"Physics inquires whether the world is eternal, or perpetual, or had a beginning and will have an end in time, or whether none of these alternatives is accurate." (John of Salisbury, "Metalogicon", 1159)
"Physics must be sharply distinguished from mathematics. The former must stand in clear independence, penetrating into the sacred life of nature in common with all the forces of love, veneration and devotion. The latter, on the other hand, must declare its independence of all externality, go its own grand spiritual way, and develop itself more purely than is possible so long as it tries to deal with actuality and seeks to adapt itself to things as they really are." (Johann Wolfgang von Goethe, "Schriften zur Naturwissenschaft" ["Writing on Natural Sciences"], cca. 1810)
"The domain of physics is no proper field for mathematical pastimes. The best security would be in giving a geometrical training to physicists, who need not then have recourse to mathematicians, whose tendency is to despise experimental science. By this method will that union between the abstract and the concrete be effected which will perfect the uses of mathematical, while extending the positive value of physical science. Meantime, the uses of analysis in physics is clear enough. Without it we should have no precision, and no co-ordination; and what account could we give of our study of heat, weight, light, etc.? We should have merely series of unconnected facts, in which we could foresee nothing but by constant recourse to experiment; whereas, they now have a character of rationality which fits them for purposes of prevision." (Auguste Comte, "The Positive Philosophy", 1830)
"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." (John S Mill, "A System of Logic, Ratiocinative and
Inductive", 1843)
"So
intimate is the union between Mathematics and Physics that probably by far the
larger part of the accessions to our mathematical knowledge have been obtained
by the efforts of mathematicians to solve the problems set to them by
experiment, and to create for each successive class phenomena a new calculus or
a new geometry, as the case might be, which might prove not wholly inadequate
to the subtlety of nature. Sometimes the mathematician has been before the
physicist, and it has happened that when some great and new question has
occurred to the experimentalist or the observer, he has found in the armory of
the mathematician the weapons which he needed ready made to his hand. But much
oftener, the questions proposed by the physicist have transcended the utmost
powers of the mathematics of the time, and a fresh mathematical creation has
been needed to supply the logical instrument requisite to interpret the new
enigma." (Henry J S Smith, Nature, Volume 8, 1873)
"That
branch of physics which is at once the oldest and the simplest and which is
therefore treated as introductory to other departments of this science, is
concerned with the motions and equilibrium of masses. It bears the name of
mechanics." (Ernst Mach, "The Science of Mechanics: A Critical and
Historical Account of Its Development", 1893)
"The atomic theory plays a part in physics similar to that of certain auxiliary concepts in mathematics: it is a mathematical model for facilitating the mental reproduction of facts. Although we represent vibrations by the harmonic formula, the phenomena of cooling by exponentials, falls by squares of time, etc, no one would fancy that vibrations in themselves have anything to do with circular functions, or the motion of falling bodies with squares." (Ernst Mach, "The Science of Mechanic", 1893)
"In
this sense the fundamental ideas of mechanics, together with the principles
connecting them, represent the simplest image which physics can produce of
things in the sensible world and the processes which occur in it. By varying
the choice of the propositions which we take as fundamental, we can give various
representations of the principles of mechanics. Hence we can thus obtain
various images of things; and these images we can test and compare with each
other in respect of permissibility, correctness, and appropriateness."
(Heinrich Hertz, "The Principles of Mechanics Presented in a New
Form", 1894)
"In
addition to this it [mathematics] provides its disciples with pleasures similar
to painting and music. They admire the delicate harmony of the numbers and the
forms; they marvel when a new discovery opens up to them an unexpected vista;
and does the joy that they feel not have an aesthetic character even if the
senses are not involved at all? […] For this reason I do not hesitate to say
that mathematics deserves to be cultivated for its own sake, and I mean the
theories which cannot be applied to physics just as much as the others."
(Henri Poincaré, 1897)
"Mathematicians
will do well to observe that a reasonable acquaintance with theoretical physics
at its present stage of development, to mention only such broad subjects as
electricity, elastics, hydrodynamics, etc., is as much as most of us can keep
permanently assimilated. It should also be remembered that the step from the
formal elegance of theory to the brute arithmetic of the special case is always
humiliating, and that this labor usually falls to the lot of the
physicist." (Carl Barus, "The Mathematical Theory of the Top",
1898)
"Chemistry
and physics are experimental sciences; and those who are engaged in attempting
to enlarge the boundaries of science by experiment are generally unwilling to
publish speculations; for they have learned, by long experience, that it is
unsafe to anticipate events. It is true, they must make certain theories and
hypotheses. They must form some kind of mental picture of the relations between
the phenomena which they are trying to investigate, else their experiments
would be made at random, and without connection." (William Ramsay,
"Radium and Its Products", Harper’s Magazine, 1904)
"The
mathematical formula is the point through which all the light gained by science
passes in order to be of use to practice; it is also the point in which all
knowledge gained by practice, experiment, and observation must be concentrated
before it can be scientifically grasped. The more distant and marked the point,
the more concentrated will be the light coming from it, the more unmistakable
the insight conveyed. All scientific thought, from the simple gravitation
formula of Newton, through the more complicated formulae of physics and
chemistry, the vaguer so called laws of organic and animated nature, down to
the uncertain statements of psychology and the data of our social and
historical knowledge, alike partakes of this characteristic, that it is an attempt
to gather up the scattered rays of light, the different parts of knowledge, in
a focus, from whence it can be again spread out and analyzed, according to the
abstract processes of the thinking mind. But only when this can be done with a
mathematical precision and accuracy is the image sharp and well-defined, and
the deductions clear and unmistakable. As we descend from the mechanical,
through the physical, chemical, and biological, to the mental, moral, and
social sciences, the process of focalization becomes less and less perfect, -
the sharp point, the focus, is replaced by a larger or smaller circle, the
contours of the image become less and less distinct, and with the possible
light which we gain there is mingled much darkness, the sources of many mistakes
and errors. But the tendency of all scientific thought is toward clearer and
clearer definition; it lies in the direction of a more and more extended use of
mathematical measurements, of mathematical formulae." (John T Merz,
"History of European Thought in the 19th Century" Vol. 1, 1904)
