[randallsquared]

The Babylonians used based 60 for at least some things, but even that seems unwieldy, and even taking everything in between as equally useful provides only 58 distinct sequences of digits in pi.

The control implied is basically the power to create all the universes laws (and the math we can learn in it) from scratch.

[jecel]

It has been a very long time since I read the book, but if I remember correctly the first message was actually found in base 11 (a picture of a circle).

Back then it hadn't been decided yet if the distribution of the digits of pi are such that all finite numbers can be found in it or not. Some years ago I read about some proof that they can. That means that "Carl Sagan was right!" in whatever encoding you like can be found in pi is you look deep enough.

The thing is what does "deep enough" mean? If we consider some two digit decimal number, like 27, then the chance that it isn't the first two digits is 99%. The chance that it isn't the first two nor the second and third digits is 98.01% and so on. The chance of not finding it among the first 500 digits is less than 0.6%. But unlikely things can still happen, so finding a message "too near the start" might convince some people that pi was created by an intelligence but wouldn't really be a good proof.

[RustyRussell]

Yes, your recollection matches mine. Various bases were searched, after being given a hint.

The point was that this is what proof of a Creator would look like (and the aliens suggested there were others).

It was, IMHO, a giant gauntlet thrown down to religious folk. And elegantly done, too.

[kevinventullo]

Back then it hadn't been decided yet if the distribution of the digits of pi are such that all finite numbers can be found in it or not. Some years ago I read about some proof that they can.

I would be curious to hear more. As far as I know that is still a conjecture.

[jecel]

I was not able to find the reference and I didn't read it carefully back then so might have misunderstood what was being proved.