandeur and the leaves themselves their meaning.
There is not a discovery in science, however revolutionary, however sparkling with insight, that does not arise out of what went before. “If I have seen further than other men,” said Isaac Newton, “it is because I have stood on the shoulders of giants.”
I was sorry of the man who, it seemed to me, was forced to hover about the edges of science. He was compelled to shiver endlessly in the outskirts, getting only feeble warmth from the distant sun of science- in-progress; while I, just beginning my research, was bathed in the heady liquid heat up at the very center of the glow.
In a lifetime of being wrong at many a point, I was never more wrong. It was I, not he, who was wandering in the periphery. It was he, not I, who lived in the blaze.
I had fallen victim to the fallacy of the “growing edge;” the belief that only the very frontier of scientific advance counted; that everything that had been left behind by that advance was faded and dead.
But is that true? Because a tree in spring buds and comes greenly into leaf, are those leaves therefore the tree? If the newborn twigs and their leaves were all that existed, they would form a vague halo of green suspended in mid-air, but surely that is not the tree. The leaves, by themselves, are no more than trivial fluttering decoration. It is the trunk and limbs that give the tree its grandeur and the leaves themselves their meaning.
There is not a discovery in science, however revolutionary, however sparkling with insight, that does not arise out of what went before. “If I have seen further than other men,” said Isaac Newton, “it is because I have stood on the shoulders of giants.”
Absolute space, that is to say, the mark to which it would be necessary to refer the earth to know whether it really moves, has no objective existence…. The two propositions: “The earth turns round” and “it is more convenient to suppose the earth turns round” have the same meaning; there is nothing more in the one than in the other.
Acute [diseases] meaning those of which God is the author, chronic meaning those that originate in ourselves.
Again and again in reading even his [William Thomson] most abstract writings one is struck by the tenacity with which physical ideas control in him the mathematical form in which he expressed them. An instance of this is afforded by … an example of a mathematical result that is, in his own words, “not instantly obvious from the analytical form of my solution, but which we immediately see must be the case by thinking of the physical meaning of the result.”
Among all the liberal arts, the first is logic, and specifically that part of logic which gives initial instruction about words. … [T]he word “logic” has a broad meaning, and is not restricted exclusively to the science of argumentative reasoning. [It includes] Grammar [which] is “the science of speaking and writing correctly—the starting point of all liberal studies.”
Among the multitude of animals which scamper, fly, burrow and swim around us, man is the only one who is not locked into his environment. His imagination, his reason, his emotional subtlety and toughness, make it possible for him not to accept the environment, but to change it. And that series of inventions, by which man from age to age has remade his environment, is a different kind of evolution—not biological, but cultural evolution. I call that brilliant sequence of cultural peaks The Ascent of Man. I use the word ascent with a precise meaning. Man is distinguished from other animals by his imaginative gifts. He makes plans, inventions, new discoveries, by putting different talents together; and his discoveries become more subtle and penetrating, as he learns to combine his talents in more complex and intimate ways. So the great discoveries of different ages and different cultures, in technique, in science, in the arts, express in their progression a richer and more intricate conjunction of human faculties, an ascending trellis of his gifts.
Among the older records, we find chapter after chapter of which we can read the characters, and make out their meaning: and as we approach the period of man’s creation, our book becomes more clear, and nature seems to speak to us in language so like our own, that we easily comprehend it. But just as we begin to enter on the history of physical changes going on before our eyes, and in which we ourselves bear a part, our chronicle seems to fail us—a leaf has been torn out from nature's record, and the succession of events is almost hidden from our eyes.
An equation means nothing to me unless it expresses a thought of God.
As an Art, Mathematics has its own standard of beauty and elegance which can vie with the more decorative arts. In this it is diametrically opposed to a Baroque art which relies on a wealth of ornamental additions. Bereft of superfluous addenda, Mathematics may appear, on first acquaintance, austere and severe. But longer contemplation reveals the classic attributes of simplicity relative to its significance and depth of meaning.
As far as the meaning of life in general, or in the abstract, as far as I can see, there is none. If all of life were suddenly to disappear from earth and anywhere else it may exist, or if none had ever formed in the first place, I think the Universe would continue to exist without perceptible change. However, it is always possible for an individual to invest his own life with meaning that he can find significant. He can so order his life that he may find as much beauty and wisdom in it as he can, and spread as much of that to others as possible.
As I strayed into the study of an eminent physicist, I observed hanging against the wall, framed like a choice engraving, several dingy, ribbon-like strips of, I knew not what... My curiosity was at once aroused. What were they? ... They might be shreds of mummy-wraps or bits of friable bark-cloth from the Pacific, ... [or] remnants from a grandmother’s wedding dress... They were none of these... He explained that they were carefully-prepared photographs of portions of the Solar Spectrum. I stood and mused, absorbed in the varying yet significant intensities of light and shade, bordered by mystic letters and symbolic numbers. As I mused, the pale legend began to glow with life. Every line became luminous with meaning. Every shadow was suffused with light shining from behind, suggesting some mighty achievement of knowledge; of knowledge growing more daring in proportion to the remoteness of the object known; of knowledge becoming more positive in its answers, as the questions which were asked seemed unanswerable. No Runic legend, no Babylonish arrowhead, no Egyptian hieroglyph, no Moabite stone, could present a history like this, or suggest thoughts of such weighty import or so stimulate and exalt the imagination.
At first it seems obvious, but the more you think about it the stranger the deductions from this axiom seem to become; in the end you cease to understand what is meant by it.
Attaching significance to invariants is an effort to recognize what, because of its form or colour or meaning or otherwise, is important or significant in what is only trivial or ephemeral. A simple instance of failing in this is provided by the poll-man at Cambridge, who learned perfectly how to factorize a²-b² but was floored because the examiner unkindly asked for the factors of p²–q².
But although in theory physicists realize that their conclusions are ... not certainly true, this ... does not really sink into their consciousness. Nearly all the time ... they ... act as if Science were indisputably True, and what's more, as if only science were true.... Any information obtained otherwise than by the scientific method, although it may be true, the scientists will call “unscientific,” using this word as a smear word, by bringing in the connotation from its original [Greek] meaning, to imply that the information is false, or at any rate slightly phony.
But does Man have any “right” to spread through the universe? Man is what he is, a wild animal with the will to survive, and (so far) the ability, against all competition. Unless one accepts that, anything one says about morals, war, politics, you name it, is nonsense. Correct morals arise from knowing what man is, not what do-gooders and well-meaning old Aunt Nellies would like him to be. The Universe will let us know—later—whether or not Man has any “right” to expand through it.
By far the most important consequence of the conceptual revolution brought about in physics by relativity and quantum theory lies not in such details as that meter sticks shorten when they move or that simultaneous position and momentum have no meaning, but in the insight that we had not been using our minds properly and that it is important to find out how to do so.
Cayley was singularly learned in the work of other men, and catholic in his range of knowledge. Yet he did not read a memoir completely through: his custom was to read only so much as would enable him to grasp the meaning of the symbols and understand its scope. The main result would then become to him a subject of investigation: he would establish it (or test it) by algebraic analysis and, not infrequently, develop it so to obtain other results. This faculty of grasping and testing rapidly the work of others, together with his great knowledge, made him an invaluable referee; his services in this capacity were used through a long series of years by a number of societies to which he was almost in the position of standing mathematical advisor.
Curiosity that inborn property of man, daughter of ignorance and mother of knowledge when wonder wakens our minds, has the habit, wherever it sees some extraordinary phenomenon of nature, a comet for example, a sun-dog, or a midday star, of asking straightway what it means.
Darwin grasped the philosophical bleakness with his characteristic courage. He argued that hope and morality cannot, and should not, be passively read in the construction of nature. Aesthetic and moral truths, as human concepts, must be shaped in human terms, not ‘discovered’ in nature. We must formulate these answers for ourselves and then approach nature as a partner who can answer other kinds of questions for us–questions about the factual state of the universe, not about the meaning of human life. If we grant nature the independence of her own domain–her answers unframed in human terms–then we can grasp her exquisite beauty in a free and humble way. For then we become liberated to approach nature without the burden of an inappropriate and impossible quest for moral messages to assuage our hopes and fears. We can pay our proper respect to nature’s independence and read her own ways as beauty or inspiration in our different terms.
Darwin’s book is very important and serves me as a basis in natural science for the class struggle in history. One has to put up with the crude English method of development, of course. Despite all deficiencies not only is the death-blow dealt here for the first time to “teleology” in the natural sciences, but their rational meaning is empirically explained.
Death is what gives life meaning. To know your days are numbered. Your time is short.
— Movie
Divers of Hermetic Books have such involv’d Obscuritys that they may justly be compar’d to Riddles written in Cyphers. For after a Man has surmounted the difficulty of decyphering the Words & Terms, he finds a new & greater difficulty to discover ye meaning of the seemingly plain Expression.
Does there truly exist an insuperable contradiction between religion and science? Can religion be superseded by science? The answers to these questions have, for centuries, given rise to considerable dispute and, indeed, bitter fighting. Yet, in my own mind there can be no doubt that in both cases a dispassionate consideration can only lead to a negative answer. What complicates the solution, however, is the fact that while most people readily agree on what is meant by ‘science,’ they are likely to differ on the meaning of ‘religion.’
Dr. Paget was conducting a school examination, and in the course of his questions he happened to ask a small child the meaning of “Average.” He was utterly bewildered by the reply, “The thing that hens lay on,” until the child explained that he had read in a book that hens lay on an average so many eggs a year.