"The science of physics does not only give us [mathematicians] an opportunity to solve problems, but helps us also to discover the means of solving them, and it does this in two ways: it leads us to anticipate the solution and suggests suitable lines of argument." (Henri Poincaré, "La valeur de la science" ["The Value of Science"], 1905)
"[...] as for physics, it has developed remarkably as a precision science, in such a way that we can justifiably claim that the majority of all the greatest discoveries in physics are very largely based on the high degree of accuracy which can now be obtained in measurements made during the study of physical phenomena. [... Accuracy of measurement] is the very root, the essential condition, of our penetration deeper into the laws of physics - our only way to new discoveries." (K Bernhard Hasselberg, [Nobel Lecture] 1907)
"If the aim of physical theories is to explain experimental laws, theoretical physics is not an autonomous science; it is subordinate to metaphysics." (Pierre-Maurice-Marie DuhemDuhem, "The Aim and Structure of Physical Theory", 1908)
"It is impossible to follow the march of one of the greatest theories of physics, to see it unroll majestically its regular deductions starting from initial hypotheses, to see its consequences represent a multitude of experimental laws down to the smallest detail, without being charmed by the beauty of such a construction, without feeling keenly that such a creation of the human mind is truly a work of art." (Pierre-Maurice-Marie DuhemDuhem, "The Aim and Structure of Physical Theory", 1908)
"[...] physics makes progress because experiment constantly causes new disagreements to break out between laws and facts, and because physicists constantly touch up and modify laws in order that they may more faithfully represent the facts." (Pierre-Maurice-Marie Duhem, "The Aim and Structure of Physical Theory", 1908)
"The
laws of physics are therefore provisional in that the symbols they relate too
simple to represent reality completely." (Pierre-Maurice-Marie Duhem,
"The Aim and Structure of Physical Theory", 1908)
"Though the ultimate state of the universe may be its vital and psychical extinction, there is nothing in physics to interfere with the hypothesis that the penultimate state might be the millennium - in other words a state in which a minimum of difference of energy - level might have its exchanges so skillfully canalises that a maximum of happy and virtuous consciousness would be the only result." (William James, [Letter to Henry Adams] 1910)" (William James, [Letter to Henry Adams] 1910)
"Physics
is not a machine one can take apart; one cannot try each piece in isolation and
wait, to adjust it, until its solidity has been minutely checked. Physical
science is a system that must be taken as a whole. It is an organism no part of
which can be made to function without the remotest parts coming into play, some
more, some less, but all in some degree." (Pierre-Maurice-Marie Duhem,
1914)
"[…]
science deals with but a partial aspect of reality, and there is no faintest
reason for supposing that everything science ignores is less real than what it
accepts. [...] Why is it that science forms a closed system? Why is it that the
elements of reality it ignores never come in to disturb it? The reason is that
all the terms of physics are defined in terms of one another. The abstractions
with which physics begins are all it ever has to do with." (John W N
Sullivan, "The Limitations of Science", 1915)
"It behooves us always to remember that in physics it has taken great men to discover simple things." (D'Arcy W Thompson, "On Growth and Form", 1917)
"[...] the future of thought and therefore of history lies in the hands of physicists, and therefore the future historian must seek his education in the world of mathematical physics." (Henry Adams, "The Degradation of the Democratic Dogma", 1920)
"The
scene of action of reality is not a three-dimensional Euclidean space but
rather a four-dimensional world, in which space and time are linked together
indissolubly. However deep the chasm may be that separates the intuitive nature
of space from that of time in our experience, nothing of this qualitative
difference enters into the objective world which physics endeavors to
crystallize out of direct experience. It is a four-dimensional continuum, which
is neither 'time' nor 'space'. Only the consciousness that passes on in one
portion of this world experiences the detached piece which comes to meet it and
passes behind it as history, that is, as a process that is going forward in time
and takes place in space." (Hermann Weyl, "Space, Time, Matter",
1922)
"And so in its actual procedure physics studies not these inscrutable qualities, but pointer-readings which we can observe, The readings, it is true, reflect the fluctuations of the world-qualities; but our exact knowledge is of the readings, not of the qualities. The former have as much resemblance to the latter as a telephone number has to a subscriber." (Arthur S Eddington, "The Domain of Physical Science", 1925)
"We
wish to obtain a representation of phenomena and form an image of them in our
minds. Till now, we have always attempted to form these images by means of the
ordinary notions of time and space. These notions are perhaps innate; in any
case they have been developed by our daily observations. For me, these notions
are clear, and I confess that I am unable to gain any idea of physics without
them. […] I would like to retain this ideal of other days and describe
everything that occurs in this world in terms of clear pictures." (Hendrik
A Lorentz, [Fifth Solvay Conference] 1927)
"It
seems to be the impression among students that mathematical physics consists in
deriving a large number of partial differential equations and then solving
them, individually, by an assortment of special mutually unrelated devices. It
has not been made clear that there is any underlying unity of method and one
has often been left entirely in the dark as to what first suggested a
particular device to the mind of its inventor." (Arthur G Webster,
"Partial Differential Equations of Mathematical Physics", 1927)
"Physics has progressed because, in the first place, she accepted the uniformity of nature; because, in the next place, she early discovered the value of exact measurements; because, in the third place, she concentrated her attention on the regularities that underlie the complexities of phenomena as they appear to us; and lastly, and not the least significant, because she emphasized the importance of the experimental method of research. An ideal or crucial experiment is a study of an event, controlled so as to give a definite and measurable answer to a question - an answer in terms of specific theoretical ideas, or better still an answer in terms of better understood relations." (Thomas H Morgan, "The Relation of Biology to Physics", Science Vol. LXV (1679), 1927)
"Physics
is mathematical not because we know so much about the physical world, but
because we know so little: it is only its mathematical properties that we can
discover." (Bertrand Russell, "An Outline of Philosophy", 1927)
"It is
unreasonable to expect science to produce a system of ethics - ethics are a
kind of highway code for traffic among mankind - and the fact that in physics
atoms which were yesterday assumed to be square are now assumed to be round is
exploited with unjustified tendentiousness by all who are hungry for faith; so
long as physics extends our dominion over nature, these changes ought to be a
matter of complete indifference to you." (Sigmund Freud, [Letter to Oskar
Pfister] 1928)
"So
far as physics is concerned, time's arrow is a property of entropy alone."
