[On Oxygen, Chlorine, Iodine, Fluorine:] The most important division of ponderable substances seems to be that which represents their electrical energies or their respective inherent states. When the poles of a voltaic apparatus are introduced into a mixture of the simple substances, it is found that four of them go to the positive, while the rest evince their state by passing to the negative pole. As this division coincides with one resulting from a consideration of their most important properties, it is that which I shall adopt as the first.

An idea must not be condemned for being a little shy and incoherent; all new ideas are shy when introduced first among our old ones. We should have patience and see whether the incoherency is likely to wear off or to wear on, in which latter case the sooner we get rid of them the better.

An optical unit has been devised which will convey optical images along a flexible axis. The unit comprises a bundle of fibres of glass, or other transparent material, and it therefore appears appropriate to introduce the term 'fibrescope' to denote it.
Co-author with Indian-American physicist Narinder Singh Kapany..

Astronomy is the most ancient of all the sciences, and has been the introducer of vast knowledge.

Cells are required to stick precisely to the point. Any ambiguity, any tendency to wander from the matter at hand, will introduce grave hazards for the cells, and even more for the host in which they live. … There is a theory that the process of aging may be due to the cumulative effect of imprecision, a gradual degrading of information. It is not a system that allows for deviating.

Chemical analysis and synthesis go no farther than to the separation of particles one from another, and to their reunion. No new creation or destruction of matter is within the reach of chemical agency. We might as well attempt to introduce a new planet into the solar system, or to annihilate one already in existence, as to create or destroy a particle of hydrogen.

Equations are Expressions of Arithmetical Computation, and properly have no place in Geometry, except as far as Quantities truly Geometrical (that is, Lines, Surfaces, Solids, and Proportions) may be said to be some equal to others. Multiplications, Divisions, and such sort of Computations, are newly received into Geometry, and that unwarily, and contrary to the first Design of this Science. For whosoever considers the Construction of a Problem by a right Line and a Circle, found out by the first Geometricians, will easily perceive that Geometry was invented that we might expeditiously avoid, by drawing Lines, the Tediousness of Computation. Therefore these two Sciences ought not to be confounded. The Ancients did so industriously distinguish them from one another, that they never introduced Arithmetical Terms into Geometry. And the Moderns, by confounding both, have lost the Simplicity in which all the Elegance of Geometry consists. Wherefore that is Arithmetically more simple which is determined by the more simple Equation, but that is Geometrically more simple which is determined by the more simple drawing of Lines; and in Geometry, that ought to be reckoned best which is geometrically most simple.

Euclid avoids it [the treatment of the infinite]; in modern mathematics it is systematically introduced, for only then is generality obtained.

Exactness cannot be established in the arguments unless it is first introduced into the definitions.

Given any rule, however “fundamental” or “necessary” for science, there are always circumstances when it is advisable not only to ignore the rule, but to adopt its opposite. For example, there are circumstances when it is advisable to introduce, elaborate and defend ad hoc hypotheses, or hypotheses which contradict well-established and generally accepted experimental results, or hypotheses whose content is smaller than the content of the existing and empirically adequate alternative, or self-inconsistent hypotheses, and so on.

Given one has before oneself a strong, healthy, youth rich in spirited blood and a powerless, weak, cachectic old man scarcely capable of breathing. If now the physician wishes to practise the rejuvenating art on the latter, he should make silver tubes which fit into each other: open then the artery of the healthy person and introduce one of the tubes into it and fasten it into the artery; thereupon he opens also the artery of the ill person...
[First detailed description of blood transfusion (1615)]

How do we discover the individual laws of Physics, and what is their nature? It should be remarked, to begin with, that we have no right to assume that any physical law exists, or if they have existed up to now, that they will continue to exist in a similar manner in the future. It is perfectly conceivable that one fine day Nature should cause an unexpected event to occur which would baffle us all; and if this were to happen we would be powerless to make any objection, even if the result would be that, in spite of our endeavors, we should fail to introduce order into the resulting confusion. In such an event, the only course open to science would be to declare itself bankrupt. For this reason, science is compelled to begin by the general assumption that a general rule of law dominates throughout Nature.

I am ashamed to say that C. P. Snow's “two cultures” debate smoulders away. It is an embarrassing and sterile debate, but at least it introduced us to Medawar's essays. Afterwards, not even the most bigoted aesthete doubted that a scientist could be every inch as cultivated and intellectually endowed as a student of the humanities.

