as an infinte random string of values, the digits of pi will, sooner or later, contain any specific string of values.
i think it was Sagan’s “Contact” where aliens sent a message to read the digits of pi from the x th place to the y th place, and that stretch could be read as instructions on how to build a machine to reply.
It is believed that pi is “absolutely normal” in the strict mathematical definition: that in any base numbering system, any finite sequence of digits appears as frequently as any other sequence of that length. If that’s true, then yes, a particular binary string, including one that corresponds to a particular digital file (like a particular mp4 file), can be found in pi.
That said, it hasn’t actually been proven that pi is normal. If it’s not normal, then the number can be infinitely non-repeating and still never hit that particular sequence of digits.
as an infinte random string of values, the digits of pi will, sooner or later, contain any specific string of values.
i think it was Sagan’s “Contact” where aliens sent a message to read the digits of pi from the x th place to the y th place, and that stretch could be read as instructions on how to build a machine to reply.
It is believed that pi is “absolutely normal” in the strict mathematical definition: that in any base numbering system, any finite sequence of digits appears as frequently as any other sequence of that length. If that’s true, then yes, a particular binary string, including one that corresponds to a particular digital file (like a particular mp4 file), can be found in pi.
That said, it hasn’t actually been proven that pi is normal. If it’s not normal, then the number can be infinitely non-repeating and still never hit that particular sequence of digits.