During the three years which I spent at Cambridge my time was wasted, as far as the academical studies were concerned…. I attempted mathematics, … but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish…
Engineering is the art of construction; but to limit it to this would be to restrict its meaning much within the range of the ordinary use of the word. In a broader sense, engineering includes all operations whose object is the utilization of the forces of nature in the interests of man.
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.
Every time we get slapped down, we can say, “Thank you Mother Nature,” because it means we’re about to learn something important.
Face this world. Learn its ways, watch it, be careful of too hasty guesses at its meaning. In the end you will find clues to it all.
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.
For, in mathematics or symbolic logic, reason can crank out the answer from the symboled equations—even a calculating machine can often do so—but it cannot alone set up the equations. Imagination resides in the words which define and connect the symbols—subtract them from the most aridly rigorous mathematical treatise and all meaning vanishes. Was it Eddington who said that we once thought if we understood 1 we understood 2, for 1 and 1 are 2, but we have since found we must learn a good deal more about “and”?
Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it is the truth.
Godless science reads nature only as Milton's daughters did Hebrew, rightly syllabling the sentences, but utterly ignorant of the meaning.
Good applied science in medicine, as in physics, requires a high degree of certainty about the basic facts at hand, and especially about their meaning, and we have not yet reached this point for most of medicine.
He who has never been deceived by a lie does not know the meaning of bliss.
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.”
I also require much time to ponder over the matters themselves, and particularly the principles of mechanics (as the very words: force, time, space, motion indicate) can occupy one severely enough; likewise, in mathematics, the meaning of imaginary quantities, of the infinitesimally small and infinitely large and similar matters.
I can conceive few human states more enviable than that of the man to whom, panting in the foul laboratory, or watching for his life under the tropic forest, Isis shall for a moment lift her sacred veil, and show him, once and for ever, the thing he dreamed not of; some law, or even mere hint of a law, explaining one fact; but explaining with it a thousand more, connecting them all with each other and with the mighty whole, till order and meaning shoots through some old Chaos of scattered observations.
I can hear the sizzle of newborn stars, and know anything of meaning, of the fierce magic emerging here. I am witness to flexible eternity, the evolving past, and I know we will live forever, as dust or breathe in the face of stars, in the shifting pattern of winds.
I despise Birth-Control first because it is ... an entirely meaningless word; and is used so as to curry favour even with those who would first recoil from its real meaning. The proceeding these quack doctors recommend does not control any birth. ... But these people know perfectly well that they dare not write the plain word Birth-Prevention, in any one of the hundred places where they write the hypocritical word Birth-Control. They know as well as I do that the very word Birth-Prevention would strike a chill into the public... Therefore they use a conventional and unmeaning word, which may make the quack medicine sound more innocuous. ... A child is the very sign and sacrament of personal freedom. He is a fresh will added to the wills of the world; he is something that his parents have freely chosen to produce ... he is their own creative contribution to creation.
I have now reached the point where I may indicate briefly what to me constitutes the essence of the crisis of our time. It concerns the relationship of the individual to society. The individual has become more conscious than ever of his dependence upon society. But he does not experience this dependence as a positive asset, as an organic tie, as a protective force, but rather as a threat to his natural rights, or even to his economic existence. Moreover, his position in society is such that the egotistical drives of his make-up are constantly being accentuated, while his social drives, which are by nature weaker, progressively deteriorate. All human beings, whatever their position in society, are suffering from this process of deterioration. Unknowingly prisoners of their own egotism, they feel insecure, lonely, and deprived of the naive, simple, and unsophisticated enjoyment of life. Man can find meaning in life, short and perilous as it is, only through devoting himself to society.
I maintain there is much more wonder in science than in pseudoscience. And in addition, to whatever measure this term has any meaning, science has the additional virtue, and it is not an inconsiderable one, of being true.
I must confess, I am dreading today’s elections, … because no matter what the outcome, our government will still be a giant bonfire of partisanship. It is ironic since whenever I have met with our elected officials they are invariably thoughtful, well-meaning people. And yet collectively 90% of their effort seems to be focused on how to stick it to the other party.
I myself, a professional mathematician, on re-reading my own work find it strains my mental powers to recall to mind from the figures the meanings of the demonstrations, meanings which I myself originally put into the figures and the text from my mind. But when I attempt to remedy the obscurity of the material by putting in extra words, I see myself falling into the opposite fault of becoming chatty in something mathematical.
I once spoke to a human geneticist who declared that the notion of intelligence was quite meaningless, so I tried calling him unintelligent. He was annoyed, and it did not appease him when I went on to ask how he came to attach such a clear meaning to the notion of lack of intelligence. We never spoke again.
I require a term to express those bodies which can pass to the electrodes, or, as they are usually called, the poles. Substances are frequently spoken of as being electro-negative, or electro-positive, according as they go under the supposed influence of a direct attraction to the positive or negative pole. But these terms are much too significant for the use to which I should have to put them; for though the meanings are perhaps right, they are only hypothetical, and may be wrong; and then, through a very imperceptible, but still very dangerous, because continual, influence, they do great injury to science, by contracting and limiting the habitual view of those engaged in pursuing it. I propose to distinguish these bodies by calling those anions which go to the anode of the decomposing body; and those passing to the cathode, cations; and when I have occasion to speak of these together, I shall call them ions.
I specifically paused to show that, if there were such machines with the organs and shape of a monkey or of some other non-rational animal, we would have no way of discovering that they are not the same as these animals. But if there were machines that resembled our bodies and if they imitated our actions as much as is morally possible, we would always have two very certain means for recognizing that, none the less, they are not genuinely human. The first is that they would never be able to use speech, or other signs composed by themselves, as we do to express our thoughts to others. For one could easily conceive of a machine that is made in such a way that it utters words, and even that it would utter some words in response to physical actions that cause a change in its organs—for example, if someone touched it in a particular place, it would ask what one wishes to say to it, or if it were touched somewhere else, it would cry out that it was being hurt, and so on. But it could not arrange words in different ways to reply to the meaning of everything that is said in its presence, as even the most unintelligent human beings can do. The second means is that, even if they did many things as well as or, possibly, better than anyone of us, they would infallibly fail in others. Thus one would discover that they did not act on the basis of knowledge, but merely as a result of the disposition of their organs. For whereas reason is a universal instrument that can be used in all kinds of situations, these organs need a specific disposition for every particular action.
I think it is a peculiarity of myself that I like to play about with equations, just looking for beautiful mathematical relations which maybe don’t have any physical meaning at all. Sometimes they do.
At age 60.
At age 60.
I venture to assert that the feelings one has when the beautiful symbolism of the infinitesimal calculus first gets a meaning, or when the delicate analysis of Fourier has been mastered, or while one follows Clerk Maxwell or Thomson into the strange world of electricity, now growing so rapidly in form and being, or can almost feel with Stokes the pulsations of light that gives nature to our eyes, or track with Clausius the courses of molecules we can measure, even if we know with certainty that we can never see them I venture to assert that these feelings are altogether comparable to those aroused in us by an exquisite poem or a lofty thought.
If a specific question has meaning, it must be possible to find operations by which an answer may be given to it ... I believe that many of the questions asked about social and philosophical subjects will be found to be meaningless when examined from the point of view of operations.
If any philosopher had been asked for a definition of infinity, he might have produced some unintelligible rigmarole, but he would certainly not have been able to give a definition that had any meaning at all.
If education really educates, there will, in time, be more and more citizens who understand that relics of the old West add meaning and value to the new. Youth yet unborn will pole up the Missouri with Lewis and Clark, or climb the Sierras with James Capen Adams, and each generation in turn will ask: Where is the big white bear? It will be a sorry answer to say he went under while conservationists weren’t looking.
If I am given a sign [formula], and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?
If I were asked to name the most needed of all reforms in the spirit of education, I should say: “Cease conceiving of education as mere preparation for later life, and make it the full meaning of the present life.”
[This is widely seen quoted in a paraphrased form: Education is not preparation for life; education is life itself.]
[This is widely seen quoted in a paraphrased form: Education is not preparation for life; education is life itself.]
If Louis Pasteur were to come out of his grave because he heard that the cure for cancer still had not been found, NIH would tell him, “Of course we'll give you assistance. Now write up exactly what you will be doing during the three years of your grant.” Pasteur would say, “Thank you very much,” and would go back to his grave. Why? Because research means going into the unknown. If you know what you are going to do in science, then you are stupid! This is like telling Michelangelo or Renoir that he must tell you in advance how many reds and how many blues he will buy, and exactly how he will put those colors together.
If the question were, “What ought to be the next objective in science?” my answer would be the teaching of science to the young, so that when the whole population grew up there would be a far more general background of common sense, based on a knowledge of the real meaning of the scientific method of discovering truth.
If the universe is not meaningless, what is its meaning? For me, this meaning is to be found in the structure of the universe, which happens to be such as to produce thought by way of life and mind. Thought, in turn, is a faculty whereby the universe can reflect upon itself, discover its own structure, and apprehend such immanent entities as truth, beauty, goodness, and love. Such is the meaning of the universe, as I see it.
If the whole universe has no meaning, we should never have found out that it has no meaning: just as, if there were no light in the universe and therefore no creatures with eyes, we should never know it was dark. Dark would be without meaning.
