I’m always on the lookout for non-rigorous, ‘pictorial’ explanations of abstract mathematical topics. Because ones that are good, and also mostly correct, are difficult to find. And also I am not particularly fond of learning mathematics by plodding through theorems in a book. I find that only with the appropriate picture does a particularly daunting [...]
Archive for April, 2009
20 Apr
Topology Apology
In lieu of actually delving into this, I’ll just give a short description and let you go look it up on Wikipedia.
There’s a way of classifying or generating seemingly complicated surfaces using a sort of surface (or shape, I guess) that isn’t really that complicated.
The way you do it is this: Take one vector [...]
16 Apr
The Lawyer’s Expert Opinion
Andrew McCarthy, noted retard, writes about the release today of four torture memos written under the presidency and administration of George W. Bush (also a noted retard):
A terrible decision, pushed for aggressively by AG Eric Holder… Holder’s press release, which suggests that the interrogators are in fact guilty of torture (“‘The President has halted [...]
15 Apr
Oh, Well That’s Gone
To the person who broke into my car and stole my GPS:
I appreciate that you did not steal the pants lying in the back seat, though you clearly rifled through them.
I must remark, however, that the theft of my umbrella was a pretty dick thing to do.
Today it rained, and I did not have [...]
12 Apr
Tensors
See here for a very friendly introduction to tensors (~25 pages).
See here and then here for a very friendly introduction to the Levi-Civita tensor (~3 pages).
9 Apr
Blatant Huckster is Blatant
You might think that a moderator should not, when introducing the parameters of a supposedly intellectual debate on the existence of the so-called Kerishten deity, first plug his own book, and then go on to offer the audience a magazine subscription, and then try and whore out religious pamphlets to college students. Within the first [...]
7 Apr
Homotopy Classes and the Fundamental Group
If you imagine a hole on a plane—say, a circular one with radius —as being an infinitely tall column rising above the plane, you can determine how many holes exist on that surface in the following natural way:
Suppose that you take a string, tie it into a loop, and lay it on the surface. If [...]
6 Apr
The Dangers of Visualizing Abstract Things
To follow on to my last post, a big part of visualizing abstract mathematics is, ironically, accepting that you can’t completely visualize it. Sometimes you have to settle with what you know. For instance, you can imagine points in , which is the vector space of square-integrable functions. You just imagine or (the [...]
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