What's always captured my wonder is this kind of ambiguity between math and physical reality. Sometimes it almost seems to me that you can say physical reality is math, or that it is an intrinsic part. Matter and energy come in discrete quantized forms which can be added, subtracted, multiplied, ect. If you add or subtract 1 electron from an atom, it will exhibit specific properties. A charged particle exhibits the behavior of being acted on by 1/4 of it's original force when it is twice as far away from an opposite charge. This seems to be much more than merely a description, these patterns and ratios seem to be the organization of nature.
The thing with that is, there has always been clouds of mystery on the horizon of our best conception of reality and our mathematical description of it. Space was well described by Euclidean geometry until Einstein unraveled one of the "two small clouds of mystery" Lord Kelvin mentioned, and completely changed the mathematical description of space to a geometry which Bernhard Riemann discovered purely for math itself. Now, even the reality of this (mostly) working description of space seems to be obscured by two clouds on the horizon, dark matter and dark energy. Does our best mathematical description of reality only work when we sweep those well contained and isolated areas of mystery under the rug? Will mathematical sureness always flow out into something new when those mysteries are uncapped?
Does a paradox between sure mathematical description and the unknown forever reform and evolve science? Will it eventually end in sure mathematical description (is reality at it's core mathematical organization?), or will we just use our best mathematical structures as stepping stones to forever ascend into new mysteries (is reality at it's core the ineffable unknown?). If the latter is true, where is the math coming from if not from physical reality? Is it something uniquely neurological? Are we just projecting neurological structures onto the rest of the observable universe? However, our brains are constructions of the universe: physics, chemistry, ect, so surely whatever our brains do must be akin to properties of the rest of nature, perhaps a kind of primordial math of which we discover being an intrinsic one, this would seem to make the former possible. Could it be possible that an intrinsic part of human experience is that both are true in a conserved dual awareness kind of way? This has been in the back of my mind forever lol.
Quantum Mechanics is a prime example of this kind of ambiguity. Is math really the core of this reality we observe, or is it mystery? There is heated debate on both sides.


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