If the world has begun with a single quantum, the notions of space and would altogether fail to have any meaning at the beginning; they would only begin to have a sensible meaning when the original quantum had been divided into a sufficient number of quanta. If this suggestion is correct, the beginning of the world happened a little before the beginning of space and time. I think that such a beginning of the world is far enough from the present order of Nature to be not at all repugnant. It may be difficult to follow up the idea in detail as we are not yet able to count the quantum packets in every case. For example, it may be that an atomic nucleus must be counted as a unique quantum, the atomic number acting as a kind of quantum number. If the future development of quantum theory happens to turn in that direction, we could conceive the beginning of the universe in the form of a unique atom, the atomic weight of which is the total mass of the universe. This highly unstable atom would divide in smaller and smaller atoms by a kind of super-radioactive process.
If there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators and sit at their desks for endless hours working out the meaning of the data they gather.
If we consider that part of the theory of relativity which may nowadays in a sense be regarded as bone fide scientific knowledge, we note two aspects which have a major bearing on this theory. The whole development of the theory turns on the question of whether there are physically preferred states of motion in Nature (physical relativity problem). Also, concepts and distinctions are only admissible to the extent that observable facts can be assigned to them without ambiguity (stipulation that concepts and distinctions should have meaning). This postulate, pertaining to epistemology, proves to be of fundamental importance.
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.
In 1963, when I assigned the name “quark” to the fundamental constituents of the nucleon, I had the sound first, without the spelling, which could have been “kwork.” Then, in one of my occasional perusals of Finnegans Wake, by James Joyce, I came across the word “quark” in the phrase “Three quarks for Muster Mark.” Since “quark” (meaning, for one thing, the cry of a gull) was clearly intended to rhyme with “Mark,” as well as “bark” and other such words, I had to find an excuse to pronounce it as “kwork.” But the book represents the dreams of a publican named Humphrey Chimpden Earwicker. Words in the text are typically drawn from several sources at once, like the “portmanteau words” in Through the Looking Glass. From time to time, phrases occur in the book that are partially determined by calls for drinks at the bar. I argued, therefore, that perhaps one of the multiple sources of the cry “Three quarks for Muster Mark” might be pronunciation for “Three quarts for Mister Mark,” in which case the pronunciation “kwork” would not be totally unjustified. In any case, the number three fitted perfectly the way quarks occur in nature.
In despair, I offer your readers their choice of the following definitions of entropy. My authorities are such books and journals as I have by me at the moment.
(a) Entropy is that portion of the intrinsic energy of a system which cannot be converted into work by even a perfect heat engine.—Clausius.
(b) Entropy is that portion of the intrinsic energy which can be converted into work by a perfect engine.—Maxwell, following Tait.
(c) Entropy is that portion of the intrinsic energy which is not converted into work by our imperfect engines.—Swinburne.
(d) Entropy (in a volume of gas) is that which remains constant when heat neither enters nor leaves the gas.—W. Robinson.
(e) Entropy may be called the ‘thermal weight’, temperature being called the ‘thermal height.’—Ibid.
(f) Entropy is one of the factors of heat, temperature being the other.—Engineering.
I set up these bald statement as so many Aunt Sallys, for any one to shy at.
[Lamenting a list of confused interpretations of the meaning of entropy, being hotly debated in journals at the time.]
(a) Entropy is that portion of the intrinsic energy of a system which cannot be converted into work by even a perfect heat engine.—Clausius.
(b) Entropy is that portion of the intrinsic energy which can be converted into work by a perfect engine.—Maxwell, following Tait.
(c) Entropy is that portion of the intrinsic energy which is not converted into work by our imperfect engines.—Swinburne.
(d) Entropy (in a volume of gas) is that which remains constant when heat neither enters nor leaves the gas.—W. Robinson.
(e) Entropy may be called the ‘thermal weight’, temperature being called the ‘thermal height.’—Ibid.
(f) Entropy is one of the factors of heat, temperature being the other.—Engineering.
I set up these bald statement as so many Aunt Sallys, for any one to shy at.
[Lamenting a list of confused interpretations of the meaning of entropy, being hotly debated in journals at the time.]
In my work on Fossil Bones, I set myself the task of recognizing to which animals the fossilized remains which fill the surface strata of the earth belong. ... As a new sort of antiquarian, I had to learn to restore these memorials to past upheavals and, at the same time, to decipher their meaning. I had to collect and put together in their original order the fragments which made up these animals, to reconstruct the ancient creatures to which these fragments belonged, to create them once more with their proportions and characteristics, and finally to compare them to those alive today on the surface of the earth. This was an almost unknown art, which assumed a science hardly touched upon up until now, that of the laws which govern the coexistence of forms
of the various parts in organic beings.
In physics we deal with states of affairs much simpler than those of psychology and yet we again and again learn that our task is not to investigate the essence of things—we do not at all know what this would mean&mash;but to develop those concepts that allow us to speak with each other about the events of nature in a fruitful manner.
In science, each of us knows that what he has accomplished will be antiquated in ten, twenty, fifty years. That is the fate to which science is subjected; it is the very meaning of scientific work, to which it is devoted in a quite specific sense, as compared with other spheres of culture for which in general the same holds. Every scientific “fulfilment” raises new “questions”; it asks to be “surpassed” and outdated. Whoever wishes to serve science has to resign himself to this fact. Scientific works certainly can last as “gratifications” because of their artistic quality, or they may remain important as a means of training. Yet they will be surpassed scientifically—let that be repeated—for it is our common fate and, more our common goal. We cannot work without hoping that others will advance further than we have. In principle, this progress goes on ad infinitum.
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 printed page the only real things are the paper and the ink; the white spaces play the same part in aiding the eye to take in the meaning of the print as do the black letters.
In the world of human thought generally, and in physical science particularly, the most important and fruitful concepts are those to which it is impossible to attach a well-defined meaning.
In this communication I wish first to show in the simplest case of the hydrogen atom (nonrelativistic and undistorted) that the usual rates for quantization can be replaced by another requirement, in which mention of “whole numbers” no longer occurs. Instead the integers occur in the same natural way as the integers specifying the number of nodes in a vibrating string. The new conception can be generalized, and I believe it touches the deepest meaning of the quantum rules.
In this respect mathematics fails to reproduce with complete fidelity the obvious fact that experience is not composed of static bits, but is a string of activity, or the fact that the use of language is an activity, and the total meanings of terms are determined by the matrix in which they are embedded.
Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”
It [mathematics] is in the inner world of pure thought, where all entia dwell, where is every type of order and manner of correlation and variety of relationship, it is in this infinite ensemble of eternal verities whence, if there be one cosmos or many of them, each derives its character and mode of being,—it is there that the spirit of mathesis has its home and its life.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
Is it a restricted home, a narrow life, static and cold and grey with logic, without artistic interest, devoid of emotion and mood and sentiment? That world, it is true, is not a world of solar light, not clad in the colours that liven and glorify the things of sense, but it is an illuminated world, and over it all and everywhere throughout are hues and tints transcending sense, painted there by radiant pencils of psychic light, the light in which it lies. It is a silent world, and, nevertheless, in respect to the highest principle of art—the interpenetration of content and form, the perfect fusion of mode and meaning—it even surpasses music. In a sense, it is a static world, but so, too, are the worlds of the sculptor and the architect. The figures, however, which reason constructs and the mathematic vision beholds, transcend the temple and the statue, alike in simplicity and in intricacy, in delicacy and in grace, in symmetry and in poise. Not only are this home and this life thus rich in aesthetic interests, really controlled and sustained by motives of a sublimed and supersensuous art, but the religious aspiration, too, finds there, especially in the beautiful doctrine of invariants, the most perfect symbols of what it seeks—the changeless in the midst of change, abiding things hi a world of flux, configurations that remain the same despite the swirl and stress of countless hosts of curious transformations.
It has become a cheap intellectual pastime to contrast the infinitesimal pettiness of man with the vastnesses of the stellar universes. Yet all such comparisons are illicit. We cannot compare existence and meaning; they are disparate. The characteristic life of a man is itself the meaning of vast stretches of existences, and without it the latter have no value or significance. There is no common measure of physical existence and conscious experience because the latter is the only measure there is of the former. The significance of being, though not its existence, is the emotion it stirs, the thought it sustains.
It is admitted by all that a finished or even a competent reasoner is not the work of nature alone; the experience of every day makes it evident that education develops faculties which would otherwise never have manifested their existence. It is, therefore, as necessary to learn to reason before we can expect to be able to reason, as it is to learn to swim or fence, in order to attain either of those arts. Now, something must be reasoned upon, it matters not much what it is, provided it can be reasoned upon with certainty. The properties of mind or matter, or the study of languages, mathematics, or natural history, may be chosen for this purpose. Now of all these, it is desirable to choose the one which admits of the reasoning being verified, that is, in which we can find out by other means, such as measurement and ocular demonstration of all sorts, whether the results are true or not. When the guiding property of the loadstone was first ascertained, and it was necessary to learn how to use this new discovery, and to find out how far it might be relied on, it would have been thought advisable to make many passages between ports that were well known before attempting a voyage of discovery. So it is with our reasoning faculties: it is desirable that their powers should be exerted upon objects of such a nature, that we can tell by other means whether the results which we obtain are true or false, and this before it is safe to trust entirely to reason. Now the mathematics are peculiarly well adapted for this purpose, on the following grounds:
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
1. Every term is distinctly explained, and has but one meaning, and it is rarely that two words are employed to mean the same thing.
2. The first principles are self-evident, and, though derived from observation, do not require more of it than has been made by children in general.
3. The demonstration is strictly logical, taking nothing for granted except self-evident first principles, resting nothing upon probability, and entirely independent of authority and opinion.
