http://www.timesonline.co.uk/tol/news/uk/science/article1533648.ece

doubt many people care about it, but definitely interesting for some.

Quote :

"For four years they have locked themselves away in their laboratories, poring over some of the most abstract calculations known to mankind. But today 18 leading mathematicians will emerge, blinking, into the public glare, to tell the American Institute of Mathematics that they have mapped E8, one of the most complicated mathematical structures. Although it has no immediate uses, and you may need a PhD in maths to understand what it means, the group has solved a 120-year-old problem previously thought impossible. If the calculations were written on paper it would cover an area the size of Manhattan. E8 is an example of a Lie (pronounced “lee”) group. The brainchild of Sophus Lie, a 19th-century Norwegian mathematician, Lie groups explain the manner in which symmetrical objects could be rotated while still looking the same. It is relatively simple to imagine a three-dimensional sphere rotating around its axes, while looking identical from every angle. E8, however, explains the symmetry of a 57-dimensional object. And for a reason known only to advanced mathematicians, E8 itself has 248 dimensions. Jeffrey Adams, a professor of mathematics at the University of Maryland and the project’s leader, said: “It’s like the human genome project. DNA has all the information coded in it, which was mapped for the genome project. “What we’ve done is to map the structure of E8, showing all its different manifestations. If people say we’re mad, in some sense they’re right. But it’s mathematics of the highest character. It’s the most interesting thing I can imagine thinking about.” The human genome project needs one gigabyte of disk space to be stored. E8 needs 60 GBs, the equivalent of 45 days of continuous MP3s. There are few clues as to E8’s use. Professor Adams believes it may help to explain some problems facing physicists. “Amazingly, E8 comes up in physics — in string theory. Some physicists believe that plays a fundamental role in explaining the theory of matter. It may be that some day this calculation can help physicists to understand the universe.” One of the main problems was the volume of data that the group’s calculations would produce. It took two years to programme the formula into a computer, then a further year to find a computer powerful enough to do the calculations. In the end a supercomputer, Sage, at the University of Washington, took 77 hours to compute the answer. “It was an enormous effort but an enormous amount of fun,” said David Vogan, a professor of mathematics at Massachusetts Institute of Technology. “Once you get halfway up the mountain you want to get to the top. It was such a delight to be working for it.” In the matrix — The result of the E8 calculation is a matrix, or grid, with 453,060 rows and columns — While many scientific projects involve processing large amounts of data, the E8 calculation is different: the size of the input is small, but the answer itself is enormous, and very dense — The E8 root system consists of 240 vectors in an eight-dimensional space, illustrated above Source: American Institute of Mathematics"

3/19/2007 5:05:47 PM

See, this is why I can't go into higher-level mathematics (PhD and such). Math just gets too stupid. Though this is kinda cool.

3/19/2007 5:09:36 PM

Quote :

"Math just gets too stupid."

Math 425 got too abstract for me.. I can't imagine PhD shit

3/19/2007 5:16:12 PM

Quote :

"Lie groups explain the manner in which symmetrical objects could be rotated while still looking the same. "

3/19/2007 5:17:08 PM

Awesome. I'm working on a project for my sr thesis. It generates about 30kb's worth of equations, I thought that was a pain...

3/19/2007 5:17:11 PM

yeah i wish i were smart enough to do that stuff

3/19/2007 5:17:14 PM

who is paying them to do this

3/19/2007 5:20:32 PM

us

3/19/2007 5:21:49 PM

Quote :

"Math 425 got too abstract for me.. I can't imagine PhD shit"

exactly, and this stuff they have done is like 10 x any PhD stuff

Quote :

"yeah i wish i were smart enough to do that stuff"

me too that would make my life so much easier

[Edited on March 19, 2007 at 5:25 PM. Reason : \/ no you are not smart enough to understand what they have done]

3/19/2007 5:23:54 PM

I'm smart enough, but this is what separates me from these mathematicians:

Quote :

" It’s the most interesting thing I can imagine thinking about."

