Complex Quotes (202 quotes)
… our “Physick” and “Anatomy” have embraced such infinite varieties of being, have laid open such new worlds in time and space, have grappled, not unsuccessfully, with such complex problems, that the eyes of Vesalius and of Harvey might be dazzled by the sight of the tree that has grown out of their grain of mustard seed.
“Complex” is a relative term
That’s rarely applied to a worm
But a worm that’s coelomic
Can be rather comic
It can burrow and wriggle and squirm.
That’s rarely applied to a worm
But a worm that’s coelomic
Can be rather comic
It can burrow and wriggle and squirm.
“If there are two theories, one simpler man the other, the simpler one is to be preferred.” At first sight this does not seem quite so bad, but a little thought shows that our tendency to prefer the simpler possibility is psychological rather than scientific. It is less trouble to think that way. Experience invariably shows that the more correct a theory becomes, the more complex does it seem. … So this … interpretation of [Ockham’s Razor] is … worthless.
[All phenomena] are equally susceptible of being calculated, and all that is necessary, to reduce the whole of nature to laws similar to those which Newton discovered with the aid of the calculus, is to have a sufficient number of observations and a mathematics that is complex enough.
[My favourite fellow of the Royal Society is the Reverend Thomas Bayes, an obscure 18th-century Kent clergyman and a brilliant mathematician who] devised a complex equation known as the Bayes theorem, which can be used to work out probability distributions. It had no practical application in his lifetime, but today, thanks to computers, is routinely used in the modelling of climate change, astrophysics and stock-market analysis.
[The] complex pattern of the misallocation of credit for scientific work must quite evidently be described as “the Matthew effect,” for, as will be remembered, the Gospel According to St. Matthew puts it this way: For unto every one that hath shall be given, and he shall have abundance: but from him that hath not shall be taken away even that which he hath. Put in less stately language, the Matthew effect consists of the accruing of greater increments of recognition for particular scientific contributions to scientists of considerable repute and the withholding of such recognition from scientists who have not yet made their mark.
~~[Misattributed]~~ The shortest path between two truths in the real domain passes through the complex domain.
In fact, this quote is a paraphrase from Paul Painlevé.
In fact, this quote is a paraphrase from Paul Painlevé.
A cell has a history; its structure is inherited, it grows, divides, and, as in the embryo of higher animals, the products of division differentiate on complex lines. Living cells, moreover, transmit all that is involved in their complex heredity. I am far from maintaining that these fundamental properties may not depend upon organisation at levels above any chemical level; to understand them may even call for different methods of thought; I do not pretend to know. But if there be a hierarchy of levels we must recognise each one, and the physical and chemical level which, I would again say, may be the level of self-maintenance, must always have a place in any ultimate complete description.
A cell of a higher organism contains a thousand different substances, arranged in a complex system. This great organized system was not discovered by chemical or physical methods; they are inadequate to its refinement and delicacy and complexity.
A central lesson of science is that to understand complex issues (or even simple ones), we must try to free our minds of dogma and to guarantee the freedom to publish, to contradict, and to experiment. Arguments from authority are unacceptable.
A clinician is complex. He is part craftsman, part practical scientist, and part historian.
A modern branch of mathematics, having achieved the art of dealing with the infinitely small, can now yield solutions in other more complex problems of motion, which used to appear insoluble. This modern branch of mathematics, unknown to the ancients, when dealing with problems of motion, admits the conception of the infinitely small, and so conforms to the chief condition of motion (absolute continuity) and thereby corrects the inevitable error which the human mind cannot avoid when dealing with separate elements of motion instead of examining continuous motion. In seeking the laws of historical movement just the same thing happens. The movement of humanity, arising as it does from innumerable human wills, is continuous. To understand the laws of this continuous movement is the aim of history. … Only by taking an infinitesimally small unit for observation (the differential of history, that is, the individual tendencies of man) and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.
A physician’s subject of study is necessarily the patient, and his first field for observation is the hospital. But if clinical observation teaches him to know the form and course of diseases, it cannot suffice to make him understand their nature; to this end he must penetrate into the body to find which of the internal parts are injured in their functions. That is why dissection of cadavers and microscopic study of diseases were soon added to clinical observation. But to-day these various methods no longer suffice; we must push investigation further and, in analyzing the elementary phenomena of organic bodies, must compare normal with abnormal states. We showed elsewhere how incapable is anatomy alone to take account of vital phenenoma, and we saw that we must add study of all physico-chemical conditions which contribute necessary elements to normal or pathological manifestations of life. This simple suggestion already makes us feel that the laboratory of a physiologist-physician must be the most complicated of all laboratories, because he has to experiment with phenomena of life which are the most complex of all natural phenomena.
A single ray of light from a distant star falling upon the eye of a tyrant in bygone times, may have altered the course of his life, may have changed the destiny of nations, may have transformed the surface of the globe, so intricate, so inconceivably complex are the processes of nature.
A tool is but the extension of a man’s hand, and a machine is but a complex tool. He that invents a machine augments the power of a man and the well being of mankind.
Accordingly the primordial state of things which I picture is an even distribution of protons and electrons, extremely diffuse and filling all (spherical) space, remaining nearly balanced for an exceedingly long time until its inherent instability prevails. We shall see later that the density of this distribution can be calculated; it was about one proton and electron per litre. There is no hurry for anything to begin to happen. But at last small irregular tendencies accumulate, and evolution gets under way. The first stage is the formation of condensations ultimately to become the galaxies; this, as we have seen, started off an expansion, which then automatically increased in speed until it is now manifested to us in the recession of the spiral nebulae.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life.
As the matter drew closer together in the condensations, the various evolutionary processes followed—evolution of stars, evolution of the more complex elements, evolution of planets and life.
All knowledge is profitable; profitable in its ennobling effect on the character, in the pleasure it imparts in its acquisition, as well as in the power it gives over the operations of mind and of matter. All knowledge is useful; every part of this complex system of nature is connected with every other. Nothing is isolated. The discovery of to-day, which appears unconnected with any useful process, may, in the course of a few years, become the fruitful source of a thousand inventions.
All scientists must focus closely on limited targets. Whether or not one’s findings on a limited subject will have wide applicability depends to some extent on chance, but biologists of superior ability repeatedly focus on questions the answers to which either have wide ramifications or lead to new areas of investigation. One procedure that can be effective is to attempt both reduction and synthesis; that is, direct a question at a phenomenon on one integrative level, identify its mechanism at a simpler level, then extrapolate its consequences to a more complex level of integration.
Amoebas at the start Were not complex; They tore themselves apart And started Sex.
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.
An atom must be at least as complex as a grand piano.
An immune system of enormous complexity is present in all vertebrate animals. When we place a population of lymphocytes from such an animal in appropriate tissue culture fluid, and when we add an antigen, the lymphocytes will produce specific antibody molecules, in the absence of any nerve cells. I find it astonishing that the immune system embodies a degree of complexity which suggests some more or less superficial though striking analogies with human language, and that this cognitive system has evolved and functions without assistance of the brain.
And do you know what “the world” is to me? Shall I show it to you in my mirror? This world: a monster of energy, without beginning, without end; a firm, iron magnitude of force that does not grow bigger or smaller, that does not expend itself but only transforms itself; as a whole, of unalterable size, a household without expenses or losses, but likewise without increase or income; enclosed by “nothingness”' as by a boundary; not by something blurry or wasted, not something endlessly extended, but set in a definite space as a definite force, and not a space that might be “empty” here or there, but rather as force throughout, as a play of forces and waves of forces, at the same time one and many, increasing here and at the same time decreasing there; a sea of forces flowing and rushing together, eternally changing, eternally flooding back, with tremendous years of recurrence, with an ebb and a flood of its forms; out of the simplest forms striving toward the most complex, out of the stillest, most rigid, coldest forms toward the hottest, most turbulent, most self-contradictory, and then again returning home to the simple out of this abundance, out of the play of contradictions back to the joy of concord, still affirming itself in this uniformity of its courses and its years, blessing itself as that which must return eternally, as a becoming that knows no satiety, no disgust, no weariness: this, my Dionysian world of the eternally self-creating, the eternally self-destroying, this mystery world of the twofold voluptuous delight, my “beyond good and evil,” without goal, unless the joy of the circle itself is a goal; without will, unless a ring feels good will toward itself-do you want a name for this world? A solution for all its riddles? A light for you, too, you best-concealed, strongest, most intrepid, most midnightly men?—This world is the will to power—and nothing besides! And you yourselves are also this will to power—and nothing besides!
Any intelligent fool can make things bigger, more complex, and more violent. It takes a touch of genius - and a lot of courage - to move in the opposite direction.
As a nation, we are too young to have true mythic heroes, and we must press real human beings into service. Honest Abe Lincoln the legend is quite a different character from Abraham Lincoln the man. And so should they be. And so should both be treasured, as long as they are distinguished. In a complex and confusing world, the perfect clarity of sports provides a focus for legitimate, utterly unambiguous support or disdain. The Dodgers are evil, the Yankees good. They really are, and have been for as long as anyone in my family can remember.
