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We detected music and video encoded in radio signals from Alpha Centauri. We want to aim a large radio telescope there and blast them with something that's going to get their attention, something simple that shows we're intelligent.

That header would be followed by complex information that would be more difficult to decrypt.

One way would be to transmit a series of pulses representing prime numbers, repeatedly. But there has been discussion on the philosophy stax about whether that is necessarily an artificial sequence. Like, harmonics night cause it.

If you wanted to transmit the first n digits of Pi and transmitted it as 3, 1, 4, 1... That would be easily recognizable, but only to creatures who use base 10.

So how would you transmit it? How can you indicate where the decimal point goes?

There's a simple n-digit magic number that acts like an ID card for intelligence. All you have to do is transmit it, with no other information.

Is it even possible to encode Pi so it's recognizable as Pi?

Or does this belong in the world-building stax?

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    $\begingroup$ It is recognisable as base 10 (once you transmit enough digits) because there are only 10 distinct symbols $\endgroup$
    – Benjamin Wang
    Commented Dec 3 at 8:02
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    $\begingroup$ I think this would be a better fit on world building. As stated I don't think there is a unique correct answer. $\endgroup$
    – quarague
    Commented Dec 3 at 8:39
  • $\begingroup$ Hi, this has a possible answer here: puzzling.stackexchange.com/questions/120109/… $\endgroup$
    – David
    Commented Dec 3 at 10:09
  • $\begingroup$ It's going to make a difference if you can understand or influence Alpha Centauri's culture or calendar. $\endgroup$
    – David
    Commented Dec 3 at 10:12
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    $\begingroup$ @BenjaminWang > == EEE-YESS! I think that's the answer. Just do it in base 10. $\endgroup$
    – Miss Understands
    Commented Dec 3 at 12:42

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I have to go now, so I expect to extend my answer when I shall return, but a natural idea is

to encode $\pi$ in binary as $11.001\dots$.

To avoid the decimal point encoding problem we can

to encode $\pi/4$ instead as $.11001\dots$.

PS. But if we already know how music and video are encoded in their radio signals then

we can send to them already prepared Voyager_Golden_Record.

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