Summary: The microcosm is an infinitely deep non-mathematical ocean. The sub-atomic level as we know it barely scrapes the surface.
The Mathematical Map
Consider the equation Force = Mass X Acceleration.
Is it what is actually happening in reality?
Or is it just a mathematical description of what's happening, using references, concepts, terms, that we find convenient?
This equation is just a map of reality. It maps a certain natural process, that, in itself is *not* mathematical.
Nature does not flow in terms of numbers. Nature does not calculate the weight and chemical composition of a rock before creating it.
Nature did not precalculate/predecide the voltage range of lightening, or the pH level of the dead sea or any sea for that matter. Nor did it calculate the mass of the sun and the planets before creating the solar system.
Nature flows in a smooth, continuous, non mathematical flow. Like a song. The mathematical map of a song, in terms of numbers, amplitudes, frequencies...is that a complete expression/representation of the song?
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Nature has no 'mechanism'. It is not a machine that runs logically and mathematically.
Building a mathematical model of a process, extrapolating it, and expecting the process to manifest in the same manner or manner similar to your extrapolation can never lead to correct results. Because nature does not 'extrapolate itself mathematically'. We think it is this way because we confuse the map with the territory.
Mathematics, no matter how evolved, no matter how refined....will always remain just a map.
A fractal mathematical map of corals(below)...can never 'predict' how a 'real coral' will manifest next. For the abovementioned reasons.
Photo Ctsy. Miqel.Com.
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The Infinite Microcosm
The GAP between the scientific map of nature and the actual flow of nature can never go away because the microcosm is infinitely deep AND because the microcosm/macrocosm is not mathematical.
The cosmos will throw our way deeper and deeper mysteries, even if mankind survives a billion trillion years without forgetting its knowledge.
We can 'see' things at the nano level (10
-9m) using existing technology.
I do not agree that it is impossible to see below 10-35m...i.e. Planck Length.
The day we see at 10 X nano level (10
-90m), we'll see newer things.
The day we 'see' at 100 X Nano level (10
-900m) we'll see newer things.
There would certainly be things going on at 1000 X Nano level (10
-9000m).
And the 100,000 X Nano level (10
-900000m).....Ad Infinitum.
As we dive deeper and deeper into the microcosm....the complexity and the richness will keep on INCREASING. This conclusion of mine is based on my understanding of the "FRACTAL GEOMETRY OF NATURE".
And...assuming that the things we see at the 100,000 X Nano level (10
-900000m) will be a repetition of the things we have seen at the nano level (10
-9m).....this assumption would not be a wise assumption.
Electrons, protons, neutrons...these mathematical maps just barely scrape the surface of the infinite microcosm.
These concepts 'electrons, protons, neutrons' could approximate certain formations on the sub atomic scale, but these sub atomic formations are not the end of it. Nothing 'fundamental' about them.
The microcosm cannot be anything but infinitely deep.
The cosmos was, is, and will remain...forever mystical.
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Further Reading:
Being And Quirkiness