I beg to introduce myself to you as a clerk in the Accounts Department of the Port Trust Office at Madras on a salary of only £20 per annum. I am now about 23 years of age. … After leaving school I have been employing the spare time at my disposal to work at Mathematics.

I should rejoice to see … Euclid honourably shelved or buried “deeper than did ever plummet sound” out of the schoolboys’ reach; morphology introduced into the elements of algebra; projection, correlation, and motion accepted as aids to geometry; the mind of the student quickened and elevated and his faith awakened by early initiation into the ruling ideas of polarity, continuity, infinity, and familiarization with the doctrines of the imaginary and inconceivable.

I think, and I am not the only one who does, that it is important never to introduce any conception which may not be completely defined by a finite number of words. Whatever may be the remedy adopted, we can promise ourselves the joy of the physician called in to follow a beautiful pathological case [beau cas pathologique].

I was introduced to Mr. Davy, who has rooms adjoining mine (in the Royal Institution); he is a very agreeable and intelligent young man, and we have interesting conversation in an evening; the principal failing in his character as a philosopher is that he does not smoke.

I wish people would more generally bring back the seeds of pleasing foreign plants and introduce them broadcast, sowing them by our waysides and in our fields, or in whatever situation is most likely to suit them. It is true, this would puzzle botanists, but there is no reason why botanists should not be puzzled. A botanist is a person whose aim is to uproot, kill and exterminate every plant that is at all remarkable for rarity or any special virtue, and the rarer it is the more bitterly he will hunt it down.

I wished to show that Pythagoras, the first founder of the vegetable regimen, was at once a very great physicist and a very great physician; that there has been no one of a more cultured and discriminating humanity; that he was a man of wisdom and of experience; that his motive in commending and introducing the new mode of living was derived not from any extravagant superstition, but from the desire to improve the health and the manners of men.

I'd climb in the car as it went down the assembly line and introduce myself. Then I'd ask for ideas.
[How, as Ford manager of development for the Taurus car, he sought input from Ford production employees.]

If E is considered to be a continuously divisible quantity, this distribution is possible in infinitely many ways. We consider, however—this is the most essential point of the whole calculation—E to be composed of a well-defined number of equal parts and use thereto the constant of nature h = 6.55 ×10^-27 erg sec. This constant multiplied by the common frequency ν of the resonators gives us the energy element ε in erg, and dividing E by ε we get the number P of energy elements which must be divided over the N resonators.
[Planck’s constant, as introduced in 1900; subsequently written e = hν.]

If one of these elements, heat, becomes predominant in any body whatsoever, it destroys and dissolves all the others with its violence. …Again if too much moisture enters the channels of a body, and thus introduces disproportion, the other elements, adulterated by the liquid, are impaired, and the virtues of the mixture dissolved. This defect, in turn, may arise from the cooling properties of moist winds and breezes blowing upon the body. In the same way, increase or diminution of the proportion of air or of the earthy which is natural to the body may enfeeble the other elements.

In Euclid each proposition stands by itself; its connection with others is never indicated; the leading ideas contained in its proof are not stated; general principles do not exist. In modern methods, on the other hand, the greatest importance is attached to the leading thoughts which pervade the whole; and general principles, which bring whole groups of theorems under one aspect, are given rather than separate propositions. The whole tendency is toward generalization. A straight line is considered as given in its entirety, extending both ways to infinity, while Euclid is very careful never to admit anything but finite quantities. The treatment of the infinite is in fact another fundamental difference between the two methods. Euclid avoids it, in modern mathematics it is systematically introduced, for only thus is generality obtained.

In Melvin Calvin’s office there were four photographs: Michael Polanyi, Joel Hildebrand, Gilbert N. Lewis, and Ernest O. Lawrence. These scientists were his mentors: Polanyi for introducing him to the chemistry of phthalocyanine; Hildebrand for bringing him to Berkeley; Lewis, perhaps his most influential teacher; and Lawrence, who provided him the opportunity to work with the new scientific tool of radioactive carbon, which enabled the search for the path of carbon in photosynthesis to be successful.

