Friends, I am afraid my bullshit detector is chiming a bit. In my spare time I hunt for multiply-perfect numbers, so I am used to thinking of integers as finite sequences of prime exponents. I'm skeptical of these pictures because of the inexplicable decision to throw away all information about the exponents except whether they are zero or nonzero. OEIS tells me that there are 507 different integers, not exceeding one million, of the form 2^a * 3^b * 5^c. According to the explanation given, these 507 integers would all be displayed at the same point. I think the artist is not doing that -- instead, integers that ought to be displayed at the same place are jiggled a little bit, creating those long "snakes". That is, I suspect that those twisty shapes are completely arbitrary, and say nothing about the structure of the set of integers. And this leads me to be skeptical of the rest of the image as well: who knows what other arbitrary jiggery-pokery is going on here? Well, it's a github project, so I assume we can inspect the source. But my hopes are not high. A new Mandelbrot set this ain't. On Thu, Aug 23, 2018 at 8:32 AM Fred Lunnon <fred.lunnon@gmail.com> wrote:
We can chuck out all those expensive telescopes and pesky dark matter/energy then --- all you need to understand the universe is large enough table of primes and (presumably) PCA ... WFL
On 8/23/18, Brent Meeker <meekerdb@verizon.net> wrote:
A fascinating display of mathematical fireworks.
Brent
-------- Forwarded Message --------
Each integer is represented as a vector of its prime factors, in a high-dimensionality representation such that:
[1 0 1 0 0 0 0 ...] means that the number has factors 2 and 5 (first and third primes). Then they apply a dimensionality reduction algorithm to transform these vectors into 2D vectors with real-valued coordinates.
I think the result is beautiful: https://johnhw.github.io/umap_primes/index.md.html
Cheers
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