“We have assumed that the laws of nature must be capable of expression in a form which is invariant for all possible transformations of the space-time co-ordinates”

— Gerald James Whitrow

The Structure of the Universe: An Introduction to Cosmology (1949)
Context: The philosophical consequences of the General Theory of Relativity are perhaps more striking than the experimental tests. As Bishop Barnes has reminded us, "The astonishing thing about Einstein's equations is that they appear to have come out of nothing." We have assumed that the laws of nature must be capable of expression in a form which is invariant for all possible transformations of the space-time co-ordinates and also that the geometry of space-time is Riemannian. From this exiguous basis, formulae of gravitation more accurate than those of Newton have been derived. As Barnes points out...

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Gerald James Whitrow 39

British mathematician 1912–2000

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“Each of the most basic physical laws that we know corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. …whilst leaving some underlying theme unchanged. …for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time… the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to directional orientation… discovery of conservation laws indicated that Nature possessed built-in sustaining principles which prevented the world from just ceasing to be. There were fewer roles for the Deity to play…”

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[Lectures on Celestial Mechanics, https://books.google.com/books?id=mZtrCQAAQBAJ&pg=PA1] (p. 1)

“I can see no excuse for doubting that all are co-ordinated terms of Nature's great progression, from the formless to the formed—from the inorganic to the organic—from blind force to conscious intellect and will.”

Thomas Henry Huxley (1825–1895) English biologist and comparative anatomist

Source: 1860s, Evidence as to Man's Place in Nature (1863), Ch.1 (1884 edition) http://books.google.com/books?id=1Z9DGVKfXuQC p. 28
Context: The whole analogy of natural operations furnishes so complete and crushing an argument against the intervention of any but what are termed secondary causes, in the production of all the phenomena of the universe; that, in view of the intimate relations between Man and the rest of the living world; and between the forces exerted by the latter and all other forces, I can see no excuse for doubting that all are co-ordinated terms of Nature's great progression, from the formless to the formed—from the inorganic to the organic—from blind force to conscious intellect and will.

“The sequence of different positions of the same particle at different times forms a one-dimensional continuum in the four-dimensional space-time, which is called the world-line of the particle. All that physical experiments or observations can teach us refers to intersections of world-lines of different material particles, light-pulsations, etc., and how the course of the world-line is between these points of intersection is entirely irrelevant and outside the domain of physics. The system of intersecting world-lines can thus be twisted about at will, so long as no points of intersection are destroyed or created, and their order is not changed. It follows that the equations expressing the physical laws must be invariant for arbitrary transformations.”

Willem de Sitter (1872–1934) Dutch cosmologist

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Source: Reality; The Search for Objectivity or the Quest for a Compelling Argument (1988), p. 48 as cited in: Vincent Kenny (1989) " Life, the Multiverse and Everything; an Introduction to the Ideas of. Humberto Maturana http://www.oikos.org/vinclife.htm".

“That nature will follow to-morrow the same laws that she follows to-day is, they all admit, a truth which no man can know; but in the interests of cognition as well as of action we must postulate or assume it.”

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Context: The necessity of faith as an ingredient in our mental attitude is strongly insisted on by the scientific philosophers of the present day; but by a singularly arbitrary caprice they say that it is only legitimate when used in the interests of one particular proposition, — the proposition, namely, that the course of nature is uniform. That nature will follow to-morrow the same laws that she follows to-day is, they all admit, a truth which no man can know; but in the interests of cognition as well as of action we must postulate or assume it.

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“Since space is continuous, it follows that there must be an immediate community of feeling between parts of mind infinitesimally close together. Without this, I believe it would have been impossible for any co-ordination to be established in the action of the nerve-matter of one brain.”

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“We have assumed that the laws of nature must be capable of expression in a form which is invariant for all possible transformations of the space-time co-ordinates”

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Gerald James Whitrow 39

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