4. When the conclusion is obtained by reasoning, its truth or falsehood can be ascertained, in geometry by actual measurement, in algebra by common arithmetical calculation. This gives confidence, and is absolutely necessary, if, as was said before, reason is not to be the instructor, but the pupil.
5. There are no words whose meanings are so much alike that the ideas which they stand for may be confounded. Between the meaning of terms there is no distinction, except a total distinction, and all adjectives and adverbs expressing difference of degrees are avoided.
It is difficult even to attach a precise meaning to the term “scientific truth.” So different is the meaning of the word “truth” according to whether we are dealing with a fact of experience, a mathematical proposition or a scientific theory. “Religious truth” conveys nothing clear to me at all.
It is evident that scientists and philosophers can help each other. For the scientist sometimes wants a new idea, and the philosopher is enlightened as to meanings by the study of the scientific consequences.
It is not failure but success that is forcing man off this earth. It is not sickness but the triumph of health... Our capacity to survive has expanded beyond the capacity of Earth to support us. The pains we are feeling are growing pains. We can solve growth problems in direct proportion to our capacity to find new worlds... If man stays on Earth, his extinction is sure even if he lasts till the sun expands and destroys him... It is no longer reasonable to assume that the meaning of life lies on this earth alone. If Earth is all there is for man, we are reaching the foreseeable end of man.
It is possible that the deepest meaning and aim of Newtonianism, or rather, of the whole scientific revolution of the seventeenth century, of which Newton is the heir and the highest expression, is just to abolish the world of the 'more or less', the world of qualities and sense perception, the world of appreciation of our daily life, and to replace it by the (Archimedean) universe of precision, of exact measures, of strict determination ... This revolution [is] one of the deepest, if not the deepest, mutations and transformations accomplished—or suffered—by the human mind since the invention of the cosmos by the Greeks, two thousand years before.
It is sages and grey-haired philosophers who ought to sit up all night reading Alice in Wonderland in order to study that darkest problem of metaphysics, the borderland between reason and unreason, and the nature of the most erratic of spiritual forces, humour, which eternally dances between the two. That we do find a pleasure in certain long and elaborate stories, in certain complicated and curious forms of diction, which have no intelligible meaning whatever, is not a subject for children to play with; it is a subject for psychologists to go mad over.
It is the constant aim of the mathematician to reduce all his expressions to their lowest terms, to retrench every superfluous word and phrase, and to condense the Maximum of meaning into the Minimum of language.
It will be noticed that the fundamental theorem proved above bears some remarkable resemblances to the second law of thermodynamics. Both are properties of populations, or aggregates, true irrespective of the nature of the units which compose them; both are statistical laws; each requires the constant increase of a measurable quantity, in the one case the entropy of a physical system and in the other the fitness, measured by m, of a biological population. As in the physical world we can conceive the theoretical systems in which dissipative forces are wholly absent, and in which the entropy consequently remains constant, so we can conceive, though we need not expect to find, biological populations in which the genetic variance is absolutely zero, and in which fitness does not increase. Professor Eddington has recently remarked that “The law that entropy always increases—the second law of thermodynamics—holds, I think, the supreme position among the laws of nature.” It is not a little instructive that so similar a law should hold the supreme position among the biological sciences. While it is possible that both may ultimately be absorbed by some more general principle, for the present we should note that the laws as they stand present profound differences—-(1) The systems considered in thermodynamics are permanent; species on the contrary are liable to extinction, although biological improvement must be expected to occur up to the end of their existence. (2) Fitness, although measured by a uniform method, is qualitatively different for every different organism, whereas entropy, like temperature, is taken to have the same meaning for all physical systems. (3) Fitness may be increased or decreased by changes in the environment, without reacting quantitatively upon that environment. (4) Entropy changes are exceptional in the physical world in being irreversible, while irreversible evolutionary changes form no exception among biological phenomena. Finally, (5) entropy changes lead to a progressive disorganization of the physical world, at least from the human standpoint of the utilization of energy, while evolutionary changes are generally recognized as producing progressively higher organization in the organic world.
It would be possible to describe absolutely everything scientifically, but it would make no sense. It would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure.
Just finding out something new is not by itself sufficient justification for research. It needs to mean something when we find it.
Language is simply alive, like an organism. We all tell each other this, in fact, when we speak of living languages, and I think we mean something more than an abstract metaphor. We mean alive. Words are the cells of language, moving the great body, on legs. Language grows and evolves, leaving fossils behind. The individual words are like different species of animals. Mutations occur. Words fuse, and then mate. Hybrid words and wild varieties or compound words are the progeny. Some mixed words are dominated by one parent while the other is recessive. The way a word is used this year is its phenotype, but it has deeply immutable meanings, often hidden, which is its genotype.... The separate languages of the Indo-European family were at one time, perhaps five thousand years ago, maybe much longer, a single language. The separation of the speakers by migrations had effects on language comparable to the speciation observed by Darwin on various islands of the Galapagos. Languages became different species, retaining enough resemblance to an original ancestor so that the family resemblance can still be seen.
Leo Szilard’s Ten Commandments:
1. Recognize the connections of things and the laws of conduct of men, so that you may know what you are doing.
2. Let your acts be directed towards a worthy goal, but do not ask if they will reach it; they are to be models and examples, not means to an end.
3. Speak to all men as you do to yourself, with no concern for the effect you make, so that you do not shut them out from your world; lest in isolation the meaning of life slips out of sight and you lose the belief in the perfection of the creation.
4. Do not destroy what you cannot create.
5. Touch no dish, except that you are hungry.
6. Do not covet what you cannot have.
7. Do not lie without need.
8. Honor children. Listen reverently to their words and speak to them with infinite love.
9. Do your work for six years; but in the seventh, go into solitude or among strangers, so that the memory of your friends does not hinder you from being what you have become.
10. Lead your life with a gentle hand and be ready to leave whenever you are called.
1. Recognize the connections of things and the laws of conduct of men, so that you may know what you are doing.
2. Let your acts be directed towards a worthy goal, but do not ask if they will reach it; they are to be models and examples, not means to an end.
3. Speak to all men as you do to yourself, with no concern for the effect you make, so that you do not shut them out from your world; lest in isolation the meaning of life slips out of sight and you lose the belief in the perfection of the creation.
4. Do not destroy what you cannot create.
5. Touch no dish, except that you are hungry.
6. Do not covet what you cannot have.
7. Do not lie without need.
8. Honor children. Listen reverently to their words and speak to them with infinite love.
9. Do your work for six years; but in the seventh, go into solitude or among strangers, so that the memory of your friends does not hinder you from being what you have become.
10. Lead your life with a gentle hand and be ready to leave whenever you are called.
Lives with no more sense of spiritual meaning than that provided by shopping malls, ordinary television, and stagnant workplaces are barren lives indeed.
Man does not limit himself to seeing; he thinks and insists on learning the meaning of phenomena whose existence has been revealed to him by observation. So he reasons, compares facts, puts questions to them, and by the answers which he extracts, tests one by another. This sort of control, by means of reasoning and facts, is what constitutes experiment, properly speaking; and it is the only process that we have for teaching ourselves about the nature of things outside us.
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 a structure providing observers with a framework upon which to base healthy, informed, and intelligent judgment. Data and information are slung about us from all directions, and we are to use them as a basis for informed decisions. … Ability to critically analyze an argument purported to be logical, free of the impact of the loaded meanings of the terms involved, is basic to an informed populace.
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.
My life has been a continuous fulfillment of dreams. It appears that everything I saw and did has a new, and perhaps, more significant meaning, every time I see it. The earth is good. It is a privilege to live thereon.
No more harmful nonsense exists than the common supposition that deepest insight into great questions about the meaning of life or the structure of reality emerges most readily when a free, undisciplined, and uncluttered (read, rather, ignorant and uneducated) mind soars above mere earthly knowledge and concern.
No one really understood music unless he was a scientist, her father had declared, and not just a scientist, either, oh, no, only the real ones, the theoreticians, whose language mathematics. She had not understood mathematics until he had explained to her that it was the symbolic language of relationships. “And relationships,” he had told her, “contained the essential meaning of life.”
No one thinks of concealing the truth from a cardiac patient: there is nothing shameful about a heart attack. Cancer patients are lied to, not just because the disease is (or is thought to be) a death sentence, but because it is felt to be obscene—in the original meaning of that word: ill-omened, abominable, repugnant to the senses.
Not only are there meaningless questions, but many of the problems with which the human intellect has tortured itself turn out to be only 'pseudo problems,' because they can be formulated only in terms of questions which are meaningless. Many of the traditional problems of philosophy, of religion, or of ethics, are of this character. Consider, for example, the problem of the freedom of the will. You maintain that you are free to take either the right- or the left-hand fork in the road. I defy you to set up a single objective criterion by which you can prove after you have made the turn that you might have made the other. The problem has no meaning in the sphere of objective activity; it only relates to my personal subjective feelings while making the decision.
Not that we may not, to explain any Phenomena of Nature, make use of any probable Hypothesis whatsoever: Hypotheses, if they are well made, are at least great helps to the Memory, and often direct us to new discoveries. But my Meaning is, that we should not take up anyone too hastily, (which the Mind, that would always penetrate into the Causes of Things, and have Principles to rest on, is very apt to do,) till we have very well examined Particulars, and made several Experiments, in that thing which we would explain by our Hypothesis, and see whether it will agree to them all; whether our Principles will carry us quite through, and not be as inconsistent with one Phenomenon of Nature, as they seem to accommodate and explain another.