In one department of his [Joseph Black’s] lecture he exceeded any I have ever known, the neatness and unvarying success with which all the manipulations of his experiments were performed. His correct eye and steady hand contributed to the one; his admirable precautions, foreseeing and providing for every emergency, secured the other. I have seen him pour boiling water or boiling acid from a vessel that had no spout into a tube, holding it at such a distance as made the stream’s diameter small, and so vertical that not a drop was spilt. While he poured he would mention this adaptation of the height to the diameter as a necessary condition of success. I have seen him mix two substances in a receiver into which a gas, as chlorine, had been introduced, the effect of the combustion being perhaps to produce a compound inflammable in its nascent state, and the mixture being effected by drawing some string or wire working through the receiver's sides in an air-tight socket. The long table on which the different processes had been carried on was as clean at the end of the lecture as it had been before the apparatus was planted upon it. Not a drop of liquid, not a grain of dust remained.

In organic chemistry there exist certain types which are conserved even when, in place of hydrogen, equal volumes of chlorine, of bromine, etc. are introduced.

In the summer after kindergarten, a friend introduced me to the joys of building plastic model airplanes and warships. By the fourth grade, I graduated to an erector set and spent many happy hours constructing devices of unknown purpose where the main design criterion was to maximize the number of moving parts and overall size. The living room rug was frequently littered with hundreds of metal “girders” and tiny nuts and bolts surrounding half-finished structures. An understanding mother allowed me to keep the projects going for days on end.

It is a temptation for philosophers that they should weave a fairy tale of the adjustment of factors; and then as an appendix introduce the notion of frustration, as a secondary aspect. I suggest to you that this is the criticism to be made on the monistic idealisms of the nineteenth century, and even of the great Spinoza. It is quite incredible that the Absolute, as conceived in monistic philosophy, should evolve confusion about its own details.

It is the task of science, as a collective human undertaking, to describe from the external side, (on which alone agreement is possible), such statistical regularity as there is in a world “in which every event has a unique aspect, and to indicate where possible the limits of such description. It is not part of its task to make imaginative interpretation of the internal aspect of reality—what it is like, for example, to be a lion, an ant or an ant hill, a liver cell, or a hydrogen ion. The only qualification is in the field of introspective psychology in which each human being is both observer and observed, and regularities may be established by comparing notes. Science is thus a limited venture. It must act as if all phenomena were deterministic at least in the sense of determinable probabilities. It cannot properly explain the behaviour of an amoeba as due partly to surface and other physical forces and partly to what the amoeba wants to do, with out danger of something like 100 per cent duplication. It must stick to the former. It cannot introduce such principles as creative activity into its interpretation of evolution for similar reasons. The point of view indicated by a consideration of the hierarchy of physical and biological organisms, now being bridged by the concept of the gene, is one in which science deliberately accepts a rigorous limitation of its activities to the description of the external aspects of events. In carrying out this program, the scientist should not, however, deceive himself or others into thinking that he is giving an account of all of reality. The unique inner creative aspect of every event necessarily escapes him.

It is very desirable to have a word to express the Availability for work of the heat in a given magazine; a term for that possession, the waste of which is called Dissipation. Unfortunately the excellent word Entropy, which Clausius has introduced in this connexion, is applied by him to the negative of the idea we most naturally wish to express. It would only confuse the student if we were to endeavour to invent another term for our purpose. But the necessity for some such term will be obvious from the beautiful examples which follow. And we take the liberty of using the term Entropy in this altered sense ... The entropy of the universe tends continually to zero.

It is very different to make a practical system and to introduce it. A few experiments in the laboratory would prove the practicability of system long before it could be brought into general use. You can take a pipe and put a little coal in it, close it up, heat it and light the gas that comes out of the stem, but that is not introducing gas lighting. I'll bet that if it were discovered to-morrow in New York that gas could be made out of coal it would be at least five years before the system would be in general use.

It seems perfectly clear that Economy, if it is to be a science at all, must be a mathematical science. There exists much prejudice against attempts to introduce the methods and language of mathematics into any branch of the moral sciences. Most persons appear to hold that the physical sciences form the proper sphere of mathematical method, and that the moral sciences demand some other method—I know not what.

