Susskind's answer
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In mathematics, particularly in differential topology, there are two Whitney embedding theorems, named after Hassler Whitney:
The strong Whitney embedding theorem states that any smooth real m-dimensional manifold (required also to be Hausdorff and second-countable) can be smoothly embedded in the real 2m-space (R2m), if m > 0. This is the best linear bound on the smallest-dimensional Euclidean space that all m-dimensional manifolds embed in, as the real projective spaces of dimension m cannot be embedded into real (2m − 1)-space if m is a power of two (as can be seen from a characteristic class argument, also due to Whitney).
Weinberg - Is Mathematics Invented or Discovered?
find the question to which the universe is the answer
Calilasseia wrote:Because at bottom, mathematics is the study of reliably repeatable interactions and well-defined entities taking part therein.
It is a logical system that builds an internally consistent set of rules that are amazingly useful in describing the world around us. ... You could argue that mathematics is a construct of the human mind.
(such that they can't, for example, be enumerated).
Macdoc wrote:(such that they can't, for example, be enumerated).
Yet Pi cannot be fully enumerated yet is very useful and what it is approximating can be easily seen.
Mathematics is a useful, transmittable way/language of preserving a description of the universe that can be acted on by others...or a CAM machine. IMNSHO
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