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That "log(e^i x pi) = i x pi" is not self-evident at all. The only reason you know it is because you attended a math class and your professor made you solve 60

That "log(e^i x pi) = i x pi" is not self-evident at all. The only reason you know it is because you attended a math class and your professor made you solve 60 problems from a $1,000 textbook until you memorized it. I don't even know what "e^i x pi" means. How does that translate into C notation? Is it pow(e, i) * pi, or is it pow(e, i) * x * pi, or is it something else entirely?

tsimionescu 6y ago
Unfortunately, the text inputs I have available are not good enough to represent the actual maths notation, which is extremely clear in this respect: it would have an e, and then in the superscript, i π. Since this is such a well known formula (Euler's Identity), I didn't think it would be a problem. In C notation, this would be pow(e, i * π). Or maybe pow(i*π, e), I don't remember and the notation is pretty bad. And the point about exponentiation is very simple, and I didn't need to do hundreds of exercises to remember: the natural logarithm of e raised to some X is X, whatever that X may be. The other commenter's note was that raising some constant to an imaginary number is a very obscure way of expressing the geometric operation that this represents (multiplying by e^iπ is equivalent to rotating a complex number by a half circle). I was pointing out that, while that is true, it loses the algebraic interpretation, which also has value.
- oalae5niMiel7qu 6y ago
  I agree with the other poster. If you can memorize log(e^N) = N, you could have memorized other notations for expressing the same. Math notation doesn't make Euler's Identity self-evident, and can be used to obscure the geometric operations taking place. To those who haven't memorized Euler's Identity (I'm aware of it due to your comment, but will probably forget it in a day or two), this "self-evident" truth is invisible no matter which notation is used. C notation is bad, but has the advantage of being precisely representable in ASCII. To post math notation you'd need to upload a PNG somewhere.

tsimionescu 6y ago

Unfortunately, the text inputs I have available are not good enough to represent the actual maths notation, which is extremely clear in this respect: it would have an e, and then in the superscript, i π. Since this is such a well known formula (Euler's Identity), I didn't think it would be a problem. In C notation, this would be pow(e, i * π). Or maybe pow(i*π, e), I don't remember and the notation is pretty bad. And the point about exponentiation is very simple, and I didn't need to do hundreds of exercises to remember: the natural logarithm of e raised to some X is X, whatever that X may be. The other commenter's note was that raising some constant to an imaginary number is a very obscure way of expressing the geometric operation that this represents (multiplying by e^iπ is equivalent to rotating a complex number by a half circle). I was pointing out that, while that is true, it loses the algebraic interpretation, which also has value.

oalae5niMiel7qu 6y ago
I agree with the other poster. If you can memorize log(e^N) = N, you could have memorized other notations for expressing the same. Math notation doesn't make Euler's Identity self-evident, and can be used to obscure the geometric operations taking place. To those who haven't memorized Euler's Identity (I'm aware of it due to your comment, but will probably forget it in a day or two), this "self-evident" truth is invisible no matter which notation is used. C notation is bad, but has the advantage of being precisely representable in ASCII. To post math notation you'd need to upload a PNG somewhere.