As a scientist and geneticist I started to feel that science would probably soon reach the point where its interference into the life processes would be counterproductive if a properly designed governing policy was not implemented. A heavily overcrowded planet, ninety-five percent urbanized with nuclear energy as the main source of energy and with all aspects of life highly computerized, is not too pleasant a place for human life. The life of any individual soon will be predictable from birth to death. Medicine, able to cure almost everything, will make the load of accumulated defects too heavy in the next two or three centuries. The artificial prolongation of life, which looked like a very bright idea when I started research in aging about twenty-five years ago, has now lost its attractiveness for me. This is because I now know that the aging process is so multiform and complex that the real technology and chemistry of its prevention by artificial interference must be too complex and expensive. It would be the privilege of a few, not the method for the majority. I also was deeply concerned about the fact that most research is now either directly or indirectly related to military projects and objectives for power.
As soon as we touch the complex processes that go on in a living thing, be it plant or animal, we are at once forced to use the methods of this science [chemistry]. No longer will the microscope, the kymograph, the scalpel avail for the complete solution of the problem. For the further analysis of these phenomena which are in flux and flow, the investigator must associate himself with those who have labored in fields where molecules and atoms, rather than multicellular tissues or even unicellular organisms, are the units of study.
At terrestrial temperatures matter has complex properties which are likely to prove most difficult to unravel; but it is reasonable to hope that in the not too distant future we shall be competent to understand so simple a thing as a star.
Before a complex of sensations becomes a recollection placeable in time, it has ceased to be actual. We must lose our awareness of its infinite complexity, or it is still actual ... It is only after a memory has lost all life that it can be classed in time, just as only dissected flowers find their way into the herbarium of a botanist.
Between two truths of the real domain, the easiest and shortest path quite often passes through the complex domain.
Borel makes the amusing supposition of a million monkeys allowed to play upon the keys of a million typewriters. What is the chance that this wanton activity should reproduce exactly all of the volumes which are contained in the library of the British Museum? It certainly is not a large chance, but it may be roughly calculated, and proves in fact to be considerably larger than the chance that a mixture of oxygen and nitrogen will separate into the two pure constituents. After we have learned to estimate such minute chances, and after we have overcome our fear of numbers which are very much larger or very much smaller than those ordinarily employed, we might proceed to calculate the chance of still more extraordinary occurrences, and even have the boldness to regard the living cell as a result of random arrangement and rearrangement of its atoms. However, we cannot but feel that this would be carrying extrapolation too far. This feeling is due not merely to a recognition of the enormous complexity of living tissue but to the conviction that the whole trend of life, the whole process of building up more and more diverse and complex structures, which we call evolution, is the very opposite of that which we might expect from the laws of chance.
But of all environments, that produced by man’s complex technology is perhaps the most unstable and rickety. In its present form, our society is not two centuries old, and a few nuclear bombs will do it in.
To be sure, evolution works over long periods of time and two centuries is far from sufficient to breed Homo technikos… .
The destruction of our technological society in a fit of nuclear peevishness would become disastrous even if there were many millions of immediate survivors.
The environment toward which they were fitted would be gone, and Darwin’s demon would wipe them out remorselessly and without a backward glance.
To be sure, evolution works over long periods of time and two centuries is far from sufficient to breed Homo technikos… .
The destruction of our technological society in a fit of nuclear peevishness would become disastrous even if there were many millions of immediate survivors.
The environment toward which they were fitted would be gone, and Darwin’s demon would wipe them out remorselessly and without a backward glance.
But, as we consider the totality of similarly broad and fundamental aspects of life, we cannot defend division by two as a natural principle of objective order. Indeed, the ‘stuff’ of the universe often strikes our senses as complex and shaded continua, admittedly with faster and slower moments, and bigger and smaller steps, along the way. Nature does not dictate dualities, trinities, quarterings, or any ‘objective’ basis for human taxonomies; most of our chosen schemes, and our designated numbers of categories, record human choices from a cornucopia of possibilities offered by natural variation from place to place, and permitted by the flexibility of our mental capacities. How many seasons (if we wish to divide by seasons at all) does a year contain? How many stages shall we recognize in a human life?
By destroying the biological character of phenomena, the use of averages in physiology and medicine usually gives only apparent accuracy to the results. From our point of view, we may distinguish between several kinds of averages: physical averages, chemical averages and physiological and pathological averages. If, for instance, we observe the number of pulsations and the degree of blood pressure by means of the oscillations of a manometer throughout one day, and if we take the average of all our figures to get the true or average blood pressure and to learn the true or average number of pulsations, we shall simply have wrong numbers. In fact, the pulse decreases in number and intensity when we are fasting and increases during digestion or under different influences of movement and rest; all the biological characteristics of the phenomenon disappear in the average. Chemical averages are also often used. If we collect a man's urine during twenty-four hours and mix all this urine to analyze the average, we get an analysis of a urine which simply does not exist; for urine, when fasting, is different from urine during digestion. A startling instance of this kind was invented by a physiologist who took urine from a railroad station urinal where people of all nations passed, and who believed he could thus present an analysis of average European urine! Aside from physical and chemical, there are physiological averages, or what we might call average descriptions of phenomena, which are even more false. Let me assume that a physician collects a great many individual observations of a disease and that he makes an average description of symptoms observed in the individual cases; he will thus have a description that will never be matched in nature. So in physiology, we must never make average descriptions of experiments, because the true relations of phenomena disappear in the average; when dealing with complex and variable experiments, we must study their various circumstances, and then present our most perfect experiment as a type, which, however, still stands for true facts. In the cases just considered, averages must therefore be rejected, because they confuse, while aiming to unify, and distort while aiming to simplify. Averages are applicable only to reducing very slightly varying numerical data about clearly defined and absolutely simple cases.
By their very nature chemical controls are self-defeating, for they have been devised and applied without taking into account the complex biological systems against which they have been blindly hurled.
Combining in our survey then, the whole range of deposits from the most recent to the most ancient group, how striking a succession do they present:– so various yet so uniform–so vast yet so connected. In thus tracing back to the most remote periods in the physical history of our continents, one system of operations, as the means by which many complex formations have been successively produced, the mind becomes impressed with the singleness of nature's laws; and in this respect, at least, geology is hardly inferior in simplicity to astronomy.
Complex organisms cannot be construed as the sum of their genes, nor do genes alone build particular items of anatomy or behavior by them selves. Most genes influence several aspects of anatomy and behavior–as they operate through complex interactions with other genes and their products, and with environmental factors both within and outside the developing organism. We fall into a deep error, not just a harmful oversimplification, when we speak of genes ‘for’ particular items of anatomy or behavior.
Complexes are psychic contents which are outside the control of the conscious mind. They have been split off from consciousness and lead a separate existence in the unconscious, being at all times ready to hinder or to reinforce the conscious intentions.
Conformity-enforcing packs of vicious children and adults gradually shape the social complexes we know as religion, science, corporations, ethnic groups, and even nations. The tools of our cohesion include ridicule, rejection, snobbery, self-righteousness, assault, torture, and death by stoning, lethal injection, or the noose. A collective brain may sound warm and fuzzily New Age, but one force lashing it together is abuse.
Continents are complexes of crustal scar tissue.
Contrary to the legend, Darwin's finches do not appear to have inspired his earliest theoretical views on evolution, even after he finally became an evolutionist in 1837; rather it was his evolutionary views that allowed him, retrospectively, to understand the complex case of the finches.
Culture is not a biologically transmitted complex.
Everything is controlled by immutable mathematical laws, from which there is, and can be, no deviation whatsoever. We learn the complex from the simple. We arrive at the abstract by way of the concrete.
For a smart material to be able to send out a more complex signal it needs to be nonlinear. If you hit a tuning fork twice as hard it will ring twice as loud but still at the same frequency. That’s a linear response. If you hit a person twice as hard they’re unlikely just to shout twice as loud. That property lets you learn more about the person than the tuning fork. - When Things Start to Think, 1999.
For every complex question there is a simple answer–and it's wrong.
For it is necessary in every practical science to proceed in a composite (i.e. deductive) manner. On the contrary in speculative science, it is necessary to proceed in an analytical manner by breaking down the complex into elementary principles.
For many of us, water simply flows from a faucet, and we think little about it beyond this point of contact. We have lost a sense of respect for the wild river, for the complex workings of a wetland, for the intricate web of life that water supports.
From Pythagoras (ca. 550 BC) to Boethius (ca AD 480-524), when pure mathematics consisted of arithmetic and geometry while applied mathematics consisted of music and astronomy, mathematics could be characterized as the deductive study of “such abstractions as quantities and their consequences, namely figures and so forth” (Aquinas ca. 1260). But since the emergence of abstract algebra it has become increasingly difficult to formulate a definition to cover the whole of the rich, complex and expanding domain of mathematics.
