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Images Created from Prime Numbers

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Re: Images Created from Prime Numbers

#91

Post by nkrisc »

javajosh wrote: post #73
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".

It just occurred to me how strange it is that you can get to some numbers by addition that you cannot get to by multiplying any subset of the earlier sequence. Emotionally, it feels like addition and multiplication are arguing over who's better, and multiplication is like "I'm so fast", and addition is like, "I'm slow but, I can go places you can't ". It'd be cool, if there was a Maker, that they make it so that some…

> Why not have a SETI-in-the-primes project, after all?

Sure, it can run alongside SETI-in-the-burn-marks-on-toast and SETI-the-flour-spilled-on-the-table projects.

Re: Images Created from Prime Numbers

#92

Post by jedimastert »

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…

This is why I love the idea of the "Library of Babel". The basic idea is that it's a vast "library" of every permutation of letters and punctuation in a book. Almost every book would be complete gibberish, but there much also be every book ever written, already created and waiting to be discovered.

Is any idea truly created, or simply discovered first? Or is the simple fact of having too many possibilities man that there's no possible way you can "discover" anything at all, and anything much be invented first to be looked for?

Re: Images Created from Prime Numbers

#93

Post by infradig »

hwillis wrote: post #68
baddox wrote: post #61

Earlier quoted context omitted.

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.

It looks better on a calculator.

Re: Images Created from Prime Numbers

#94

Post by jameshart »

jedimastert wrote: post #92
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…

This is why I love the idea of the "Library of Babel". The basic idea is that it's a vast "library" of every permutation of letters and punctuation in a book. Almost every book would be complete gibberish, but there much also be every book ever written, already created and waiting to be discovered. Is any idea truly created, or simply discovered first? Or is the simple fact of having too many possibilities man that t…

well, among other things that library contains an infinite number of proofs that P=NP. Also an infinite number of proofs of the opposite. Also an infinite number of base64-encoded FLACs of the original cast recording of a rock opera based on each of those proofs, performed by David Bowie and Justin Bieber. Obviously, an infinite number of them contain logical flaws. An infinite number of them are surprisingly listenable.

You’re welcome to devote time to trying to discover them...

Re: Images Created from Prime Numbers

#95

Post by zeveb »

skissane wrote: post #82
javajosh wrote: post #73

Earlier quoted context omitted.

It just occurred to me how strange it is that you can get to some numbers by addition that you cannot get to by multiplying any subset of the earlier sequence. Emotionally, it feels like addition and multiplication are arguing over who's better, and multiplication is like "I'm so fast", and addition is like, "I'm slow but, I can go places you can't ". It'd be cool, if there was a Maker, that they make it so that some…

> It'd be cool, if there was a Maker, that they make it so that some very large prime number is a message to all intelligent life capable of computing and deciphering it Every possible message is already there. Just like how Borges’ Library of Babel contains every possible book (within its limits of size and format)

> Just like how Borges’ Library of Babel contains every possible book (within its limits of size and format)

You're welcome to look around for messages here: https://libraryofbabel.info/

I don't know if anyone has ever found one, though.

Re: Images Created from Prime Numbers

#96

Post by javajosh »

nkrisc wrote: post #91
javajosh wrote: post #73

Earlier quoted context omitted.

It just occurred to me how strange it is that you can get to some numbers by addition that you cannot get to by multiplying any subset of the earlier sequence. Emotionally, it feels like addition and multiplication are arguing over who's better, and multiplication is like "I'm so fast", and addition is like, "I'm slow but, I can go places you can't ". It'd be cool, if there was a Maker, that they make it so that some…

> Why not have a SETI-in-the-primes project, after all? Sure, it can run alongside SETI-in-the-burn-marks-on-toast and SETI-the-flour-spilled-on-the-table projects.

Ah, but that's not quite the same. A message encoded in number theory itself is a far more difficult to author than just adjusting the position of 10^23 atoms.

Re: Images Created from Prime Numbers

#97

Post by skissane »

javajosh wrote: post #88
skissane wrote: post #82

Earlier quoted context omitted.

> It'd be cool, if there was a Maker, that they make it so that some very large prime number is a message to all intelligent life capable of computing and deciphering it Every possible message is already there. Just like how Borges’ Library of Babel contains every possible book (within its limits of size and format)

That cannot be true. It does not contain the message '4'. (Or any of the non-primes.) In fact it seems like there must be many more non-primes than primes over any finite interval (for the simple reason that multiplication gets a lot of whacks at the piñata, e.g. producing a product landing in that finite interval.) So to answer your implied question ("why bother commucating with primes anwyay?") I guess the value of…

> That cannot be true. It does not contain the message '4'. (Or any of the non-primes.)

Any finite message (containing a finite number of symbols drawn from a finite alphabet) can be represented as a positive integer.

Any positive integer n can be encoded in a prime, even a composite integer.

Use the following encoding system: write 1 n times, followed by a zero, followed by an arbitrary bit string.

For example, for 4: 11110xxxxxxxxxxxxx...

Using that encoding system, there will be an infinite number of primes that encode 4 - all the primes which start with 11110 in binary.

Thus, the set of all primes contains an infinite number of copies of every possible finite message.

Re: Images Created from Prime Numbers

#99

Post by OJFord »

askvictor wrote: post #60
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 ...…

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 [...]'.

Re: Images Created from Prime Numbers

#100

Post by criddell »

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…

> with an infinite numbers of primes available to us, nothing is hidden

Just because there's an infinite number of primes, it doesn't necessarily mean that everything is in there, does it? For example, would you expect to find Romeo and Juliet in pi? It might be there, but I don't think it has to be there, does it?

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