...(o)(o) is the most interesting thing I can imagine thinking about.

3/19/2007 5:23:59 PM

Quote :

"E8 needs 60 GBs, the equivalent of 45 days of continuous MP3s. "

i've commented on this phenomenon before - in the past couple years, the MP3 has become the de facto standard for measuring hard drive space to the normal person. kind of like "football field" is used to describe how large things are in area or length, or measuring weight in "number of elephants"

3/19/2007 5:26:51 PM

this function will be built into excel in 5 years.

3/19/2007 6:09:04 PM

i can't imagine being a math PhD and finding a project, knowing that all the "easy" stuff has been done already

[Edited on March 19, 2007 at 6:26 PM. Reason : ]

3/19/2007 6:26:28 PM

Quote :

"i've commented on this phenomenon before - in the past couple years, the MP3 has become the de facto standard for measuring hard drive space to the normal person. kind of like "football field" is used to describe how large things are in area or length, or measuring weight in "number of elephants""

http://www.somethingawful.com/d/guides/guide-understanding-tv.php

3/19/2007 6:44:03 PM

Quote :

"yeah i wish i were smart enough to do that stuff"

3/19/2007 6:46:33 PM

sru wins the thread

3/19/2007 7:00:15 PM

and blinking step into the sun?


seriously tho the first thing I thought IRT rotating an object and having it look the same was cloaking devices. That and beam transporters.

3/19/2007 7:15:28 PM

10/10.B.

3/19/2007 7:48:36 PM

finding the solution is the easy part
finding a practical use for a 60gb matrix is the hard part

3/19/2007 7:59:03 PM

that's a lotta dimensions

3/19/2007 8:02:05 PM

my penis is so big it's the equivalent of 46 days of continuous mp3s. That's an awful lot of football fields and elephants there.

3/19/2007 8:26:01 PM

I think I have finally figured it out. GW Bush is actually a super genious(hehe) kind of guy.

All those times we have been turning the corner, everyone just assumed it was a square.

But now its coming clear to me, we actually getting somewhere!!!

3/19/2007 8:32:48 PM

Quote :

"i can't imagine being a math PhD and finding a project, knowing that all the "easy" stuff has been done already"

there is still easy stuff out there ( I can do it, it can't be that hard ) you just have to learn about twenty courses of calculus worth of math then twist something a little. That's what most of us do, the really good ones come up with something new which casts new understanding on the old mathematics.

For example there is this program of using Lie symmetries to solve partial differential equations(PDE) (ma 401, but on crack), when they finish there program it will revolutionize our understanding of certain kinds of PDEs making it way easier to understand the intrinsic structure of ugly equations. This to me is very cool because these sort of PDEs have been investigated at least 200 years now and yet they are still finding new facts about them.

3/20/2007 1:26:01 AM

You need a PhD in maths to understand this.

3/20/2007 6:23:34 AM

I cant help but read this and think of Deep Thought, the computer that was built to calculate the Ultimate Answer to the Great Question of Life, the Universe, and Everything

42

3/20/2007 10:05:44 AM

Quote :

"If the calculations were written on paper it would cover an area the size of Manhattan. "

manhattan = 20 sq miles

20 sq miles x (5280x12)^2 = 80,289,792,000 sq inches

one sheet of letter size paper = 8.5 x 11 = 93.5 sq inches

manhattan area / sheet area = almost 860 million sheets of paper

3/20/2007 10:16:51 AM

I'm much happier doing a PhD in APPLIED math, using existing mathematical tools (in my case, a system of differential equations) to better understand or represent ideas from the sciences.

3/20/2007 10:16:59 AM

Quote :

"The human genome project needs one gigabyte of disk space to be stored."

