4 ms·

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".

javajosh 7y ago
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 very large prime number is a message to all intelligent life capable of computing and deciphering it. This kind of message would penetrate even nested, simulated universes, and could only come from World 0, assuming the properties of numbers are independent of physical constants. Why not have a SETI-in-the-primes project, after all?
- skissane 7y ago
  > 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)
  - javajosh 7y ago
    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 limiting your message to "a really big prime number" is to make discovery hard, but still tenable. It should be pretty big, like big enough for a good bible sized book, say 1 gigabyte, and start with something really obviously artificial, or unexpected looking, like starting as a 1 with 20,000 zeroes, or maybe better, 20k perfect 010101 and then after a few thousand, 00110011, and from there establish a language protocol, and write the book. But you'd have to expect people to check only primes for these simple patterns, because it's really easy to produce meaningful sequences with addition, and really hard with multiplication (AFAIK).
    - skissane 7y ago
      > 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.
      - javajosh 7y ago
        I meant that the entire message is "4", not just part of the message. Obviously we can pick a subset of digits of any large prime and find anything we want. However, the odds of a very large prime (like a gigabyte) looking intentionally ordered over its entire length seems vanishingly small. The only reason to limit ourselves to primes is because its trivial to produce a meaningful composite, and very difficult to produce a meaningful prime. Take this message; if I was to associate it with a number (say by joining its characters as 7-bit ASCII), my money is that it's composite. (Not sure what the odds are, but I'd take 100:1 odds). EDIT: period is `01110`, which is even, so I win.
        skissane 7y ago
        > 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 though it is very small compared to the number of composite gigabyte-sized numbers, it is still unimaginably large in absolute terms.
        javajosh 7y ago
  - zeveb 7y ago
    > 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/ https://libraryofbabel.info/ I don't know if anyone has ever found one, though.
- nkrisc 7y ago
  > 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.
  - javajosh 7y ago
    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.
    - nkrisc 7y ago
      Then it shouldn't take nearly as long!
Tainnor 7y ago
that's not mathematical induction though. it's what philosophers call "induction", i.e. building theories out of empirical observations (as opposed to deduction; mathematical induction is weirdly named because it's actually purely deductive)
OJFord 7y ago
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 [...]'.
- askvictor 7y ago
  Yes, I know. It's a joke. Making fun of mathematicians, physicists and engineers.
JKCalhoun 7y ago
You heard that in your engineering course.....

javajosh 7y ago

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 very large prime number is a message to all intelligent life capable of computing and deciphering it. This kind of message would penetrate even nested, simulated universes, and could only come from World 0, assuming the properties of numbers are independent of physical constants. Why not have a SETI-in-the-primes project, after all?

skissane 7y ago
> 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)
- javajosh 7y ago
  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 limiting your message to "a really big prime number" is to make discovery hard, but still tenable. It should be pretty big, like big enough for a good bible sized book, say 1 gigabyte, and start with something really obviously artificial, or unexpected looking, like starting as a 1 with 20,000 zeroes, or maybe better, 20k perfect 010101 and then after a few thousand, 00110011, and from there establish a language protocol, and write the book. But you'd have to expect people to check only primes for these simple patterns, because it's really easy to produce meaningful sequences with addition, and really hard with multiplication (AFAIK).
  - skissane 7y ago
    > 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.
    - javajosh 7y ago
      I meant that the entire message is "4", not just part of the message. Obviously we can pick a subset of digits of any large prime and find anything we want. However, the odds of a very large prime (like a gigabyte) looking intentionally ordered over its entire length seems vanishingly small. The only reason to limit ourselves to primes is because its trivial to produce a meaningful composite, and very difficult to produce a meaningful prime. Take this message; if I was to associate it with a number (say by joining its characters as 7-bit ASCII), my money is that it's composite. (Not sure what the odds are, but I'd take 100:1 odds). EDIT: period is `01110`, which is even, so I win.
      - skissane 7y ago
        > 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 though it is very small compared to the number of composite gigabyte-sized numbers, it is still unimaginably large in absolute terms.
        javajosh 7y ago
- zeveb 7y ago
  > 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/ https://libraryofbabel.info/ I don't know if anyone has ever found one, though.
nkrisc 7y ago
> 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.
- javajosh 7y ago
  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.
  - nkrisc 7y ago
    Then it shouldn't take nearly as long!

Tainnor 7y ago

that's not mathematical induction though. it's what philosophers call "induction", i.e. building theories out of empirical observations (as opposed to deduction; mathematical induction is weirdly named because it's actually purely deductive)

OJFord 7y ago

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 [...]'.

askvictor 7y ago
Yes, I know. It's a joke. Making fun of mathematicians, physicists and engineers.

JKCalhoun 7y ago

You heard that in your engineering course.....