14 ms·
Images Created from Prime Numbers
- aj7 7y agoWhat are the image errors?
- uyaij 7y agoExplanation from an article referenced by the linked article[1]: Most of the digits were fixed while the rest could be brute-forced using some useful properties. [1] https://www.futilitycloset.com/2017/09/10/trinity-hall-prime/ https://www.futilitycloset.com/2017/09/10/trinity-hall-prime...
- kijin 7y agoFrom the link: > approximately one in every 6200 2688-digit numbers is prime. So if you're lucky, you only need to brute force the last 4 digits! Maybe 5 if you're unlucky. In either case, that's a lot less work than I imagined. And of course you can skip all the even numbers.
- krackers 7y agoHow did you get 4 digits? Wouldn't that mean 1 in every 2^4 = 16 is prime? For 1 in every 6200 shouldn't it be 12 digits?
- pcmaffey 7y agoYou can skip all multiples of 3 also.
- BubRoss 7y agoYou skip all multiples of anything, but evens are easy to check.
- danwills 7y agoKinda more 'primes from images' (w/a tiny area that can't be used) than 'images from primes'. Still cool though!
- kff55 7y agoYou can generate these from any image here: https://geonnave.github.io/primg/ https://geonnave.github.io/primg/
- miguelmota 7y agoPretty cool although it struggled with certain very basic 2d images.
- nayuki 7y agoReminds me of this classic number: https://en.wikipedia.org/wiki/Illegal_prime https://en.wikipedia.org/wiki/Illegal_prime Basically: DeCSS source code (illegal) → compress → pad → add constant to make it prime.
- lonelappde 7y agoThat article talks about specious attempt to hack the legal system, by claiming information can never be legally restricted because it can encode numbers, but doesn't say the result of the attempt.
- cyborgx7 7y agoCopyright does make numbers illegal. I think it is less about "hacking" the legal system, and more about demonstrating how nonsensical it is.
- dTal 7y agoWhich it doesn't actually do. Whatever you think of copyright law, the nonsense lies in our contradictory intuition that information is "special" and numbers, even large ones, aren't. But beyond about, oh say, 128 bits[1], numbers take on all the properties we expect of "special" information. I can, for instance, encode a picture of you doing something embarrassing as a very large prime[2] number. Yet my protest of "it's just a prime number, bro!" isn't likely to calm you when I start passing it around to all your friends. Information is information. It's not unreasonable to have rules about the flow of information, however cleverly you've encoded it. [1] https://qntm.org/number https://qntm.org/number [2] The primality is of course totally irrelevant, but it makes it seem more "mathy"
- c3534l 7y agoIf I ever get a tattoo, I think it's going to be of that.
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- extr 7y agoWow. 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.
- ardit33 7y agoyou can encode any arbitrary information into a one dimensional value.... eg: a large enough number can encode the whole universe.... But decoding any meaningful information has to be at least in two dimensions.... In two dimensions, you can describe everything.... the other dimensions are not needed (and perhaps just emerging, according to the holographic principle)....
- lonelappde 7y ago> But decoding any meaningful information has to be at least in two dimensions.... What does this mean?
- goldenkey 7y agoIt's the uncertainty principle and principle of orthogonal observables. Energy vs time for example. You need two dimensions for a comparison. One dimension is static.
- jodrellblank 7y ago1GB of storage is a single number with 2^8billion binary digits. Everything we do in computers is encoding information in long numbers. Every character is a single number, every file is, every disk image is, every state of RAM, every database, every cache, every piece of source code.
- lonelappde 7y agoNot encoded as, but can be interpreted as. Any precisely specified object can be interpreted as a number.
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- snowwrestler 7y agoThere’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 images could be “hidden” in the primes... in the very structure of mathematics! But then I realized that with an infinite numbers of primes available to us, nothing is hidden. It’s more like the primes are simply building blocks for us to use in constructing images of whatever we want.
- lonelappde 7y agoNot quite true. Sagan's version was better than that analysis suggests: http://kasmana.people.cofc.edu/MATHFICT/mf55-spoiler.html 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.
- jon_richards 7y agoI’ve always assumed that was also the inspiration for one of the earliest xkcd’s: https://xkcd.com/10/ https://xkcd.com/10/
- EvanAnderson 7y agoI'd never read that analysis of the ending of Contact. Thanks for sharing!
- yesenadam 7y agoIt 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 infamous “Drake equation” for computing the probability of ETIs), who was raised “Very strong Baptist. Sunday school every Sunday,” made this observation: “A strong influence on me, and I think on a lot of SETI people, was the extensive exposure to fundamentalist religion. You find when you talk to people who have been active in SETI that there seems to be that thread. They were either exposed or bombarded with fundamentalist religion. So to some extent it is a reaction to firm religious upbringing”. Similarly, John Kraus recalled: “We were very strong churchgoers, members of the Methodist church. I was brought up in a very religious atmosphere…there was never any thought of conflict between science and religion in my thinking or in my upbringing. Science and religion were simply both seeking ultimate truth but using different ways of going at it”. ... ... One might speculate that SETI, as a highbrow, elitist revolution, contains within it quasi-religious and spiritual overtones, in the sense that these scientists, while not believing in God, do believe in ETIs, uniformly portrayed as higher intelligences who, having survived what might be a tendency in species toward self-destruction once advanced technologies are created, must also be morally superior. To the extent that religion involves belief in and hope for transcendence or transcendent beings, SETI is a high-cultural form of religion, and UFOs a low-cultural form of religion. The Measure Of A Life: Carl Sagan and the Science of Biography http://www.theeway.com/skepticc/newsworthy06.html http://www.theeway.com/skepticc/newsworthy06.html P.S. I was very much a child of Sagan and SETI! I was 15 when Cosmos aired, and read every Sagan book I could get my hands on, got a large telescope, became obsessed with astronomy for years... Reading about this religious dimension years later surprised me, it had never occurred to me. (My family was atheist)
- Causality1 7y agoReminds 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.