Now it came to me: … the independence of the gravitational acceleration from the nature of the falling substance, may be expressed as follows: In a gravitational field (of small spatial extension) things behave as they do in a space free of gravitation. … This happened in 1908. Why were another seven years required for the construction of the general theory of relativity? The main reason lies in the fact that it is not so easy to free oneself from the idea that coordinates must have an immediate metrical meaning.
Numbers have neither substance, nor meaning, nor qualities. They are nothing but marks, and all that is in them we have put into them by the simple rule of straight succession.
Objective Science is that which has as its conscious purpose the investigating of the meaning and aim of existence.
Obviously, what our age has in common with the age of the Reformation is the fallout of disintegrating values. What needs explaining is the presence of a receptive audience. More significant than the fact that poets write abstrusely, painters paint abstractly, and composers compose unintelligible music is that people should admire what they cannot understand; indeed, admire that which has no meaning or principle.
On careful examination the physicist finds that in the sense in which he uses language no meaning at all can be attached to a physical concept which cannot ultimately be described in terms of some sort of measurement. A body has position only in so far as its position can be measured; if a position cannot in principle be measured, the concept of position applied to the body is meaningless, or in other words, a position of the body does not exist. Hence if both the position and velocity of electron cannot in principle be measured, the electron cannot have the same position and velocity; position and velocity as expressions of properties which an electron can simultaneously have are meaningless.
On the theory of natural selection we can clearly understand the full meaning of that old canon in natural history, “Natura non facit saltum.” This canon, if we look only to the present inhabitants of the world, is not strictly correct, but if we include all those of past times, it must by my theory be strictly true.
One cannot ignore half of life for the purposes of science, and then claim that the results of science give a full and adequate picture of the meaning of life. All discussions of “life” which begin with a description of man's place on a speck of matter in space, in an endless evolutionary scale, are bound to be half-measures, because they leave out most of the experiences which are important to use as human beings.
One dictionary that I consulted remarks that “natural history” now commonly means the study of animals and plants “in a popular and superficial way,” meaning popular and superficial to be equally damning adjectives. This is related to the current tendency in the biological sciences to label every subdivision of science with a name derived from the Greek. “Ecology” is erudite and profound; while “natural history” is popular and superficial. Though, as far as I can see, both labels apply to just about the same package of goods.
One of the hardest things in the world is to convey a meaning accurately from one mind to another.
One of the principal obstacles to the rapid diffusion of a new idea lies in the difficulty of finding suitable expression to convey its essential point to other minds. Words may have to be strained into a new sense, and scientific controversies constantly resolve themselves into differences about the meaning of words. On the other hand, a happy nomenclature has sometimes been more powerful than rigorous logic in allowing a new train of thought to be quickly and generally accepted.
Only for you, children of doctrine and learning, have we written this work. Examine this book, ponder the meaning we have dispersed in various places and gathered again; what we have concealed in one place we have disclosed in another, that it may be understood by your wisdom.
Our story of evolution ended with a stirring in the brain-organ of the latest of Nature’s experiments; but that stirring of consciousness transmutes the whole story and gives meaning to its symbolism. Symbolically it is the end, but looking behind the symbolism it is the beginning.
Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world. In our endeavour to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility or the meaning of such a comparison. But he certainly believes that, as his knowledge increases, his picture of reality will become simpler and simpler and will explain a wider and wider range of his sensuous impressions. He may also believe in the existence of the ideal limit of knowledge and that it is approached by the human mind. He may call this ideal limit the objective truth.
Physical misery is great everywhere out here [Africa]. Are we justified in shutting our eyes and ignoring it because our European newspapers tell us nothing about it? We civilised people have been spoilt. If any one of us is ill the doctor comes at once. Is an operation necessary, the door of some hospital or other opens to us immediately. But let every one reflect on the meaning of the fact that out here millions and millions live without help or hope of it. Every day thousands and thousands endure the most terrible sufferings, though medical science could avert them. Every day there prevails in many and many a far-off hut a despair which we could banish. Will each of my readers think what the last ten years of his family history would have been if they had been passed without medical or surgical help of any sort? It is time that we should wake from slumber and face our responsibilities!
Physics tries to discover the pattern of events which controls the phenomena we observe. But we can never know what this pattern means or how it originates; and even if some superior intelligence were to tell us, we should find the explanation unintelligible.
Poets say science takes away from the beauty of the stars—mere globs of gas atoms. Nothing is “mere.” I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination—stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern—of which I am a part. … What is the pattern, or the meaning, or the “why?” It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
Positive, objective knowledge is public property. It can be transmitted directly from one person to another, it can be pooled, and it can be passed on from one generation to the next. Consequently, knowledge accumulates through the ages, each generation adding its contribution. Values are quite different. By values, I mean the standards by which we judge the significance of life. The meaning of good and evil, of joy and sorrow, of beauty, justice, success-all these are purely private convictions, and they constitute our store of wisdom. They are peculiar to the individual, and no methods exist by which universal agreement can be obtained. Therefore, wisdom cannot be readily transmitted from person to person, and there is no great accumulation through the ages. Each man starts from scratch and acquires his own wisdom from his own experience. About all that can be done in the way of communication is to expose others to vicarious experience in the hope of a favorable response.
Positivism stands or falls with the principle of scientism, that is that the meaning of knowledge is defined by what the sciences do and can thus be adequately explicated through the methodological analysis of scientific procedures.
Probability is the most important concept in modern science, especially as nobody has the slightest notion of what it means.
Quantity is that which is operated with according to fixed mutually consistent laws. Both operator and operand must derive their meaning from the laws of operation. In the case of ordinary algebra these are the three laws already indicated [the commutative, associative, and distributive laws], in the algebra of quaternions the same save the law of commutation for multiplication and division, and so on. It may be questioned whether this definition is sufficient, and it may be objected that it is vague; but the reader will do well to reflect that any definition must include the linear algebras of Peirce, the algebra of logic, and others that may be easily imagined, although they have not yet been developed. This general definition of quantity enables us to see how operators may be treated as quantities, and thus to understand the rationale of the so called symbolical methods.
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 and science ... constitute deep-rooted and ancient efforts to find richer experience and deeper meaning than are found in the ordinary biological and social satisfactions. As pointed out by Whitehead, religion and science have similar origins and are evolving toward similar goals. Both started from crude observations and fanciful concepts, meaningful only within a narrow range of conditions for the people who formulated them of their limited tribal experience. But progressively, continuously, and almost simultaneously, religious and scientific concepts are ridding themselves of their coarse and local components, reaching higher and higher levels of abstraction and purity. Both the myths of religion and the laws of science, it is now becoming apparent, are not so much descriptions of facts as symbolic expressions of cosmic truths.
Religion reveals the meaning of life, and science only applies this meaning to the course of circumstances.
Science and mathematics [are] much more compelling and exciting than the doctrines of pseudoscience, whose practitioners were condemned as early as the fifth century B.C. by the Ionian philosopher Heraclitus as “night walkers, magicians, priests of Bacchus, priestesses of the wine-vat, mystery-mongers.” But science is more intricate and subtle, reveals a much richer universe, and powerfully evokes our sense of wonder. And it has the additional and important virtue—to whatever extent the word has any meaning—of being true.
Science develops best when its concepts and conclusions are integrated into the broader human culture and its concerns for ultimate meaning and value. Scientists cannot, therefore, hold themselves entirely aloof from the sorts of issues dealt with by philosophers and theologians. By devoting to these issues something of the energy and care they give to their research in science, they can help others realize more fully the human potentialities of their discoveries. They can also come to appreciate for themselves that these discoveries cannot be a genuine substitute for knowledge of the truly ultimate.
Science gives us the grounds of premises from which religious truths are to be inferred; but it does not set about inferring them, much less does it reach the inference; that is not its province. It brings before us phenomena, and it leaves us, if we will, to call them works of design, wisdom, or benevolence; and further still, if we will, to proceed to confess an Intelligent Creator. We have to take its facts, and to give them a meaning, and to draw our own conclusions from them. First comes Knowledge, then a view, then reasoning, then belief. This is why Science has so little of a religious tendency; deductions have no power of persuasion. The heart is commonly reached, not through the reason, but through the imagination, by means of direct impressions, by the testimony of facts and events, by history, by description. Persons influence us, voices melt us, looks subdue us, deeds inflame us. Many a man will live and die upon a dogma; no man will be a martyr for a conclusion.
Science itself is badly in need of integration and unification. The tendency is more and more the other way ... Only the graduate student, poor beast of burden that he is, can be expected to know a little of each. As the number of physicists increases, each specialty becomes more self-sustaining and self-contained. Such Balkanization carries physics, and indeed, every science further away, from natural philosophy, which, intellectually, is the meaning and goal of science.
Science repudiates philosophy. In other words, it has never cared to justify its truth or explain its meaning.
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 modes of thought cannot be developed and become generally accepted unless people renounce their primary, unreflecting, and spontaneous attempt to understand all their experience in terms of its purpose and meaning for themselves. The development that led to more adequate knowledge and increasing control of nature was therefore, considered from one aspect, also a development toward greater self-control by men.
Scientists don’t really ever grow up. I read, as a 10-or-so-year-old, a book for kids by Einstein. I think it was The Meaning of Relativity. It was exciting! Science was compared to a detective story, replete with clues, and the solution was the search for a coherent account of all the known events. Then I remember some very entrapping biographies: Crucibles, by Bernard Jaffe, was the story of chemistry told through the lives of great chemists; Microbe Hunters, by Paul de Kruif, did the same for biologists. Also, the novel Arrowsmith, by Sinclair Lewis, about a medical researcher. These books were a crucial component of getting hooked into science.