It was his [Leibnitz’s] love of method and order, and the conviction that such order and harmony existed in the real world, and that our success in understanding it depended upon the degree and order which we could attain in our own thoughts, that originally was probably nothing more than a habit which by degrees grew into a formal rule. This habit was acquired by early occupation with legal and mathematical questions. We have seen how the theory of combinations and arrangements of elements had a special interest for him. We also saw how mathematical calculations served him as a type and model of clear and orderly reasoning, and how he tried to introduce method and system into logical discussions, by reducing to a small number of terms the multitude of compound notions he had to deal with. This tendency increased in strength, and even in those early years he elaborated the idea of a general arithmetic, with a universal language of symbols, or a characteristic which would be applicable to all reasoning processes, and reduce philosophical investigations to that simplicity and certainty which the use of algebraic symbols had introduced into mathematics.
A mental attitude such as this is always highly favorable for mathematical as well as for philosophical investigations. Wherever progress depends upon precision and clearness of thought, and wherever such can be gained by reducing a variety of investigations to a general method, by bringing a multitude of notions under a common term or symbol, it proves inestimable. It necessarily imports the special qualities of number—viz., their continuity, infinity and infinite divisibility—like mathematical quantities—and destroys the notion that irreconcilable contrasts exist in nature, or gaps which cannot be bridged over. Thus, in his letter to Arnaud, Leibnitz expresses it as his opinion that geometry, or the philosophy of space, forms a step to the philosophy of motion—i.e., of corporeal things—and the philosophy of motion a step to the philosophy of mind.

It would be wrong to assume that one must stay with a research programme until it has exhausted all its heuristic power, that one must not introduce a rival programme before everybody agrees that the point of degeneration has probably been reached.

John Bahcall, an astronomer on the Institute of Advanced Study faculty since 1970 likes to tell the story of his first faculty dinner, when he found himself seated across from Kurt Gödel, … a man dedicated to logic and the clean certainties of mathematical abstraction. Bahcall introduced himself and mentioned that he was a physicist. Gödel replied, “I don’t believe in natural science.”

Mathematicians attach great importance to the elegance of their methods and their results. This is not pure dilettantism. What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details. But this is exactly what yields great results, in fact the more we see this aggregate clearly and at a single glance, the better we perceive its analogies with other neighboring objects, consequently the more chances we have of divining the possible generalizations. Elegance may produce the feeling of the unforeseen by the unexpected meeting of objects we are not accustomed to bring together; there again it is fruitful, since it thus unveils for us kinships before unrecognized. It is fruitful even when it results only from the contrast between the simplicity of the means and the complexity of the problem set; it makes us then think of the reason for this contrast and very often makes us see that chance is not the reason; that it is to be found in some unexpected law. In a word, the feeling of mathematical elegance is only the satisfaction due to any adaptation of the solution to the needs of our mind, and it is because of this very adaptation that this solution can be for us an instrument. Consequently this esthetic satisfaction is bound up with the economy of thought.

Modern theories did not arise from revolutionary ideas which have been, so to speak, introduced into the exact sciences from without. On the contrary they have forced their way into research which was attempting consistently to carry out the programme of classical physics—they arise out of its very nature. It is for this reason that the beginnings of modern physics cannot be compared with the great upheavals of previous periods like the achievements of Copernicus. Copernicus’s idea was much more an import from outside into the concepts of the science of his time, and therefore caused far more telling changes in science than the ideas of modern physics are creating to-day.

My impression about the Panama Canal is that the great revolution it is going to introduce in the trade of the world is in the trade between the east and the west coast of the United States.

One day when the whole family had gone to a circus to see some extraordinary performing apes, I remained alone with my microscope, observing the life in the mobile cells of a transparent star-fish larva, when a new thought suddenly flashed across my brain. It struck me that similar cells might serve in the defence of the organism against intruders. Feeling that there was in this something of surpassing interest, I felt so excited that I began striding up and down the room and even went to the seashore in order to collect my thoughts.
I said to myself that, if my supposition was true, a splinter introduced into the body of a star-fish larva, devoid of blood-vessels or of a nervous system, should soon be surrounded by mobile cells as is to be observed in a man who runs a splinter into his finger. This was no sooner said than done.
There was a small garden to our dwelling, in which we had a few days previously organised a 'Christmas tree' for the children on a little tangerine tree; I fetched from it a few rose thorns and introduced them at once under the skin of some beautiful star-fish larvae as transparent as water.
I was too excited to sleep that night in the expectation of the result of my experiment, and very early the next morning I ascertained that it had fully succeeded.
That experiment formed the basis of the phagocyte theory, to the development of which I devoted the next twenty-five years of my life.

Science can be introduced to children well or poorly. If poorly, children can be turned away from science; they can develop a lifelong antipathy; they will be in a far worse condition than if they had never been introduced to science at all.

