FROM : Jens Alfke
DATE : Sun May 25 21:51:15 2008
On 25 May '08, at 11:58 AM, Hamish Allan wrote:
> What this thread has reminded me of is an ongoing conversation I have
> with a friend of mine, who refuses to countenance the square root of
> minus one, because he doesn't think it means anything.
It also reminded me of the fact that Isaac Asimov never managed to
learn calculus; he said it seemed like some conceptual wall he
couldn't get over. Didn't stop him from getting a Ph.D in
biochemistry, inventing thiotimoline and positronic AI, and writing a
few hundred books on science...
I hit a similar wall in number theory, trying to understand finite
fields. I managed to visualize how they worked for an hour or two
while working on a homework set, but lost it after that, like some
ecstatic vision of Heaven shown to a mystic, which he can never
remember the details of afterwards.
In my case I dropped the class, and later my math major*. I hope that
doesn't sound too discouraging. I somehow found plenty of interesting
things to work on that didn't involve bijective isomorphisms of finite
abelian groups.
I don't know what to suggest, Jonny ... I think we've all hit the
limits of how vigorously we can wave our hands about the concept in an
email thread. Taking a break from it would be a good idea, for all of
us.
—Jens
* to be honest, the math major dropped me. I was kind of crushed,
actually. But she later saw the error of her ways, though I eventually
married an astronomer.
DATE : Sun May 25 21:51:15 2008
On 25 May '08, at 11:58 AM, Hamish Allan wrote:
> What this thread has reminded me of is an ongoing conversation I have
> with a friend of mine, who refuses to countenance the square root of
> minus one, because he doesn't think it means anything.
It also reminded me of the fact that Isaac Asimov never managed to
learn calculus; he said it seemed like some conceptual wall he
couldn't get over. Didn't stop him from getting a Ph.D in
biochemistry, inventing thiotimoline and positronic AI, and writing a
few hundred books on science...
I hit a similar wall in number theory, trying to understand finite
fields. I managed to visualize how they worked for an hour or two
while working on a homework set, but lost it after that, like some
ecstatic vision of Heaven shown to a mystic, which he can never
remember the details of afterwards.
In my case I dropped the class, and later my math major*. I hope that
doesn't sound too discouraging. I somehow found plenty of interesting
things to work on that didn't involve bijective isomorphisms of finite
abelian groups.
I don't know what to suggest, Jonny ... I think we've all hit the
limits of how vigorously we can wave our hands about the concept in an
email thread. Taking a break from it would be a good idea, for all of
us.
—Jens
* to be honest, the math major dropped me. I was kind of crushed,
actually. But she later saw the error of her ways, though I eventually
married an astronomer.
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