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The problem is that such a language may have a mathematical basis but that alone wouldn't be able to convey anything besides mathematics. It can demonstrate intelligence, as used in Carl Sagan's novel Contact by broadcasting a sequence of prime numbers — but that doesn't exactly constitute a language.

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You could probably move from math to chemistry/physics. Of course all the 'constants' are arbitrary numbers based on the measuring system used, but going from elements to DNA to cloning to emotion should at least in theory be possible if you had enough time and intelligence.

This is, in fact, solvable; you can use plank units, which result from setting universal constants to 1. As an example, setting the speed of light to 1 means that time can now be measured in meters.

https://en.wikipedia.org/wiki/Planck_units

You still have the challenge of choosing a base system. Remember we are base 10 simply because of biology. Our alien friends may be on a different number base because they have 7 fingers.

It ought to be possible to deal with that by enumerating each possible digit. And then showing a representation of some kind of fundamental concept like PI/TAU that's easy to make a diagram of. Each side shows their digits and their representation and at that point we can determine conversions between the bases.

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