When asked by Discover magazine what books helped inspire his passion as a scientist.
When asked by Discover magazine what books helped inspire his passion as a scientist.
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.
Shall an invention be patented or donated to the public freely? I have known some well-meaning scientific men to look askance at the patenting of inventions, as if it were a rather selfish and ungracious act, essentially unworthy. The answer is very simple. Publish an invention freely, and it will almost surely die from lack of interest in its development. It will not be developed and the world will not be benefited. Patent it, and if valuable, it will be taken up and developed into a business.
Some things mankind can finish and be done with, but not ... science, that persists, and changes from ancient Chaldeans studying the stars to a new telescope with a 200-inch reflector and beyond; not religion, that persists, and changes from old credulities and world views to new thoughts of God and larger apprehensions of his meaning.
Somewhere in the arrangement of this world there seems to be a great concern about giving us delight, which shows that, in the universe, over and above the meaning of matter and forces, there is a message conveyed through the magic touch of personality. ...
Is it merely because the rose is round and pink that it gives me more satisfaction than the gold which could buy me the necessities of life, or any number of slaves. ... Somehow we feel that through a rose the language of love reached our hearts.
Is it merely because the rose is round and pink that it gives me more satisfaction than the gold which could buy me the necessities of life, or any number of slaves. ... Somehow we feel that through a rose the language of love reached our hearts.
Strictly speaking, it is really scandalous that science has not yet clarified the nature of number. It might be excusable that there is still no generally accepted definition of number, if at least there were general agreement on the matter itself. However, science has not even decided on whether number is an assemblage of things, or a figure drawn on the blackboard by the hand of man; whether it is something psychical, about whose generation psychology must give information, or whether it is a logical structure; whether it is created and can vanish, or whether it is eternal. It is not known whether the propositions of arithmetic deal with those structures composed of calcium carbonate [chalk] or with non-physical entities. There is as little agreement in this matter as there is regarding the meaning of the word “equal” and the equality sign. Therefore, science does not know the thought content which is attached to its propositions; it does not know what it deals with; it is completely in the dark regarding their proper nature. Isn’t this scandalous?
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.
Symmetry, as wide or as narrow as you may define its meaning, is one idea by which man through the ages has tried to comprehend and create order, beauty and perfection.
That is how the atom is split. But what does it mean? To us who think in terms of practical use it means—Nothing!
Deity Htreld (June 27, |»J2)
That small word “Force,” they make a barber's block,
Ready to put on
Meanings most strange and various, fit to shock
Pupils of Newton....
The phrases of last century in this
Linger to play tricks—
Vis viva and Vis Mortua and Vis Acceleratrix:—
Those long-nebbed words that to our text books still
Cling by their titles,
And from them creep, as entozoa will,
Into our vitals.
But see! Tait writes in lucid symbols clear
One small equation;
And Force becomes of Energy a mere
Space-variation.
Ready to put on
Meanings most strange and various, fit to shock
Pupils of Newton....
The phrases of last century in this
Linger to play tricks—
Vis viva and Vis Mortua and Vis Acceleratrix:—
Those long-nebbed words that to our text books still
Cling by their titles,
And from them creep, as entozoa will,
Into our vitals.
But see! Tait writes in lucid symbols clear
One small equation;
And Force becomes of Energy a mere
Space-variation.
The ‘mad idea’ which will lie at the basis of a future fundamental physical theory will come from a realization that physical meaning has some mathematical form not previously associated with reality. From this point of view the problem of the ‘mad idea’ is the problem of choosing, not of generating, the right idea. One should not understand that too literally. In the 1960s it was said (in a certain connection) that the most important discovery of recent years in physics was the complex numbers. The author [Yuri Manin] has something like that in mind.
The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.
The anxious precision of modern mathematics is necessary for accuracy, … it is necessary for research. It makes for clearness of thought and for fertility in trying new combinations of ideas. When the initial statements are vague and slipshod, at every subsequent stage of thought, common sense has to step in to limit applications and to explain meanings. Now in creative thought common sense is a bad master. Its sole criterion for judgment is that the new ideas shall look like the old ones, in other words it can only act by suppressing originality.
The argument of the ‘long view’ may be correct in some meaninglessly abstract sense, but it represents a fundamental mistake in categories and time scales. Our only legitimate long view extends to our children and our children’s children’s children–hundreds or a few thousands of years down the road. If we let the slaughter continue, they will share a bleak world with rats, dogs, cockroaches, pigeons, and mosquitoes. A potential recovery millions of years later has no meaning at our appropriate scale.
The assumption we have made … is that marriages and the union of gametes occur at random. The validity of this assumption may now be examined. “Random mating” obviously does not mean promiscuity; it simply means, as already explained above, that in the choice of mates for marriage there is neither preference for nor aversion to the union of persons similar or dissimilar with respect to a given trait or gene. Not all gentlemen prefer blondes or brunettes. Since so few people know what their blood type is, it is even safer to say that the chances of mates being similar or dissimilar in blood type are determined simply by the incidence of these blood types in a given Mendelian population.
[Co-author with Theodosius Dobzhansky]
[Co-author with Theodosius Dobzhansky]
The belief that mathematics, because it is abstract, because it is static and cold and gray, is detached from life, is a mistaken belief. Mathematics, even in its purest and most abstract estate, is not detached from life. It is just the ideal handling of the problems of life, as sculpture may idealize a human figure or as poetry or painting may idealize a figure or a scene. Mathematics is precisely the ideal handling of the problems of life, and the central ideas of the science, the great concepts about which its stately doctrines have been built up, are precisely the chief ideas with which life must always deal and which, as it tumbles and rolls about them through time and space, give it its interests and problems, and its order and rationality. That such is the case a few indications will suffice to show. The mathematical concepts of constant and variable are represented familiarly in life by the notions of fixedness and change. The concept of equation or that of an equational system, imposing restriction upon variability, is matched in life by the concept of natural and spiritual law, giving order to what were else chaotic change and providing partial freedom in lieu of none at all. What is known in mathematics under the name of limit is everywhere present in life in the guise of some ideal, some excellence high-dwelling among the rocks, an “ever flying perfect” as Emerson calls it, unto which we may approximate nearer and nearer, but which we can never quite attain, save in aspiration. The supreme concept of functionality finds its correlate in life in the all-pervasive sense of interdependence and mutual determination among the elements of the world. What is known in mathematics as transformation—that is, lawful transfer of attention, serving to match in orderly fashion the things of one system with those of another—is conceived in life as a process of transmutation by which, in the flux of the world, the content of the present has come out of the past and in its turn, in ceasing to be, gives birth to its successor, as the boy is father to the man and as things, in general, become what they are not. The mathematical concept of invariance and that of infinitude, especially the imposing doctrines that explain their meanings and bear their names—What are they but mathematicizations of that which has ever been the chief of life’s hopes and dreams, of that which has ever been the object of its deepest passion and of its dominant enterprise, I mean the finding of the worth that abides, the finding of permanence in the midst of change, and the discovery of a presence, in what has seemed to be a finite world, of being that is infinite? It is needless further to multiply examples of a correlation that is so abounding and complete as indeed to suggest a doubt whether it be juster to view mathematics as the abstract idealization of life than to regard life as the concrete realization of mathematics.
The central task of science is to arrive, stage by stage, at a clearer comprehension of nature, but this does not mean, as it is sometimes claimed to mean, a search for mastery over nature.
The century after the Civil War was to be an Age of Revolution—of countless, little-noticed revolutions, which occurred not in the halls of legislatures or on battlefields or on the barricades but in homes and farms and factories and schools and stores, across the landscape and in the air—so little noticed because they came so swiftly, because they touched Americans everywhere and every day. Not merely the continent but human experience itself, the very meaning of community, of time and space, of present and future, was being revised again and again, a new democratic world was being invented and was being discovered by Americans wherever they lived.
The constant conditions which are maintained in the body might be termed equilibria. That word, however, has come to have fairly exact meaning as applied to relatively simple physico-chemical states, in closed systems, where known forces are balanced. The coordinated physiological processes which maintain most of the steady states in the organism are so complex and so peculiar to living beings—involving, as they may, the brain and nerves, the heart, lungs, kidneys and spleen, all working cooperatively—that I have suggested a special designation for these states, homeostasis. The word does not imply something set and immobile, a stagnation. It means a condition—a condition which may vary, but which is relatively constant.
The cosmogonist has finished his task when he has described to the best of his ability the inevitable sequence of changes which constitute the history of the material universe. But the picture which he draws opens questions of the widest interest not only to science, but also to humanity. What is the significance of the vast processes it portrays? What is the meaning, if any there be which is intelligible to us, of the vast accumulations of matter which appear, on our present interpretations of space and time, to have been created only in order that they may destroy themselves.
The difference between science and Congress is that in science facts mean everything and the illusions mean nothing. And in politics, it’s just the opposite.
The extensive literature addressed to the definition or characterization of science is filled with inconsistent points of view and demonstrates that an adequate definition is not easy to attain. Part of the difficulty arises from the fact that the meaning of science is not fixed, but is dynamic. As science has evolved, so has its meaning. It takes on a new meaning and significance with successive ages.
