Alert! We've struck a Snoreburg; We're Taking on Sleep, and Sinking Rapidly!

[swestrup]

... Actually I think I said it all in the title.

I'm now a very sleeply Sti, and plan to head off to bed as soon as my teeth are brushed. On the good side of things, I finally have (I believe) postfix correctly configured in all of the various particulars. On the other hand, I just discovered that there is something wrong in my courier-imap setup.  :-/

Oh well, it only affects a class of accounts that I'm not using at the moment, and it should be easy enough to find and fix tomorrow.

Comments

Here's a math paradox for you

[(Anonymous)]

Wed, 4 Aug 2004 10:15:00 EDT (-0400)

Stirling,

While you sleep, here's a math paradox for you...

I suddenly started wondering about the term e^(2*pi*i).

This prompted me to think:
One to the power of anything is still one, right? ie 1^x = 1.
(a^b)^c = a^(b*c), right?
e^(i*pi) = -1, right?
so e^(2*i*pi) = 1, because the square of negative one is one, right?
and e^(ix) can equal e^[2*pi*i*(x/(2*pi)] anytime, right?
This equals [e^(2*pi*i)]^[x/(2*pi)] = [1]^[x/(2*pi)] = 1, right? (??)
So how can e^(ix) ever be anything but 1?

Can you spot the fallacy? I'm stumped right now.

I know that e^(i*pi) = cos(x) + i*sin(x) and could be evaluated
that way, but math should generally be consistent, right? Are we
hitting Godel's theorem already?

I don't suppose I've just disproved all of electronic
communication theory and sinusoidal steady state (S^3 or S^4)
alternating current theory. That's it! No wonder we never use
this stuff out in the real world!

-Jim

Re: Here's a math paradox for you

[(Anonymous)]

Wed, 4 Aug 2004 15:07:00 EDT (-0400)
>I know that e^(i*pi) = cos(x) + i*sin(x)
whoops -- that's "x", not "pi".

I found some information using Al Gore's wonderful invention, and
posted it on my own website:
http://www.geocities.com/jameswi.geo/Science/expParadox.htm
(see http://groups.google.ca/groups?q=exp(i+always+equals+1&hl=en&lr=&ie=UTF-8&selm=1993Nov13.163828.28823%40galois.mit.edu&rnum=6)
-Jim