(Arthur S Eddington, "The Nature of the Physical World", 1928)
"If
to-day you ask a physicist what he has finally made out the æther or the
electron to be, the answer will not be a description in terms of billiard balls
or fly-wheels or anything concrete; he will point instead to a number of
symbols and a set of mathematical equations which they satisfy. What do the
symbols stand for? The mysterious reply is given that physics is indifferent to
that; it has no means of probing beneath the symbolism. To understand the
phenomena of the physical world it is necessary to know the equations which the
symbols obey but not the nature of that which is being symbolised [...]"
(Arthur S Eddington, "Science and the Unseen World", 1929)
"The
methods of progress in theoretical physics have undergone a vast change during
the present century. The classical tradition has been to consider the world to
be an association of observable objects (particles, fluids, fields, etc.)
moving about according to definite laws of force, so that one could form a
mental picture in space and time of the whole scheme. This led to a physics
whose aim was to make assumptions about the mechanism and forces connecting
these observable objects, to account for their behaviour in the simplest
possible way. It has become increasingly evident in recent times, however, that
nature works on a different plan. Her fundamental laws do not govern the world
as it appears in our mental picture in any very direct way, but instead they
control a substratum of which we cannot form a mental picture without
introducing irrelevancies. (Paul A M Dirac, "The Principles of Quantum
Mechanics", 1930)
"The
chain of cause and effect could be quantitatively verified only if the whole
universe were considered as a single system - but then physics has vanished,
and only a mathematical scheme remains. The partition of the world into
observing and observed system prevents a sharp formulation of the law of cause
and effect." (Werner K Heisenberg, "The Physical Principles of the
Quantum Theory", 1930)
"The
classical tradition has been to consider the world to be an association of
observable objects (particles, fluids, fields, etc.) moving according to
definite laws of force, so that one could form a mental picture in space and
time of the whole scheme. This led to a physics whose aim was to make
assumptions about the mechanism and forces connecting these observable objects
in the simplest possible way. It has become increasingly evident in recent
times, however, that nature works on a different plan. Her fundamental laws do
not govern the world as it appears in our mental picture in any very direct
way, but instead they control a substratum of which we cannot form a mental
picture without introducing irrelevancies." (Paul A M Dirac, "The
Principles of Quantum Mechanics", 1930)
"The
steady progress of physics requires for its theoretical formulation a
mathematics which get continually more advanced. […] it was expected that
mathematics would get more and more complicated, but would rest on a permanent
basis of axioms and definitions, while actually the modern physical developments
have required a mathematics that continually shifts its foundation and gets
more abstract. Non-Euclidean geometry and noncommutative algebra, which were at
one time were considered to be purely fictions of the mind and pastimes of
logical thinkers, have now been found to be very necessary for the description
of general facts of the physical world. It seems likely that this process of
increasing abstraction will continue in the future and the advance in physics
is to be associated with continual modification and generalisation of the
axioms at the base of mathematics rather than with a logical development of any
one mathematical scheme on a fixed foundation." (Paul A M Dirac,
"Quantities singularities in the electromagnetic field", Proceedings
of the Royal Society of London, 1931)
"Physics is the attempt at the conceptual construction of a model of the real world and its lawful structure." (Albert Einstein, [letter to Moritz Schlick] 1931)
"Few spectacles are as beautiful and moving for the mind as that of physics thus advancing toward its destiny like a huge throbbing ship." (Jacques Maritain, "Distinguer pour unir, ou Les degres du savoir" ["Distinguish to Unite, or The Degrees of Knowledge"], 1932)
"The supreme task of the physicist is the discovery of the
most general elementary laws from which the world-picture can be deduced
logically. But there is no logical way to the discovery of these elemental
laws. There is only the way of intuition, which is helped by a feeling for the
order lying behind the appearance, and this Einfühlung [literally, empathy or
'feeling one's way in'] is developed by experience." (Albert Einstein, [Preface
to Max Planck's "Where is Science Going?"], 1933)
"[...]
the mathematical physicist [...] obtains much prestige from the physicists
because they are impressed with the amount of mathematics he knows, and much
prestige from the mathematicians, because they are impressed with the amount of
physics he knows." (William F G Swann, "The Architecture of the Universe",
1934)
"Let us now discuss the extent of the mathematical quality in Nature. According to the mechanistic scheme of physics or to its relativistic modification, one needs for the complete description of the universe not merely a complete system of equations of motion, but also a complete set of initial conditions, and it is only to the former of these that mathematical theories apply. The latter are considered to be not amenable to theoretical treatment and to be determinable only from observation." (Paul A M Dirac, "The Relation Between Mathematics And Physics", Proceedings of the Royal Society of Edinburgh", 1938-1939)
"The classical physics seemed to bolt and bar the door leading to any sort of freedom of the will; the new physics hardly does this; it almost seems to suggest that the door may be unlocked—if only we could find the handle. The old physics showed us a universe which looked more like a prison than a dwelling place. The new physics shows us a universe which looks as though it might conceivably form a suitable dwelling place for free men, and not a mere shelter for brutes - a home in which it may at least be possible for us to mould events to our desires and live lives of endeavor and achievement." (Sir James Jeans, "Physics and Philosophy", 1942)
"Yet a
review of receipt physics has shown that all attempts at mechanical models or
pictures have failed and must fail. For a mechanical model or picture must
represent things as happening in space and time, while it has recently become
clear that the ultimate processes of nature neither occur in, nor admit of
representation in, space and time. Thus an understanding of the ultimate
processes of nature is for ever beyond our reach: we shall never be able - even
in imagination - to open the case of our watch and see how the wheels go round.
