"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."
"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."
"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."
"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."
"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."
"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."
"[..] 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."
"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."
"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)
"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."
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