nLab Nature conformable to herself


Nature conformable to herself is the name of an article written by Murray Gell-Mann which takes its title from the writings of Isaac Newton:

For Nature is very consonant and conformable to her self… For we must learn from the phaenomena of nature what bodies attract one another, and what are the laws and properties of the attraction, before we enquire the cause by which the attraction is perform’d, the attractions of gravity, magnetism and electricity, react to very sensible distances, and so have been observed by vulgar eyes, and there may be others which reach to so small distances as hitherto escape observation; and perhaps electrical attraction may react to such small distances, even without being excited by friction. (Opticks, Gell-Mann 96, p. 11)

Gell-Mann comments on this passage:

What a wealth of wisdom is contained in these words! Newton suggests that at small distances electrical interactions may play an important role, going far beyond the attraction of bits of paper to an amber rod rubbed against a cat’s fur. He anticipates the existence of a multitude of short-range forces such as we now know to exist. (Indeed, theoretical considerations now point to an infinite number of such forces.) He points out how empirical laws generally precede detailed dynamical explanations. And he seems to think of the various “Phaenomena” as exhibiting conformability among themselves as well as within each one. The last idea is the key to understanding why the criterion of simplicity should be helpful in the search for the fundamental laws of physics. (Gell-Mann 96, p. 11)

Conformity between the physical principles operating at neighboring levels allows for their discovery:

As we peel the skins of the onion, penetrating to deeper and deeper levels of the structure of the elementary particle system, mathematics with which we become familiar because of its utility at one level suggests new mathematics, some of which may be applicable at the next level down or to another phenomenon at the same level. Sometimes even the old mathematics is sufficient. (Gell-Mann 96, p. 11)


Gell-Mann’s ideas are developed by James Hartle in (Hartle 19) in the context of their joint work on the decoherent histories approach to quantum mechanics. Layers of what Gell-Mann calls the ‘onion’ are given as:

Quantum Spacetime; Classical Spacetime, the Quasiclassical Realm, and Copenhagen Quantum Mechanics; Elementary Particles; Big Bang Nucleosynthesis; Recombination; Large Scale Structure – Galaxies, Stars, Planets, Black Holes; Approximately Isolated Subsystems and their Frozen Accidents.

Again, we find an explanation for the applicability of mathematics across levels:

In this model it is not surprising that the mathematics useful at one level is related to that at another level. There is only one mathematics underlying the unified theory… Different parts of this mathematics may be more useful than others at different levels but they are all partial expressions of the same mathematical structure. The closer the mathematics at one level is to the mathematics of the next, the simpler it is to make connections between them, to augment them, or to invent any new mathematics needed. (Hartle 19, p. 7)


category: reference

Last revised on December 20, 2019 at 16:01:40. See the history of this page for a list of all contributions to it.