The true object of scientific study can never be the realities of nature, but
only our own observations on nature." (James H Jeans, "Physics and
Philosophy", 1942)
"Good physics is made a priori. Theory precedes fact. Experience is useless because before any experience we are already in possession of the knowledge we are seeking for. Fundamental laws of motion (and of rest), laws that determine the spatio-temporal behavior of material bodies, are laws of a mathematical nature. Of the same nature as those which govern relations and laws of figures and numbers. We find and discover them not in Nature, but in ourselves, in our mind, in our memory, as Plato long ago has taught us." (Alexander Koyre, "Galileo and the Scientific Revolution of the Seventeenth Century", The Philosophical Review Vol. 52 (3), 1943)
"It
will probably be the new mathematical discoveries which are suggested through
physics that will always be the most important, for, from the beginning Nature
has led the way and established the pattern which mathematics, the Language of
Nature, must follow." (George D Birkhoff, "Mathematical Nature of
Physical Theories" American Scientific Vol. 31 (4), 1943)
"In
time they [physicists] hoped to devise a model which would reproduce all the
phenomena of physics, and so make it possible to predict them all. […] To-day
we not only have no perfect model, but we know that it is of no use to search
for one - it could have no intelligible meaning for us. For we have found out
that nature does not function in a way that can be made comprehensible to the
human mind through models or pictures. […] Although we can never devise a
pictorial representation which shall be both true to nature and intelligible to
our minds, we may still be able to make partial aspects of the truth
comprehensible through pictorial representations or parables. As the whole
truth does not admit of intelligible representation, every such pictorial
representation or parable must fail somewhere. The physicist of the last
generation was continually making pictorial representations and parables, and also
making the mistake of treating the half-truths of pictorial representations and
parables as literal truths." (James H Jeans, "Physics and
Philosophy" 3rd Ed., 1943)
"An
isolated system or a system in a uniform environment (which for the present
consideration we do best to include as a part of the system we contemplate)
increases its entropy and more or less rapidly approaches the inert state of
maximum entropy. We now recognize this fundamental law of physics to be just
the natural tendency of things to approach the chaotic state (the same tendency
that the books of a library or the piles of papers and manuscripts on a writing
desk display) unless we obviate it. (The analogue of irregular heat motion, in
this case, is our handling those objects now and again without troubling to put
them back in their proper places.) (Erwin Schrödinger, "What is
Life?", 1944)
"There
is no concept in the whole field of physics which is more difficult to
understand than is the concept of entropy, nor is there one which is more
fundamental." (Francis W Sears, "Mechanics, Heat and Sound",
1944)
"I
cannot seriously believe in [the quantum theory] because it cannot be
reconciled with the idea that physics should represent a reality in time and
space, free from spooky actions at a distance." (Albert Einstein, [Letter
to Max Born] 1948)
"It
seems significant that according to quantum physics the indestructibility of
energy on one hand - which expresses its timeless existence - and the
appearance of energy in space and time on the other hand correspond to two
contradictory (complementary) aspects of reality. In fact, both are always
present, but in individual cases the one or the other may be more pronounced. (Wolfgang
Pauli, "Moderne Beispiele zur Hintergrundsphysik" ["Modern
Examples of Background Physics", 1948)
"Physics is not about the real world, it is about ‘abstractions’ from the real world, and this is what makes it so scientific." (Anthony Standen, "Science is a Sacred Cow", 1950)
"Physics
too deals with mathematical concepts; however, these concepts attain physical
content only by the clear determination of their relation to the objects of
experience." (Albert Einstein, "Out of My Later Years", 1950)
"The
first thing to realize about physics […] is its extraordinary indirectness. […]
For physics is not about the real world, it is about 'abstractions' from the
real world, and this is what makes it so scientific. […] Theoretical physics
runs merrily along with these unreal abstractions, but its conclusions are
checked, at every possible point, by experiments." (Anthony Standen,
"Science is a Sacred Cow", 1950)
"Common
sense […] may be thought of as a series of concepts and conceptual schemes
which have proved highly satisfactory for the practical uses of mankind. Some
of those concepts and conceptual schemes were carried over into science with
only a little pruning and whittling and for a long time proved useful. As the
recent revolutions in physics indicate, however, many errors can be made by
failure to examine carefully just how common sense ideas should be defined in
terms of what the experimenter plans to do." (James B Conant,
"Science and Common Sense", 1951)
"Automata
have begun to invade certain parts of mathematics too, particularly but not
exclusively mathematical physics or applied mathematics. The natural systems
(e.g., central nervous system) are of enormous complexity and it is clearly
necessary first to subdivide what they represent into several parts that to a
certain extent are independent, elementary units. The problem then consists of
understanding how these elements are organized as a whole. It is the latter
problem which is likely to attract those who have the background and tastes of
the mathematician or a logician. With this attitude, he will be inclined to
forget the origins and then, after the process of axiomatization is complete,
concentrate on the mathematical aspects." (John Von Neumann, "The
General and Logical Theory of Automata", 1951)
"In
the realm of physics it is perhaps only the theory of relativity which has made
it quite clear that the two essences, space and time, entering into our
intuition, have no place in the world constructed by mathematical physics.
Colours are thus 'really' not even æther-vibrations, but merely a series of
values of mathematical functions in which occur four independent parameters
corresponding to the three dimensions of space, and the one of time."