Really? I know that's still huge, but I never figured it was like "oh here let me give you the human genome on my memory stick"

3/20/2007 11:03:16 AM

Quote :

"i can't imagine being a math PhD and finding a project, knowing that all the "easy" stuff has been done already "

welcome to the sciences

3/20/2007 11:26:29 AM

2d pictures

http://aimath.org/E8/mcmullen.html

3/20/2007 11:54:38 AM

^ nice, thanks.

details of calculation:

http://aimath.org/E8/computerdetails.html



p.s. article on bbc:

http://news.bbc.co.uk/2/hi/science/nature/6466129.stm

[Edited on March 20, 2007 at 12:47 PM. Reason : ]

3/20/2007 12:22:45 PM

I think I want that on a t-shirt ... but just one, because two side by side would look like
(o)(o)

3/20/2007 2:46:11 PM

Does this E8 thing have any usefulness?

3/20/2007 3:37:43 PM

^ plz to read the article, and also http://aimath.org/E8/e8andphysics.html and this:

Quote :

"Like the Human Genome Project, these results are just the beginning. According to project leader Jeffrey Adams, "This is basic research which will have many implications, most of which we don't understand yet. Just as the human genome does not instantly give you a new miracle drug, our results are a basic tool which people will use to advance research in other areas." This could have unforeseen implications in mathematics and physics which do not appear for years. According to Hermann Nicolai, Director of the Albert Einstein Institute in Bonn, Germany (not affiliated with the project), "This is an impressive achievement. While mathematicians have known for a long time about the beauty and the uniqueness of E8, we physicists have come to appreciate its exceptional role only more recently --- yet, in our attempts to unify gravity with the other fundamental forces into a consistent theory of quantum gravity, we now encounter it at almost every corner! Thus, understanding the inner workings of E8 is not only a great advance for pure mathematics, but may also help physicists in their quest for a unified theory." "

**************************************************************************

remember this:

The result of the E8 calculation is a matrix, or grid, with 453,060 rows and columns

i thought the 205,263,363,600 matrix entries were just numbers, but they are huge polynomials!!! :

Quote :

"The size of the answer The result of the E8 calculation is a matrix, or grid, with 453,060 rows and columns. There are 205,263,363,600 entries in the matrix, each of which is a polynomial. The largest entry in the matrix is: 152 q^22 + 3,472 q^21 + 38,791 q^20 + 293,021 q^19 + 1,370,892 q^18 + 4,067,059 q^17 + 7,964,012 q^16 + 11,159,003 q^15 + 11,808,808 q^14 + 9,859,915 q^13 + 6,778,956 q^12 + 3,964,369 q^11 + 2,015,441 q^10 + 906,567 q^9 + 363,611 q^8 + 129,820 q^7 + 41,239 q^6 + 11,426 q^5 + 2,677 q^4 + 492 q^3 + 61 q^2 + 3 q If each entry was written in a one inch square, then the entire matrix would measure more than 7 miles on each side. "

here is a bigger picture:

http://aimath.org/E8/images/4_21_300.pdf

[Edited on March 20, 2007 at 4:19 PM. Reason : ]

3/20/2007 4:18:26 PM

seems pretty useless to me. congrats nerdy mathmaticians you wasted a bunch of time and money on jack shit

3/20/2007 4:30:10 PM

it takes a good thing to recongnize a good thing.

Quote :

"Major : Partying "

3/20/2007 4:31:34 PM

how could this have been discovered over 100 years ago, but not solved until this year? I don't understand that type of shit.

3/20/2007 5:45:08 PM

i don't think they had too many supercomputers 100 years ago

3/20/2007 5:52:16 PM

There are a lot of problems which have never been solved or proven.

A pretty famous one, posed several hundred years ago by Euler or somebody, just got solved in the past few years. They proved that for any n > 2, A^n != B^n + C^n, or some shit like that.

3/20/2007 5:59:20 PM

how can it be discovered if it can't be solved by the person who discovered it

3/20/2007 6:02:09 PM

^^that's Fermat's Last Theorem.

