29 May 2021

Clifford Truesdell - Collected Quotes

"Pedantry and sectarianism aside, the aim of theoretical physics is to construct mathematical models such as to enable us, from the use of knowledge gathered in a few observations, to predict by logical processes the outcomes in many other circumstances. Any logically sound theory satisfying this condition is a good theory, whether or not it be derived from 'ultimate' or 'fundamental' truth. It is as ridiculous to deride continuum physics because it is not obtained from nuclear physics as it would be to reproach it with lack of foundation in the Bible." (Clifford Truesdell & Walter Noll, "The Non-Linear Field Theories of Mechanics", 1965)

"The task of the theorist is to bring order into the chaos of the phenomena of nature, to invent a language by which a class of these phenomena can be described efficiently and simply." (Clifford Truesdell & Walter Noll, "The Non-Linear Field Theories of Mechanics", 1965)

"A mathematical theorem cannot be escaped by denying its truth or by forgetting it for vague, intuitive reasons that blur the edges of all rational processes. The way to escape an unpleasant theorem is to prove another one." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"As mechanics is the science of motions and forces, so thermodynamics is the science of forces and entropy. What is entropy? Heads have split for a century trying to define entropy in terms of other things. Entropy, like force, is an undefined object, and if you try to define it, you will suffer the same fate as the force definers of the seventeenth and eighteenth centuries: Either you will get something too special or you will run around in a circle." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Despite two centuries of study, the integrals of general dynamical systems remain covered with darkness. To save the classical thermostatics, the practical success of which is shown by the wide use to which it has been put, we must find a way out. That is, we must find some mathematical connection between time averages of the functions of physical interest and the corresponding simple canonical averages." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Formerly, the beginner was taught to crawl through the underbrush, never lifting his eyes to the trees; today he is often made to focus on the curvature of the universe, missing even the earth." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"In all of natural philosophy, the most deeply and repeatedly studied part, next to pure geometry, is mechanics. […] The picture of nature as a whole given us by mechanics may be compared to a black-and-white photograph: It neglects a great deal, but within its limitations, it can be highly precise. Developing sharper and more flexible black-and-white photography has not attained pictures in color or three-dimensional casts, but it serves in cases where color and thickness are irrelevant, presently impossible to get in the required precision, or distractive from the true content." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Mathematicians, on the other hand, often regard all of physics as a kind of divine revelation or trickery, where mathematical morals are irrelevant, so that if they enter this red-light district at all, it is only to get what they want as cheaply as possible before returning to the respectability of problems purely mathematical in the older sense: analysis, probability, differential geometry, etc." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Mechanics seeks to connect these three elements -body, motion, and force -in such a way as to yield good models for the behavior of the materials in nature." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Nature does not seem full of circles and triangles to the ungeometrical; rather, mastery of the theory of triangles and circles, and later of conic sections, has taught the theorist, the experimenter, the carpenter, and even the artist to find them everywhere, from the heavenly motions to the pose of a Venus." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"[..] principle of equipresence: A quantity present as an independent variable in one constitutive equation is so present in all, to the extent that its appearance is not forbidden by the general laws of Physics or rules of invariance. […] The principle of equipresence states, in effect, that no division of phenomena is to be laid down by constitutive equations." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Rational mechanics is mathematics, just as geometry is mathematics. […] Mechanics cannot, any more than geometry, exhaust the properties of the physical universe. […] Mechanics presumes geometry and hence is more special; since it attributes to a sphere additional properties beyond its purely geometric ones, the mechanics of spheres is not only more complicated and detailed but also, on the grounds of pure logic, necessarily less widely applicable than geometry. This, again, is no reproach; geometry is not despised because it is less widely applicable than topology. A more complicated theory, such as mechanics, is less likely to apply to any given case; when it does apply, it predicts more than any broader, less specific theory." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"The purpose of statistical mechanics, for phenomena of equilibrium, is to calculate time averages, and the ensemble theory is useful only as a tool enabling us to calculate time averages without knowing how to integrate the equations of motion. The ensemble theory is a mathematical device; we are wasting our time if we try to explain it by itself." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"There is nothing that can be said by mathematical symbols and relations which cannot also be said by words. The converse, however, is false. Much that can be and is said by words cannot successfully be put into equations, because it is nonsense." (Clifford A Truesdell, "Six Lectures on Modern Natural Philosophy", 1966) 

"Thermostatics, which even now is usually called thermodynamics, has an unfortunate history and a cancerous tradition. It arose in a chaos of metaphysical and indeed irrational controversy, the traces of which drip their poison even today. As compared with the older science of mechanics and the younger science of electromagnetism, its mathematical structure is meager. Though claims for its breadth of application are often extravagant, the examples from which its principles usually are inferred are most special, and extensive mathematical developments based on fundamental equations, such as typify mechanics and electromagnetism, are wanting. The logical standards acceptable in thermostatics fail to meet the criteria of other exact sciences [...]." (Clifford Truesdell, "Six Lectures on Modern Natural Philosophy", 1966)

"Nothing is harder to surmount than a corpus of true but too special knowledge; to reforge the tradition of his forebears is the greatest originality a man can have." (Clifford Truesdell, The Creation and Unfolding of the Concept of Stress'' [in "Essays in the History of Mechanics"] , 1968) 

"Now a mathematician has a matchless advantage over general scientists, historians, politicians, and exponents of other professions: He can be wrong. A fortiori, he can also be right. [...] A mistake made by a mathematician, even a great one, is not a 'difference of a point of view' or 'another interpretation of the data' or a 'dictate of a conflicting ideology', it is a mistake. The greatest of all mathematicians, those who have discovered the greatest quantities of mathematical truths, are also those who have published the greatest numbers of lacunary proofs, insufficiently qualified assertions, and flat mistakes." (Clifford Truesdell, "Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton's Principia" [in "Essays in the History of Mechanics"], 1968)

"The mistakes made by a great mathematician are of two kinds: first, trivial slips that anyone can correct, and, second, titanic failures reflecting the scale of the struggle which the great mathematician waged. Failures of this latter kind are often as important as successes, for they give rise to major discoveries by other mathematicians. One error of a great mathematician has often done more for science than a hundred impeccable little theorems proved by lesser men." (Clifford Truesdell, "Late Baroque Mechanics to Success, Conjecture, Error, and Failure in Newton's Principia" [in "Essays in the History of Mechanics"], 1968)

"Every physicist knows exactly what the first and the second law mean, but [...] no two physicists agree about them." (Clifford Truesdell)

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