Furthermore, it’s equally evident that what goes on is actually one degree better than self-reproduction, for organisms appear to have gotten more elaborate in the course of time. Today's organisms are phylogenetically descended from others which were vastly simpler than they are, so much simpler, in fact, that it’s inconceivable, how any kind of description of the latter, complex organism could have existed in the earlier one. It’s not easy to imagine in what sense a gene, which is probably a low order affair, can contain a description of the human being which will come from it. But in this case you can say that since the gene has its effect only within another human organism, it probably need not contain a complete description of what is to happen, but only a few cues for a few alternatives. However, this is not so in phylogenetic evolution. That starts from simple entities, surrounded by an unliving amorphous milieu, and produce, something more complicated. Evidently, these organisms have the ability to produce something more complicated than themselves.
Genes make enzymes, and enzymes control the rates of chemical processes. Genes do not make ‘novelty seeking’ or any other complex and overt behavior. Predisposition via a long chain of complex chemical reactions, mediated through a more complex series of life’s circumstances, does not equal identification or even causation.
Human societies are everywhere complex, for living at peace with ourselves requires a vast multiplicity of rules.
I believe that there is but one way to learn any subject, and that is through study. The very name student tells what the person so named should be doing; and with a natural science, dealing with a most complex object, extending through three dimensions of space, any other method besides studying the object is practically useless.
I believed that, instead of the multiplicity of rules that comprise logic, I would have enough in the following four, as long as I made a firm and steadfast resolution never to fail to observe them.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.
The first was never to accept anything as true if I did not know clearly that it was so; that is, carefully to avoid prejudice and jumping to conclusions, and to include nothing in my judgments apart from whatever appeared so clearly and distinctly to my mind that I had no opportunity to cast doubt upon it.
The second was to subdivide each on the problems I was about to examine: into as many parts as would be possible and necessary to resolve them better.
The third was to guide my thoughts in an orderly way by beginning, as if by steps, to knowledge of the most complex, and even by assuming an order of the most complex, and even by assuming an order among objects in! cases where there is no natural order among them.
And the final rule was: in all cases, to make such comprehensive enumerations and such general review that I was certain not to omit anything.
The long chains of inferences, all of them simple and easy, that geometers normally use to construct their most difficult demonstrations had given me an opportunity to think that all the things that can fall within the scope of human knowledge follow from each other in a similar way, and as long as one avoids accepting something as true which is not so, and as long as one always observes the order required to deduce them from each other, there cannot be anything so remote that it cannot be reached nor anything so hidden that it cannot be uncovered.
I do not claim that intelligence, however defined, has no genetic basis–I regard it as trivially true, uninteresting, and unimportant that it does. The expression of any trait represents a complex interaction of heredity and environment ... a specific claim purporting to demonstrate a mean genetic deficiency in the intelligence of American blacks rests upon no new facts whatever and can cite no valid data in its support. It is just as likely that blacks have a genetic advantage over whites. And, either way, it doesn’t matter a damn. An individual can’t be judged by his group mean.
I don’t think we’re yet evolved to the point where we’re clever enough to handle a complex a situation as climate change.… The inertia of humans is so huge that you can’t really do anything meaningful.
I have often been amused by our vulgar tendency to take complex issues, with solutions at neither extreme of a continuum of possibilities, and break them into dichotomies, assigning one group to one pole and the other to an opposite end, with no acknowledgment of subtleties and intermediate positions–and nearly always with moral opprobrium attached to opponents.
I recall my own emotions: I had just been initiated into the mysteries of the complex number. I remember my bewilderment: here were magnitudes patently impossible and yet susceptible of manipulations which lead to concrete results. It was a feeling of dissatisfaction, of restlessness, a desire to fill these illusory creatures, these empty symbols, with substance. Then I was taught to interpret these beings in a concrete geometrical way. There came then an immediate feeling of relief, as though I had solved an enigma, as though a ghost which had been causing me apprehension turned out to be no ghost at all, but a familiar part of my environment.
I recognize nothing that is not material. In physics, chemistry and biology I see only mechanics. The Universe is nothing but an infinite and complex mechanism. Its complexity is so great that it borders on willfulness, suddenness, and randomness; it gives the illusion of free will possessed by conscious beings.
I should like to call the number of atom groups, with which an elementary atom coordinates … to form a complex radical, the coordination number of the atom in question … We must differentiate between valence number and coordination number. The valence number indicates the maximum number of monovalent atoms which can be bound directly to the atom in question without the participation of other elementary atoms … Perhaps this concept [of coordination number] is destined to serve as a basis for the theory of the constitution of inorganic compounds, just as valence theory formed the basis for the constitutional theory of carbon compounds.
I think each individual is never a plane but a polyhedron. Naturally, whenever a ray of light falls on a face, a vertex, an edge of this polyhedron; the arc that it reflects is undoubtedly variable, very complex and single or multicoloured. I don’t believe in plane men, I think we’re all multiple. We don’t have a double life, we have a multiple life. However, it is no less true that we’re thought to have a common denominator. I think I am or I aspire to be an honest man that tries not to bother too many people in this valley of tears.
I thought existing zoo programmes were really not doing animals justice. They all looked like oddities, like bizarre stage things, when, really, in their own environment, they are wonderful answers to very complex questions.
I wish that one would be persuaded that psychological experiments, especially those on the complex functions, are not improved [by large studies]; the statistical method gives only mediocre results; some recent examples demonstrate that. The American authors, who love to do things big, often publish experiments that have been conducted on hundreds and thousands of people; they instinctively obey the prejudice that the persuasiveness of a work is proportional to the number of observations. This is only an illusion.
I would ... change the accepted rule that the nature of a complex molecule is determined by the nature, quantity, and position of its elementary component parts, by the following statement: the chemical nature of a complex molecule is determined by the nature of its elementary component parts, their quantity and chemical structure.
I’m sure that science can’t ever explain everything and I can give you the reasons for that decision … I believe that scientific knowledge has fractal properties; that no matter how much we learn, whatever is left, however small it may seem, is just as infinitely complex as the whole was to start with. That, I think is the secret of the universe.
If a photographic plate under the center of a lens focused on the heavens is exposed for hours, it comes to reveal stars so far away that even the most powerful telescopes fail to reveal them to the naked eye. In a similar way, time and concentration allow the intellect to perceive a ray of light in the darkness of the most complex problem.
If in physics there’s something you don’t understand, you can always hide behind the uncharted depths of nature. You can always blame God. You didn’t make it so complex yourself. But if your program doesn’t work, there is no one to hide behind. You cannot hide behind an obstinate nature. If it doesn’t work, you’ve messed up.
If it could be demonstrated that any complex organ existed which could not possibly have been formed by numerous, successive slight modifications, my theory would absolutely break down.
If it were possible to transfer the methods of physical or of biological science directly to the study of man, the transfer would long ago have been made ... We have failed not for lack of hypotheses which equate man with the rest of the universe, but for lack of a hypothesis (short of animism) which provides for the peculiar divergence of man ... Let me now state my belief that the peculiar factor in man which forbids our explaining his actions upon the ordinary plane of biology is a highly specialized and unstable biological complex, and that this factor is none other than language.
If the structure that serves as a template (the gene or virus molecule) consists of, say, two parts, which are themselves complementary In structure, then each of these parts can serve as the mould for the production of a replica of the other part, and the complex of two complementary parts thus can serve as the mould for the production of duplicates of itself.
If the task of scientific methodology is to piece together an account of what scientists actually do, then the testimony of biologists should be heard with specially close attention. Biologists work very close to the frontier between bewilderment and understanding.
Biology is complex, messy and richly various, like real life; it travels faster nowadays than physics or chemistry (which is just as well, since it has so much farther to go), and it travels nearer to the ground. It should therefore give us a specially direct and immediate insight into science in the making.
Biology is complex, messy and richly various, like real life; it travels faster nowadays than physics or chemistry (which is just as well, since it has so much farther to go), and it travels nearer to the ground. It should therefore give us a specially direct and immediate insight into science in the making.
If this seems complex, the reason is because Tao is both simple and complex. It is complex when we try to understand it, and simple when we allow ourselves to experience it.
If we go back to our chequer game, the fundamental laws are rules by which the chequers move. Mathematics may be applied in the complex situation to figure out what in given circumstances is a good move to make. But very little mathematics is needed for the simple fundamental character of the basic laws. They can be simply stated in English for chequers.
If we lived on a planet where nothing ever changed, there would be little to do. There would be nothing to figure out. There would be no impetus for science. And if we lived in an unpredictable world, where things changed in random or very complex ways, we would not be able to figure things out. But we live in an in-between universe, where things change, but according to patterns, rules, or as we call them, laws of nature. If I throw a stick up in the air, it always falls down. If the sun sets in the west, it always rises again the next morning in the east. And so it becomes possible to figure things out. We can do science, and with it we can improve our lives.