(Hermann Weyl, "Space, Time, Matter", 1952)
"As
far as I can see, all a priori statements in physics have their origin in
symmetry." (Hermann Weyl, "Symmetry", 1952)
"All great discoveries in experimental physics have been due to the intuition of men who made free use of models, which were for them not products of the imagination, but representatives of real things." (Max Born, "Physical Reality", Philosophical Quarterly Vol. (11), 1953)
"It is not only the smallest features of the Universe that are controlled by the laws of physics. The behavior of matter on the very large scale that concerns us in astronomy is also determined by physics. The heavenly bodies dance like puppets on strings. If we are to understand why they dance as they do, it is necessary to find out how the strings are manipulated." (Fred Hoyle, "Frontiers of Astronomy", 1955)
"The time has come to realise that an interpretation of the universe - even a positive one - remains unsatisfying unless it covers the interior as well as the exterior of things; mind as well as matter. The true physics is that which will, one day, achieve the inclusion of man in his wholeness in a coherent picture of the world." (Pierre Tielhard de Chardin, "Le phénomène humain" ["The Phenomenon of Man"], 1955)
"The ultimate origin of the difficulty lies in the fact (or philosophical principle) that we are compelled to use the words of common language when we wish to describe a phenomenon, not by logical or mathematical analysis, but by a picture appealing to the imagination. Common language has grown by everyday experience and can never surpass these limits. Classical physics has restricted itself to the use of concepts of this kind; by analysing visible motions it has developed two ways of representing them by elementary processes; moving particles and waves. There is no other way of giving a pictorial description of motions - we have to apply it even in the region of atomic processes, where classical physics breaks down." (Max Born, "Atomic Physics", 1957)
"The
time has come to realise that an interpretation of the universe - even a
positive one - remains unsatisfying unless it covers the interior as well as
the exterior of things; mind as well as matter. The true physics is that which
will, one day, achieve the inclusion of man in his wholeness in a coherent
picture of the world." (Pierre Teilhard de Chardin, "The Phenomenon
of Man", 1959)
"Modern theoretical physics […] has put our thinking about the essence of matter in a different context. It has taken our gaze from the visible-the particles-to the underlying entity, the field. The presence of matter is merely a disturbance of the perfect state of the field at that place; something accidental, one could almost say, merely a ‘blemish’. Accordingly, there are no simple laws describing the forces between elementary particles […] Order and symmetry must be sought in the underlying field." (Walter Thirring "Urbausteine der Materie", 1960)
"Physics is to be regarded not so much as the study of something a priori given, but rather as the development of methods of ordering and surveying human experience. In this respect our task must be to account for such experience in a manner independent of individual subjective judgement and therefor objective in the sense that it can be unambiguously communicated in ordinary human language." (Niels Bohr, "The Unity of Human Knowledge", 1960)
"The enormous
usefulness of mathematics in natural sciences is something bordering on the
mysterious, and there is no rational explanation for it. It is not at all
natural that ‘laws of nature’ exist, much less that man is able to discover
them. The miracle of the appropriateness of the language of mathematics for the
formulation of the laws of physics is a wonderful gift which we neither
understand nor deserve." (Eugene P Wigner, "The Unreasonable
Effectiveness of Mathematics in the Natural Sciences," 1960)
"Books
on physics are full of complicated mathematical formulae. But thought and
ideas, not formulas, are the beginning of every physical theory." (Leopold
Infeld, "The Evolution of Physics", 1961)
"The
mathematicians and physics men Have their mythology; they work alongside the
truth, Never touching it; their equations are false But the things work. Or,
when gross error appears, They invent new ones; they drop the theory of waves
In universal ether and imagine curved space." (Robinson Jeffers," The
Beginning and the End and Other Poems, The Great Wound", 1963)
"We have ceased to expect from physics an explanation of all events, even of the gross structure of the universe, and we aim only at the discovery of the laws of nature, that is the regularities, of the events."
"In
its efforts to learn as much as possible about nature, modem physics has found
that certain things can never be ‘known’ with certainty. Much of our knowledge
must always remain uncertain. The most we can know is in terms of
probabilities." (Richard P Feynman, "The Feynman Lectures on
Physics", 1964)
"A
more problematic example is the parallel between the increasingly abstract and
insubstantial picture of the physical universe which modern physics has given
us and the popularity of abstract and non-representational forms of art and
poetry. In each case the representation of reality is increasingly removed from
the picture which is immediately presented to us by our senses." (Harvey
Brooks, "Scientific Concepts and Cultural Change", 1965)
"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)
"When
the problems in physics become difficult we may often look to the mathematician
who may already have studied such things and have prepared a line of reasoning
for us to follow. On the other hand they may not have, in which case we have to
invent our own line of reasoning, which we then pass back to the
mathematician." (Richard Feynman,"The Character of Physical
Law", 1965)
"[...] we are essentially viewing the purpose of physics as a scientific discipline as invention rather than discovery. [...] the term 'invention' implies that the physicist uses not only observation but his imaginative powers to construct points of view that identify with experience." (Robert B Lindsay, "Arbitrariness in Physics", Physics Today Vol. 120 (12), 1967)
"Conventional
physics deals only with closed systems, i.e. systems which are considered to be
isolated from their environment. [...] However, we find systems which by their
very nature and definition are not closed systems. Every living organism is
essentially an open system. It maintains itself in a continuous inflow and outflow,
a building up and breaking down of components, never being, so long as it is
alive, in a state of chemical and thermodynamic equilibrium but maintained in a
so-called steady state which is distinct from the latter." (Ludwig von
Bertalanffy, "General System Theory", 1968)
"It is impossible, and it has always been impossible, to
grasp the meaning of what we nowadays call physics independently of its
mathematical form." (Jacob Klein, "Greek Mathematical Thought and the Origin of
Algebra", 1968)
"It is
probably no exaggeration to say that all of theoretical physics proceeds by
analogy." (Jeremy Bernstein, "Elementary Particles and Their
Currents", 1968)
"Theoretical physicists live in a classical world, looking
