I want to know about .....

[omega 616]

I love to know about "cool" things, but due to my stupidity I can't so I am hoping some smartie pants on this site can help me out.

I would like a maths wizz to explain what on earth Graham's number is/used for in a very laymans way.

This is wiki's effort to inform me .... "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 either red or blue.
What is the smallest value of n for which every such colouring contains at least one single-coloured 4-vertex planar complete subgraph?"

I got lost at N-dimensional ....

Keep in mind I am just god awful with maths, christ due to my first primary school (and my lazyness, I must add) I never got taught times tables (or basic English, like you couldn't tell).

For discusions sake, what cool things do you want to know but when you look it up none of the words makes sense or your just not smart enough to get it.

EDIT: I know it's a fucking huge number that can't written down.

 

[DefunctTheory]

It seems to be a part of a overall problem... Ramsey theory.

Suppose, for example, that we know that n pigeons have been housed in m pigeonholes. How big must n be before we can be sure that at least one pigeonhole houses at least two pigeons? The answer is the pigeonhole principle: if n > m, then at least one pigeonhole will have at least two pigeons in it. Ramsey's theory generalizes this principle as explained below.

A typical result in Ramsey theory starts with some mathematical structure that is then cut into pieces. How big must the original structure be in order to ensure that at least one of the pieces has a given interesting property?

 

[Outright Villainy]

There is no layman's way to describe that, since you're getting into really technical, and purely theoretical maths.

Most maths isn't badly explained, as people would think, it just can't be expressed any more simply.

Ot: I always wanted to learn how to read music. I know literally no music theory, I'm completely self taught, and learn by ear. I can tab, but then, you could teach a monkey how to read tabs pretty quickly...

 

[Ironrose]

I think this may be one of those concepts that is a lot harder to understand when you don't have something to apply it to.

 

[omega 616]

Awww, well I guess I am out of luck, shame.

So do you guys know what it is and kind of/fully understand it's uses or are you just like "yeah, thats some top o' the line maths, right there"? 'cos I suspect only people with masters in maths can actually bend there head around this mother.

EDIT, maybe do any of you know what it's used for? Like working out how many pidgeons need a home or something?

 

[Outright Villainy]

Awww, well I guess I am out of luck, shame.

So do you guys know what it is and kind of/fully understand it's uses or are you just like "yeah, thats some top o' the line maths, right there"? 'cos I suspect only people with masters in maths can actually bend there head around this mother.

EDIT, maybe do any of you know what it's used for? Like working out how many pidgeons need a home or something?

I don't really understand it, since I've only done maths as a part of my college course, and I don't do it anymore, but it really doesn't look like half as interesting as you're expecting; it seems to be just calculating an arbitrarily large upper limit.

 

[IronCladNinja]

You should read Logicomix. It's a graphic novel about the life of Bertrand Russell, the famous logician. Has all sorts of math-free explanations of math and logic, lots of cool history and such too.

Generally advanced math can't be explained without math, you're better off reading about physics. I'm terrible at math, but I love talking about De Broglie wavelengths and the Heisenberg Uncertainty Principle.

 

[Outright Villainy]

You should read Logicomix. It's a graphic novel about the life of Bertrand Russell, the famous logician. Has all sorts of math-free explanations of math and logic, lots of cool history and such too.

Generally advanced math can't be explained without math, you're better off reading about physics. I'm terrible at math, but I love talking about De Broglie wavelengths and the Heisenberg Uncertainty Principle.

The best part is explaining relativity to people.

Blows their tiny brains.

 

[omega 616]

You should read Logicomix. It's a graphic novel about the life of Bertrand Russell, the famous logician. Has all sorts of math-free explanations of math and logic, lots of cool history and such too.

Generally advanced math can't be explained without math, you're better off reading about physics. I'm terrible at math, but I love talking about De Broglie wavelengths and the Heisenberg Uncertainty Principle.

The best part is explaining relativity to people.

Blows their tiny brains.

I love explaining Bose-Einstein condensate to people and a look of either disinterest or total bafflement creep onto there face. LOVE it.

 

[Shymer]

I am not a Maths Whizz - and you are not stupid.

Graham's number is one of a number of features of 'proofs' of a class of maths problems, collectively known as Ramsey Theory. These problems are interested in exploring the smallest number of things that are required for a certain 'interesting' order (or pattern) to appear.