If you look at a tree and think of it as a design assignment, it would be like asking you to make something that makes oxygen, sequesters carbon, fixes nitrogen, distills water, provides habitat for hundreds of species, accrues solar energy’s fuel, makes complex sugars and food, changes colors with the seasons, creates microclimates, and self-replicates.
If you want to achieve conservation, the first thing you have to do is persuade people that the natural world is precious, beautiful, worth saving and complex. If people don’t understand that and don’t believe that in their hearts, conservation doesn't stand a chance. That’s the first step, and that is what I do.
In general the actions which we see ever taking place around us are complex, or due to the simultaneous action of many causes. When, as in astronomy, we endeavour to ascertain these causes by simply watching their effects, we observe; when, as in our laboratories, we interfere arbitrarily with the causes or circumstances of a phenomenon, we are said to experiment.
In its most primitive form, life is, therefore, no longer bound to the cell, the cell which possesses structure and which can be compared to a complex wheel-work, such as a watch which ceases to exist if it is stamped down in a mortar. No, in its primitive form life is like fire, like a flame borne by the living substance;—like a flame which appears in endless diversity and yet has specificity within it;—which can adopt the form of the organic world, of the lank grass-leaf and of the stem of the tree.
In physics we have dealt hitherto only with periodic crystals. To a humble physicist’s mind, these are very interesting and complicated objects; they constitute one of the most fascinating and complex material structures by which inanimate nature puzzles his wits. Yet, compared with the aperiodic crystal, they are rather plain and dull. The difference in structure is of the same kind as that between an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity and a masterpiece of embroidery, say a Raphael tapestry, which shows no dull repetition, but an elaborate, coherent, meaningful design traced by the great master.
In this lecture I would like to conclude with … some characteristics [of] gravity … The most impressive fact is that gravity is simple. It is simple to state the principles completely and not have left any vagueness for anybody to change the ideas of the law. It is simple, and therefore it is beautiful. It is simple in its pattern. I do not mean it is simple in its action—the motions of the various planets and the perturbations of one on the other can be quite complicated to work out, and to follow how all those stars in a globular cluster move is quite beyond our ability. It is complicated in its actions, but the basic pattern or the system beneath the whole thing is simple. This is common to all our laws; they all turn out to be simple things, although complex in their actual actions.
It is certainly true that all physical phenomena are subject to strictly mathematical conditions, and mathematical processes are unassailable in themselves. The trouble arises from the data employed. Most phenomena are so highly complex that one can never be quite sure that he is dealing with all the factors until the experiment proves it. So that experiment is rather the criterion of mathematical conclusions and must lead the way.
It is given to but few men to achieve immortality, still less to achieve Olympian rank, during their own lifetime. In a generation that witnesses one of the greatest revolutions in the entire history of science [Ernest Rutherford] was universally acknowledged as the leading explorer of the vast infinitely complex universe within the atom, a universe that he was first to penetrate.
(Rutherford's death was front page news in the New York Times.)
(Rutherford's death was front page news in the New York Times.)
It is important to realize that life on this planet has spent about three-quarters of its existence in single-celled form, and even today the majority of organisms still exist as single cells. The evolutionary pressure to become complex is evidently not very great.
It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us. These laws, taken in the largest sense, being Growth with Reproduction; Inheritance which is almost implied by reproduction; Variability from the indirect and direct action of the external conditions of life, and from use and disuse; a Ratio of Increase so high as to lead to a Struggle for Life, and as a consequence to Natural Selection, entailing Divergence of Character and the Extinction of less-improved forms.
It is natural selection that gives direction to changes, orients chance, and slowly, progressively produces more complex structures, new organs, and new species. Novelties come from previously unseen association of old material. To create is to recombine.
It is often said that all the conditions for the first production of a living being are now present, which could ever have been present. But if (and oh what a big if) we could conceive in some warm little pond with all sort of ammonia and phosphoric salts—light, heat, electricity present, that a protein compound was chemically formed, ready to undergo still more complex changes, at the present such matter would be instantly devoured, or absorbed, which would not have been the case before living creatures were formed.
It is often said that all the conditions for the first production of a living organism are now present, which could have ever been present. But if (and oh! what a big if!) we could conceive in some warm pond, with all sorts of ammonia and phosphoric salts, light, heat, electricity, &c., present, that a proteine compound was chemically formed ready to undergo still more complex changes, at the present day such matter would be instantly devoured or absorbed, which would not have been the case before living creatures were formed.
It is probably no exaggeration to suppose that in order to improve such an organ as the eye at all, it must be improved in ten different ways at once. And the improbability of any complex organ being produced and brought to perfection in any such way is an improbability of the same kind and degree as that of producing a poem or a mathematical demonstration by throwing letters at random on a table.
[Expressing his reservations about Darwin's proposed evolution of the eye by natural selection.]
[Expressing his reservations about Darwin's proposed evolution of the eye by natural selection.]
It is tempting to wonder if our present universe, large as it is and complex though it seems, might not be merely the result of a very slight random increase in order over a very small portion of an unbelievably colossal universe which is virtually entirely in heat-death. Perhaps we are merely sliding down a gentle ripple that has been set up, accidently and very temporarily, in a quiet pond, and it is only the limitation of our own infinitesimal range of viewpoint in space and time that makes it seem to ourselves that we are hurtling down a cosmic waterfall of increasing entropy, a waterfall of colossal size and duration.
It is the individual only who is timeless. Societies, cultures, and civilizations - past and present - are often incomprehensible to outsiders, but the individual’s hunger, anxieties, dreams, and preoccupations have remained unchanged through the millennia. Thus, we are up against the paradox that the individual who is more complex, unpredictable, and mysterious than any communal entity is the one nearest to our understanding; so near that even the interval of millennia cannot weaken our feeling of kinshiIf in some manner the voice of an individual reaches us from the remotest distance of time, it is a timeless voice speaking about ourselves.
It seems to me that the view toward which we are tending is that the specificity in gene action is always a chemical specificity, probably the production of enzymes which guide metabolic processes along particular channels. A given array of genes thus determines the production of a particular kind of protoplasm with particular properties—such, for example, as that of responding to surface forces by the formation of a special sort of semipermeable membrane, and that of responding to trivial asymmetries in the play of external stimuli by polarization, with consequent orderly quantitative gradients in all physiologic processes. Different genes may now be called into play at different points in this simple pattern, either through the local formation of their specific substrates for action, or by activation of a mutational nature. In either case the pattern becomes more complex and qualitatively differentiated. Successive interactions of differentiated regions and the calling into play of additional genes may lead to any degree of complexity of pattern in the organism as a largely self-contained system. The array of genes, assembled in the course of evolution, must of course be one which determines a highly selfregulatory system of reactions. On this view the genes are highly specific chemically, and thus called into play only under very specific conditions; but their morphological effects, if any, rest on quantitative influences of immediate or remote products on growth gradients, which are resultants of all that has gone on before in the organism.
It was obvious—to me at any rate—that the answer was to why an enzyme is able to speed up a chemical reaction by as much as 10 million times. It had to do this by lowering the energy of activation—the energy of forming the activated complex. It could do this by forming strong bonds with the activated complex, but only weak bonds with the reactants or products.
Knowledge leads us from the simple to the complex; wisdom leads us from the complex to the simple.
Lavoisier was right in the deepest, almost holy, way. His passion harnessed feeling to the service of reason; another kind of passion was the price. Reason cannot save us and can even persecute us in the wrong hands; but we have no hope of salvation without reason. The world is too complex, too intransigent; we cannot bend it to our simple will.
Law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise, or at least pretends to be. Experiment is made under conditions always complex, the enunciation of the law eliminates these complications. This is what is called ‘correcting the systematic errors’.
Life arose as a living molecule or protogene, the progression from this stage to that of the ameba is at least as great as from ameba to man. All the essential problems of living organisms are already solved in the one-celled (or, as many now prefer to say, noncellular) protozoan and these are only elaborated in man or the other multicellular animals. The step from nonlife to life may not have been so complex, after all, and that from cell to multicellular organism is readily comprehensible. The change from protogene to protozoan was probably the most complex that has occurred in evolution, and it may well have taken as long as the change from protozoan to man.
Looking back over the last thousand years, one can divide the development of the machine and the machine civilization into three successive but over-lapping and interpenetrating phases: eotechnic, paleotechnic, neotechnic … Speaking in terms of power and characteristic materials, the eotechnic phase is a water-and-wood complex: the paleotechnic phase is a coal-and-wood complex… The dawn-age of our modern technics stretches roughly from the year 1000 to 1750. It did not, of course, come suddenly to an end in the middle of the eighteenth century. A new movement appeared in industrial society which had been gathering headway almost unnoticed from the fifteenth century on: after 1750 industry passed into a new phase, with a different source of power, different materials, different objectives.