The faith of scientists in the power and truth of mathematics is so implicit that their work has gradually become less and less observation, and more and more calculation. The promiscuous collection and tabulation of data have given way to a process of assigning possible meanings, merely supposed real entities, to mathematical terms, working out the logical results, and then staging certain crucial experiments to check the hypothesis against the actual empirical results. But the facts which are accepted by virtue of these tests are not actually observed at all. With the advance of mathematical technique in physics, the tangible results of experiment have become less and less spectacular; on the other hand, their significance has grown in inverse proportion. The men in the laboratory have departed so far from the old forms of experimentation—typified by Galileo's weights and Franklin's kite—that they cannot be said to observe the actual objects of their curiosity at all; instead, they are watching index needles, revolving drums, and sensitive plates. No psychology of 'association' of sense-experiences can relate these data to the objects they signify, for in most cases the objects have never been experienced. Observation has become almost entirely indirect; and readings take the place of genuine witness.
The fish trap exists because of the fish; once you’ve gotten the fish, you can forget the trap. The rabbit snare exists because of the rabbit; once you’ve gotten the rabbit, you can forget the snare. Words exist because of meaning; once you’ve gotten the meaning, you can forget the words.
The Grand Cañon of the Colorado is a great innovation in modern ideas of scenery, and in our conceptions of the grandeur, beauty, and power of nature. As with all great innovations it is not to be comprehended in a day or a week, nor even in a month. It must be dwelt upon and studied, and the study must comprise the slow acquisition of the meaning and spirit of that marvelous scenery which characterizes the Plateau Country, and of which the great chasm is the superlative manifestation.
The greatest scientists have always looked on scientific materialism as a kind of religion, as a mythology. They are impelled by a great desire to explore mystery, to celebrate mystery in the universe, to open it up, to read the stars, to find the deeper meaning.
The human mind delights in finding pattern–so much so that we often mistake coincidence or forced analogy for profound meaning. No other habit of thought lies so deeply within the soul of a small creature trying to make sense of a complex world not constructed for it.
The imaginary expression √(-a) and the negative expression -b, have this resemblance, that either of them occurring as the solution of a problem indicates some inconsistency or absurdity. As far as real meaning is concerned, both are imaginary, since 0 - a is as inconceivable as √(-a).
The imagination is … the most precious faculty with which a scientist can be equipped. It is a risky possession, it is true, for it leads him astray a hundred times for once that it conducts him to truth; but without it he has no chance at all of getting at the meaning of the facts he has learned or discovered.
The little girl had the baking of a poet in her who, being told to be sure of her meaning before she spoke, said ‘How can I know what I think till I see what I say?’
The majority of evolutive movements are degenerative. Progressive cases are exceptional. Characters appear suddenly that have no meaning in the atavistic series. Evolution in no way shows a general tendency toward progress… . The only thing that could be accomplished by slow changes would be the accumulation of neutral characteristics without value for survival. Only important and sudden mutations can furnish the material which can be utilized by selection.
The man in the street will, therefore, twist the statement that the scientist has come to the end of meaning into the statement that the scientist has penetrated as far as he can with the tools at his command, and that there is something beyond the ken of the scientist. This imagined beyond, which the scientist has proved he cannot penetrate, will become the playground of the imagination of every mystic and dreamer. The existence of such a domain will be made the basis of an orgy of rationalizing. It will be made the substance of the soul; the spirits of the dead will populate it; God will lurk in its shadows; the principle of vital processes will have its seat here; and it will be the medium of telepathic communication. One group will find in the failure of the physical law of cause and effect the solution of the age-long problem of the freedom of the will; and on the other hand the atheist will find the justification of his contention that chance rules the universe.
The meaning of geography is as much a sealed book to the person of ordinary intelligence and education as the meaning of a great cathedral would be to a backwoodsman, and yet no cathedral can be more suggestive of past history in its many architectural forms than is the land about us, with its innumerable and marvellously significant geographic forms. It makes one grieve to think of opportunity for mental enjoyment that is last because of the failure of education in this respect.
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 meaning of life is 'the ultimate questioner's vanity.'
The meaning of life is contained in every single expression of life. It is present in the infinity of forms and phenomena that exist in all of creation.
The meaning of the evolution of culture is no longer a riddle to us. It must present to us the struggle between Eros and Death, between the instincts of life and the instincts of destruction, as it works itself out in the human species.
The meaning of time has become terribly problematic in contemporary physics. The situation is so uncomfortable that by far the best thing to do is declare oneself an agnostic.
The meaning that we are seeking in evolution is its meaning to us, to man. The ethics of evolution must be human ethics. It is one of the many unique qualities of man, the new sort of animal, that he is the only ethical animal. The ethical need and its fulfillment are also products of evolution, but they have been produced in man alone.
The most striking characteristic of the written language of algebra and of the higher forms of the calculus is the sharpness of definition, by which we are enabled to reason upon the symbols by the mere laws of verbal logic, discharging our minds entirely of the meaning of the symbols, until we have reached a stage of the process where we desire to interpret our results. The ability to attend to the symbols, and to perform the verbal, visible changes in the position of them permitted by the logical rules of the science, without allowing the mind to be perplexed with the meaning of the symbols until the result is reached which you wish to interpret, is a fundamental part of what is called analytical power. Many students find themselves perplexed by a perpetual attempt to interpret not only the result, but each step of the process. They thus lose much of the benefit of the labor-saving machinery of the calculus and are, indeed, frequently incapacitated for using it.
The nineteenth century is a turning point in history, simply on account of the work of two men, Darwin and Renan, the one the critic of the Book of Nature, the other the critic of the books of God. Not to recognise this is to miss the meaning of one of the most important eras in the progress of the world.
The only distinct meaning of the word “natural” is stated, fixed, or
settled; since what is natural as much requires and presupposes an intelligent agent to render it so, i.e. to effect it continually or at stated times, as what is supernatural or miraculous does to effect it for once.
The path of a cosmonaut is not an easy, triumphant march to glory, as some people make it out to be. You have to put in a lot of work, a lot of sweat, and have to get to know the meaning not just of joy but also of grief, before being allowed in the spacecraft cabin.
The path towards sustainable energy sources will be long and sometimes difficult. But America cannot resist this transition, we must lead it. We cannot cede to other nations the technology that will power new jobs and new industries, we must claim its promise. That’s how we will maintain our economic vitality and our national treasure—our forests and waterways, our crop lands and snow-capped peaks. That is how we will preserve our planet, commanded to our care by God. That’s what will lend meaning to the creed our fathers once declared.
The popular and scientific views of “race” no longer coincide. The word “race,” as applied scientifically to human groupings, has lost any sharpness of meaning. To-day it is hardly definable in scientific terms, except as an abstract concept which may, under certain conditions, very different from those now prevalent, have been realized approximately in the past and might, under certain other but equally different conditions, be realized in the distant future.
Co-author with British anthropologist Alfred Cort Haddon (1855-1940).
Co-author with British anthropologist Alfred Cort Haddon (1855-1940).
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 psychiatric interviewer is supposed to be doing three things: considering what the patient could mean by what he says; considering how he himself can best phrase what he wishes to communicate to the patient; and, at the same time, observing the general pattern of the events being communicated. In addition to that, to make notes which will be of more than evocative value, or come anywhere near being a verbatim record of what is said, in my opinion is beyond the capacity of most human beings.
The recent ruling by the Supreme Court restricting obscenity in books, magazines and movies, requires that we re-examine our own journals for lewd contents. The recent chemical literature provides many examples of words and concepts whose double meaning and thinly veiled overtones are an affront to all clean chemists. What must a layman think of ‘coupling constants’, ‘tickling techniques’, or indeed ‘increased overlap’? The bounds of propriety are surely exceeded when heterocyclic chemists discuss homoenolization.
The saying of Protagoras is like the views we have mentioned; he said that man is the measure of all things, meaning simply that that which seems to each man assuredly is. If this is so, it follows that the same thing both is and is not, and is bad and good, and that the contents of all other opposite statements are true, because often a particular thing appears beautiful to some and ugly to others, and that which appears to each man is the measure
The saying often quoted from Lord Kelvin… that “where you cannot measure your knowledge is meagre and unsatisfactory,” as applied in mental and social science, is misleading and pernicious. This is another way of saying that these sciences are not science in the sense of physical science and cannot attempt to be such without forfeiting their proper nature and function. Insistence on a concretely quantitative economics means the use of statistics of physical magnitudes, whose economic meaning and significance is uncertain and dubious. (Even wheat is approximately homogeneous only if measured in economic terms.) And a similar statement would even apply more to other social sciences. In this field, the Kelvin dictum very largely means in practice, “if you cannot measure, measure anyhow!”
The sense that the meaning of the universe had evaporated was what seemed to escape those who welcomed Darwin as a benefactor of mankind. Nietzsche considered that evolution presented a correct picture of the world, but that it was a disastrous picture. His philosophy was an attempt to produce a new world-picture which took Darwinism into account but was not nullified by it.
The student should read his author with the most sustained attention, in order to discover the meaning of every sentence. If the book is well written, it will endure and repay his close attention: the text ought to be fairly intelligible, even without illustrative examples. Often, far too often, a reader hurries over the text without any sincere and vigorous effort to understand it; and rushes to some example to clear up what ought not to have been obscure, if it had been adequately considered. The habit of scrupulously investigating the text seems to me important on several grounds. The close scrutiny of language is a very valuable exercise both for studious and practical life. In the higher departments of mathematics the habit is indispensable: in the long investigations which occur there it would be impossible to interpose illustrative examples at every stage, the student must therefore encounter and master, sentence by sentence, an extensive and complicated argument.
