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Images Created from Prime Numbers

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Re: Images Created from Prime Numbers

#11

Post by ardit33 »

extr wrote: post #9

Wow. I feel like the fact that you can encoding arbitrary information in long numbers is such a far reaching concept in math/computer science, it's really satisfying to see it demonstrated in such an intuitive way.

you can encode any arbitrary information into a one dimensional value.... eg: a large enough number can encode the whole universe....

But decoding any meaningful information has to be at least in two dimensions....

In two dimensions, you can describe everything.... the other dimensions are not needed (and perhaps just emerging, according to the holographic principle)....

Re: Images Created from Prime Numbers

#12

Post by jodrellblank »

extr wrote: post #9

Wow. I feel like the fact that you can encoding arbitrary information in long numbers is such a far reaching concept in math/computer science, it's really satisfying to see it demonstrated in such an intuitive way.

1GB of storage is a single number with 2^8billion binary digits.

Everything we do in computers is encoding information in long numbers. Every character is a single number, every file is, every disk image is, every state of RAM, every database, every cache, every piece of source code.

Re: Images Created from Prime Numbers

#13

Post by BubRoss »

pcmaffey wrote: post #10
kijin wrote: post #5

Earlier quoted context omitted.

From the link: > approximately one in every 6200 2688-digit numbers is prime. So if you're lucky, you only need to brute force the last 4 digits! Maybe 5 if you're unlucky. In either case, that's a lot less work than I imagined. And of course you can skip all the even numbers.

You can skip all multiples of 3 also.

You skip all multiples of anything, but evens are easy to check.

Re: Images Created from Prime Numbers

#14

Post by ShorsHammer »

extr wrote: post #9

Wow. I feel like the fact that you can encoding arbitrary information in long numbers is such a far reaching concept in math/computer science, it's really satisfying to see it demonstrated in such an intuitive way.

The entire Library of Babel is encoded in Pi.

https://en.wikipedia.org/wiki/The_Library_of_Babel

Re: Images Created from Prime Numbers

#16

Post by kvakil »

ShorsHammer wrote: post #14
extr wrote: post #9

Wow. I feel like the fact that you can encoding arbitrary information in long numbers is such a far reaching concept in math/computer science, it's really satisfying to see it demonstrated in such an intuitive way.

The entire Library of Babel is encoded in Pi. https://en.wikipedia.org/wiki/The_Library_of_Babel

This assumes that pi is a normal number [0], a fact that is widely believed but has not been proven.

[0]: https://en.wikipedia.org/wiki/Normal_number

Re: Images Created from Prime Numbers

#17

Post by [deleted] »

ShorsHammer wrote: post #14
extr wrote: post #9

Wow. I feel like the fact that you can encoding arbitrary information in long numbers is such a far reaching concept in math/computer science, it's really satisfying to see it demonstrated in such an intuitive way.

The entire Library of Babel is encoded in Pi. https://en.wikipedia.org/wiki/The_Library_of_Babel

[deleted]

Re: Images Created from Prime Numbers

#18

Post by snowwrestler »

There’s a great scene in the end of the book “Contact” by Carl Sagan where the main character uses super powerful computers to find a raster image of a circle hidden deep in the digits of pi. This is supposed to be a moment of deep spiritual significance.

But in fact, it’s basically an expected outcome given what we think we know about pi.

At first glance these images were startling to me; that such recognizable images could be “hidden” in the primes... in the very structure of mathematics! But then I realized that with an infinite numbers of primes available to us, nothing is hidden. It’s more like the primes are simply building blocks for us to use in constructing images of whatever we want.

Re: Images Created from Prime Numbers

#19

Post by lonelappde »

nayuki wrote: post #4

Reminds me of this classic number: https://en.wikipedia.org/wiki/Illegal_prime Basically: DeCSS source code (illegal) → compress → pad → add constant to make it prime.

That article talks about specious attempt to hack the legal system, by claiming information can never be legally restricted because it can encode numbers, but doesn't say the result of the attempt.

Re: Images Created from Prime Numbers

#20

Post by Causality1 »

Reminds me of a thought I had a while back that given sufficient computational power you could describe any dataset using only two place values in an irrational number and an interpretation rule. For example, the complete data for an h265 copy of Avengers Endgame exists somewhere in the digital expression of the value of Pi. It might be googleplexes of digits deep, but it's there somewhere.
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