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Images Created from Prime Numbers

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Re: Images Created from Prime Numbers

#61

Post by baddox »

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…

The way I would describe it is that the primality of a number is almost completely unrelated to these images. The image is chosen beforehand, then a set of integers is chosen that each looks recognizably close to that image, then that set is searched for one that is prime (which is not unusual). Primality is the chosen attribute simply because it’s widely known and considered to be interesting in popular mathematics. People would be less impressed by images constructed with the binary representation of numbers divisible by 1,000,000, even though that may be a rarer property than primality for the magnitude of numbers considered.

Re: Images Created from Prime Numbers

#62

Post by jacobush »

yesenadam wrote: post #40
lonelappde wrote: post #24

Earlier quoted context omitted.

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.

It seems there was a large (unconscious?) religious dimension to SETI. Michael Shermer: [David Swift in his 1990 book SETI Pioneers ] asked each of the SETI pioneers about their parents’ religiosity... most were raised in a religious household but that not one believes in anything like the traditional Judeo-Christian God... Astronomer Frank Drake, ostensively the SETI pioneer if there was one (and creator of the infa…

Not saying you are from that background, but I think any upbringing that beats you over the head with something akin to "who are you going to believe, your deceiving eyes or me?" will prime you for SETI or similar "religion" later in life. That beating over the head could be an abusive parent, boarding school or whatever.

(Not saying most religious practice is abusive or anything. But it can be.)

Re: Images Created from Prime Numbers

#63

Post by yesenadam »

yesenadam wrote: post #40
lonelappde wrote: post #24

Earlier quoted context omitted.

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.

It seems there was a large (unconscious?) religious dimension to SETI. Michael Shermer: [David Swift in his 1990 book SETI Pioneers ] asked each of the SETI pioneers about their parents’ religiosity... most were raised in a religious household but that not one believes in anything like the traditional Judeo-Christian God... Astronomer Frank Drake, ostensively the SETI pioneer if there was one (and creator of the infa…

Also, if you loved (Sagan's) Cosmos - Dimitri Martin did a spoof version, Our Fascinating Planet, which is absolutely hilarious.

https://www.youtube.com/watch?v=fYo-OdQ-5ic&list=PLRcB4n4CGc...

Re: Images Created from Prime Numbers

#64

Post by dmurray »

I was sure that the original inspiration for this would be this [0] comic and reddit post from 2015, about a 4096-bit prime number that looks like a giraffe [1].

[0] https://www.reddit.com/r/math/comments/7qpfls/does_there_exi...

[1] A reddit commenter also found a "minimalist giraffe": 7.

Re: Images Created from Prime Numbers

#66

Post by [deleted] »

goldenkey wrote: post #55
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.

Dimensions can always be compressed and uncompressed. Naturals: https://en.wikipedia.org/wiki/Pairing_function Reals: https://en.wikipedia.org/wiki/Space-filling_curve The caveat is that a function, like the evolution of the universe, General Relativity, differential equations, would be possibly unwieldy and unaesthetic when written on lower dimensions, and locality might also be lost. Some techniques try to preserve…

[deleted]

Re: Images Created from Prime Numbers

#67

Post by Agentlien »

dmurray wrote: post #64

I was sure that the original inspiration for this would be this [0] comic and reddit post from 2015, about a 4096-bit prime number that looks like a giraffe [1]. [0] https://www.reddit.com/r/math/comments/7qpfls/does_there_exi... [1] A reddit commenter also found a "minimalist giraffe": 7.

That comic was oddly apropros. I just messaged my father explaining what a perfect number is (He'd asked me because of a question on a game show). That comic made for a great footnote.

Re: Images Created from Prime Numbers

#68

Post by hwillis »

baddox wrote: post #61
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…

The way I would describe it is that the primality of a number is almost completely unrelated to these images. The image is chosen beforehand, then a set of integers is chosen that each looks recognizably close to that image, then that set is searched for one that is prime (which is not unusual). Primality is the chosen attribute simply because it’s widely known and considered to be interesting in popular mathematics.…

truly it is an amazing congruence of mathematics and linguistics that one of my favorite words appears in the real series: 8008135.

Re: Images Created from Prime Numbers

#69

Post by goldenkey »

goldenkey wrote: post #55
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.

Dimensions can always be compressed and uncompressed. Naturals: https://en.wikipedia.org/wiki/Pairing_function Reals: https://en.wikipedia.org/wiki/Space-filling_curve The caveat is that a function, like the evolution of the universe, General Relativity, differential equations, would be possibly unwieldy and unaesthetic when written on lower dimensions, and locality might also be lost. Some techniques try to preserve…

Replying to the dead comment by saschag:

Respectfully, your argument just boils down to whether the real numbers actually "exist." And I airquote exist because even that term is loaded.

This HN delved into it: https://news.ycombinator.com/item?id=14080024

It really just boils down to the nature of incompressible infinities.

You may enjoy this video that explores some of the issues with unresolvable infinities:

https://youtu.be/Szd6RBsWntg

Re: Images Created from Prime Numbers

#70

Post by contravariant »

tanelpoder wrote: post #45
mc3 wrote: post #39

Earlier quoted context omitted.

Nonetheless, it's freaky that our deepest secrets are encoded into pi. If pi is normal.

Also, there will be multiple copies of data, some uncompressed, some compressed in different formats like gzip, lzo, etc.

And each copy will occur infinitely often.
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