Mathematics, the science of the ideal, becomes the means of investigating, understanding and making known the world of the real. The complex is expressed in terms of the simple. From one point of view mathematics may be defined as the science of successive substitutions of simpler concepts for more complex.
Most complex object in mathematics? The Mandelbrot Set, named after Benoit Mandelbrot, is represented by a unique pattern plotted from complex number coordinates. … A mathematical description of the shape’s outline would require an infinity of information and yet the pattern can be generated from a few lines of computer code. Used in the study of chaotic behavior, Mandelbrot’s work has found applications in fields such as fluid mechanics, economics and linguistics.
My main thesis will be that in the study of the intermediate processes of metabolism we have to deal not with complex substances which elude ordinary chemical methods, but with the simple substances undergoing comprehensible reactions... I intend also to emphasise the fact that it is not alone with the separation and identification of products from the animal that our present studies deal; but with their reactions in the body; with the dynamic side of biochemical phenomena.
My method consists in allowing the mind to play freely for a very brief period, until a couple or so of ideas have passed through it, and then, while the traces or echoes of those ideas are still lingering in the brain, to turn the attention upon them with a sudden and complete awakening; to arrest, to scrutinise them, and to record their exact appearance... The general impression they have left upon me is like that which many of us have experienced when the basement of our house happens to be under thorough sanitary repairs, and we realise for the first time the complex system of drains and gas and water pipes, flues, bell-wires, and so forth, upon which our comfort depends, but which are usually hidden out of sight, and with whose existence, so long as they acted well, we had never troubled ourselves.
My own thinking (and that of many of my colleagues) is based on two general principles, which I shall call the Sequence Hypothesis and the Central Dogma. The direct evidence for both of them is negligible, but I have found them to be of great help in getting to grips with these very complex problems. I present them here in the hope that others can make similar use of them. Their speculative nature is emphasized by their names. It is an instructive exercise to attempt to build a useful theory without using them. One generally ends in the wilderness.
The Sequence Hypothesis
This has already been referred to a number of times. In its simplest form it assumes that the specificity of a piece of nucleic acid is expressed solely by the sequence of its bases, and that this sequence is a (simple) code for the amino acid sequence of a particular protein...
The Central Dogma
This states that once 'information' has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein. This is by no means universally held—Sir Macfarlane Burnet, for example, does not subscribe to it—but many workers now think along these lines. As far as I know it has not been explicitly stated before.
The Sequence Hypothesis
This has already been referred to a number of times. In its simplest form it assumes that the specificity of a piece of nucleic acid is expressed solely by the sequence of its bases, and that this sequence is a (simple) code for the amino acid sequence of a particular protein...
The Central Dogma
This states that once 'information' has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein. This is by no means universally held—Sir Macfarlane Burnet, for example, does not subscribe to it—but many workers now think along these lines. As far as I know it has not been explicitly stated before.
Nature becomes fertile only by virtue of laws that oblige matter to organize itself into one of a number of necessarily very simple primitive forms. Because of their very simplicity, these are capable of constituting the basis for increasingly complex bodies, by the addition of organs calculated according to identical laws of possibility.
Nature seems to take advantage of the simple mathematical representations of the symmetry laws. When one pauses to consider the elegance and the beautiful perfection of the mathematical reasoning involved and contrast it with the complex and far-reaching physical consequences, a deep sense of respect for the power of the symmetry laws never fails to develop.
Never believe that the atom is a complex mystery—it is not. The atom is what we find when we look for the underlying architecture in nature, whose bricks are as few, as simple and orderly as possible.
No doubt, a scientist isn’t necessarily penalized for being a complex, versatile, eccentric individual with lots of extra-scientific interests. But it certainly doesn't help him a bit.
No video, no photographs, no verbal descriptions, no lectures can provide the enchantment that a few minutes out-of-doors can: watch a spider construct a web; observe a caterpillar systematically ravaging the edge of a leaf; close your eyes, cup your hands behind your ears, and listen to aspen leaves rustle or a stream muse about its pools and eddies. Nothing can replace plucking a cluster of pine needles and rolling them in your fingers to feel how they’re put together, or discovering that “sedges have edges and grasses are round,” The firsthand, right-and-left-brain experience of being in the out-of-doors involves all the senses including some we’ve forgotten about, like smelling water a mile away. No teacher, no student, can help but sense and absorb the larger ecological rhythms at work here, and the intertwining of intricate, varied and complex strands that characterize a rich, healthy natural world.
Nobody knows more than a tiny fragment of science well enough to judge its validity and value at first hand. For the rest he has to rely on views accepted at second hand on the authority of a community of people accredited as scientists. But this accrediting depends in its turn on a complex organization. For each member of the community can judge at first hand only a small number of his fellow members, and yet eventually each is accredited by all. What happens is that each recognizes as scientists a number of others by whom he is recognized as such in return, and these relations form chains which transmit these mutual recognitions at second hand through the whole community. This is how each member becomes directly or indirectly accredited by all. The system extends into the past. Its members recognize the same set of persons as their masters and derive from this allegiance a common tradition, of which each carries on a particular strand.
Not every collision,
not every punctilious trajectory
by which billiard-ball complexes
arrive at their calculable meeting places
lead to reaction. ...
Men (and women) are not
as different from molecules
as they think.
not every punctilious trajectory
by which billiard-ball complexes
arrive at their calculable meeting places
lead to reaction. ...
Men (and women) are not
as different from molecules
as they think.
Nothing in our experience suggests the introduction of [complex numbers]. Indeed, if a mathematician is asked to justify his interest in complex numbers, he will point, with some indignation, to the many beautiful theorems in the theory of equations, of power series, and of analytic functions in general, which owe their origin to the introduction of complex numbers. The mathematician is not willing to give up his interest in these most beautiful accomplishments of his genius.
Now, a living organism is nothing but a wonderful machine endowed with the most marvellous properties and set going by means of the most complex and delicate mechanism.
Now, in the development of our knowledge of the workings of Nature out of the tremendously complex assemblage of phenomena presented to the scientific inquirer, mathematics plays in some respects a very limited, in others a very important part. As regards the limitations, it is merely necessary to refer to the sciences connected with living matter, and to the ologies generally, to see that the facts and their connections are too indistinctly known to render mathematical analysis practicable, to say nothing of the complexity.
Now, we propose in the first place to show, that this law of organic progress is the law of all progress. Whether it be in the development of the Earth, in the development in Life upon its surface, in the development of Society, of Government, of Manufactures, of Commerce, of Language, Literature, Science, Art, this same evolution of the simple into the complex, through a process of continuous differentiation, holds throughout. From the earliest traceable cosmical changes down to the latest results of civilization, we shall find that the transformation of the homogeneous into the heterogeneous is that in which Progress essentially consists.
On the other hand, ethnic psychology must always come to the assistance of individual psychology, when the developmental forms of the complex mental processes are in question.
Order is not sufficient. What is required, is something much more complex. It is order entering upon novelty; so that the massiveness of order does not degenerate into mere repetition; and so that the novelty is always reflected upon a background of system.
Organisms are not billiard balls, propelled by simple and measurable external forces to predictable new positions on life’s pool table. Sufficiently complex systems have greater richness. Organisms have a history that constrains their future in myriad, subtle ways.
Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relationship to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring.
Perhaps randomness is not merely an adequate description for complex causes that we cannot specify. Perhaps the world really works this way, and many events are uncaused in any conventional sense of the word. Perhaps our gut feeling that it cannot be so reflects only our hopes and prejudices, our desperate striving to make sense of a complex and confusing world, and not the ways of nature.
Physicists still tend to regard biologists as men condemned by their lack of mathematics to follow an imprecise science. Some biologists think that, life is too complex to be amenable to mathematical study.
Physics is becoming so unbelievably complex that it is taking longer and longer to train a physicist. It is taking so long, in fact, to train a physicist to the place where he understands the nature of physical problems that he is already too old to solve them.
Plasma seems to have the kinds of properties one would like for life. It’s somewhat like liquid water—unpredictable and thus able to behave in an enormously complex fashion. It could probably carry as much information as DNA does. It has at least the potential for organizing itself in interesting ways.
Primates stand at a turning point in the course of evolution. Primates are to the biologist what viruses are to the biochemist. They can be analysed and partly understood according to the rules of a simpler discipline, but they also present another level of complexity: viruses are living chemicals, and primates are animals who love and hate and think.
Psychoanalysis makes quite simple people feel they’re complex.
Realizing how often ingenious speculation in the complex biological world has led nowhere and how often the real advances in biology as well as in chemistry, physics and astronomy have kept within the bounds of mechanistic interpretation, we geneticists should rejoice, even with our noses on the grindstone (which means both eyes on the objectives), that we have at command an additional means of testing whatever original ideas pop into our heads.
Reproduction is so primitive and fundamental a function of vital organisms that the mechanism by which it is assured is highly complex and not yet clearly understood. It is not necessarily connected with sex, nor is sex necessarily connected with reproduction.
