Simon asks: << What would be the best way to write them down in a universal language because for ET the equation exp(Pi*i)+1=0 means nothing at all if we can't explain what is Pi, e, 1, 0 and the equal sign, isn't?
Cool question! It may be self-evident that multiple vertical strokes signify 1,2,3,...: |, ||, |||, . . . A few simple equations like | + | = || and || + ||| = ||||| should reveal the meanings of + and =. A circle with one diameter drawn in, labeled | could reveal pi by showing a sequence of increasingly unrolled circles, culminating in a straight line, all the while keeping its length constant. This straight line can be labeled with the symbol pi. (The meaning of labeling could be explained by showing two diameters end to end labeled ||, three labeled |||, etc.) If E.T. knows anything about exp, then by this point they will recognize the series definition for exp(z) (for simplicity, call it e(z)) without further explanation: e(z) = | + z/(|) + zz/(|| |) + zzz/(||| || |) + ... Now writing | + -| = -| + | = should explain the minus sign, and finally i i = -| should yield the (ambiguous) meaning of i. Finally, e(pi i) + | = ought to be clear to any being who's familiar with it, irrespective of their symbology for it (assuming they use symbols!). --Dan