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You might be surprised to learn that π! (pi factorial) is a thing that makes sense
π! = 7.1880827289760327020821943451247587185593017639684371624100356994...
If you use a external pallete (one that is not coming from the pi digits themselves) I don't think it's that interesting. With any random set of data you can find a pallete that approximates the desired result
I converted the smallest valid GIF file[1] (35 bytes) into decimal number: 540959129019042423917857241427143195931235689921032801204995597056286563376232988672
It's nowhere to be found in PI :) I couldn't even find "GIF87a". So, fuzzy search seems to be a must.
[1] https://stackoverflow.com/questions/2570633/smallest-filesiz...
It’s kind of obvious that they are cheating: 23,074,248th through 23,075,235th hexadecimal digits is approximately 500 bytes. Finding 500 exact bytes in a random sequence would take a very long expected sequence :-) They do explain what they do: https://kundor.github.io/Cheating-images/
I find their methodology for evaluating candidate Waldos to be as sufficient as any other.
What I mean is, they could certainly choose a much harder evaluation criteria and fail, but that's not much of a blog.
This deeply reminds me of Carl Sagan's science fiction novel, Contact.
(spoilers to the novel follow, so avoid if you haven't read it)
The film adaptation missed out on so much, and the treatment of pi is one such unfortunate omission (or simplification).
The novel's aliens were advanced, but they told the main character that even they were stumped by the clear messages left encoded deep within the universe's constants.
It made the ending to the book so much more profound and touching than the film.
Carl was a master of making us feel small, all the while opening up our imaginations to infinities beyond measure.
> The pixel data in this gif are the 23,074,248th through 23,075,235th hexadecimal digits of π! You might be surprised to learn that π! (pi factorial) is a thing that makes sense π! = 7.1880827289760327020821943451247587185593017639684371624100356994... https://www.wolframalpha.com/input?i=pi%21
> The pixel data in this gif are the 23,074,248th through 23,075,235th hexadecimal digits of π! You might be surprised to learn that π! (pi factorial) is a thing that makes sense π! = 7.1880827289760327020821943451247587185593017639684371624100356994... https://www.wolframalpha.com/input?i=pi%21
It’s kind of obvious that they are cheating: 23,074,248th through 23,075,235th hexadecimal digits is approximately 500 bytes. Finding 500 exact bytes in a random sequence would take a very long expected sequence :-) They do explain what they do: https://kundor.github.io/Cheating-images/
But they're not finding exact bytes, they're finding something that very vaguely looks like something very vague. It also helps a lot that it's a face and human brains are very good at identifying faces.
The number of 500 bytes that would "look like" waldo is a lot higher than 1.
If you use a external pallete (one that is not coming from the pi digits themselves) I don't think it's that interesting. With any random set of data you can find a pallete that approximates the desired result
So often, people observe patterns in nature that appear to be so unlikely as to be by design. I have family members that are superstitious: if a light flickers at the same time that they mention a recently deceased loved one, it must be "a sign". Similarly, they will point to some overwhelmingly unlikely occurrence in the news, and ask, "how do you explain that?" The answer is usually random chance (if not deceit). And this exercise is a good illustration of that.
"Waldo, in the digits of pi?!? What are the odds??" - To the outsider who is not scientifically minded, this just looks so coincidental as to be magic. But almost any pattern can be found in randomness. It's just that the size of the necessary search space explodes as the query becomes larger / more specific.
The average HN reader knows all this, but the Waldo story is still a cool way to describe it to other people.
If you use a external pallete (one that is not coming from the pi digits themselves) I don't think it's that interesting. With any random set of data you can find a pallete that approximates the desired result
Can someone explain to me where the palette is defined? If it's not in the bytes of waldo.gif, is it provided by the website itself? If I save the gif file, I still see it as the same on my computer. Is it not true that the bytes of the gif actually 100% match the bytes of pi? Is there some extra metadata not included in the bytes of the file itself? If I were to send those bytes over the wire and save them to a file…
The GIF file as stored on disk has extra headers, and the pixel data's been compressed. So the whole file isn't found in the digits of π, just the pixel data itself.
I'd guess the chance of actually finding a correctly formatted full GIF file in contiguous bytes of π is effectively nil.