Near the end of the book, Contact, by Carl Sagan, the main character is told there are messages hidden deep in the base-11 digits of π.

From the Wikipedia article:

Acting on the suggestion of "Ted", Ellie works on a program to compute the digits of π to heretofore-unprecedented lengths. When Ellie looks at what the computer has found, she sees a circle rasterized from 0's and 1's that appear after 10^20 places in the base 11 representation of π. This not only provides evidence of her journey, but suggests that intelligence is behind the universe itself.

Somebody as smart as Carl Sagan should know that the creator(s) of the universe can no more change the value of π than they can change any other fact. Math itself must precede both the universe and anything or anyone that created it.

I could better believe a deity chose to hide a message inside the Fine-Structure Constant than in π.

Did Carl Sagan ever provide an explanation for how a deity would embed hidden messages deep inside the value of π?

I am looking for answers from the novel or from Carl Sagan's writings or interviews. I don't want answers from the movie, Contact, since that does not mention any messages hidden in the value of π.

  • 7
    Can you please clarify why you think God modified pi rather than just starting the universe with that particular value of pi? Or is that what you mean by "Math itself must precede both the universe and anything or anyone that created it."? Jul 10, 2018 at 6:56
  • 9
    @RichS - In philosophical terms, an omnipotent deity can change anything, even fundamental concepts. Or else it isn't omnipotent
    – Valorum
    Jul 10, 2018 at 7:06
  • 3
    I've voted to close. It looks like you're seeking a scientific explanation for how a deity would muck with fundamental concepts (e.g. whether it's actually possible).
    – Valorum
    Jul 10, 2018 at 7:10
  • 4
    @Valorum I am not asking for a scientific explanation. I am asking if the author provided an explanation for a logically impossible plot event. I don't see this as much different than asking how a different authors may explain faster-than-light travel in their stories, which is believed to be physically impossible.
    – RichS
    Jul 10, 2018 at 7:13
  • 5
    I'm not sure why I'd need an author statement to explain a material fact. Any more than I need one to say the sky is blue.
    – Jontia
    Jul 10, 2018 at 7:17

2 Answers 2



The whole point of the story was that the message in π was inexplicable. In other words, that it was a genuine miracle, real and irrefutable evidence for the existence of God.

Your story has been foretold. It's happened before. Somewhere inside of you, you must have known. None of your details are in the Book of Genesis. Of course not. How could they be? The Genesis account was right for the time of Jacob. Just as your witness is right for this time, for our time.

(Chapter 23, Reprogramming.)

Any attempt at explaining the inexplicable, describing the mechanism behind a miracle in human terms, would have fatally undermined the story. Granted, authors do occasionally undermine their own stories, but I consider it unlikely in this particular case.

To expand on that a little, I suspect that this quote from your question summarizes the reason that you feel there ought to be an explanation of some sort:

Math itself must precede both the universe and anything or anyone that created it.

... but that isn't a falsifiable statement; there is no meaningful way to argue either in favour or against this proposition. There is therefore no particular reason to believe that Dr. Sagan considered your proposition to be so obviously and objectively true that it did not make sense to even speculate about a universe in which it is not.

It is of course your prerogative to consider him wrong in that respect. But even if that is so, even very smart people can be wrong sometimes. It is more likely in my opinion that he simply didn't consider it to be a problem than that he believed it to be a problem but had come up with some complicated excuse to put it in the story anyway.

I leave you with The Parable of Hemlock:

Logic never dictates any empirical question; it never settles any real-world query which could, by any stretch of the imagination, go either way.

  • All that said, I will of course delete this answer if someone finds a quote that contradicts me. Jul 11, 2018 at 0:56
  • 1
    This is as silly as saying 1+1=3. If Sagan put "1+1=3" into his story, would you defend that as a miracle?
    – user89104
    Jul 11, 2018 at 5:34
  • 1
    You say "1+1=3" means the universe would be incomprehensible, but believe a message can be hidden in pi? You can't change pi any more than you can make 1+1=3. They are both wrong.
    – user89104
    Jul 11, 2018 at 6:57
  • 1
    @LincolnMan, but you're perfectly happy with direwolves? I find that baffling. Jul 11, 2018 at 8:19
  • 4
    @LincolnMan, we know that 1+1 does not equal 3. so this can't be our universe. we do not know (yet) if there's a message hidden in pi.
    – ths
    Jul 11, 2018 at 8:51

My original comment said;

The digits of pi are infinite and the message is only "part" of the value. Given that as a starting point and complete freedom to describe the method of encoding any message you like can be hidden within the value of pi.

Now bear in mind we've only calculated the 2,000,000,000,000,000th position of pi. That's 2*10^15 in base 10. That's 1 million times smaller than the starting point for Sagan's message. And most online pi searches cap out a lot lower.

If we use a simple A1Z26 encoding, that is replace the letter A with 1, B with 2 and so on with Z as 26. I can find the RichS written in Pi at 10,319,866.

Encoder RichS = 1893819
Searcher Your name is at; Position 10,319,866 counting from the first digit after the decimal point. The 3. is not counted.

Given more flexibility, the choice of base, more digits to work from and different ciphers, quite literally every message is in there somewhere.

  • 2
    @user14111 I saw that in the comments above. I guess my response is why would he need to? To quote Vernor Vinge from the great Marooned in Realtime. "You can find any message you want in there if the coding scheme is nutty enough".
    – Jontia
    Jul 10, 2018 at 7:22
  • 6
    This answer is not even wrong. It missed the point of the question.
    – user89104
    Jul 10, 2018 at 7:25
  • 3
    @user14111 there's not even any evidence that anyone has made this critique before, so why would the author respond to it? Further, the critique is based on a false premise / misunderstanding. It's like asking "what did Sagan have to say about spelling Contact with a C?" - well, nothing, because that's how it's spelled.
    – OrangeDog
    Jul 10, 2018 at 11:17
  • 6
    The point made by this answer is addressed and refuted within the story itself. The important thjng is not that the message exists (as is pointed out, all finite messages exist somewhere in pi), but that it occurs inexplicably early, whereas the expected position of such a message is many orders of magnitude further into the sequence.
    – Jules
    Jul 10, 2018 at 12:40
  • 2
    (Now, I personally am not comfortable with this argument which seems non conclusive to me, but then again reflecting on the theme of the book I suspect I'm not supposed to be comfortable with it. But the point remains that Sagan seems to be suggesting that it was possible that the message was intentionally placed there, therefore the question is valid: how did he believe this would have been achieved?)
    – Jules
    Jul 10, 2018 at 12:45

Not the answer you're looking for? Browse other questions tagged or ask your own question.