Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Images Created from Prime Numbers

futilitycloset.com

Post reply on HN
Print view View original

21–30 of 131 posts

Re: Images Created from Prime Numbers

#21

Post by lonelappde »

ardit33 wrote: post #11
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)....

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

What does this mean?

Re: Images Created from Prime Numbers

#22

Post by lonelappde »

jodrellblank wrote: post #12
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.

Not encoded as, but can be interpreted as. Any precisely specified object can be interpreted as a number.

Re: Images Created from Prime Numbers

#23

Post by lonelappde »

This is yet another case where "prime" is bolted onto something for no particular reason to make it superficially more interesting. IMO this confused mathematical understanding.

Approximately 1/n of all n-bit pieces of data (including bimaps) are prime.

Re: Images Created from Prime Numbers

#24

Post by lonelappde »

snowwrestler wrote: post #18

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 imag…

Not quite true. Sagan's version was better than that analysis suggests: http://kasmana.people.cofc.edu/MATHFICT/mf55-spoiler.html

> as Sagan puts it in the story itself, the surprise is not that it appears that it appears "so early" in the sequence.

Re: Images Created from Prime Numbers

#25

Post by MontyCarloHall »

Causality1 wrote: post #20

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.

Only if that irrational number is also normal (https://en.wikipedia.org/wiki/Normal_number), which pi has not been proven to be.

Re: Images Created from Prime Numbers

#26

Post by kvakil »

MontyCarloHall wrote: post #25
Causality1 wrote: post #20

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.

Only if that irrational number is also normal ( https://en.wikipedia.org/wiki/Normal_number ), which pi has not been proven to be.

In addition, even if a normal number was used, it's far simpler to describe the data by just using a single number alone. For example, a binary encoding of the data (perhaps using a prefix-free code). Using a normal number and two "positions" is just more complicated.

Re: Images Created from Prime Numbers

#27

Post by jon_richards »

lonelappde wrote: post #24
snowwrestler wrote: post #18

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 imag…

Not quite true. Sagan's version was better than that analysis suggests: http://kasmana.people.cofc.edu/MATHFICT/mf55-spoiler.html > as Sagan puts it in the story itself, the surprise is not that it appears that it appears "so early" in the sequence.

I’ve always assumed that was also the inspiration for one of the earliest xkcd’s: https://xkcd.com/10/

Re: Images Created from Prime Numbers

#28

Post by war1025 »

Semi-related, but reading this article and thinking about it made me wonder if there is any study at all of "gray code" primes, for lack of a better word.

Basically, prime numbers that differ by exactly one binary digit in their representation.

Probably nothing about that relationship that would be interesting enough to look into beyond just "I ran some calculations and found these numbers that fit the pattern"

Re: Images Created from Prime Numbers

#29

Post by EvanAnderson »

lonelappde wrote: post #24
snowwrestler wrote: post #18

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 imag…

Not quite true. Sagan's version was better than that analysis suggests: http://kasmana.people.cofc.edu/MATHFICT/mf55-spoiler.html > as Sagan puts it in the story itself, the surprise is not that it appears that it appears "so early" in the sequence.

I'd never read that analysis of the ending of Contact. Thanks for sharing!
Post reply on HN