The Samovar


10 dimensional spheres are odder than you might think
February 14, 2007, 2:14 am
Filed under: Mathematics

Read this blog if you want to know why (it’s not at all technical and it’s quite amazing).

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10 Comments

That’s a fascinating rave review. I’ve no idea why you’re so excited by it – but I trust you that it’s exciting. It’s one of those times where I really wish I had the equipment to understand just why something is so good. I’ve managed it with Captain Beefheart. And Oysters. I haven’t figured out Opera yet.

Comment by Edward the Bonobo

Fair enough. Tricky one. Not sure I can explain why it’s interesting. Maybe 10-dimensional spheres aren’t everyone’s cup of tea?

Comment by Dan Goodman

It’s not so much that. I can kind of understand why the end result is cool. And it doesn’t bother me too much that I’ve no way in hell of visualising cases for n>3…I gather that even you folk who are good at sums can’t do that. I’ve come to the conclusion that the problem is that I don’t understand the working out along the way. We earthbound souls who don’t use higher maths in our everyday lives are simply unused to expressing things in mathematical terms. I’d need someone to take me throug, very carefully, step by step and explain basic things like why the first matrix goes from +2 to -2. I fear it would feel a little like talking to a four year old.

Not that I couldn’t learn. I used to do some of this stuff. I’m just out of practice.

Comment by Edward the Bonobo

Hmm, perhaps after 8 years of maths my definition of “not at all technical” is slightly out of touch with the rest of the world? 😉

Comment by Dan Goodman

Indeed! 🙂

In any field of expertise, the experts internalise so many ‘blindingly obvious’ things that it can be difficult to get back to first principles. I encounterd an example recently. An engineer I work with had been on a Communications course, and he learned that…different people have different ways of thinking about things. That had honestly never occured to him before.

Comment by Edward the Bonobo

Seen this yet?

Math for the Masses

Now you can show off properly. 😉

Comment by azahar

Hey cool, I wonder if it works in comments?

$e^{i\pi}=-1$

Comment by Dan Goodman

Hmm did that wrong, try again:

e^{i\pi}=-1

Comment by Dan Goodman

So no then.

Still cool though! 🙂

Comment by Dan Goodman

It’s fairly weird even in 5d where the inner sphere is larger than the outer ones. I think you’re right Dan about the cause being that unit n-spheres have small volume as n gets large.

Comment by Simon Judes




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