Rules of Thumb
Thumb’s First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb’s Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Thumb’s First Postulate: It is better to use a crude approximation and know the truth, plus or minus 10 percent, than demand an exact solution and know nothing at all.
Thumb’s Second Postulate: An easily understood, workable falsehood is more useful than a complex incomprehensible truth.
Science has now been for a long time—and to an ever-increasing extent—a collective enterprise. Actually, new results are always, in fact, the work of specific individuals; but, save perhaps for rare exceptions, the value of any result depends on such a complex set of interrelations with past discoveries and possible future researches that even the mind of the inventor cannot embrace the whole.
Science helps us before all things in this, that it somewhat lightens the feeling of wonder with which Nature fills us; then, however, as life becomes more and more complex, it creates new facilities for the avoidance of what would do us harm and the promotion of what will do us good.
Science is complex and chilling. The mathematical language of science is understood by very few. The vistas it presents are scary—an enormous universe ruled by chance and impersonal rules, empty and uncaring, ungraspable and vertiginous. How comfortable to turn instead to a small world, only a few thousand years old, and under God's personal; and immediate care; a world in which you are His peculiar concern.
Since an organism is inseparable from its environment, any person who attempts to understand an organism’s distribution must keep constantly in mind that the item being studied is neither a stuffed skin, a pickled specimen, nor a dot on a map. It is not even the live organism held in the hand, caged in a laboratory, or seen in the field. It is a complex interaction between a self-sustaining physicochemical system and the environment. An obvious corollary is that to know the organism it is necessary to know its environment.
Technical skill is mastery of complexity while creativity is mastery of simplicity.
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 act of smelling something, anything, is remarkably like the act of thinking. Immediately at the moment of perception, you can feel the mind going to work, sending the odor around from place to place, setting off complex repertories through the brain, polling one center after another for signs of recognition, for old memories and old connection.
The advance from the simple to the complex, through a process of successive differentiations, is seen alike in the earliest changes of the Universe to which we can reason our way back, and in the earliest changes which we can inductively establish; it is seen in the geologic and climatic evolution of the Earth; it is seen in the unfolding of every single organism on its surface, and in the multiplication of kinds of organisms; it is seen in the evolution of Humanity, whether contemplated in the civilized individual, or in the aggregate of races; it is seen in the evolution of Society in respect alike of its political, its religious, and its economical organization; and it is seen in the evolution of all those endless concrete and abstract products of human activity which constitute the environment of our daily life. From the remotest past which Science can fathom, up to the novelties of yesterday, that in which Progress essentially consists, is the transformation of the homogeneous into the heterogeneous.
The advances of biology during the past 20 years have been breathtaking, particularly in cracking the mystery of heredity. Nevertheless, the greatest and most difficult problems still lie ahead. The discoveries of the 1970‘s about the chemical roots of memory in nerve cells or the basis of learning, about the complex behavior of man and animals, the nature of growth, development, disease and aging will be at least as fundamental and spectacular as those of the recent past.
The aim of science is to seek the simplest explanations of complex facts. We are apt to fall into the error of thinking that the facts are simple because simplicity is the goal of our quest. The guiding motto in the life of every natural philosopher should be, Seek simplicity and distrust it.
The beauty of physics lies in the extent which seemingly complex and unrelated phenomena can be explained and correlated through a high level of abstraction by a set of laws which are amazing in their simplicity.
The chemical compounds are comparable to a system of planets in that the atoms are held together by chemical affinity. They may be more or less numerous, simple or complex in composition, and in the constitution of the materials, they play the same role as Mars and Venus do in our planetary system, or the compound members such as our earth with its moon, or Jupiter with its satellites... If in such a system a particle is replaced by one of different character, the equilibrium can persist, and then the new compound will exhibit properties similar to those shown by the original substance.
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 dog [in Pavlov’s experiments] does not continue to salivate whenever it hears a bell unless sometimes at least an edible offering accompanies the bell. But there are innumerable instances in human life where a single association, never reinforced, results in the establishment of a life-long dynamic system. An experience associated only once with a bereavement, an accident, or a battle, may become the center of a permanent phobia or complex, not in the least dependent on a recurrence of the original shock.
The fact that this chain of life existed [at volcanic vents on the seafloor] in the black cold of the deep sea and was utterly independent of sunlight—previously thought to be the font of all Earth’s life—has startling ramifications. If life could flourish there, nurtured by a complex chemical process based on geothermal heat, then life could exist under similar conditions on planets far removed from the nurturing light of our parent star, the Sun.
The famous set of pictures taken from the moon, [celebrate] the birth of a global consciousness that will help build a peaceful future for humankind. That future is in the hands of those who dedicate their lives to explore Teilhard de Chardin’s three infinities: the infinitely big, the infinitely small, and the infinitely complex. And from all the beauty they discover while crossing perpetually receding frontiers, they develop for nature and for humankind an infinite love.
The fundamental laws necessary for the mathematical treatment of a large part of physics and the whole of chemistry are thus completely known, and the difficulty lies only in the fact that application of these laws leads to equations that are too complex to be solved.
The great basic thought that the world is not to be comprehended as a complex of ready-made things, but as a complex of processes, in which the things apparently stable no less than their mind-images in our heads, the concepts, go through an uninterrupted change of coming into being and passing away, in which, in spite of all seeming accidents and of all temporary retrogression, a progressive development asserts itself in the end—this great fundamental thought has, especially since the time of Hegel, so thoroughly permeated ordinary consciousness that in this generality it is scarcely ever contradicted.
The great beauty of Darwin’s theory of evolution is that it explains how complex, difficult to understand things could have arisen step by plausible step, from simple, easy to understand beginnings. We start our explanation from almost infinitely simple beginnings: pure hydrogen and a huge amount of energy. Our scientific, Darwinian explanations carry us through a series of well-understood gradual steps to all the spectacular beauty and complexity of life.
The greater the mind, the greater are the truths self-evident to it, and the greater also is its power to induce complex from simple truths—complex truths of which we may be as certain
as we are of the primary self-evident truths themselves.
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 ingenuity and effective logic that enabled chemists to determine complex molecular structures from the number of isomers, the reactivity of the molecule and of its fragments, the freezing point, the empirical formula, the molecular weight, etc., is one of the outstanding triumphs of the human mind.
The interactions of man with his environment are so complex that only an ecological approach to nutrition permits an understanding of the whole spectrum of factors determining the nutritional problems that exist in human societies.
The investigation of causal relations between economic phenomena presents many problems of peculiar difficulty, and offers many opportunities for fallacious conclusions. Since the statistician can seldom or never make experiments for himself, he has to accept the data of daily experience, and discuss as best he can the relations of a whole group of changes; he cannot, like the physicist, narrow down the issue to the effect of one variation at a time. The problems of statistics are in this sense far more complex than the problems of physics.
The last level of metaphor in the Alice books is this: that life, viewed rationally and without illusion, appears to be a nonsense tale told by an idiot mathematician. At the heart of things science finds only a mad, never-ending quadrille of Mock Turtle Waves and Gryphon Particles. For a moment the waves and particles dance in grotesque, inconceivably complex patterns capable of reflecting on their own absurdity.
The method of science depends on our attempts to describe the world with simple theories: theories that are complex may become untestable, even if they happen to be true. Science may be described as the art of systematic over-simplification—the art of discerning what we may with advantage omit.
The more the subject is examined the more complex must we suppose the constitution of matter in order to explain the remarkable effects observed.
The more you understand the significance of evolution, the more you are pushed away from the agnostic position and towards atheism. Complex, statistically improbable things are by their nature more difficult to explain than simple, statistically probable things.
The nervous system is the most complex and delicate instrument on our planet, by means of which relations, connections are established between the numerous parts of the organism, as well as between the organism, as a highly complex system, and the innumerable, external influences. If the closing and opening of electric current is now regarded as an ordinary technical device, why should there be any objection to the idea that the same principle acts in this wonderful instrument? On this basis the constant connection between the external agent and the response of the organism, which it evokes, can be rightly called an unconditioned reflex, and the temporary connection—a conditioned reflex.
The new mathematics is a sort of supplement to language, affording a means of thought about form and quantity and a means of expression, more exact, compact, and ready than ordinary language. The great body of physical science, a great deal of the essential facts of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of the great complex world-wide States that are now developing, it is as necessary to be able to compute, to think in averages and maxima and minima, as it is now to be able to read and write.
The open society, the unrestricted access to knowledge, the unplanned and uninhibited association of men for its furtherance—these are what may make a vast, complex, ever growing, ever changing, ever more specialized and expert technological world, nevertheless a world of human community.
The physicist is like someone who’s watching people playing chess and, after watching a few games, he may have worked out what the moves in the game are. But understanding the rules is just a trivial preliminary on the long route from being a novice to being a grand master. So even if we understand all the laws of physics, then exploring their consequences in the everyday world where complex structures can exist is a far more daunting task, and that’s an inexhaustible one I'm sure.
