That is, being a normalized random string of infinite digits, if one converted the string to binary, ascii, or what have you, as the myth goes: If you search long enough you can find the complete works of Shakespeare, an image of the Titanic as it’s sinking, the movie π encoded in h264, plans to build a nuke, images of life on another planet, or even the equations of the grand unified theory, etc.
But, of course, you’d need to know what to look for, and might need next to an infinite amount of time, as well as weed through an infinite amount of gibberish. Despite that, has anybody attempted to find something—anything—even if it just be the words, “Never tell me the odds.” or this emoticon: ?
On average, for a search string of length n bits, you’d expect to have to look through something on the order of 2^n bits of pi before you found it (though of course, you might find it earlier or later). The string “Never tell me the odds.”, assuming ASCII encoding, would be 184 bits, meaning you’d need 2^184 bits of pi, or 2.5e55, to have a reasonable expectation of finding it. Nobody’s searched anywhere remotely near that far, so I highly doubt that that string has ever been found. On the other hand, “:)” is only 16 bits (again, assuming ASCII encoding, and also assuming that we want the characters and not the image), so you’d expect to find it somewhere in the first 66000 or so digits, more or less. That much, people have done, so the smiley face probably has been found.
Sounds like this could be the basis for a hobby: The Pi Searchers Club. You try out different coding schemes and, when you find something interesting, you share it online. Maybe “disco sucks” or a 16-pixel portrait of Abraham Lincoln.
I believe that those are the odds of finding that specific 184 bit phrase. It you look for any 184 bit phrase that is meaningful in English (or in any other language) then the odds grow much, much better.
Assuming there’s tools on the net that have pi converted to ASCII, let’s do it! 66-thousand digits doesn’t seem like it’d take long at all to search. Hell, a million should be a breeze, no?
Anyone want to take a crack at finding the ASCII encoded characters for this .gif in pi?
The problem is that whatever coding scheme you use is going to be arbitrary—you could use one in which “[noparse]:)[/noparse]” maps to “14”, then it’s right there in the beginning. (Nevertheless, what Chronos says remains true, statistically, for any appropriate—say, Shannon-Fano—code.)
I remember reading about this phenomena in a scientific research magazine while waiting in a doctor’s office a few years back. The researchers, mainly graduate students from MIT, I think, had discovered bit string that translated into an image that eerily resembled Richard Nixon. Here’s a link to the image: LINK.
search string found at binary index = 2729541692
binary pi : 1100100001010011000110000000000010000010000101111111110011111110
binary string: 0101001100011000000000001000
hex pi : 4d3f224e5763dfd833a3fc85318008217fcfe5503a4a1545
hex string: 5318008
Has every possible three digit sequence been found? Four?
What is the longest string of the same number consecutive? The same number however many times in a row might be where the idea that every possible sequence will come out eventually. Can we know what is the theoretical longest possible string of the same number in a consecutively?
What, other than convention, singles out the .gif format, as opposed to other formats like .jpeg, .bmp and so on? Or something else entirely?
Ultimately, that picture is just a set of pixels lighting up on a screen. How you code for that is (within the limits that make a code reasonable) entirely arbitrary. A code exists such that the first few digits of π represent the image, a code exists such that it only occurs after the umptillionth one, and so on.
There is no theoretical longest possible string of the same consecutive digit. If pi is indeed normal (and maybe even if it’s not) its digits could contain consecutive sequences of any particular finite length.
?
in pi?