For another example of a more familiar problem which was discovered long before being proved with a computer, see the Four Color Theorem, which is the fact that any map can be colored with four colors in a way so that no two adjoining regions have the same color. That was conjectured back in 1852, but a satisfactory proof wasn't developed until the mid-1990's.


^it's a similar thing to the human genome project; to discover the genome is one thing, but mapping it out was a tremendous challenge for years. discovering this mathematical structure in theory is one thing, but it was only recently that we had the computational power to determine every representation of it.


[Edited on March 20, 2007 at 6:06 PM. Reason : ]

3/20/2007 6:04:29 PM

well think of it like mapping the human genome. we KNOW that dna is made up of certain sequences, but for a long time, we didn't have the ability to map billions of them. but we knew it could be done in theory. and now we can do it. as technology progresses, our capabilities to use that technology to solve more problems increases as well. 120 years ago they KNEW that this problem could be solved, but they couldn't practically do the billions of calculations (or whatever - just keeping with the dna analogy) by hand to solve it

[Edited on March 20, 2007 at 6:06 PM. Reason : ^ i knew you would appear in this thread ]

3/20/2007 6:06:18 PM

this is really the most extreme case of symmetry.

3/20/2007 6:06:38 PM

Quote :

"They proved that for any n > 2, A^n != B^n + C^n, or some shit like that."

Fermat's Last Theorem

basically pythagoras theorem in higher dimensions.

everybody knows pythagoras theorem:

you can find integers to fit a^2 = b^2 + c^2 (and they form the sides of right angled triangles)

there are infinite values, for eg:

5^2 = 4^2 + 3^2
13^2 = 12^2 + 5^2

etc

Fermat's Last theorem says that you can't find integers to fit the equation if the powers are greater than 2, i.e.:

a^3 = b^3 + c^3
a^4 = b^4 + c^4
.
.
.

Fermat in his book postulated the theorem in his book before his death in the 19th century, and he put it at the end of the book and said i have the proof, but there isn't enough space left in the margins at the end to put the proof

Quote :

"Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et generaliter nullam in infinitum ultra quadratum potestatem in duos eiusdem nominis fas est dividere cuius rei demonstrationem mirabilem sane detexi. Hanc marginis exiguitas non caperet. (It is impossible to separate a cube into two cubes, or a fourth power into two fourth powers, or in general, any power higher than the second into two like powers. I have discovered a truly marvellous proof of this, which this margin is too narrow to contain.) "

no one had found any numbers (integers) to fit the equation with powers greater than 2 since his death, and people kne there were no numbers that could fit it, but no one had a PROOF.

well this british guy (andrew wiles http://en.wikipedia.org/wiki/Andrew_Wiles) from princeton proved it a few years back and won a lot of money for it.

the proof was some 200 pages long.

[Edited on March 20, 2007 at 6:07 PM. Reason : damn i was typing for 2 long]

[Edited on March 20, 2007 at 6:19 PM. Reason : http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem]

3/20/2007 6:06:45 PM

this speaks to the larger body of open problems in mathematics. riemann's hypothesis is my favorite, but there are lots.

3/20/2007 6:44:16 PM

not to mention

message_topic.aspx?topic=467439

[Edited on March 20, 2007 at 8:03 PM. Reason : though i see 0EPII1 has already referenced the disparity in these two problems]

3/20/2007 7:54:32 PM

To ActOfGod: I'm out of my element here, but that's a fractal, right? I'm asking and I'm interested because the symbolic, patterned, and epistemological aspects of the E8 structure have implications that both support and transcend mathematics.

3/20/2007 9:40:57 PM

no, it's not a fractal

3/20/2007 9:44:11 PM

^ Because the patterns don't repeat?

3/20/2007 10:20:48 PM

So what I understand from this, I can create a mathematics equation that I cannot prove and no one can currently prove and some how people will spend their lives trying to prove it even when I myself as the creator has no proof to its validity?

3/20/2007 10:30:45 PM