Posted on 03/19/2007 8:34:38 PM PDT by LibWhacker
Roger Highfield describes a heroic mathematical enterprise that could lay bare the fundamentals of the cosmos
Mathematicians have successfully scaled their equivalent of Mount Everest. Today they unveil the answer to a problem that, if written out in tiny print, would cover an area the size of Manhattan.
At the most basic level, the calculation is an arcane investigation of symmetry – in this case of an object that is 57 dimensional, rather than the usual three dimensional ones that we are familiar with. Although this object was first discovered in the 19th century. there is evidence that it could contain the structure of the cosmos.
Mathematicians are known for their solitary style of working, but the combined assault on what is described as "one of the largest and most complicated structures in mathematics" required the effort of 18 mathematicians from America and Europe for an intensive four-year collaboration.
The feat may baffle most people but could have unforeseen implications in mathematics and physics, which won’t be evident for years to come, said the American Institute of Mathematics.
"The group of symmetries of this strange geometry called E8 is one of the most intriguing structures that Nature has left for the mathematician to play with," commened Prof Marcus du Sautoy of Oxford University, currently in Auckland. "Most of the time mathematical objects fit into nice patterns that we can order and classify. But this one just sits there like a huge Everest." advertisement
What makes this group of symmetries so exciting is that Nature also seems to have embedded it at the heart of many bits of physics. One interpretation of why we have such a quirky list of fundamental particles is because they all result from different facets of the strange symmetries of E8. I find it rather extraordinary that of all the symmetries that mathematician’s have discovered, it is this exotic exceptional object that Nature has used to build the fabric of the universe. The symmetries are so intricate and complex that today’s announcement of the complete mapping of E8 is a significant moment in our exploration of symmetry."
For the feat, the team used a mix of theoretical mathematics and intricate computer programming to successfully map E8, (pronounced "E eight") which is an example of a Lie (pronounced "Lee") group. Lie groups were invented by the 19th century Norwegian mathematician Sophus Lie to study symmetry.
Underlying any symmetrical object, such as a sphere, is a Lie group. Balls, cylinders or cones are familiar examples of symmetric three-dimensional objects. Today’s feat rests on the drive by mathematicians to study symmetries in higher dimensions. E8 is the symmetries of a geometric object that is 57-dimensional. E8 itself is 248-dimensional.
"E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood," said Prof Jeffrey Adams, Project Leader, at the University of Maryland. "This groundbreaking achievement is significant both as an advance in basic knowledge, as well as a major advance in the use of large scale computing to solve complicated mathematical problems."
"This is an exciting breakthrough," said Prof Peter Sarnak at Princeton University. "Understanding and classifying the representations of E8 and Lie groups has been critical to understanding phenomena in many different areas of mathematics and science including algebra, geometry, number theory, physics and chemistry. This project will be invaluable for future mathematicians and scientists."
The ways that E8 manifests itself as a symmetry group are called representations. The goal is to describe all the possible representations of E8. These representations are extremely complicated, but mathematicians describe them in terms of basic building blocks. The new result is a complete list of these building blocks for the representations of E8, and a precise description of the relations between them, all encoded in a matrix, or grid, with 453,060 rows and columns. There are 205,263,363,600 entries in all, each a mathematical expression called a polynomial. If each entry was written in a one inch square, then the entire matrix would measure more than seven miles on each side.
The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes in size. This is enough to store 45 days of continuous music in MP3-format. If written out on paper, the answer would cover an area the size of Manhattan. The computation required sophisticated new mathematical techniques and computing power not available even a few years ago.
"This is an impressive achievement," said Hermann Nicolai, Director of the Albert Einstein Institute in Potsdam, Germany. "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," he said, referring to efforts to combine the theory of the very big (general relativity) with the very small (quantum mechanics). "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."
Faith in what?
Why when I read this article am I reminded of the Tower of Babel?
ping
I think it is safe to say that no one understands quantum mechanics... In fact, it is often stated that of all the theories proposed in this century, the silliest is quantum theory. Some say that the only thing that quantum theory has going for it, in fact, is that it is unquestionably correct
Now thats faith..
What we need is imagination. We have to find a new view of the world. Richard Feynman
Well said!
"Mathematics is the language God used to write the universe."
I read this somewhere recently; don't remember who said it; very probably Albert Einstein.
Even if so, how would it differ from God?
His rising poll numbers will soon rate him an E8 symmetrical asterisk.
Physics is to math what sex is to masturbation.
Richard Feynman (1918 - 1988)
Looks like both that guy from e Harmony, Dr. Neil Clark Warren, with his multiple dimensions of compatability, has picked up on this, not to mention Teresa Heinz Kerry with her varieties. The important thing, for selling ANY product ,or idea, is that you have to have lots and lots of ......something.....or other.....just remember to have LOTS//
Denim.
Math research team maps E8A fairly comprehensive glimpse of the work from the American Institute of Mathematics (AIM) website, with informative sidebar links and a photo of the mathematicans involved in the work:
Mathematicians Map E8
Wwow......that is a GOOD one....Feynman was really something. But only Einstein could have explained that
whacking off has its own physics.
Galileo.
... but the Divine intellect, by a simple apprehension of the circles's essence, knows without time-consuming reasoning all the infinity of its properties. Next, all these properties are in effect virtually included in the definitions of all things; and ultimately, through being infinite, are perhaps but one in their essence and in the Divine mind. Nor is all the above entirely unknown to the human mind either, but it is clouded with deep and thick mists ...
- Salviati at the end of the First Day of Dialogues
Concerning the Two Chief World Systems
Despite their innocuous character, these passages were seized upon as one of the textual points offensive to the Church. ... "That he asserted some equality between the Divine and the human mind in geometrical matters."
- from the notes to the Stillman Drake edition
... so tread lightly !
Read it again. They lied about 248 dimensions. I'm suing. :)
After the "heroic", I lost interest.Sea rescues are heroic, saving your buddies under fire is heroic.
Math can never be heroic until someone works 40 days and nights determining if an asteroid will demolish Earth and how to avoid it.
This is more Eeyore than E8.
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