out into a quantum-mechanical world. The latter we describe only subjectively,
in terms of procedures and results in our classical domain." (John S Bell,
"Introduction to the hidden-variable question", 1971)
"Physics
is not a finished logical system. Rather, at any moment it spans a great
confusion of ideas, some that survive like folk epics from the heroic periods
of the past, and others that arise like utopian novels from our dim
premonitions of a future grand synthesis." (Steven Weinberg,
"Gravitation and Cosmology: Principles and Applications of the General
Theory of Relativity", 1972)
"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." (Melvin Schwartz,
"In Principles of Electrodynamics", 1972)
"One
aim of the physical sciences has been to give an exact picture of the material
world. One achievement of physics in the twentieth century has been to prove
that that aim is unattainable." (Jacob Bronowski, "The Ascent of
Man", 1973)
"Whenever
the Eastern mystics express their knowledge in words - be it with the help of
myths, symbols, poetic images or paradoxical statements-they are well aware of
the limitations imposed by language and 'linear' thinking. Modern physics has
come to take exactly the same attitude with regard to its verbal models and
theories. They, too, are only approximate and necessarily inaccurate. They are
the counterparts of the Eastern myths, symbols and poetic images, and it is at
this level that I shall draw the parallels. The same idea about matter is
conveyed, for example, to the Hindu by the cosmic dance of the god Shiva as to
the physicist by certain aspects of quantum field theory. Both the dancing god
and the physical theory are creations of the mind: models to describe their
authors' intuition of reality." (Fritjof Capra, "The Tao of Physics:
An Exploration of the Parallels Between Modern Physics and Eastern
Mysticism", 1975)
"The
chief difficulty of modern theoretical physics resides not in the fact that it
expresses itself almost exclusively in mathematical symbols, but in the
psychological difficulty of supposing that complete nonsense can be seriously
promulgated and transmitted by persons who have sufficient intelligence of some
kind to perform operations in differential and integral calculus […]"
(Celia Green, "The Decline and Fall of Science", 1976)
"Mathematical physics represents the purest image that the
view of nature may generate in the human mind; this image presents all the
character of the product of art; it begets some unity, it is true and has the
quality of sublimity; this image is to physical nature what music is to the
thousand noises of which the air is full […]" (Théophile de Donder, 1977)
"Modern physics is not experimental physics because it applies apparatus to the questioning of nature. Rather the reverse is true. Because physics, indeed already as pure theory, sets nature up to exhibit itself as a coherence of forces calculable in advance, it therefore orders its experiments precisely for the purpose of asking whether and how nature reports itself when set up in this way." (Martin Heidegger, "The Question Concerning Technology and other Essays", 1977)
"There is another fundamental difference between the old physics and the new physics. The old phvsics assumes that there is an external world which exists apart from us. It further assumes that we can observe measure and speculate about the external world without changing it. According to the old physics the external world is indifferent to us and to our needs. [...] The new physics, quantum mechanics, tells us clearly that it is not possible to observe reality without changing it. If we observe a certain particle collision experiment, not only do we have no way of proving that the result would have been the same if we had not been watching it, all that we know indicates that it would not have been the same, because the result that we got was affected by the fact that we were looking for it." (Gary Zukav, "The Dancing Wu Li Masters", 1979)
"Unfortunately, when most people think of 'physics', they think of chalkboards covered with undecipherable symbols of an unknown mathematics. The fact is that physics is not mathematics. Physics, in essence, is simple wonder at the way things are and a divine (some call it compulsive) interest in how that is so. Mathematics is the tool of physics. Stripped of mathematics, physics becomes pure enchantment." (Gary Zukav, "The Dancing Wu Li Masters", 1979)
"Since
the beginning of physics, symmetry considerations have provided us with an
extremely powerful and useful tool in our effort to understand nature.
Gradually they have become the backbone of our theoretical formulation of
physical laws." (Tsung-Dao Lee, "Particle Physics and Introduction to
Field Theory", 1981)
"In
physics it is usual to give alternative theoretical treatments of the same
phenomenon. We construct different models for different purposes, with
different equations to describe them. Which is the right model, which the
'true' set of equations? The question is a mistake. One model brings out some
aspects of the phenomenon; a different model brings out others. Some equations
give a rougher estimate for a quantity of interest, but are easier to solve. No
single model serves all purposes best." (Nancy Cartwright, "How the
Laws of Physics Lie", 1983)
"Physics
is like that. It is important that the models we construct allow us to draw the
right conclusions about the behaviour of the phenomena and their causes. But it
is not essential that the models accurately describe everything that actually
happens; and in general it will not be possible for them to do so, and for much
the same reasons. The requirements of the theory constrain what can be
literally represented. This does not mean that the right lessons cannot be
drawn. Adjustments are made where literal correctness does not matter very much
in order to get the correct effects where we want them; and very often, as in
the staging example, one distortion is put right by another. That is why it
often seems misleading to say that a particular aspect of a model is false to
reality: given the other constraints that is just the way to restore the
representation." (Nancy Cartwright, "How the Laws of Physics
Lie", 1983)
"The physicist […] engages in complex and difficult
calculations, involving the manipulating of ideal, mathematical quantities
that, at first glance, are wholly lacking in the music of the living world and
the beauty of the resplendent cosmos. It would seem as if there exists no
relationship between these quantities and reality. Yet these ideal numbers that
cannot be grasped by one's senses, these numbers that only are meaningful from
within the system itself, only meaningful as part of abstract mathematical
functions, symbolize the image of existence. […] As a result of scientific
man's creativity there arises an ordered, illumined, determined world,
imprinted with the stamp of creative intellect, of pure reason and clear cognition.
From the midst of the order and lawfulness we hear a new song, the song of the
creature to the Creator, the song of the cosmos to its Maker." (Joseph B Soloveitchik, "Halakhic Man", 1983)
"The
equations of physics have in them incredible simplicity, elegance and beauty.
