What is a Riemannian Manifold?

Mr. Tea

Shub-Niggurath, Please
Staff member
How many months did this take?/How many hits of acid?

No, I don't believe either of you.
Couple of weeks.

No acid, but I did read a bit of it while otherwise intoxicated - dunno if it make any more sense, but I don't think it made any less.
 

nomadthethird

more issues than Time mag
Couple of weeks.

No acid, but I did read a bit of it while otherwise intoxicated - dunno if it make any more sense, but I don't think it made any less.
I was gonna say, don't waste good acid!

I just thought within the first 30 pages-- ok I get it. Maybe I just have ADD, or did at the time.
 

Mr. Tea

Shub-Niggurath, Please
Staff member
I suppose Advanced Dungeons & Dragons tournaments do eat into one's time somewhat.
 

IdleRich

IdleRich
"But they do not get to grips with the basics of calculus; they learn how to perform certain operations, and so the knowledge they acquire is for the most part purely procedural. A major problem with undergraduate maths courses is that the lack of conceptual knowledge doesn't prepare them well for the transition to HE programmes that rely on maths. There is quite a literature on this."
But didn't the operations come first historically? The (rigorous) philosophy of it came later when people realised that it was a handy tool and the explanations as they stood weren't adequate. So in a sense people are learning it in an order that is somewhat justfiable.

I read Cyclonopedia to the end - although I didn't really enjoy it so I'm not sure why really.
 

vimothy

yurp
I'm not arguing for Philosophy, just conceptual understanding. It's a question of connecting one procedure to the others, so that you can understand it as a concept -- a mathematical, not philosophical concept -- as well as a procedure. But there are time constraints imposed because everyone needs to know enough procedures to pass the exam.
 

IdleRich

IdleRich
"I'm not arguing for Philosophy, just conceptual understanding. It's a question of connecting one procedure to the others, so that you can understand it as a concept -- a mathematical, not philosophical concept -- as well as a procedure. But there are time constraints imposed because everyone needs to know enough procedures to pass the exam."
Well, when we started doing differentiation we did derive it in a way that made sense. It's just that at university we did it in a different way as we had a more subtle understanding of various types of limits and things. But my understanding is that that derivation came later so I don't have a problem with seeing them that way round. What I'm saying is that I certainly don't feel as though the methodology of calculus was just plucked out of the blue when I was doing my a-levels - although we had a very good teacher, maybe that wasn't the usual experience.
I didn't think that you were arguing for a philosophical description as such but rather something that went further than "this seems to work and although we're not totally sure why and the derivation is a bit dodgy who cares?" - and I agree with you, but I felt that I did get the first steps of that.
 

vimothy

yurp
That's cool. Obviously, it varies. I guess at A level it's the prior knowledge of the class versus the constraint of the exam. A really good, homogeneous class can probably do a lot.
 

IdleRich

IdleRich
"That's cool. Obviously, it varies. I guess at A level it's the prior knowledge of the class versus the constraint of the exam. A really good, homogeneous class can probably do a lot."
Well, it's interesting, I did maths and further maths at a-level and in the further maths group there were only about six or eight of us who were all quite bright (if I can say that) and everyone was obviously interested enough to do maths twice; on the other hand the normal maths group was very mixed ability and about thirty people and it was in this that we first studied differentation obviously. I think the justification was most likely presented along the lines of "you may not stricly need to know this for the exam but here it is". It was certainly a far cry from "You don't need to know this so shut the fuck up".
In fact, I never really found that was the caes studying maths. In a desperate attempt to find some focus to my "career" I started studying CIMA (accountancy) and found this attitude rife - I gave up very quickly 'cause that made it so fucking boring.
 

Mr. Tea

Shub-Niggurath, Please
Staff member
I'm not arguing for Philosophy, just conceptual understanding. It's a question of connecting one procedure to the others, so that you can understand it as a concept -- a mathematical, not philosophical concept -- as well as a procedure. But there are time constraints imposed because everyone needs to know enough procedures to pass the exam.
Yes, I've seen this quite often with my students - I'll say something like "Oh come on, I know you can do this, it's just a fraction!" and they respond "Oh, I didn't know this was a fractions question...". As if maths (or any subject) is naturally divided up into nice discrete, non-overlapping topics. Which is, probably unavoidably, how it's taught of course.

I'm also hearing you on procedure vs. understanding. They'll get stumped on some really trivial problem because it's not presented to them in exactly the format they're used to, and they don't know what to do - then when I give them a nudge in the right direction they can (usually) solve it using their familiar techniques.

I think I have once had a student say those terrible words "But I don't have to understand it though, do I?". :mad: Poor girl, I mean it's just a symptom of her teachers' (and the entire system's) approach. Though she was an unusually bad case - rich parents, ergo possibly a lot of pressure to get those precious grades at that expensive school.* Edit: though I should add this cropped up more often in her physics work than in the maths.


*not to imply that my less well-off students' parents didn't want their kids to do well too, of course - they presumably wouldn't have hired me in that case.
 
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nomadthethird

more issues than Time mag
I suppose Advanced Dungeons & Dragons tournaments do eat into one's time somewhat.
But you don't understand, this is the only place I can spazz out and be a dork. My friends have all read theory and stuff but they don't really care about it--beyond a few extremely cracked out/impressionistic remarks here and there-- because they are artists, which means they mostly care about a) being hot/looking good b) fucking other scenesters and c) maintaining a base-level of abject poverty that doesn't quite match their earning potential.

These days I prefer to be alone where I can wallow in depression without having to bother with full make-up or cover charges. I'd rather dole out exp points here than live like that anyway. :D
 

pajbre

Well-known member
erm, i read all of cyclonopedia (during the day, mostly, at night the girlfriend would look at some of the illustrations and say 'don't go to the darkside!')... one thing that helped was realizing that if one emailed reza with questions, he would respond with almost ridiculously generous explanations/provocations.
 
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