Since Pi is believed to be normal in the sense that any numerical sequence in it’s decimal expansion should appear randomly, and because we currently know the decimal expansion of Pi to 31 trillion digits, then given some suitable scheme for translating digits into letters are there any known short phrases appearing in Pi? Something like “Hello John” for example?
ETA: especially if you expressed Pi in base-26 perhaps.
If you don’t have the hardware to work it out in base 26, you may as well make up any scheme you want. For instance, A = 01, B = 02, … Or 7-bit ASCII for the binary expansion of pi…
Instead of using base-26, why not just treat the bits of pi as an arithmetic code, and “decrypt” that “compressed file” using the trigraph statistics of King James’ Bible. I happen to have code that does just that right here, next to my fingertips.
Doing this with the first million bits of pi I get about 1000 lines of text, of which this excerpt is typical:
I tried seeding with Shakespeare’s Complete Works rather than the King James Bible.
I just googled <pi base-26 messages> and the first hit lists some of the first few messages, with a lot of info on the supporting mathematics and other observations.
Note though that they don’t seem to have noticed that the very first 5 characters after the decimal place are “Dr SQL”…I googled *that *and incredibly, there is no product yet so named…
If you use A=01, B=02, … Z=26 and " "=00 then
John (10150814) appears at digit 95,782,881
Hello (0805121215) sadly does not appear in the first 100 million digits.
I’ve often wondered what sort of message one might hope for. I envisage something like:
“Hello! You got here at last! There now follow instructions on how to make an anti-gravity machine…”
Of course the fact it was in English might be even more notable.
I was thinking Latin, or Aramaic, or some cro-magon language.
I looked out to a billion digits.
Hello (0805121215) appears at position 390,990,395.
John (10150814) appears 12 times in the first billion digits.
God (071504) first appears at 386,707, then at 396,745, 1,222,168, 1,735,723, etc. I count 1007 occurrences of God in the first billion digits. That guy is always scribbling his name on everything. In fact, YHVH (25082208) occurs 8 times too. And Allah (0112120108) appears once at 596,539,269.
Of the people posting in this thread, only DPRK appears, at positions 16,285,229 and 93,869,933.
What about the other 8,999,999,997 names?
From Post #3 above:
So that’s straight-up Chaucer!
I’m expecting “So long and thanks for all the fish.”
About twenty years ago, there was an Internet program that you could run to simulate a large number of monkeys typing randomly to see if any random string corresponded with text from Shakespeare’s plays. After a ridiculous amount of simulated time (billions of years) passed, the best result was about 24 characters.
Monkeys had a damn union.
The OP is a major plot point in the novel Contact by Carl Sagan.
Of course, with a ‘suitable’ coding scheme, you can get whatever result you want. Here, I’m going to use a scheme where I pick 1,000 common English words (and given names) and assign each one a three-decimal-digit number from 000 to 999. I just made my list and it turns out “Hello” ends up as 314, and 151 encodes to John. Mathematically, this is no more arbitrary than 01=“a”, etc.
So, look, we can find “Hello John” immediately! How amazing!. Unless you think we should only start after the decimal point. In my system 141 is the word “random” and 519 decodes to “noise”, so we get quite a different result. Hmm
But even though it’s just arbitrary, just for fun I’d still like someone to do some emoji-result decoding of Pi’s digits.
Yes, the OP specifically said ‘letters’, not word-by-word, but it’s a lot easier to make the point this way.
That’s because “Pi is shy”. 
And septimus’s encoding scheme is designed to make it easy to get common English words, so it’s no surprise that most of it looks mostly like English words.
One interesting experiment would convert the digits of Pi to letters in a way that was statistically consistent with normal language. Just writing Pi in base 26 means all the letters should come up about equally, but that’s not typical. In typical texts, certain letters come up more often than most. According to this table, E is 11.2%, A is 8.5%, R is 7.6%… For example, write Pi in base 1000. Then 112 of the digits would be assigned to E, 85 digits would be assigned to A, 76 digits assigned to R, and so on. This should produce text that was much more likely to correspond to actual words and phrases.
Isn’t this kinda-sorta what septimus is doing in Post #3, and which Chronos notes in the post just above?
Can you explain all of that please? What are trigraphs, what does it mean to have them on a King James Bible, why that book and not some other book, and why do you have this at all?
Maybe. I suppose it could be. I guess I didn’t understand what was meant when septimus said “Instead of using base-26, why not just treat the bits of pi as an arithmetic code, and “decrypt” that “compressed file” using the trigraph statistics of King James’ Bible”