The plan followed by nature in producing animals clearly comprises a predominant prime cause. This endows animal life with the power to make organization gradually more complex, and to bring increasing complexity and perfection not only to the total organization but also to each individual apparatus when it comes to be established by animal life. This progressive complication of organisms was in effect accomplished by the said principal cause in all existing animals. Occasionally a foreign, accidental, and therefore variable cause has interfered with the execution of the plan, without, however, destroying it. This has created gaps in the series, in the form either of terminal branches that depart from the series in several points and alter its simplicity, or of anomalies observable in specific apparatuses of various organisms.
The possibility that the infective agent may not contain nucleic acid and consist only of a peptide or peptide-polysaccharide complex which has replication properties within susceptible cells is intriguing. If peptides, short-chain proteins, or peptide/fatty-acid/ polysaccharide complexes activate nucleic-acid template activity in the host genes to produce identical infective particles, this would invalidate the accepted dogma of present-day molecular biology in which D.N.A. and R.N.A. templates control all biological activity.
The precise equivalence of the chromosomes contributed by the two sexes is a physical correlative of the fact that the two sexes play, on the whole, equal parts in hereditary transmission, and it seems to show that the chromosomal substance, the chromatin, is to be regarded as the physical basis of inheritance. Now, chromatin is known to be closely similar to, if not identical with, a substance known as nuclein (C29H49N9O22, according to Miescher), which analysis shows to be a tolerably definite chemical compased of nucleic acid (a complex organic acid rich in phosphorus) and albumin. And thus we reach the remarkable conclusion that inheritance may, perhaps, be effected by the physical transmission of a particular chemical compound from parent to offspring.
The results of ethnic psychology constitute, at the same time, our chief source of information regarding the general psychology of the complex mental processes.
The Struggle for Existence amongst all organic beings throughout the world, which inevitably follows from their high geometrical powers of increase ... This is the doctrine of Malthus, applied to the whole animal and vegetable kingdoms. As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected. From the strong principle of inheritance, any selected variety will tend to propagate its new and modified form.
The three of us have worked on the development of the small and totally harmless fruit fly, Drosophila. This animal has been extremely cooperative in our hands - and has revealed to us some of its innermost secrets and tricks for developing from a single celled egg to a complex living being of great beauty and harmony. ... None of us expected that our work would be so successful or that our findings would ever have relevance to medicine.
The totality of life, known as the biosphere to scientists and creation to theologians, is a membrane of organisms wrapped around Earth so thin it cannot be seen edgewise from a space shuttle, yet so internally complex that most species composing it remain undiscovered. The membrane is seamless. From Everest's peak to the floor of the Mariana Trench, creatures of one kind or another inhabit virtually every square inch of the planetary surface.
The underlying concepts that unlock nature must be shown to arise early and in the simplest cultures of man from his basic and specific faculties. And the development of science which joins them in more and more complex conjunctions must be seen to be equally human: discoveries are made by men, not merely by minds, so that they are alive and charged with individuality.
The understanding of a complex problem such as atherosclerosis requires the tools of basic science. We are fortunate to live at a time when the methods of basic science are so powerful that they can be applied directly to clinical problems. … [T]he two attributes that are required – basic training and technical courage.
The universe is simple; it’s the explanation that’s complex.
The value of mathematical instruction as a preparation for those more difficult investigations, consists in the applicability not of its doctrines but of its methods. Mathematics will ever remain the past perfect type of the deductive method in general; and the applications of mathematics to the simpler branches of physics furnish the only school in which philosophers can effectually learn the most difficult and important of their art, the employment of the laws of simpler phenomena for explaining and predicting those of the more complex. These grounds are quite sufficient for deeming mathematical training an indispensable basis of real scientific education, and regarding with Plato, one who is … as wanting in one of the most essential qualifications for the successful cultivation of the higher branches of philosophy
Theories rarely arise as patient inferences forced by accumulated facts. Theories are mental constructs potentiated by complex external prods (including, in idealized cases, a commanding push from empirical reality) . But the prods often in clude dreams, quirks, and errors–just as we may obtain crucial bursts of energy from foodstuffs or pharmaceuticals of no objective or enduring value. Great truth can emerge from small error. Evolution is thrilling, liberating, and correct. And Macrauchenia is a litoptern.
There are, as we have seen, a number of different modes of technological innovation. Before the seventeenth century inventions (empirical or scientific) were diffused by imitation and adaption while improvement was established by the survival of the fittest. Now, technology has become a complex but consciously directed group of social activities involving a wide range of skills, exemplified by scientific research, managerial expertise, and practical and inventive abilities. The powers of technology appear to be unlimited. If some of the dangers may be great, the potential rewards are greater still. This is not simply a matter of material benefits for, as we have seen, major changes in thought have, in the past, occurred as consequences of technological advances.
There is always a well-known solution to every human problem—neat, plausible, and wrong.
There is deposited in them [plants] an enormous quantity of potential energy [Spannkräfte], whose equivalent is provided to us as heat in the burning of plant substances. So far as we know at present, the only living energy [lebendige Kraft] absorbed during plant growth are the chemical rays of sunlight… Animals take up oxygen and complex oxidizable compounds made by plants, release largely as combustion products carbonic acid and water, partly as simpler reduced compounds, thus using a certain amount of chemical potential energy to produce heat and mechanical forces. Since the latter represent a relatively small amount of work in relation to the quantity of heat, the question of the conservation of energy reduces itself roughly to whether the combustion and transformation of the nutritional components yields the same amount of heat released by animals.
There is no area in our minds reserved for superstition, such as the Greeks had in their mythology; and superstition, under cover of an abstract vocabulary, has revenged itself by invading the entire realm of thought. Our science is like a store filled with the most subtle intellectual devices for solving the most complex problems, and yet we are almost incapable of applying the elementary principles of rational thought. In every sphere, we seem to have lost the very elements of intelligence: the ideas of limit, measure, degree, proportion, relation, comparison, contingency, interdependence, interrelation of means and ends. To keep to the social level, our political universe is peopled exclusively by myths and monsters; all it contains is absolutes and abstract entities. This is illustrated by all the words of our political and social vocabulary: nation, security, capitalism, communism, fascism, order, authority, property, democracy. We never use them in phrases such as: There is democracy to the extent that… or: There is capitalism in so far as… The use of expressions like “to the extent that” is beyond our intellectual capacity. Each of these words seems to represent for us an absolute reality, unaffected by conditions, or an absolute objective, independent of methods of action, or an absolute evil; and at the same time we make all these words mean, successively or simultaneously, anything whatsoever. Our lives are lived, in actual fact, among changing, varying realities, subject to the casual play of external necessities, and modifying themselves according to specific conditions within specific limits; and yet we act and strive and sacrifice ourselves and others by reference to fixed and isolated abstractions which cannot possibly be related either to one another or to any concrete facts. In this so-called age of technicians, the only battles we know how to fight are battles against windmills.
There is thus a possibility that the ancient dream of philosophers to connect all Nature with the properties of whole numbers will some day be realized. To do so physics will have to develop a long way to establish the details of how the correspondence is to be made. One hint for this development seems pretty obvious, namely, the study of whole numbers in modern mathematics is inextricably bound up with the theory of functions of a complex variable, which theory we have already seen has a good chance of forming the basis of the physics of the future. The working out of this idea would lead to a connection between atomic theory and cosmology.
These facts shaw that mitosis is due to the co-ordinate play of an extremely complex system of forces which are as yet scarcely comprehended. Its purpose is, however, as obvious as its physiological explanation is difficult. It is the end of mitosis to divide every part of the chromatin of the mother-cell equally between the daughter-nuclei. All the other operations are tributary to this. We may therefore regard the mitotic figure as essentially an apparatus for the distribution of the hereditary substance, and in this sense as the especial instrument of inheritance.
This science, Geometry, is one of indispensable use and constant reference, for every student of the laws of nature; for the relations of space and number are the alphabet in which those laws are written. But besides the interest and importance of this kind which geometry possesses, it has a great and peculiar value for all who wish to understand the foundations of human knowledge, and the methods by which it is acquired. For the student of geometry acquires, with a degree of insight and clearness which the unmathematical reader can but feebly imagine, a conviction that there are necessary truths, many of them of a very complex and striking character; and that a few of the most simple and self-evident truths which it is possible for the mind of man to apprehend, may, by systematic deduction, lead to the most remote and unexpected results.
Thus science strips off, one after the other, the more or less gross materialisations by which we endeavour to form an objective image of the soul, till men of science, speculating, in their non-scientific intervals, like other men on what science may possibly lead to, have prophesied that we shall soon have to confess that the soul is nothing else than a function of certain complex material systems.
To bring scientific investigation to a happy end once appropriate methods have been determined, we must hold firmly in mind the goal of the project. The object here is to focus the train of thought on more and more complex and accurate associations between images based on observation and ideas slumbering in the unconscious.
