Math: Useful Tool or Satans Cock.

For me a useful tool but then I study engineering and that is basically applied maths. I gain no pleasure from it though, apart from possibly imaginary numbers which are kewl as a concept but a pain in the arse in practice.

Maths (plural as it is a shortening of Mathematics which is plural) is fantastic at school and starts becoming less compelling when you do it for a degree. Degree level maths certainly doesn't help you balance your chequebook - you don't see numbers except on the answer paper. I got deeply in to the crossover area in Philosophy Of Maths (especially infinity) - but this was pretty much the time I also got deeply into bouze. So Maths Classic - but not as classic as bouze.

What do you call a fruit that commutes? An abelian grape.

Ironically I used to vehemently despise all maths, except geometry.

I think Maths teachers should be pretty poor at it, as long as they can do it. I would be a loiusy teacher because I get how hathes works. I would habve no patience with a kid who does not see the internal logic of say Pythagoras' Theorem, and how can you not understand differential equations.

I was being self centred merely because that was what worked in my case. I think a maths teacher who understands differential equations (as you would hope any qualified maths teacher would) but may have had trouble with them at school would be a much better teacher than me. They can identify with the problem and also know what there particular epiphany was. Or even better give kids the techniques to get past these blocks until the epiphany comes. Quadratic equations are a good example of this. There is after all a formula with which you can solve all quadratic equations - but they don't give you this until you have fannied around using guesswork methods. Now your average 16 year old is never going to devise said formula (say they) so its good that people are given techniques which make them understand it. But in this case the formula is the calculator. Give it and move on.

I agree that Maths teaching has undergone so many ideological changes over the last thirty years that it is difficult to spot a coherent trend. However it is also possibly useful to note that some people just do not get maths and will be very difficult to teach whatever the situation.

Admittedly I am always worried when a PE teachers second subject ins Maths though...

http://upload.wikimedia.org/math/3/8/0/380b08b0117cdea8d0f48b8eb62f19fa.png

There is another way of looking at it...
http://upload.wikimedia.org/math/2/9/2/2922879252c9d6d8402dcb267a02cb2e.png

or even just G.

Graham's number is much larger than other well known large numbers such as a googol and a googolplex, and even larger than Moser's number, another well-known large number.

uh

Maths amazes me even though I haven't the faintest idea what's going on with it...

Graham's number is connected to the following problem in the branch of mathematics known as Ramsey theory:

Consider an n-dimensional hypercube, and connect each pair of vertices to obtain a complete graph on 2n vertices. Then colour each of the edges of this graph using only the colours red and black. What is the smallest value of n for which every possible such colouring must necessarily contain a single-coloured complete sub-graph with 4 vertices which lie in a plane?

Although the solution to this problem is not yet known, Graham's number is the smallest known upper bound for it. This bound was found by Graham and B. L. Rothschild (see (GR), corollary 12). They also provided the lower bound 6, adding the qualifying understatement: "Clearly, there is some room for improvement here."

In Penrose Tiles to Trapdoor Ciphers, Martin Gardner wrote, "Ramsey-theory experts believe the actual Ramsey number for this problem is probably 6, making Graham's number perhaps the worst smallest-upper-bound ever discovered." More recently Geoff Exoo of Indiana State University has shown (in 2003) that it must be at least 11 and provided evidence that it is larger.

You can't but wonder at how the "answer" to this "problem" could be 6, 11 or a number so big that even the digits in the exponent would exceed the number of particles in the observable universe.

It has been proven that Moser's number, although extremely large, is smaller than Graham's number.

