This was a group of physicists, after all! The problem with some beautiful physics equations is that -- properly interpreted -- they can be trivial. They may have taken the whole human race thousands of years to figure them out, but once we get our heads screwed on straight, they are not only obvious, but so necessary that they are built into the foundations of nature. E.g., F=ma is no longer an equation, but a definition. Euler's equation is apparently a favorite of kooks here in Southern California -- last year a nut scrawled this on the windshields of 50 or so brand new SUV's that he trashed. The problem with "imaginary numbers" is that other civilizations might not attach the same importance to them that we do. We like them (as opposed to quaternion, for instance), because they lead to a much richer calculus & analysis. But some other civilization might consider them just one of a whole spectrum of "numbers" that can be derived from matrix representations. The whole "geometric algebra" movement might end up transforming "school math" in a revolution similar to the vector revolution of Gibbs, et al. Although many would claim that "geometric algebra" provides no new theorems, its regularization (i.e., the elimination of so many special cases) of geometric calculations may lead to its quick uptake among engineers and computer software people. So, I think a proper illustration of Euler's equation might be something akin to the "proofs without words" that one finds in some math publications, so that the beauty isn't lost to someone who doesn't understand the notation. I've looked through a number of old books on math -- e.g., translations of Cardano, etc. -- and much of their idea of beauty in these equations is not evident to modern eyes, because they deal with special cases, not the "general" case. Other civilizations looking at Euler's equation may feel the same way, because they have discovered an even more profound equation, of which Euler's is only a special case. At 11:54 AM 10/8/2004, Simon Plouffe wrote:
Hello,
they made a poll asking what are the most beautiful equations to a group of people.
http://news.bbc.co.uk/1/hi/magazine/3721406.stm
Euler's equation came second : exp(Pi * i) + 1 = 0.
Maxwell equation came first. I think that these people are in physics.
Nevertheless, I am wondering what if we would make a kind of message to extra-terrestrial intelligence and we would like to show them that we know all these things.
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?
Any clue?
ps : E = Mc^2 is only the 6'th.
Simon Plouffe