Mathematics

josef k.

Dangerous Mystagogue
I recently became obsessed with mathematics. I lie awake at night, thinking of patterns. I have discovered the following things.

1) Points. Points are pure positions.

2) Lines. Lines trace relationships between points.

3) Angles. Angles describe relationships between lines.

That is as far as I've got. I am currently trying to figure out volume. I may be going insane.
 

vimothy

yurp
Me too. Actually, I'm studying maths at the Open University. It's near the end of semester 1. Haven't got as far as volume yet.

It's not the maths that's driving me insane, though, it's the Quantitative Research Methods module I'm also taking. I lie awake at night and think about questionnaire design. How demented is that?
 

Mr. Tea

Let's Talk About Ceps
That's where Russell and Whitehead went wrong - the fundamental basis of mathematics is not irreducible axioms but questionnaire design.

Josef, if you have three vectors A, B, C delineating a parallelopiped (a cuboid which is allowed to be 'wonky'; the most general volumetric shape three vectors can define) then the volume is given by the magnitude of A . (B x C), where '.' is the scalar (or 'dot') product and 'x' is the vector (or 'cross') product. This seems like a reasonable place to start if you want to think about volume once you've got some idea of vectors and angles, maybe.

Edit: there's a fairly decent diagram on the Wiki page I linked to...
 
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don_quixote

Trent End
massive massive book recommendation:

mathematics and the imagination by edward kasner. it's from the 30s but it's spectacular.

oooh here we go:
http://books.google.co.uk/books?hl=...CzxpyU&sa=X&oi=book_result&resnum=5&ct=result

since we're here... in that book it says something about terminating decimals, claiming everything we've been told in school maths is wrong - they don't terminate?

i'm sure you've heard 0.99999... = 1 right? well he claims hence 0.125 = 1.249999... so irrationals are the only numbers which never reach a recurrence.

not sure why this is lost in school though - because two results would be too confusing?
 

Mr. Tea

Let's Talk About Ceps
i'm sure you've heard 0.99999... = 1 right? well he claims hence 0.125 = 1.249999... so irrationals are the only numbers which never reach a recurrence.

I'm not I get this: irrationals are the only non-terminating, non-repeating numbers by definition. Well actually the definiton is that they can't be written as the ratio of one finite integer to another, but it's trivial to show that this is equivalent to a non-terminating string of decimals.

I derived the fundamental theory of calculus for one of my A-level students last night, which was pretty cool. Well, for differentiation anyway, integration will have to wait til next week. :)
 

josef k.

Dangerous Mystagogue
Curves. Curves are very interesting. Also, wiggly lines. How the fuck do you analyze a wiggly line?
 

IdleRich

IdleRich
"since we're here... in that book it says something about terminating decimals, claiming everything we've been told in school maths is wrong - they don't terminate?
i'm sure you've heard 0.99999... = 1 right? well he claims hence 0.125 = 1.249999... so irrationals are the only numbers which never reach a recurrence."
I don't get what you're saying here? Recurring decimals don't terminate, they recur and any numbers which can't be written as a ratio (ie are irrational) are non-terminating and non-recurring.
 

Mr. Tea

Let's Talk About Ceps

Well that's just a wriggly line with no rhyme or reason - I thought you meant sine waves and stuff like that.

Though you could still differentiate that curve, or integrate it, or express it as a Fourier series, or draw tangents to it at selected points...

Edit: actually you couldn't, as it goes back on itself at a couple of points. You could still parameterise it as a trajectory or something, I dunno.
 
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IdleRich

IdleRich
"It depends how it wiggles."
And what you mean by analyze. I suspect that you mean find the function that generates it - which in the case of the line that you've just linked to would be, as Mr Tea says, rather hard and possibly pointless because any function that gave that line would be completely ad hoc. I guess you could find something that approximates it though if that's what you wanted.
 

josef k.

Dangerous Mystagogue
I have put it in a cage... I am now examining it.

PS - By analyze, I just mean figure out its relationship to other stuff. As in, wobbly lines exist. How do people understand them mathematically? What mathematical operations are performed on them in order to try and understand them? I don't really care about this particular line. But please don't tell it I said that.
 
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Mr. Tea

Let's Talk About Ceps
I have put it in a cage... I am now examining it.

PS - By analyze, I just mean figure out its relationship to other stuff. As in, wobbly lines exist. How do people understand them mathematically? I don't really care about this particular line, although please don't tell it I said that.

Hm, I can see what you mean, but in a way it's a bit like a kid drawing a totally surreal fantasy animal and the asking an adult what real animals it's related to, if you get me. There's no reason why it should have a relationship to other stuff. In the same way that hfyeuieoffjsgrepl could be considered a 'word', since I can write it using the same letters I use spell real words that have a meaning - but that certainly doesn't endow it with a meaning of its own.
 

josef k.

Dangerous Mystagogue
Interesting...

So, is it that, wobbly lines do not exist? Or that, when they do, it is never arbitrary, as this one is.

Take the path of a kite through a sky on a rainy day. The path traced by the kite. How do people mathematically analyze this?
 

josef k.

Dangerous Mystagogue
ps - in the case of the fantasy animal, experts conclude: it is three-headed, lamalian, behorned and tigroid, scale-necked and beastish, amphibious, zebrine, duck-billed and bewinged.
 

Mr. Tea

Let's Talk About Ceps
Interesting...

So, is it that, wobbly lines do not exist? Or that, when they do, it is never arbitrary, as this one is.

Take the path of a kite through a sky on a rainy day. The path traced by the kite. How do people mathematically analyze this?

Of course they exist! In the same way the nonsense string of letters typed exists. It's a question of whether it means anything deeper.

To what extent is anything 'arbitrary'? The path of a kite is determined by gusts of wind and tugs on the string, just as the shape of that line was determined by the movement of the muscles of your hand, in turn produced by electrical signals in your brain and spinal column. These things can all be analysed according to well understood physical laws, which of course have a rigorous mathematical basis. That doesn't mean your kite is going to trace a perfect ellipse in the sky or that you're going to draw a nice neat sine wave; the processes are extremely complex (stochastic, loosely 'chaotic') and cannot, for practical purposes, be predicted - in other words it's non-deterministic.
 
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Mr. Tea

Let's Talk About Ceps
ps - in the case of the fantasy animal, experts conclude: it is three-headed, lamalian, behorned and tigroid, scale-necked and beastish, amphibious, zebrine, duck-billed and bewinged.

Is it partly rugose and partly squamous?
 
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