A simple example related to Graham's number is if you connect a number of points on a paper together with lines, and arbitrarily colour those lines one of two colours, how many points would you need to absolutely guarantee that you will have drawn at least one complete triangle of a single colour.

Wikipedia gives a more concrete example of this is the answer to the question "How many people you would need to invite to a party to ensure that there were either three complete strangers, or three mutual acquaintances."

Graham's number appears when you take this simple 2-dimensional idea (connecting dots and looking for patterns - or indeed inviting people to parties) and considers a more general case (ie. N-dimensional problems). At this point the theory transforms from something tangible that most people can grasp, to something abstract that is pleasing to some people's minds to manipulate, but is otherwise out of reach and irrelevant for most people.

Graham's number is interesting because it is so vast, but it has a specific meaning (the upper bound of the N-dimensional problem described above), and the final digits can be calculated. However, to most people it has no purpose other than as a curiosity. Perhaps it represents humanity's obsession with finding pattern and order (beauty) in vastly complex systems of thought. Finding structure and order can be a comfort.

Perhaps it also can highlight the general human needs to be right, to win and to gain recognition from other people.

 

[Owlslayer]

i like math, but I'm not in a Uni yet, so i don't really know what you're talking about.
And also, my linguistic capabilities in understanding English fail horribly when reading math. You know, cause i haven't heard such words before. I mean, all the math I've learned, I've learned it in my language...

 

[karplas]

I've never heard of this before nor am I an expert at mathematics, so please don't take my interpretation as an expert's. Anyway from what I can understand from this website: http://www.daviddarling.info/encyclopedia/G/Grahams_number.html
I might be able to clarify a thing or two. (Once again though, I'm no expert, so I might very well be saying things which are not true).

From the website:

A stupendously large number that found its way in to the Guinness Book of Records as the biggest number ever obtained as part of a mathematical proof; it is named after its discoverer, Ronald Graham. Graham's number is the upper bound solution to a very exotic problem in Ramsey theory, namely: What is the smallest dimension n of a hypercube such that if the lines joining all pairs of corners are two-colored, a planar complete graph K4 of one color will be forced?

This is exactly equivalent to a problem that can be stated in plain language: Take any number of people, list every possible committee that can be formed from them, and consider every possible pair of committees. How many people must be in the original group so that no matter how the assignments are made, there will be four committees in which all the pairs fall in the same group, and all the people belong to an even number of committees.

I think the connection between the 'mathematical'-formulation of the problem and the 'plain-language'-formulation is as follows:

"Take any number of people" corresponds to "[any] n-dimension", i.e. the number of people you choose to take is the same number of dimensions of the hypercube.

"Every possible committee that can be formed from them" is equivalent to all the points on the hypercube. For example, choose n=3 (i.e. let there be 3 people). Let a '1' mean that a person is in the committee. Let '0' mean that a person isn't. Then for example (1,1,1) means that all three people are in a committee. (0,0,0) means that no person is in the committee. (1,0,0) means that person 1 is in the committee and that person 2 and person 3 are not. Now think of these coordinates as points in three-dimensional space. Then "[the] list [of] every possible committee that can be formed from them" are exactly the coordinates that form a cube: {(0,0,0), (1,0,0), (0,1,0), (1,1,0), (0,0,1), (1,0,1), (0,1,1), (1,1,1)} Similarly, if you chose n=4, you'd get coordinates in four dimensions, for example (1,0,0,1), which would form a 4-dimensional hypercube.

In this analogy, each possible committee is represented as a point in n-space. These points form a hypercube, hence: "[consider] the lines joining all pairs of corners" corresponds to "consider every possible pair of committees". The fact that "the lines joining all pairs of corners are two-colored" means that there are two groups of paired committees, hence the statement "there will be four committees in which all the pairs fall in the same group" is equivalent to "a planar complete graph K4 of one color will be forced".

I'm not sure though how exactly "a planar complete graph K4" exactly translates to "four committees in which [...] all the people belong to an even number of committees", but I hope I managed to help you a bit anyway

 

[EHKOS]

I know a little about cars and computer intereer...wow my brain just shut down on that one. Interior. Oh and a very comprehensive knowlegde of the Windows 98 and Vista Operating Systems...out of necesity. Freakin' won't run Red Faction until I root around in your guts...