Science is a human activity, and the best way to understand it is to understand the individual human beings who practise it. Science is an art form and not a philosophical method. The great advances in science usually result from new tools rather than from new doctrines. ... Every time we introduce a new tool, it always leads to new and unexpected discoveries, because Nature's imagination is richer than ours.

The comparatively small progress toward universal acceptance made by the metric system seems to be due not altogether to aversion to a change of units, but also to a sort of irrepressible conflict between the decimal and binary systems of subdivision.
[Remarking in 1892 (!) that although decimal fractions were introduced about 1585, America retains measurements in halves, quarters, eights and sixteenths in various applications such as fractions of an inch, the compass or used by brokers.]

The concept of an independent system is a pure creation of the imagination. For no material system is or can ever be perfectly isolated from the rest of the world. Nevertheless it completes the mathematician’s “blank form of a universe” without which his investigations are impossible. It enables him to introduce into his geometrical space, not only masses and configurations, but also physical structure and chemical composition. Just as Newton first conclusively showed that this is a world of masses, so Willard Gibbs first revealed it as a world of systems.

The concepts of ‘soul’ or ‘life’ do not occur in atomic physics, and they could not, even indirectly, be derived as complicated consequences of some natural law. Their existence certainly does not indicate the presence of any fundamental substance other than energy, but it shows only the action of other kinds of forms which we cannot match with the mathematical forms of modern atomic physics ... If we want to describe living or mental processes, we shall have to broaden these structures. It may be that we shall have to introduce yet other concepts.

The endeavour to observe oneself must inevitably introduce changes into the course of mental events,—changes which could not have occurred without it, and whose usual consequence is that the very process which was to have been observed disappears from consciousness.

The origin of a science is usually to be sought for not in any systematic treatise, but in the investigation and solution of some particular problem. This is especially the case in the ordinary history of the great improvements in any department of mathematical science. Some problem, mathematical or physical, is proposed, which is found to be insoluble by known methods. This condition of insolubility may arise from one of two causes: Either there exists no machinery powerful enough to effect the required reduction, or the workmen are not sufficiently expert to employ their tools in the performance of an entirely new piece of work. The problem proposed is, however, finally solved, and in its solution some new principle, or new application of old principles, is necessarily introduced. If a principle is brought to light it is soon found that in its application it is not necessarily limited to the particular question which occasioned its discovery, and it is then stated in an abstract form and applied to problems of gradually increasing generality.
Other principles, similar in their nature, are added, and the original principle itself receives such modifications and extensions as are from time to time deemed necessary. The same is true of new applications of old principles; the application is first thought to be merely confined to a particular problem, but it is soon recognized that this problem is but one, and generally a very simple one, out of a large class, to which the same process of investigation and solution are applicable. The result in both of these cases is the same. A time comes when these several problems, solutions, and principles are grouped together and found to produce an entirely new and consistent method; a nomenclature and uniform system of notation is adopted, and the principles of the new method become entitled to rank as a distinct science.

The result of teaching small parts of a large number of subjects is the passive reception of disconnected ideas, not illuminated with any spark of vitality. Let the main ideas which are introduced into a child’s education be few and important, and let them be thrown into every combination possible.

The word, “Vitamine,” served as a catchword which meant something even to the uninitiated, and it was not by mere accident that just at that time, research developed so markedly in this direction. Our view as to the fortunate choice of this name is strengthened, on the one hand, because it has become popular (and a badly chosen catchword, like a folksong without feeling, can never become popular), and on the other, because of the untiring efforts of other workers to introduce a varied nomenclature, for example, “accessory food factors, food hormones, water-soluble B and fat-soluble A, nutramine, and auximone” (for plants). Some of these designations are certainly not better, while others are much worse than “Vitamine.”

Those who would legislate against the teaching of evolution should also legislate against gravity, electricity and the unreasonable velocity of light, and also should introduce a clause to prevent the use of the telescope, the microscope and the spectroscope or any other instrument of precision which may in the future be invented, constructed or used for the discovery of truth.

To demonstrate experimentally that a microscopic organism actually is the cause of a disease and the agent of contagion, I know no other way, in the present state of Science, than to subject the microbe (the new and happy term introduced by M. Sédillot) to the method of cultivation out of the body.

