#prime factorization

DIVE

DIVE is a 2048 variant found at https://alexfink.github.io/dive/index.html

Strategems

Spelled with an E in the sixth letter, not an A, it's a deckbuilder found at https://playcebo.itch.io/strategems

2024 is definitely divisible by four, because 24 is and any multiple of 100 is. Actually dividing gives us 506. That's divisible by 2 (because last digit is even) leaving 253. That's...hmm. Not divisible by two or five, or three. Or seven (253+7 = 260, 260 = 13*2*10 and integers have unique factorization so that's not divisible by 7, and that means anything 7 away from it also won't be.) It's...oh, of course. It's divisible by 11.

(If you sort of zipper out the digits and add them up and they add up to the same number, or are a multiple of 11 apart, the original number is divisible by 11.)

It's 11*23, in fact. 23 is prime. So we got:

(Sorry for the incoming word salad gibberish.)

A basic idea about encryption and decryption - and what makes them different in their kind/degree of difficulty (this also relates to entropy and why disorder rather increases than decreases in complex systems) [I might create a plain infographic or short article for that one later...]

[^ignore the random scribbles of numbers at the bottom of that page]

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The following stuff/photos depicts/expresses re-distribution of information, so to speak/per this interpretation.

It's mostly statistical inference.

It tries to depict/express non-linear causal networks - or merely, some symmetries in the motion/dynamics of chaotic systems.

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It relates to stuff I made earlier that year (march):

I drew a 3D plot of a fourier transform - Fraunhofer diffraction.

^Imagine the z axis as the time axis: it depicts how it alters itself in course of time. (That's basically what a transform is, if we "translate it" into our imagination and basic language.)

And somehow, I indulged in another conception of that plot. The height of each thingy depicted above, is now the radius of each circle in the depiction below:

A delightful visualization of prime factorizations for the numbers 1 through 49. 

As per the Fundamental Theorem of Arithmetic, for every natural number, there exists a unique prime factorization (in the naturals). Each and every number can be broken down into basic, irreducible components--or is itself irreducible (i.e. it cannot be factored; it is prime). 

I liken this to chemistry: the primes are the periodic table, an array of atomically indivisible elements. (Of course, the elements are “divisible subatomically” (into rationals or reals), but that is outside our focus). 

Following this analogy, all compound numbers are like chemical compounds, where bonds are multiplication. The properties and relationships of “numerical chemicals” are due to their structures. Insofar as the complexity of our natural world is (to some extent) attributable to fundamental chemical relationships, so too are many of mathematics’ exotic objects and qualities the result of “numerical chemistry” amongst the primes. 

As you examine the structures of the images above, I encourage you to consider the numbers of dots, “sub-groupings of dots,” and their overall symmetries. You will notice that the primes cannot be broken down into “sub-groupings” (i.e. they cannot be factored). As for the compound numbers, you will observe that their number of symmetries is related to the number of dots. The reader is encouraged to consider why this is, comparing the diagrams with the numerical details of the various prime factorizations.