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."
57
As in "varieties"?
As in 3 times.... 19 ??
"Able was I ere I saw this crappy little island."
E8 -> SO(16) -> SO(10) X SO(6) -> SU(5) X SU(3)
The gauge group of superstrings is E8 X E8 after compactification of higher dimensions. The string is a heterotic string, and E8 X E8 encompasses the Standard Model.
A tree is known by its fruit. Where is the FRUIT here?
E8 is bunk. E9 is also so Passe. Don't these pseudo scientists know it's all about Mobius Strips - non-orientable finite infinity with only one plane. Mobius was God. An invention Better than the wheel!
Harry Thingo even created Mobius Doors which he used to travel great distances - like localised star gates - in the Wamphyri book series. Mobius himself taught him how to make the doors. I read it, it must be true.
Idiots with 180 IQs.....
This is all nice and well, but will it stop my buttered bread from landing buttered side down when I accidentally drop it?
ping
Quantum mechanics has been repeatedly demonstrated through actual experiments.
Yeah... I see it... thanks for the ping.
Now, this is really funny, I think...
Looking at this link describing this work of the "Atlas Group"
http://aimath.org/E8/
Clicking on the link apparently describing this incredibly powerful supercomputer used to do the calculations: http://sage.math.washington.edu/sage.html ,
I got this message --- (twice)
The connection has timed out -
The server at sage.math.washington.edu is taking too long to respond.
* The site could be temporarily unavailable or too busy...
They must have their site hosted on a PC-XT or something to save money... LOL.
I agree.
That God has created the universe clearly comprehending the underlying structure of this type of complexity is truly a tribute to his Almighty Greatness, not in any way an invitation to blasphemy. I suspect strongly we've not yet really even touched upon the true complexity yet.
From this great article http://aimath.org/E8/ from the group's website:
"The magnitude of the E8 calculation invites comparison with the Human Genome Project. The human genome, which contains all the genetic information of a cell, is less than a gigabyte in size. The result of the E8 calculation, which contains all the information about E8 and its representations, is 60 gigabytes in size."
Quite a feat.
God is just the creator of mathmatics. I am sure he gets a good giggle when we finally figure new something out. The problem is we don't always get the fact that science and higher math points the way toward, not away from Him.
Bravo
Written for all government school graduates. LOL
"Idiots with 180 IQs....."
As opposed to the garden-variety idiots who post on threads like this?
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