- MontyCarloHall 7y agoOnly if that irrational number is also normal (https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number), which pi has not been proven to be.
- kvakil 7y agoIn addition, even if a normal number was used, it's far simpler to describe the data by just using a single number alone. For example, a binary encoding of the data (perhaps using a prefix-free code). Using a normal number and two "positions" is just more complicated.
- mc3 7y agoNonetheless, it's freaky that our deepest secrets are encoded into pi. If pi is normal.
- tanelpoder 7y agoAlso, there will be multiple copies of data, some uncompressed, some compressed in different formats like gzip, lzo, etc.
- contravariant 7y agoAnd each copy will occur infinitely often.
- lonelappde 7y agoThis is yet another case where "prime" is bolted onto something for no particular reason to make it superficially more interesting. IMO this confused mathematical understanding. Approximately 1/n of all n-bit pieces of data (including bimaps) are prime.
- mc3 7y agoIt's like a magic trick. Amazing at first, then you sort of realize how they did it.
- tromp 7y agoIf you take a binary image, of length n bits, then the probability of some single bit flip producing a prime, is approximately 1 - (1 - 1/ln(2^n))^n ~ 0.76. Allowing 2 bit flips makes finding a prime as good as certain.
- tromp 7y agoIf you take any binary image, of length n bits, then the probability of some single bit flip producing a prime, is approximately 1 - (1 - 1/ln(2^n))^n ~ 1 - e^{-1 / ln(2)} ~ 0.76.
- war1025 7y agoSemi-related, but reading this article and thinking about it made me wonder if there is any study at all of "gray code" primes, for lack of a better word. Basically, prime numbers that differ by exactly one binary digit in their representation. Probably nothing about that relationship that would be interesting enough to look into beyond just "I ran some calculations and found these numbers that fit the pattern"
- oefrha 7y agoThis is just a weaker version of the twin prime conjecture. You’re asking for primes that differ by 2^k instead of 2. Last I heard the best result was from Polymath 8a. http://michaelnielsen.org/polymath1/index.php?title=Bounded_gaps_between_primes http://michaelnielsen.org/polymath1/index.php?title=Bounded_... Edit: Actually I was wrong, differing by a binary digit is much stronger than a difference of 2^k. But that’s a starting point.
- war1025 7y agoNeat. Thanks for tying it in to something real. Makes sense now that you phrase it that way. Not something I've ever looked into much.
- oefrha 7y agoActually I replied without thinking too much, sorry... Your question is (probably a fair bit) stronger than the one I related to. Edited.
- chairmanwow1 7y agoBig side note, but what you just exhibited is one of my favorite things about this community: admitting being wrong. It wasn’t really until the workplace where I encountered level-headed people that would just shrug their shoulders and say “You are right. I was wrong” and then move on. It’s so simple, but is amazingly powerful.
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- mkl 7y agoWe discussed a similar thing a couple of years ago: https://news.ycombinator.com/item?id=16192608 https://news.ycombinator.com/item?id=16192608 Here's a prime smiley face (with code) I generated at the time: https://news.ycombinator.com/item?id=16192922 https://news.ycombinator.com/item?id=16192922
- egypturnash 7y agoMostly unrelated but this made me check to see if the Prime Number Shitting Bear is still online. It is! https://alpha61.com/primenumbershittingbear/ https://alpha61.com/primenumbershittingbear/
- JKCalhoun 7y agoThe 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 ... experimental error, 11 is prime, 13 is prime, yes, they're all prime." The engineer thinks, "3 is prime, 5 is prime, 7 is prime, 9 is prime, 11 is prime, ..."
- askvictor 7y agoThe 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 agoIt 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
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- tus88 7y agoHow on earth did they verify a 30k long number is prime?!?
- peteretep 7y agoPerl's regex engine is really fast, so presumably: perl -lne '(1x$_) =~ /^1?$|^(11+?)\1+$/ || print "$_ is prime"'
- saagarjha 7y agoFor the curious: https://www.pixelstech.net/article/1324906920-A-Perl-Regular-Expression-That-Matches-Prime-Numbers https://www.pixelstech.net/article/1324906920-A-Perl-Regular...
- amelius 7y agoAnd a prime number showing Mickey Mouse? Or is it illegal because copyright?
- DannyB2 7y agoWith Mickey Mouse the issue is more likely trademark rather than copyright.
- tealpod 7y agoUsecase: In future when computers become intelligent and we(humans) want to communicate without computers understand, we can use this means :)
- dmurray 7y agoI 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_exist_a_prime_number_whose/ https://www.reddit.com/r/math/comments/7qpfls/does_there_exi... [1] A reddit commenter also found a "minimalist giraffe": 7.
- Agentlien 7y agoThat 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.
- nailer 7y agoThis would make a great conspiracy theory - that Mona Lisa was a prime number painted by Leonardo.
- pietroppeter 7y agowhat if instead we have an approximate representation of an image through a highly composed number? we end up with a number theoretic compression technique.
- rmeertens 7y agoHalf a year ago I made the same idea but with colour: http://www.pinchofintelligence.com/painting-by-prime-number/ http://www.pinchofintelligence.com/painting-by-prime-number/. It's interesting that we both took the Mona Lisa to visualise the concept :)