That in itself is sufficient to prove to me that there must be a God who is
responsible for these laws and responsible for the universe" (Paul C W
Davies, 1984)
"[…]
the more you see how strangely Nature behaves, the harder it is to make a model
that explains how even the simplest phenomena actually work. So theoretical
physics has given up on that." (Richard P Feynman, "QED: The Strange
Theory of Light and Matter", 1985)
"If
doing mathematics or science is looked upon as a game, then one might say that
in mathematics you compete against yourself or other mathematicians; in physics
your adversary is nature and the stakes are higher." (Mark Kac,
"Enigmas Of Chance", 1985)
"The
most abstract conservation laws of physics come into their being in describing
equilibrium in the most extreme conditions. They are the most rigorous
conservation laws, the last to break down. The more extreme the conditions, the
fewer the conserved structures. [...] In a deep sense, we understand the
interior of the sun better that the interior of the earth, and the early stages
of the big bang best of all." (Frank Wilczek, "Longing for the
Harmonies: Themes and Variations from Modern Physics", 1987)
"The
world of science lives fairly comfortably with paradox. We know that light is a
wave and also that light is a particle. The discoveries made in the infinitely
small world of particle physics indicate randomness and chance, and I do not
find it any more difficult to live with the paradox of a universe of randomness
and chance and a universe of pattern and purpose than I do with light as a wave
and light as a particle. Living with contradiction is nothing new to the human
being." (Madeline L'Engle, "Two-Part Invention: The Story of a
Marriage", 1988)
"The
world of science lives fairly comfortably with paradox. We know that light is a
wave and also that light is a particle. The discoveries made in the infinitely
small world of particle physics indicate randomness and chance, and I do not
find it any more difficult to live with the paradox of a universe of randomness
and chance and a universe of pattern and purpose than I do with light as a wave
and light as a particle. Living with contradiction is nothing new to the human
being." (Madeline L'Engle, "Two-Part Invention: The Story of a
Marriage", 1988)
"Physics
is the basic science of matter and energy, and engineering is physics applied
to structures and machines. They and chemistry are the sciences that biologists
need to explain the structure and mechanism of living things." (R McNeill
Alexander, "Dynamics of Dinosaurs and Other Extinct Giants", 1989)
"Symmetry
is bound up in many of the deepest patterns of Nature, and nowadays it is
fundamental to our scientific understanding of the universe. Conservation
principles, such as those for energy or momentum, express a symmetry that (we
believe) is possessed by the entire space-time continuum: the laws of physics
are the same everywhere." (Ian Stewart & Martin Golubitsky,
"Fearful Symmetry: Is God a Geometer?", 1992)
"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." (Clifford Truesdell & Walter Noll, "The Non-Linear Field
Theories of Mechanics" 2nd Ed., 1992)
"Finite
Nature is a hypothesis that ultimately every quantity of physics, including
space and time, will turn out to be discrete and finite; that the amount of
information in any small volume of space-time will be finite and equal to one
of a small number of possibilities. [...] We take the position that Finite
Nature implies that the basic substrate of physics operates in a manner similar
to the workings of certain specialized computers called cellular
automata." (Edward Fredkin, "A New Cosmogony", PhysComp ’92:
Proceedings of the Workshop on Physics and Computation, 1993)
"The
sequence for the understanding of mathematics may be: intuition, trial, error,
speculation, conjecture, proof. The mixture and the sequence of these events
differ widely in different domains, but there is general agreement that the end
product is rigorous proof – which we know and can recognize, without the formal
advice of the logicians. […] Intuition is glorious, but the heaven of
mathematics requires much more. Physics has provided mathematics with many fine
suggestions and new initiatives, but mathematics does not need to copy the
style of experimental physics. Mathematics rests on proof - and proof is
eternal." (Saunders Mac Lan, "Reponses to …",m Bulletin of the
American Mathematical Society Vol. 30 (2), 1994)
"Physics
is not difficult; it’s just weird. […] Physics is weird because intuition is
false. To understand what an electron’s world is like, you’ve got to be an
electron, or jolly nearly. Intuition is forged in the hellish fires of the
everyday world, which makes it so eminently useful in our daily struggle for
survival. For anything else, it is hopeless." (Vincent Icke, "The
Force of Symmetry", 1995)
"As we
explore physics at higher and higher energy, revealing its structure at shorter
and shorter distances, we discover more and more symmetry." (David J
Gross, "The Role of Symmetry in Fundamental Physics", 1996)
"The
shift of paradigms requires an expansion not only of our perceptions and ways
of thinking, but also of our values. […] scientific facts emerge out of an
entire constellation of human perceptions, values, and actions-in one word, out
of a paradigm-from which they cannot be separated. […] Today the paradigm shift
in science, at its deepest level, implies a shift from physics to the life
sciences." (Fritjof Capra, "The Web of Life", 1996)
"[…] all tangible phenomena, from the birth of stars to the workings of social institutions, are based on material processes that are ultimately reducible, however long and tortuous the sequences, to the laws of physics." (Edward O Wilson, "Consilience: The Unity of Knowledge", 1998)
"The
connection of topology with physics is no passing interlude but rather
represents a length affair." (Michael I Monastyrsky, "Riemann,
Topology, and Physics", 1999)
"Zero
was at the heart of the battle between East and West. Zero was at the center of
the struggle between religion and science. Zero became the language of nature
and the most important tool in mathematics. And the most profound problems in
physics - the dark core of a black hole and the brilliant flash of the big bang
- are struggles to defeat zero." (Charles Seife ."Zero, the Biography
of a Dangerous Idea", 2000)
"Physics
builds from observations. No physical theory can succeed if it is not confirmed
by observations, and a theory strongly supported by observations cannot be
denied. (William N Cropper, Great Physicists, 2001)
"What
appear to be the most valuable aspects of the theoretical physics we have are
the mathematical descriptions which enable us to predict events. These
equations are, we would argue, the only realities we can be certain of in
physics; any other ways we have of thinking about the situation are visual aids
or mnemonics which make it easier for beings with our sort of macroscopic
experience to use and remember the equations." (Celia Green, "The
Lost Cause", 2003)
"The
concept of a random walk is simple but rich for its many applications, not only
in finance but also in physics and the description of natural phenomena. It is
arguably one of the most founding concepts in modern physics as well as in
finance, as it underlies the theories of elementary particles, which are the
building blocks of our universe, as well as those describing the complex
organization of matter around us." (Didier Sornette, "Why Stock
Markets Crash: Critical Events in Complex Systems", 2003)
"Limiting
factors in population dynamics play the role in ecology that friction does in
physics. They stop exponential growth, not unlike the way in which friction
stops uniform motion. Whether or not ecology is more like physics in a viscous
liquid, when the growth-rate-based traditional view is sufficient, is an open
question. We argue that this limit is an oversimplification, that populations
do exhibit inertial properties that are noticeable. Note that the inclusion of
inertia is a generalization - it does not exclude the regular rate-based,
first-order theories. They may still be widely applicable under a strong
immediate density dependence, acting like friction in physics." (Lev
Ginzburg & Mark Colyvan, "Ecological Orbits: How Planets Move and
Populations Grow", 2004)
"If
you assume continuity, you can open the well-stocked mathematical toolkit of
continuous functions and differential equations, the saws and hammers of
engineering and physics for the past two centuries (and the foreseeable
future)." (Benoît Mandelbrot, "The (Mis)Behaviour of Markets: A
Fractal View of Risk, Ruin and Reward", 2004)
"At
every major step physics has required, and frequently stimulated, the
introduction of new mathematical tools and concepts. Our present understanding
of the laws of physics, with their extreme precision and universality, is only
possible in mathematical terms." (Michael F Atiyah, 2005)
"A
great deal of the results in many areas of physics are presented in the form of
conservation laws, stating that some quantities do not change during evolution
of the system. However, the formulations in cybernetical physics are different.
