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NNTP-Posting-Date: Thu, 25 Apr 2024 20:35:28 +0000
Subject: Re: how
Newsgroups: sci.math
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From: Ross Finlayson <ross.a.finlayson@gmail.com>
Date: Thu, 25 Apr 2024 13:35:29 -0700
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On 04/25/2024 12:10 PM, Chris M. Thomasson wrote:
> On 4/24/2024 7:55 PM, Ross Finlayson wrote:
>> On 04/24/2024 06:16 PM, Moebius wrote:
>>> Am 25.04.2024 um 02:49 schrieb Chris M. Thomasson:
>>>
>>>> Deeper down the rabbit hole. There is an infinity between 1 and 1.25...
>>>
>>> Yeah. The real numbers (and hence the complex numbers too) ARE quite
>>> "deep".
>>>
>>> Indeed, the Mandelbrot fractal is a nice "depiction" of that fact.
>>>
>>
>> https://www.youtube.com/watch?v=ZjZr7F_kJmw&list=PLb7rLSBiE7F5_h5sSsWDQmbNGsmm97Fy5&index=34
>>
>> -
>>
>> You know if you read a derivation of the complex numbers,
>> where it gets to defining division, there's more than
>> one branch than the usual principal branch, so it sort
>> makes complex numbers a bit more complex.
>>
>> Yet, the roots of unity can also be considered a variety of ways,
>> other than complex analysis or the usual Eulerian-Gaussian analysis,
>> and, "roots of zero" is quite a deal, and the identity-dimension
>> is even a thing (in mathematics).
>>
>>
>
> Fwiw, check this out... We can store data in the n-ary roots of complex
> numbers:
>
> https://groups.google.com/g/comp.lang.c++/c/bB1wA4wvoFc/m/GdzmMd41AQAJ
>
> :^)

It seems a sort of "arithmetic coding", or, as a
sort of "addressing scheme".

Then as a sort of "arithmetization", as after an
"algebraization", or about and around that as
algebra, arithmetic, and geometry get separate
treatments while all sitting together in the numbers
and geometry their algebras, then that a "geometrization"
would also have that besides encoding offsets of
whatever interpolated sorts in the bits of the
mantissa of the complex numbers' components,
that also what's true in the geometry in the
diagram that is the complex plane about R^2,
would also be true about the things.

For example, say sometimes the alphabet is sequential,
and other times, it's like some finite ring that's
co-prime its modulus so like the roots ring around
the roots of unity, then the various sieves down
into the alphabet would have the same order.

Then it's two properties at once.