“That the existence of these motions (the "axiom of free mobility") is a desideratum, if not… a necessity, for a geometry applicable to physical space, has been forcefully argued on a priori grounds by von Helmholtz, Whitehead, Russell and others; for only in a homogeneous and isotropic space can the traditional concept of a rigid body be maintained.”

Geometry as a Branch of Physics (1949)

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Howard P. Robertson28

American mathematician and physicist 1903–1961

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

Geometry as a Branch of Physics (1949)

“"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.”

Abraham Kaplan (1918–1993) American philosopher

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

“Since we only consider the universe on a very large scale, and make abstraction of all details and local irregularities, our universe must be homogeneous and isotropic. It follows… that the three-dimensional space of it must be what mathematicians call a space of constant curvature.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“By symmetry we mean the existence of different viewpoints from which the system appears the same. It is only slightly overstating the case to say that physics is the study of symmetry. The first demonstration of the power of this idea may have been by Newton, who may have asked himself the question: What if the matter here in my hand obeys the same laws as that up in the sky—that is, what if space and matter are homogeneous and isotropic?”

Philip Warren Anderson (1923) American physicist

Source: More Is Different (1972), p. 394

“We must… maintain that mathematical geometry is not a science of space insofar as we understand by space a visual structure that can be filled with objects - it is a pure theory of manifolds.”

Hans Reichenbach (1891–1953) American philosopher

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

“Unfairness builds character and brings diversity to the otherwise homogeneous and isotropic existence.”

Newton Lee American computer scientist

Google It: Total Information Awareness, 2016

“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)

“My presentation of a general theory of living systems will employ two sorts of spaces in which they may exist, physical or geographical space and conceptual or abstract space…
The characteristics and constraints of physical space affect the action of all concrete systems, living and nonliving… Physical space is a common space because it is the only space in which all concrete systems, living and nonliving, exist (though some may exist in other spaces simultaneously). Physical space is shared by all scientific observers, and all scientific data must be collected in it. This is equally true for natural science and behavioral science.”

James Grier Miller (1916–2002) biologist

Source: Living systems, 1978, p. 9-10; As cited in: Kenneth D. Bailey (1994) Sociology and the New Systems Theory: Toward a Theoretical Synthesis. p. 262

“If we wish to express our ideas in terms of the concepts synthetic and analytic, we would have to point out that these concepts are applicable only to sentences that can be either true of false, and not to definitions. The mathematical axioms are therefore neither synthetic nor analytic, but definitions. …Hence the question of whether axioms are a priori becomes pointless since they are arbitrary.”

Hans Reichenbach (1891–1953) American philosopher

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

“The truth is that other systems of geometry are possible, yet after all, these other systems are not spaces but other methods of space measurements. There is one space only, though we may conceive of many different manifolds, which are contrivances or ideal constructions invented for the purpose of determining space.”

Paul Carus (1852–1919) American philosopher

Science, Vol. 18 (1903), p. 106, as reported in Memorabilia Mathematica; or, The Philomath's Quotation-Book https://archive.org/stream/memorabiliamathe00moriiala#page/81/mode/2up, (1914), by Robert Edouard Moritz, p. 352

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Howard P. Robertson28

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