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 introduce something altogether new would mean to begin all over, to become ignorant again, and to run the old, old risk of failing to learn.

To most ... of us, Russia was as mysterious and remote as the other side of the moon and not much more productive when it came to really new ideas or inventions. A common joke of the time [mid 1940s] said that the Russians could not surreptitiously introduce nuclear bombs in suitcases into the United States because they had not yet been able to perfect a suitcase.

We have just introduced the term gene for the hypothetical material carrier of a definite hereditary feature.

We ourselves introduce that order and regularity in the appearance which we entitle ‘nature’. We could never find them in appearances had we not ourselves, by the nature of our own mind, originally set them there.

We pass with admiration along the great series of mathematicians, by whom the science of theoretical mechanics has been cultivated, from the time of Newton to our own. There is no group of men of science whose fame is higher or brighter. The great discoveries of Copernicus, Galileo, Newton, had fixed all eyes on those portions of human knowledge on which their successors employed their labors. The certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects; and the beauty of mathematical relations and the subtlety of intellect which may be shown in dealing with them, were fitted to win unbounded applause. The successors of Newton and the Bernoullis, as Euler, Clairaut, D’Alembert, Lagrange, Laplace, not to introduce living names, have been some of the most remarkable men of talent which the world has seen.

What distinguishes the straight line and circle more than anything else, and properly separates them for the purpose of elementary geometry? Their self-similarity. Every inch of a straight line coincides with every other inch, and of a circle with every other of the same circle. Where, then, did Euclid fail? In not introducing the third curve, which has the same property—the screw. The right line, the circle, the screw—the representations of translation, rotation, and the two combined—ought to have been the instruments of geometry. With a screw we should never have heard of the impossibility of trisecting an angle, squaring the circle, etc.

What is it indeed that gives us the feeling of elegance in a solution, in a demonstration? It is the harmony of the diverse parts, their symmetry, their happy balance; in a word it is all that introduces order, all that gives unity, that permits us to see clearly and to comprehend at once both the ensemble and the details.

What is this subject, which may be called indifferently either mathematics or logic? Is there any way in which we can define it? Certain characteristics of the subject are clear. To begin with, we do not, in this subject, deal with particular things or particular properties: we deal formally with what can be said about any thing or any property. We are prepared to say that one and one are two, but not that Socrates and Plato are two, because, in our capacity of logicians or pure mathematicians, we have never heard of Socrates or Plato. A world in which there were no such individuals would still be a world in which one and one are two. It is not open to us, as pure mathematicians or logicians, to mention anything at all, because, if we do so we introduce something irrelevant and not formal.

What these two sciences of recognition, evolution and immunology, have in common is not found in nonbiological systems such as 'evolving' stars. Such physical systems can be explained in terms of energy transfer, dynamics, causes, and even 'information transfer'. But they do not exhibit repertoires of variants ready for interaction by selection to give a population response according to a hereditary principle. The application of a selective principle in a recognition system, by the way, does not necessarily mean that genes must be involved—it simply means that any state resulting after selection is highly correlated in structure with the one that gave rise to it and that the correlation continues to be propagated. Nor is it the case that selection cannot itself introduce variation. But a constancy or 'memory' of selected events is necessary. If changes occurred so fast that what was selected could not emerge in the population or was destroyed, a recognition system would not survive. Physics proper does not deal with recognition systems, which are by their nature biological and historical systems. But all the laws of physics nevertheless apply to recognition systems.

When introduced at the wrong time or place, good logic may be the worst enemy of good teaching.

You have heard of the new chemical nomenclature endeavored to be introduced by Lavoisier, Fourcroy, &c. Other chemists of this country, of equal note, reject it, and prove in my opinion that it is premature, insufficient and false. These latter are joined by the British chemists; and upon the whole, I think the new nomenclature will be rejected, after doing more harm than good. There are some good publications in it, which must be translated into the ordinary chemical language before they will be useful.

You, in this country [the USA], are subjected to the British insularity in weights and measures; you use the foot, inch and yard. I am obliged to use that system, but must apologize to you for doing so, because it is so inconvenient, and I hope Americans will do everything in their power to introduce the French metrical system. ... I look upon our English system as a wickedly, brain-destroying system of bondage under which we suffer. The reason why we continue to use it, is the imaginary difficulty of making a change, and nothing else; but I do not think in America that any such difficulty should stand in the way of adopting so splendidly useful a reform.