The subject matter of the scientist is a crowd of natural events at all times; he presupposes that this crowd is not real but apparent, and seeks to discover the true place of events in the system of nature. The subject matter of the poet is a crowd of historical occasions of feeling recollected from the past; he presupposes that this crowd is real but should not be, and seeks to transform it into a community. Both science and art are primarily spiritual activities, whatever practical applications may be derived from their results. Disorder, lack of meaning, are spiritual not physical discomforts, order and sense spiritual not physical satisfactions.
The Theory of Relativity confers an absolute meaning on a magnitude which in classical theory has only a relative significance: the velocity of light. The velocity of light is to the Theory of Relativity as the elementary quantum of action is to the Quantum Theory: it is its absolute core.
The traditional mathematics professor of the popular legend is absentminded. He usually appears in public with a lost umbrella in each hand. He prefers to face a blackboard and to turn his back on the class. He writes a, he says b, he means c, but it should be d. Some of his sayings are handed down from generation to generation:
“In order to solve this differential equation you look at it till a solution occurs to you.”
“This principle is so perfectly general that no particular application of it is possible.”
“Geometry is the science of correct reasoning on incorrect figures.”
“My method to overcome a difficulty is to go round it.”
“What is the difference between method and device? A method is a device which you used twice.”
“In order to solve this differential equation you look at it till a solution occurs to you.”
“This principle is so perfectly general that no particular application of it is possible.”
“Geometry is the science of correct reasoning on incorrect figures.”
“My method to overcome a difficulty is to go round it.”
“What is the difference between method and device? A method is a device which you used twice.”
The word “dis-aster,” in fact, means “bad star.”
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.”
Then I have more than an impression—it amounts to a certainty—that algebra is made repellent by the unwillingness or inability of teachers to explain why we suddenly start using a and b, what exponents mean apart from their handling, and how the paradoxical behavior of + and — came into being. There is no sense of history behind the teaching, so the feeling is given that the whole system dropped down readymade from the skies, to be used only by born jugglers. This is what paralyzes—with few exceptions—the infant, the adolescent, or the adult who is not a juggler himself.
Theory and fact are equally strong and utterly interdependent; one has no meaning without the other. We need theory to organize and interpret facts, even to know what we can or might observe. And we need facts to validate theories and give them substance.
There are, I believe, very few maxims in philosophy that have laid firmer hold upon the mind, than that air, meaning atmospherical air (free from various foreign matters, which were always supposed to be dissolved, and intermixed with it) is a simple elementary substance, indestructible, and unalterable, at least as much so as water is supposed to be. In the course of my enquiries, I was, however, soon satisfied that atmospherical air is not an unalterable thing; for that the phlogiston with which it becomes loaded from bodies burning in it, and animals breathing it, and various other chemical processes, so far alters and depraves it, as to render it altogether unfit for inflammation, respiration, and other purposes to which it is subservient; and I had discovered that agitation in water, the process of vegetation, and probably other natural processes, by taking out the superfluous phlogiston, restore it to its original purity.
There is a moral or metaphysical part of nature as well as a physical. A man who denies this is deep in the mire of folly. ’Tis the crown and glory of organic science that it does through final cause, link material and moral; and yet does not allow us to mingle them in our first conception of laws, and our classification of such laws, whether we consider one side of nature or the other. You have ignored this link; and, if I do not mistake your meaning, you have done your best in one or two pregnant cases to break it. Were it possible (which, thank God, it is not) to break it, humanity, in my mind, would suffer a damage that might brutalize it, and sink the human race into a lower grade of degradation than any into which it has fallen since its written records tell us of its history.
There should be no mystery in our use of the word science; it means knowledge, not theory nor speculation nor hypothesis, but hard facts, and the framework of laws to which they belong.
These microscopic organisms form an entire world composed of species, families and varieties whose history, which has barely begun to be written, is already fertile in prospects and findings of the highest importance. The names of these organisms are very numerous and will have to be defined and in part discarded. The word microbe which has the advantage of being shorter and carrying a more general meaning, and of having been approved by my illustrious friend, M. Littré, the most competent linguist in France, is one we will adopt.
Think of the image of the world in a convex mirror. ... A well-made convex mirror of moderate aperture represents the objects in front of it as apparently solid and in fixed positions behind its surface. But the images of the distant horizon and of the sun in the sky lie behind the mirror at a limited distance, equal to its focal length. Between these and the surface of the mirror are found the images of all the other objects before it, but the images are diminished and flattened in proportion to the distance of their objects from the mirror. ... Yet every straight line or plane in the outer world is represented by a straight line or plane in the image. The image of a man measuring with a rule a straight line from the mirror, would contract more and more the farther he went, but with his shrunken rule the man in the image would count out exactly the same results as in the outer world, all lines of sight in the mirror would be represented by straight lines of sight in the mirror. In short, I do not see how men in the mirror are to discover that their bodies are not rigid solids and their experiences good examples of the correctness of Euclidean axioms. But if they could look out upon our world as we look into theirs without overstepping the boundary, they must declare it to be a picture in a spherical mirror, and would speak of us just as we speak of them; and if two inhabitants of the different worlds could communicate with one another, neither, as far as I can see, would be able to convince the other that he had the true, the other the distorted, relation. Indeed I cannot see that such a question would have any meaning at all, so long as mechanical considerations are not mixed up with it.
This is the element that distinguishes applied science from basic. Surprise is what makes the difference. When you are organized to apply knowledge, set up targets, produce a usable product, you require a high degree of certainty from the outset. All the facts on which you base protocols must be reasonably hard facts with unambiguous meaning. The challenge is to plan the work and organize the workers so that it will come out precisely as predicted. For this, you need centralized authority, elaborately detailed time schedules, and some sort of reward system based on speed and perfection. But most of all you need the intelligible basic facts to begin with, and these must come from basic research. There is no other source. In basic research, everything is just the opposite. What you need at the outset is a high degree of uncertainty; otherwise it isn’t likely to be an important problem. You start with an incomplete roster of facts, characterized by their ambiguity; often the problem consists of discovering the connections between unrelated pieces of information. You must plan experiments on the basis of probability, even bare possibility, rather than certainty.
This is what writers mean when they say that the notion of cause involves the idea of necessity. If there be any meaning which confessedly belongs to the term necessity, it is unconditionalness. That which is necessary, that which must be, means that which will be, whatever supposition we may make in regard to all other things.
Though a little one, the master-word looms large in meaning. It is the open sesame to every portal, the great equalizer in the world, the true philosopher’s stone which transmutes all the base metal of humanity into gold. … The master-word is Work.
Through science or an artform—through creativity—the individual genius seems to live at the exhilarating edge of what it means to have our human mind.
Thus, be it understood, to demonstrate a theorem, it is neither necessary nor even advantageous to know what it means. The geometer might be replaced by the logic piano imagined by Stanley Jevons; or, if you choose, a machine might be imagined where the assumptions were put in at one end, while the theorems came out at the other, like the legendary Chicago machine where the pigs go in alive and come out transformed into hams and sausages. No more than these machines need the mathematician know what he does.
To be anthropocentric is to remain unaware of the limits of human nature, the significance of biological processes underlying human behavior, and the deeper meaning of long-term genetic evolution.
To be whole. To be complete. Wildness reminds us what it means to be human, what we are connected to rather than what we are separate from.
To illustrate the apparent contrast between statistics and truth … may I quote a remark I once overheard: “There are three kinds of lies: white lies, which are justifiable; common lies—these have no justification; and statistics.” Our meaning is similar when we say: “Anything can be proved by figures”; or, modifying a well-known quotation from Goethe, with numbers “all men may contend their charming systems to defend.”
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 pray is to think about the meaning of life.
To the solid ground Of Nature trusts the mind which builds for aye.
[From the first issue, and for over one hundred years, this quote appeared under the masthead of Nature journal. 'Aye' is an archaic word meaning 'always'.]
[From the first issue, and for over one hundred years, this quote appeared under the masthead of Nature journal. 'Aye' is an archaic word meaning 'always'.]
We are apt to think we know what time is because we can measure it, but no sooner do we reflect upon it than that illusion goes. So it appears that the range of the measureable is not the range of the knowable. There are things we can measure, like time, but yet our minds do not grasp their meaning. There are things we cannot measure, like happiness or pain, and yet their meaning is perfectly clear to us.
We can’t define anything precisely. If we attempt to, we get into that paralysis of thought that comes to philosophers… one saying to the other: “You don’t know what you are talking about!” The second one says: “What do you mean by know? What do you mean by talking? What do you mean by you?”
We have corrupted the term research to mean study and experiment and development toward selected objectives, and we have even espoused secret and classified projects. This was not the old meaning of university research. We need a new term, or the revival of a still older one, to refer to the dedicated activities of the scholar, the intensive study of special aspects of a subject for its own sake, motivated by the love of knowledge and truth.
We make a lot of mistakes in the environmental space. … We don’t do a good-enough job of asking, “What are the fundamentals of telling a good story?” And that is not statistics, it’s usually not science, or at least complex science. It’s people stories. … It’s got to have adventure, it’s got to be funny, it’s got to pull my heart strings, it’s got to have conflict, setting, character. It’s a story. And if it doesn’t have those things, it can be the best-meaning story in the world, and nobody’s going to buy it.
We may see how unexpectedly recondite parts of pure mathematics may bear upon physical science, by calling to mind the circumstance that Fresnel obtained one of the most curious confirmations of the theory (the laws of Circular Polarization by reflection) through an interpretation of an algebraical expression, which, according to the original conventional meaning of the symbols, involved an impossible quantity.