Re: how

On 4/25/2024 1:35 PM, Ross Finlayson wrote:

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:
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Deeper down the rabbit hole. There is an infinity between 1 and 1.25...

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Yeah. The real numbers (and hence the complex numbers too) ARE quite
"deep".
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Indeed, the Mandelbrot fractal is a nice "depiction" of that fact.
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https://www.youtube.com/watch?v=ZjZr7F_kJmw&list=PLb7rLSBiE7F5_h5sSsWDQmbNGsmm97Fy5&index=34
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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.
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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).
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Fwiw, check this out... We can store data in the n-ary roots of complex
numbers:
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https://groups.google.com/g/comp.lang.c++/c/bB1wA4wvoFc/m/GdzmMd41AQAJ
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:^)

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

Kind of... Well, it shows how data can be stored in the roots of a complex number. The fun part is that data can be within the roots that comprise escape time fractals, like the Mandelbrot and Julia sets. Fun to me.

 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.

Interesting! Btw, have you tried to compile and run it on your end?
For people that do not have a C++ compiler handy, it can be run on an online C++ compiler, here is just one of many:
https://i.ibb.co/vmfzv0M/image.png
There is an very interesting part wrt trying to get it into a state where it has errors wrt loading up data. For instance, try to store:
ABCABCABCABC instead of my name CHRIS, it gets an error:
ORIGIN POINT:(-0.75,0.059999999999999998)
LOADED POINT:(0,0)
loaded:00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000046ABCABCABCABC
load_err_sum:5.3680514269578706e-14
***** DATA CORRUPTED!!! Shi%! *****
MnWOvMQcgO.o: /tmp/MnWOvMQcgO.cpp:290: int main(): Assertion `stored == loaded' failed.
Aborted
However, if you study that error, the data is still there, right at the end!
0046ABCABCABCABC
Strange!