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Images Created from Prime Numbers

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Re: Images Created from Prime Numbers

#121

Post by skissane »

javajosh wrote: post #112
skissane wrote: post #106

Earlier quoted context omitted.

> However, the odds of a very large prime (like a gigabyte) looking intentionally ordered over its entire length seems vanishingly small. Can we estimate how many gigabyte sized primes exist? I think one can do that using the prime number theorem. Let’s call that N. What is the probability one of those N messages is meaningful? I think it is a lot higher than you think it is. I think N is a very big number, even thou…

PNT, interesting! If I'm reading it correctly you can estimate the number of N digit primes as 10^N/N. That's basically 10^N, and for N=9 (a billion), that means there's (very very roughly) a billion primes with a billion digits. I mean, it's not that many if your expecting a message from God (I say half-jokingly).

Suppose somewhere out there, there is an ISO of Bible software, and it just so happens that when expressed as an integer it turns out to be prime – proof that the Bible is God's word, or freak coincidence? I think most people would go with the second option. And, the same would be just as true if it was an ISO of some other religious scripture, such as the Quran or the Vedas.

Re: Images Created from Prime Numbers

#122

Post by c3534l »

jerrytsai wrote: post #102
JKCalhoun wrote: post #44

Earlier quoted context omitted.

The classic prime joke (saw it originally in Sci Am back in the ... 70's? 80's?). Found an approximation when I googled it: A mathematician, physicist, and engineer are taking a math test. One question asks "Are all odd numbers prime?" The mathematician thinks, "3 is prime, 5 is prime, 7 is prime, 9 is not prime -- nope, not all odd numbers are prime." The physicist thinks, "3 is prime, 5 is prime, 7 is prime, 9 ...…

Help with the joke? I understood the mathematician and the physicist, but not the engineer. What stereotype is being invoked?

9 is a prime the same way that 1/0 is +Inf.

Re: Images Created from Prime Numbers

#125

Post by javajosh »

skissane wrote: post #121
javajosh wrote: post #112

Earlier quoted context omitted.

PNT, interesting! If I'm reading it correctly you can estimate the number of N digit primes as 10^N/N. That's basically 10^N, and for N=9 (a billion), that means there's (very very roughly) a billion primes with a billion digits. I mean, it's not that many if your expecting a message from God (I say half-jokingly).

Suppose somewhere out there, there is an ISO of Bible software, and it just so happens that when expressed as an integer it turns out to be prime – proof that the Bible is God's word, or freak coincidence? I think most people would go with the second option. And, the same would be just as true if it was an ISO of some other religious scripture, such as the Quran or the Vedas.

Well it would be an impressive feat, regardless. But of course there are a lot of degrees-of-freedom if you were to attempt this. Tiny formatting and encoding decisions would all greatly influence the resulting integer. Because it's so sensitive to chosen input, I would say even if you managed to produce a prime, it's not very satisfying as a sort of Godly checksum and signature.

Much more interesting is to discover a new communication, a message encoded in a very large number that is distinguished by being prime. (What message would you send? It would be interesting if it ultimately described some sort of recursive, reactive automata, the source code for a kind of learning, communicating intelligence. A gift, then. An awesome, terrible gift.)

Re: Images Created from Prime Numbers

#126

Post by MrQuincle »

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…

I have been raised extremely religious and I completely understand obsession by the search for alien life. In some way it would "ground" at once my entire struggle to get out of this (human) religion. Sure, you can imagine an adapted religion cross the universe with multiple Jesuses etc., but it's much less convincing than the original.

Actually, the reason I'm so interested in artificial general intelligence is, I think, driven by the same reasons. If we can create fellow human beings, it somehow is like creating your own aliens on earth. That, and the idea that we need them to solve the tough problem we nowadays face as mankind.

Re: Images Created from Prime Numbers

#127

Post by askvictor »

OJFord wrote: post #99
askvictor wrote: post #60

Earlier quoted context omitted.

The version I remember has the mathematician thinking: "3 is prime, 5 is prime, 7 is prime, so by mathematical induction, all odd numbers are prime".

That's extrapolation I suppose, but not induction. For induction you'd need to say '1 is prime, n+2 is prime where n is prime, so [...]'.

Yes, I know. It's a joke. Making fun of mathematicians, physicists and engineers.

Re: Images Created from Prime Numbers

#128

Post by criddell »

SamBam wrote: post #110
criddell wrote: post #105

Earlier quoted context omitted.

This is amazing! So somewhere pi is a computer program that when run would set up a server with an entry for every person that has ever lived or ever will live with complete information on that person. You could theoretically see a real-time movie of anybody from life until death. Crazy! Do you know if k has to be finite?

K would have to be finite, yes, or there could never be another string after it. But k can be arbitrarily large. Yes, Normal Numbers are awesome to think about when you first learn them. Ever tiny detail of everything that has ever happened in the history of the world, written in incredibly beautiful prose that would bring the entire planet to its knees on reading it, is somewhere in the digits of pi. Of course, so a…

That's really fascinating.

So if you could find things in pi (or any normal number) quickly enough, then any arbitrary chunk of data could be compressed to just an offset and a length into that number. That's kind of crazy to think about.

Re: Images Created from Prime Numbers

#129

Post by dTal »

criddell wrote: post #128
SamBam wrote: post #110

Earlier quoted context omitted.

K would have to be finite, yes, or there could never be another string after it. But k can be arbitrarily large. Yes, Normal Numbers are awesome to think about when you first learn them. Ever tiny detail of everything that has ever happened in the history of the world, written in incredibly beautiful prose that would bring the entire planet to its knees on reading it, is somewhere in the digits of pi. Of course, so a…

That's really fascinating. So if you could find things in pi (or any normal number) quickly enough, then any arbitrary chunk of data could be compressed to just an offset and a length into that number. That's kind of crazy to think about.

No, not compressed - the offset would always be (much) larger than the arbitrary chunk of data. It's flawed intuition to think of the information as "in" pi - it's "in" the offset, and pi is essentially a small decryption algorithm.

Don't get carried away with pi mysticism - all this stuff is also true of the concatenation of all integers in order (0123456789101112131415...).

Re: Images Created from Prime Numbers

#130

Post by andreareina »

criddell wrote: post #128
SamBam wrote: post #110

Earlier quoted context omitted.

K would have to be finite, yes, or there could never be another string after it. But k can be arbitrarily large. Yes, Normal Numbers are awesome to think about when you first learn them. Ever tiny detail of everything that has ever happened in the history of the world, written in incredibly beautiful prose that would bring the entire planet to its knees on reading it, is somewhere in the digits of pi. Of course, so a…

That's really fascinating. So if you could find things in pi (or any normal number) quickly enough, then any arbitrary chunk of data could be compressed to just an offset and a length into that number. That's kind of crazy to think about.

It's an idea as old as time. Or 8 years, at the very least: https://github.com/philipl/pifs

In expectation, a k-digit sequence will require a k-digit number to encode its offset, so there's no compression there.

Then again, there's this gem 762 decimal places in: http://mathworld.wolfram.com/FeynmanPoint.html

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