“"Some fool has put the head of this nail on the wrong end." "You idiot, it's for the opposite wall!" To be sure, if the space of physical objects allowed motions of translation only, and not also rotations. That space has such geometry is a fantasy; experience shows otherwise. It is only experience that makes this complaint and the rejoinder a dialogue of madmen.”

Source: "The Conduct of Inquiry", p. 35.

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Abraham Kaplan8

American philosopher 1918–1993

Howard P. Robertson (1903–1961) American mathematician and physicist

Geometry as a Branch of Physics (1949)

“As the pattern of events is unaltered by motion, the mechanism must be the same when the electron is in motion as when it is at rest. But experiment shows that an electron in motion exerts additional forces which are not the same for all directions in space; if we picture this electron as moving head-foremost through space, these forces surround it like a belt around its waist.”

James Jeans (1877–1946) British mathematician and astronomer

Physics and Philosophy (1942)

“M. Desargues puts me under obligations on account of the pains that it has pleased him to have in me, in that he shows that he is sorry that I do not wish to study more in geometry, but I have resolved to quit only abstract geometry, that is to say, the consideration of questions which serve only to exercise the mind, and this, in order to study another kind of geometry, which has for its object the explanation of the phenomena of nature… You know that all my physics is nothing else than geometry.”

René Descartes (1596–1650) French philosopher, mathematician, and scientist

Letter to Marin Mersenne (July 27, 1638) as quoted by Florian Cajori, A History of Mathematics (1893) letter dated in The Philosophical Writings of Descartes Vol. 3, The Correspondence (1991) ed. John Cottingham, Robert Stoothoff, Dugald Murdoch

“Perceptual space is not a special space in addition to physical space, but physical space which we endow with a special subjective metric. …apart from the definition of congruence in physics and that based on perception, there is no third one derived from pure visualization. Any such third definition is nothing but the definition of physical congruence to which our normative function has adjusted the subjective experience of congruence.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

“Riemann has shewn that as there are different kinds of lines and surfaces, so there are different kinds of space of three dimensions; and that we can only find out by experience to which of these kinds the space in which we live belongs. In particular, the axioms of plane geometry are true within the limits of experiment on the surface of a sheet of paper, and yet we know that the sheet is really covered with a number of small ridges and furrows, upon which (the total curvature not being zero) these axioms are not true. Similarly, he says although the axioms of solid geometry are true within the limits of experiment for finite portions of our space, yet we have no reason to conclude that they are true for very small portions; and if any help can be got thereby for the explanation of physical phenomena, we may have reason to conclude that they are not true for very small portions of space.”

William Kingdon Clifford On the Space-Theory of Matter

Abstract
On the Space-Theory of Matter (read Feb 21, 1870)

“A baby has brains, but it doesn't know much. Experience is the only thing that brings knowledge, and the longer you are on earth the more experience you are sure to get.”

L. Frank Baum book The Wonderful Wizard of Oz

Source: The Wonderful Wizard of Oz

“These people seemed to think that whizzing through space in a car really altered the universe for them, but they were wrong; each one remained right in the centre of his private universe, which is the only field of knowledge of which he has any direct experience.”

Robertson Davies (1913–1995) Canadian journalist, playwright, professor, critic, and novelist

Samuel Marchbanks' Almanack (1967)
Context: Was driving through the countryside today with some people who insisted upon frequent recourse to a roadmap in order to discover, as they put it, "Just where they were." Reflected that for my part I generally have a pretty shrewd idea of just where I am; I am enclosed in the somewhat vulnerable fortress which is my body, and from that uneasy stronghold I make such sorties as I deem advisable into the realm about me. These people seemed to think that whizzing through space in a car really altered the universe for them, but they were wrong; each one remained right in the centre of his private universe, which is the only field of knowledge of which he has any direct experience.

“The objects of abstract Geometry possess in absolute precision properties which are only approximately realized in the corresponding objects of physical Geometry.”

E. W. Hobson (1856–1933) British mathematician

Source: Squaring the Circle (1913), p. 5

“It has been my experience that good theoretical physics is empowering, in that it enables thinking to take place that would otherwise not occur, and, in its highest form, facilitates experiments that would otherwise not be done.”

Robert B. Laughlin (1950) American physicist

Emergent Relativity

“Other qualities of bodies are connected with simple energy of motion and energy of position. Such is heat, which we find by experiment can be turned into work. Finding it convertible with energy, we call it a form of energy. ...But as to heat, it is further established by experiment that in this case the energy of motion does really persist as such. Thus a gas consists of molecules flying about with velocity, rotating and vibrating, and so having energy motion. All this energy of motion is what we call heat, and thus heat is a repetition of a known meaning of energy. Again, heat exists between a radiating body and the thing it warms; now the intermediate space is filled by the luminiferous ether, which, being elastic, has in its ultimate parts both energy of motion energy of position. In these forms the heat exists in the space in question.”

William Kingdon Clifford (1845–1879) English mathematician and philosopher

"Energy and Force" (Mar 28, 1873)

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Abraham Kaplan8

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