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Decius comments on The Emergence of Math - Less Wrong
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That's an interesting question, and I have no idea about the answer.. If aliens asked me to define e, I'd start talking about exponential functions that were their own derivative. But I have no idea if that's the historical motivation for noticing e.
Pi is obviously much easier, since it is part of the ratios linking circle diameter to circle perimeter and circle area.
If I had to explain Pi to real aliens that somehow understood English but not our mathematics, I would start with straight lines of a fixed length (radius) that share one (fixed) endpoint and where the other (movable) endpoints get gradually closer and closer.
Some multiple of pi is the ratio you apparently get as you compare those lengths and extrapolate for infinitely-closer-and-closer lines.
Sounds simple enough, as far as explaining abstract concepts to real aliens goes.
In my imagination, I have a chalkboard, but no other ability to communicate. So, lots of drawing circles (with emphasis on diameters and circumferences).