Later On

A blog written for those whose interests more or less match mine.

Contrast of abstract vs. concrete in physics, math, and elsewhere

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I had a few thoughts after sleeping on this article in Quanta, which describes how abstract (and unconstructable) numbers in mathematics possibly support a distorted view the physics of physical reality.

One thought concerned something that would be possible (in theory) if physical quantities could be measured precisely: Consider two metal cubes, almost identical in size. Designate the smaller’s width as 1, and the larger made so that its width is 1.000xyz…, where xyz initiates a string of 3-digit segments, with each 3 digits being the decimal value of a byte, and the bytes representing characters in Unicode UTF-8. The larger cube is constructed so the decimal expansion contains the Unicode representation of the Universal Library described by Jorge Luis Borges in The Library of Babel.

This library, though quite large (read the story to get an idea of its size), is certainly not infinite, and so the decimal string of the larger cube’s size in terms of the size of the smaller is also not an infinite decimal. It’s just a very long decimal.

That would mean that two 1mm (approximately) cubes could contain the complete range of human knowledge. But this is possible only in thought, not in reality. Reality does not even allow for such precision.

Another thought I had was the contrast between the Platonic ideal God of some branches of Christianity — a God that is eternal, unchanging, absolute, omnipotent, omniscience, unaffected by the physical universe in general and humans in particular — and the God of process theology, which is intimately involved with the evolutionary universe and humans, reacting to humans and capable of change and of learning (as in fact as described in the Holy Bible).

In both cases, the contrast is between the abstract and theoretical and the real and practical — similar to the contrast between my abstract and theoretical knowledge of the camera’s self-timer that did not make the jump to the real and practical application of the self-timer when I needed it. Abstract and theoretical knowledge is separate from real and practical and experiential knowledge, and the abstract and theoretical model of the universe in physics is separate from the real and practical (and not so precise) universe in reality.

Written by Leisureguy

8 April 2020 at 11:52 am

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