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Mathematics has the rock solid unit that doesn't change in series.
1 in 1 2 3 4 .....1325432 1325433 ....
But mathematics is a language, it's properties of the unit is singular, it abides by logical rules. There is nothing a about number has that says stop this is the limit.
In the real world,
units are multifaceted, multidimensional so interactions are physically limited by type and structure of the subunit. There are set ranges that certain sized subunits can be viable.
I proposed taking a census of all things and trying to examine them as discrete subunits. This census would range from subatomic particles, atoms, repeating crystal structures, micro-organisms, fauna and flora, geological structures, planet/ star sizes , galaxy sizes.
Does the universe go 1 2 3 .. or 1 2 7 9 12 13 14 15 21 ...*
Logically 5 exists but under construction rules of the universe not a magnitude subunit available.
The gaps might indicate the real world recursive physical patterns**.
The standard movie goes linearly from atom to web of galaxies but I not too sure that is the case.
Maybe pounds, shillings and pence was on the right track.
* Totally made up, to illustrate the idea.
** patterns that come as the small is repeatedly stacked to the large, Or as with life, the subunit pattern that is stuck between the very small and very large recursive patterns.
Vi Hart on YouTube
https://www.google....mcnjcH-VeZu4ke6VKho
Fibonacci series in nature. [RayfordSteele, Jan 14 2021]
Battle Beneath the Earth
https://www.imdb.co...87/?ref_=fn_al_tt_1
Prior Art [8th of 7, Jan 14 2021]
E series of preferred numbers
https://en.wikipedi...f_preferred_numbers
pick your level of precision, get a series of numbers [lurch, Jan 14 2021]
Explaining Benford's Law
http://www.dspguide.com/ch34.htm
Most numbers start with the digit 1 [mitxela, Jan 19 2021]
It's only a "Law" when it is applied to the right constraints...
https://www.youtube...watch?v=etx0k1nLn78
[RayfordSteele, Jan 19 2021]
[link]
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Well done, we're glad that's finally properly sorted out. Your Nobel Prize is in the post. |
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// Much of mathematics is astoundingly good at describing things we observe in nature, // |
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... except that due to neurophysiological structures, humans have an innate bias to "see" patterns - faces are the classic case - in what are actually truly random configurations, leading to the risk of self-fulfilling prophecies. |
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[zen], what you've written makes so much more sense than [wjt]'s original post- particularly about self-similarity persisting across micro to macro scales, as the Mandelbrot set demonstrates - that it's a pity that the two texts can't be exchanged ... |
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Someone should spend some time with my favorite
math channel gal, Vi Hart. Her explanations of
interesting math things are quite good. |
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Nature is less random than you think. Leaf growth
patterns are a function of simple growth hormone
maximal locations, which by their usage and
repetition make for some fascinating mathematical
patterns. See link. |
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I would just like to go on record to say that if it were possible to mentally download your understanding of the language of mathematics without having to go through all of the work it took for you to attain it... I would be good with that. |
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I understand patterns in nature have been found that have mathematical precis series or formulae like shell spirals and population interactions. |
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We all came from the expansion, how all the tiny space-time subunits unfolded/congealed to what we have now must also have a skeleton mathematical framework. Definitely not a even constant continuum. |
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And I don't think it is about repetition all the way through as combination effects can twist making a scale 'invariance' disappear.
If the scalar invariance is more about lowest/stable mass/energy ledges as scale increases , then this has been thought about, and I concede. Looking out into the world, there seems a lot of empty space with a lot of embroidery about the edges in blobs. |
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This more a general overview of whether matter/organization clumps, as scale increases, hence trying to shine a light the ultimate skeletal theory. |
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[kdf] This poor written concept, did get a well written, informed text from [zen_tom]. |
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Experimental measurements are the constraints of the mathematical language. |
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//Looking out into the world, there seems a lot of empty space
with a lot of embroidery about the edges in blobs.// |
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Stop using a doily as a COVID mask. |
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//if it were possible to mentally download your understanding of the language of mathematics without having to go through all of the work it took for you to attain it// |
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Sounds great! But I think those two clauses are more intimately linked than you suspect... a bit like trying to get from America to Europe without crossing the ocean... |
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There are the gifted, for whom the logic and symbols of the mathematical language fall into place because the subconscious does all the heavy lifting. |
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Of course, work is still needed to really utilize given talents. |
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// You would rather see nonsense in reply to a good idea than the other way around? // |
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Yes, if for no other reason than familiarity; we post excellent ideas, others post nonsense replies. |
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Or just get your bearings straight, and take the short route. |
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//this might crudely go from n^x, through a "ladder" of x^n
forms// |
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Could you provide an example, [zen_tom]? |
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// Tunnel through the Earth. // |
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The most effective place for a fixed link is the Bering Strait; a tunnel has been discussed for some time. |
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You still cross beneath the ocean |
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On most of your planet, the antipode to any given position on land is quite likely to be ocean - easy enough to calculate with a bit of basic spherical geometry. So, wherever you move on land, you're likely to be crossing ocean, albeit with the thickness of the planet in between. |
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Unless, of course, you subscribe to the view that it's "turtles all the way down" ... |
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[wjt], if I'm understanding you correctly, then something you might be interested in looking at is called the "E series of preferred numbers". It's how resistors get their weird but consistent values. |
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Thank you for the link, [zen]. |
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I read the date of posting as "March". I'm going to pretend the post let someone make a time machine, and they went back in time to edit the post and keep anyone else from discovering it. |
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A coastline is more of part of subunit . Tetonic plates I would think might be a subunit but inter planetary data might be needed on that one. Each of the subunits is going to be physically controlled by multitude of variables and physical factors but all of those dimensions emerge from the ultimate machine's underlying metal. |
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[zen_tom] Have you ever heard of Benford's Law? The idea that most numbers, in general, start with a 1. |
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The pattern is scale invariant, and base invariant - even in binary, or any base you like, most numbers start with a 1! The wikipedia page does an excellent job of only throwing further confusion on the issue, and explains nothing. |
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I can _very_ strongly recommend reading chapter 34 of the DSP Guide [link], where the author explains Benford's Law and provides an excellent explanation. It really is a magic trick, and says a lot about our human ability to see patterns everywhere. |
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// human ability to see patterns // |
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Not so much an "ability" as a propensity; it's programmed into your neural nets at a very primitive* level. It exists even in the lowliest** vision-equipped creatures, as an essential system for survival, both recognizing food and avoiding predators. |
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*Nationality can be a factor in assessing just what constitutes "primitive". |
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**Such as insects, flatworms, and P.E. teachers. |
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Benford's law is only useful as a predictor when the statistical
sampling is likely to be straddling either side of a power of
ten. It came up as a challenge to voting totals in our election
and had to be shot down by math gurus for why it was
erroneously assumed by the plaintiffs. |
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It's got some interesting applications in switched gain electrometer amplifiers for mass spectrometry, too, where the decade gain ranges don't quite overlap perfectly, or there's the problem of calibrating a SEM against a basic Faraday bucket detector. |
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The solution turned out to be to have a switched-gain amp and a logarithmic amp in parallel, and gate the A/D converter between them, but that's another story ... |
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I don't think Benford's law applies. To my thinking, Benford's rule looks inside the number set. I am trying to look outside, at the gap to other sets.
Then again, anything can be re-functioned so possibly, all the different data sets could be made to relate by a single unit and run through Benford's Law. |
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[Lurch] had my thinking right. Does nature have a baseline preferred building structure and therefore preferred numbers? Do these transform as magnitude of complexity and structure increases? |
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