You can't but wonder at how the "answer" to this "problem" could be 6, 11 or a number so big that even the digits in the exponent would exceed the number of particles in the observable universe.

yeah, this does sound weird. The deal is that you get these numbers from functions that start small but whose outputs "grow" really fast, so that the first outputs might be less than 20, but then the next outputs are gigantically big.

not bigger than satan's cock tho

it's not all been said...been said and done...
i've never slept in satan's bed
although i must admit...still visits my place
uninvited, as you know, he don't wait
funny how he always seems to fit in
funny how i always want to give in
sundays, fridays, tuesdays, thursday, the same
sometimes the special guest, he don't like to leave
already...in love...
already...in love...
already...in love...
already...
who made, who made up, made up the myth
that we were born to be covered in bliss?
who set the standard, born to be rich?
such fine examples, skinny little bitch
model, role model, roll some models in blood
get some flesh to stick, so they look like us
i shit and i stink, i'm real, join the club
i'd stop and talk, but i'm already in love
already...in love...
already...in love...
already...in love...
already...
in love...ah ha ha ha...
ah torture...follows reward...
follows torture...follows reward...
oh, oh my butt...
never shook satan's hand, look see for yourself
you'd know it if i had, that shit don't come off
i'll rise and fall, let me take credit for both
jump off a cliff, don't need your help so back off
i'll never suck satan's dick...
again, you'd see it, you know, right round the lips
i'll wait for an angel, but i won't hold my breath
'magine they're busy, think i'm doing okay...
already...in love...
already...in love...
already...in love...
already...

xp
It's genuinely wonderful. I also wondered how it could be proved that G is bigger than M. As I'm sure all of you out there are wondering also. Well, thanks to Mr Chow of MIT here's the proof...

Lemma 1

In any expression involving Knuth arrows and positive integers n > 2, the parenthisation that creates the largest number is the one that associates from the right.

For example, (a^^^b)^^c < a^^^(b^^c)

Proof: by induction.

For single arrows, or ordinary exponentiation, this is the well known result that (a^b)^c < a^(b^c), or that a^(b×c) < a^(b^c), or that b×c < b^c, which is true for b, c > 2.

Lemma 2

If n>2, then n[k+2] < n^^...^^n (2k-1 arrows)

Proof. From the details of the Moser construction, it is easy to see that n[4] = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2n terms]. From Lemma 1, this is less than the expression with n terms all associating to the right: n[4] < n^n^...^n[2^n terms]. From the definition of Knuth arrows, we have n[4] < n^^2^n

It is not hard to show, for n>2, that n^^2^n <n^^^n

Then one can proceed to the general result by induction on k, invoking Lemma 1 in the general case.

For example, when k=3 (and n>2):

n[5] = n[4]n [from definition]
= n[4][4]n-1
< (n^^^n)[4]n-1 [by Lemma 2, with k = 2]
< ((n^^^n)^^^(n^^^n))[4]n-2 [by Lemma 2 again]
...
< (...(n^^^n)^^^(n^^^n)...)^^^...^^^(...(n^^^n)^^^(n^^^n)...) (2n terms)
< n^^^^2^n [by Lemma 1]
< n^^^^^n

Proof that G >> M

M = 2[2[5]] < 3[2[5]] < 3^^...^^3 (2[5]×2 -1 arrows), by lemma 2.

Now 2[5] < 3[5] < 3^^^^^3 by lemma 2

So M < 3^^...^^3 (3^^^^^3×2-1 arrows) << G2 << G

Mr Chow I salute you.

it is easy to see that n[4] = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2n terms]
it is easy to see that n[4] = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2n terms]
it is easy to see that n[4] = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2n terms]
it is easy to see that n[4] = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2n terms]
it is easy to see that n[4] = (...(n^n)^(n^n)...)^...^(...(n^n)^(n^n)...)[2n terms]

Ramsey Theory: if the numbers won't do what you want, shout and swear at them until them do.

lol in my non-ILM life I know Mr Chow...this mixing of my two lives is going to make my brain explode...

besides, the proper answer to the thread's title question is "yes"

I knew someone would know him!

Whats he like? From his website he seems like a friendly guy.

Of course you can't really answer this question as I'm quite sure he knows how to google...

I wish I had done more maths at school.

well I just mean I know him professionally, and he's a sharp cookie

> Maths jokes are never funny.

There are 10 kinds of people in this world. Those who know binary and those who don't.

QED!

What is
http://img220.imageshack.us/img220/4941/picture1gm6.png?

Houseboat!

i fucking love math

math is hard, lol

Math: Useful Tool for measuring Satans Cock.

MATHEMAGICS

Classic Ted