To create a human through genetic engineering that is more complex, more refined, more subtle, farther from animals, than the ones we have today.
To emphasize this opinion that mathematicians would be unwise to accept practical issues as the sole guide or the chief guide in the current of their investigations, ... let me take one more instance, by choosing a subject in which the purely mathematical interest is deemed supreme, the theory of functions of a complex variable. That at least is a theory in pure mathematics, initiated in that region, and developed in that region; it is built up in scores of papers, and its plan certainly has not been, and is not now, dominated or guided by considerations of applicability to natural phenomena. Yet what has turned out to be its relation to practical issues? The investigations of Lagrange and others upon the construction of maps appear as a portion of the general property of conformal representation; which is merely the general geometrical method of regarding functional relations in that theory. Again, the interesting and important investigations upon discontinuous two-dimensional fluid motion in hydrodynamics, made in the last twenty years, can all be, and now are all, I believe, deduced from similar considerations by interpreting functional relations between complex variables. In the dynamics of a rotating heavy body, the only substantial extension of our knowledge since the time of Lagrange has accrued from associating the general properties of functions with the discussion of the equations of motion. Further, under the title of conjugate functions, the theory has been applied to various questions in electrostatics, particularly in connection with condensers and electrometers. And, lastly, in the domain of physical astronomy, some of the most conspicuous advances made in the last few years have been achieved by introducing into the discussion the ideas, the principles, the methods, and the results of the theory of functions. … the refined and extremely difficult work of Poincare and others in physical astronomy has been possible only by the use of the most elaborate developments of some purely mathematical subjects, developments which were made without a thought of such applications.
To say that mind is a product or function of protoplasm, or of its molecular changes, is to use words to which we can attach no clear conception. You cannot have, in the whole, what does not exist in any of the parts; and those who argue thus should put forth a definite conception of matter, with clearly enunciated properties, and show, that the necessary result of a certain complex arrangement of the elements or atoms of that matter, will be the production of self-consciousness. There is no escape from this dilemma—either all matter is conscious, or consciousness is something distinct from matter, and in the latter case, its presence in material forms is a proof of the existence of conscious beings, outside of, and independent of, what we term matter. The foregoing considerations lead us to the very important conclusion, that matter is essentially force, and nothing but force; that matter, as popularly understood, does not exist, and is, in fact, philosophically inconceivable. When we touch matter, we only really experience sensations of resistance, implying repulsive force; and no other sense can give us such apparently solid proofs of the reality of matter, as touch does. This conclusion, if kept constantly present in the mind, will be found to have a most important bearing on almost every high scientific and philosophical problem, and especially on such as relate to our own conscious existence.
To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest possible degree. When it was first said that the sun stood still and the world turned round, the common sense of mankind declared the doctrine false; but the old saying of Vox populi, vox Dei, as every philosopher knows, cannot be trusted in science. Reason tells me, that if numerous gradations from a perfect and complex eye to one very imperfect and simple, each grade being useful to its possessor, can be shown to exist; if further, the eye does vary ever so slightly, and the variations be inherited, which is certainly the case; and if any variation or modification in the organ be ever useful to an animal under changing conditions of life, then the difficulty of believing that a perfect and complex eye could be formed by natural selection, though insuperable by our imagination, can hardly be considered real.
Unity of plan everywhere lies hidden under the mask: of diversity of structure—the complex is everywhere evolved out of the simple.
Very little comes easily to our poor, benighted species (the first creature, after all, to experiment with the novel evolutionary inventions of self-conscious philosophy and art). Even the most ‘obvious,’ ‘accurate,’ and ‘natural’ style of thinking or drawing must be regulated by history and won by struggle. Solutions must therefore arise within a social context and record the complex interactions of mind and environment that define the possibility of human improvement.
We are not alone in the universe, and do not bear alone the whole burden of life and what comes of it. Life is a cosmic event—so far as we know the most complex state of organization that matter has achieved in our cosmos. It has come many times, in many places—places closed off from us by impenetrable distances, probably never to be crossed even with a signal. As men we can attempt to understand it, and even somewhat to control and guide its local manifestations. On this planet that is our home, we have every reason to wish it well. Yet should we fail, all is not lost. Our kind will try again elsewhere.
We divorced ourselves from the materials of the earth, the rock, the wood, the iron ore; we looked to new materials which were cooked in vats, long complex derivatives of urine which we called plastic. They had no odor of the living, ... their touch was alien to nature. ... [They proliferated] like the matastases of cancer cells.
We do not inhabit a perfected world where natural selection ruthlessly scrutinizes all organic structures and then molds them for optimal utility. Organisms inherit a body form and a style of embryonic development; these impose constraint s upon future change and adaptation. In many cases, evolutionary pathways reflect inherited patterns more than current environmental demands. These inheritances constrain, but they also provide opportunity. A potentially minor genetic change ... entails a host of complex, nonadaptive consequences ... What ‘play’ would evolution have if each structure were built for a restricted purpose and could be used for nothing else? How could humans learn to write if our brain had not evolved for hunting, social cohesion, or whatever, and could not transcend the adaptive boundaries of its original purpose?
We have hitherto considered those Ideas, in the reception whereof, the Mind is only passive, which are those simple ones received from Sensation and Reflection before-mentioned, whereof the Mind cannot make anyone to it self, nor have any Idea which does not wholy consist of them. But as these simple Ideas are observed to exist in several Combinations united together; so the Mind has a power to consider several of them united together, as one Idea; and that not only as they are united in external Objects, but as it self has joined them. Ideas thus made up of several simple ones put together, I call Complex; such as are Beauty, Gratitude, a Man, an Army, the Universe; which tough complicated various simple Ideas, made up of simple ones, yet are, when the Mind pleases, considered each by if self, as one entire thing, and signified by one name.
We inhabit a complex world. Some boundaries are sharp and permit clean and definite distinctions. But nature also includes continua that cannot be neatly parceled into two piles of unambiguous yeses and noes. Biologists have rejected, as fatally flawed in principle, all attempts by antiabortionists to define an unambiguous ‘beginning of life,’ because we know so well that the sequence from ovulation or spermatogenesis to birth is an unbreakable continuum–and surely no one will define masturbation as murder.
We live in an essential and unresolvable tension between our unity with nature and our dangerous uniqueness. Systems that attempt to place and make sense of us by focusing exclusively either on the uniqueness or the unity are doomed to failure. But we must not stop asking and questing because the answers are complex and ambiguous.
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 must not forget … that “influence” is not a simple, but on the contrary, a very complex, bilateral relation. We are not influenced by everything we read or learn. In one sense, and perhaps the deepest, we ourselves determine the influences we are submitting to; our intellectual ancestors are by no means given to, but are freely chosen by, us.
We see that each surface is really a pair of surfaces, so that, where they appear to merge, there are really four surfaces. Continuing this process for another circuit, we see that there are really eight surfaces etc and we finally conclude that there is an infinite complex of surfaces, each extremely close to one or the other of two merging surfaces.
What we call matter is only a complex of energies which we find together in the same place.
What we do see through geological time is the emergence of more complex worlds. ... [W]hen within the animal we see the emergence of larger and more complex brains, sophisticated vocalizations, echolocation, electrical perception, advanced social systems including eusociality, viviparity, warm-bloodedness, and agriculture—all of which are convergent—then to me that sounds like progress.
Whatever the subject of any investigation may be, whether poetry, biology, ethics or torpedo warfare, the same scientific method of procedure must be followed. We must first unravel the complex and heterogeneous back to first principles, and then reason forward from the simple to the complex, from the homogeneous to the heterogeneous, from what we know to what we would learn. Such are the methods pursued by all successful inventors, scientific investigators and discoverers.
When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails us. One need only think of the weather, in which case prediction even for a few days ahead is impossible. Nevertheless no one doubts that we are confronted with a causal connection whose causal components are in the main known to us.
When two texts, or two assertions, perhaps two ideas, are in contradiction, be ready to reconcile them rather than cancel one by the other; regard them as two different facets, or two successive stages, of the same reality, a reality convincingly human just because it is too complex.
When we no longer look at an organic being as a savage looks at a ship, as something wholly beyond his comprehension; when we regard every production of nature as one which has had a long history; when we contemplate every complex structure and instinct as the summing up of many contrivances, each useful to the possessor, in the same way as any great mechanical invention is the summing up of the labour, the experience, the reason, and even the blunders of numerous workmen; when we thus view each organic being, how far more interesting, I speak from experience, does the study of natural history become!
When you live in a complex world, you have to simplify it in order to understand it.
Without doubt one of the most characteristic features of mathematics in the last century is the systematic and universal use of the complex variable. Most of its great theories received invaluable aid from it, and many owe their very existence to it.
Would not [an] uncluttered mind also see the attempts to reconcile science and religion by disparaging the reduction of the complex to the simple as attempts guided by muddle-headed sentiment and intellectually dishonest emotion?