Since the results in cybernetical physics establish how the evolution of the
system can be changed by control, they should be formulated as transformation
laws, specifying the classes of changes in the evolution of the system
attainable by control function from the given class, i.e., specifying the
limits of control." (Alexander L Fradkov, "Cybernetical Physics: From
Control of Chaos to Quantum Control", 2007)
"The
methodology of feedback design is borrowed from cybernetics (control theory).
It is based upon methods of controlled system model’s building, methods of
system states and parameters estimation (identification), and methods of
feedback synthesis. The models of controlled system used in cybernetics differ
from conventional models of physics and mechanics in that they have explicitly
specified inputs and outputs. Unlike conventional physics results, often
formulated as conservation laws, the results of cybernetical physics are
formulated in the form of transformation laws, establishing the possibilities
and limits of changing properties of a physical system by means of
control." (Alexander L Fradkov, "Cybernetical Physics: From Control
of Chaos to Quantum Control", 2007)
"The
burgeoning field of computer science has shifted our view of the physical world
from that of a collection of interacting material particles to one of a
seething network of information. In this way of looking at nature, the laws of
physics are a form of software, or algorithm, while the material world - the
hardware - plays the role of a gigantic computer." (Paul C W Davies,
"Laying Down the Laws", New Scientist, 2007)
"Systematic
usage of the methods of modern control theory to study physical systems is a
key feature of a new research area in physics that may be called cybernetical
physics. The subject of cybernetical physics is focused on studying physical
systems by means of feedback interactions with the environment. Its methodology
heavily relies on the design methods developed in cybernetics. However, the
approach of cybernetical physics differs from the conventional use of feedback
in control applications (e.g., robotics, mechatronics) aimed mainly at driving
a system to a prespecified position or a given trajectory." (Alexander L
Fradkov, "Cybernetical Physics: From Control of Chaos to Quantum
Control", 2007)
"There
is nothing as dreamy and poetic, nothing as radical, subversive, and
psychedelic, as mathematics. It is every bit as mind blowing as cosmology or
physics (mathematicians conceived of black holes long before astronomers
actually found any), and allows more freedom of expression than poetry, art, or
music (which depends heavily on properties of the physical universe).
Mathematics is the purest of the arts, as well as the most misunderstood."
(Paul Lockhart, "A Mathematician's Lament", 2009)
"Much
of the recorded knowledge of physics and engineering is written in the form of
mathematical models. These mathematical models form the foundations of our
understanding of the universe we live in. Furthermore, nearly all of the
existing technology, in one way or another, rests on these models. To the
extent that we are surrounded by evidence of the technology working and being
reliable, human confidence in the validity of the underlying mathematical
models is all but unshakable." (Jerzy A Filar, "Mathematical
Models", 2009)
"[...]
according to the quantum theory, randomness is a basic trait of reality,
whereas in classical physics it is a derivative property, though an equally
objective one. Note, however, that this conclusion follows only under the
realist interpretation of probability as the measure of possibility. If, by
contrast, one adopts the subjectivist or Bayesian conception of probability as
the measure of subjective uncertainty, then randomness is only in the eye of
the beholder." (Mario Bunge, "Matter and Mind: A Philosophical
Inquiry", 2010)
"Quantum
theory may be formulated using Hilbert spaces over any of the three associative
normed division algebras: the real numbers, the complex numbers and the
quaternions. Indeed, these three choices appear naturally in a number of axiomatic
approaches. However, there are internal problems with real or quaternionic
quantum theory. Here we argue that these problems can be resolved if we treat
real, complex and quaternionic quantum theory as part of a unified structure.
Dyson called this structure the ‘three-fold way’ […] This three-fold
classification sheds light on the physics of time reversal symmetry, and it
already plays an important role in particle physics." (John C Baez,
"Division Algebras and Quantum Theory", 2011)
"[…]
the role that symmetry plays is not confined to material objects. Symmetries
can also refer to theories and, in particular, to quantum theory. For if the
laws of physics are to be invariant under changes of reference frames, the set
of all such transformations will form a group. Which transformations and which
groups depends on the systems under consideration." (William H Klink &
Sujeev Wickramasekara, "Relativity, Symmetry and the Structure of Quantum
Theory I: Galilean quantum theory", 2015)
"The passage of time and the action of entropy bring about ever-greater complexity - a branching, blossoming tree of possibilities. Blossoming disorder (things getting worse), now unfolding within the constraints of the physics of our universe, creates novel opportunities for spontaneous ordered complexity to arise." (D J MacLennan, "Frozen to Life", 2015)
"The aim of physics is not merely to tell a convincing story about every object and every event in the material universe but to produce a single epic, a coherent theory for describing nature." (Hans C von Baeyer, "QBism: The future of quantum physics", 2016)
"The goal of physics is to explain the workings of the nonliving world. At first, philosophers described the properties of real objects: the wandering of planets across the night sky, the formation of ice, or the sound of a lyre. When attention turned to things that couldn’t be seen or measured so easily, physicists invented mechanical models to take the place of real things." (Hans C von Baeyer, "QBism: The future of quantum physics", 2016)
"Mathematics began to seem too much like puzzle solving. Physics is puzzle solving, too, but of puzzles created by nature, not by the mind of man." (Maria Goeppert-Mayer)
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