Half a year ago I made the same idea but with colour: http://www.pinchofintelligence.com/painting-by-prime-number/. It's interesting that we both took the Mona Lisa to visualise the concept :)
Images Created from Prime Numbers
81–90 of 131 posts
Re: Images Created from Prime Numbers
#82Earlier 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…
> 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)
Re: Images Created from Prime Numbers
#83There’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.…
Your argument is true; though constructing images with numbers divisible by 1000000 is far easier. Take any image you want, and replace the last figures by zeroes. You'll just get a small artefact in the bottom right corner!
Re: Images Created from Prime Numbers
#84Mostly unrelated but this made me check to see if the Prime Number Shitting Bear is still online. It is! https://alpha61.com/primenumbershittingbear/
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 engineer thinks, "3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, ..."
Surely the engineer would round it to the nearest power of ten and thus discount all of the numbers?
Re: Images Created from Prime Numbers
#85How on earth did they verify a 30k long number is prime?!?
Perl's regex engine is really fast, so presumably: perl -lne '(1x$_) =~ /^1?$|^(11+?)\1+$/ || print "$_ is prime"'
For the curious: https://www.pixelstech.net/article/1324906920-A-Perl-Regular...
Re: Images Created from Prime Numbers
#86Reminds 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.
The problem is that the index itself becomes so large, even you use a dataset-optimised number instead of pi, that it's much worse than just storing the original data.
Oh certainly. I was just thinking of it as a way to get around intellectual property laws.
Re: Images Created from Prime Numbers
#87Mostly unrelated but this made me check to see if the Prime Number Shitting Bear is still online. It is! https://alpha61.com/primenumbershittingbear/
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 ...…
Surely the mathematician would think “if all odd numbers were prime then the Riemann hypothesis would be trivially false, so obviously they cannot be”.
Re: Images Created from Prime Numbers
#88Earlier 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)
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).
Re: Images Created from Prime Numbers
#89Earlier 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 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)
Re: Images Created from Prime Numbers
#90Mostly unrelated but this made me check to see if the Prime Number Shitting Bear is still online. It is! https://alpha61.com/primenumbershittingbear/
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 ...…
Yes, and the programmer thinks: "3 is prime, 5 is prime, 7 is prime, 9 is not prime, 9 is not prime, 9 is not prime, …"