E8 solved

[Pierre]

Here's an article about a math discovery that just happened.

Though I'm not qualified enough to assess the legitimacy/interest of such a result.

PALO ALTO, CA -- The American Institute of Mathematics (AIM), one of the leading math institutes in the U.S., announced today that after four years of intensive collaboration, 18 top mathematicians and computer scientists from the U.S. and Europe have successfully mapped E8, one of the largest and most complicated structures in mathematics. Partners on this project included MIT, Cornell University, University of Michigan, University of Utah and University of Maryland.

The findings will be unveiled today, Monday, March 19 at 2 p.m. Eastern, at a presentation by David Vogan, Professor of Mathematics at MIT and member of the team that mapped E8. The presentation is open to the public and is taking place at MIT, Building 1, Room 190.

E8, (pronounced "E eight") 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. Mathematicians study symmetries in higher dimensions. In fact, E8 is the symmetries of a geometric object like a sphere, cylinder or cone, but this object is 57-dimensional. E8 is itself is 248-dimensional. For details on E8 visit *http://aimath.org/E8/.

"E8 was discovered over a century ago, in 1887, and until now, no one thought the structure could ever be understood," said Jeffrey Adams, Project Leader and Mathematics Professor 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." The mapping of E8 may well have unforeseen implications in mathematics and physics which won’t be evident for years to come.

"This is an exciting breakthrough," said Peter Sarnak, Eugene Higgins Professor of Mathematics at Princeton University and Chair of AIM’s Scientific Board. "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 magnitude and nature of the E8 calculation invite 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. 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. While many scientific projects involve processing large amounts of data, the E8 calculation is very different, as the size of the input is comparatively small, but the answer itself is enormous, and very dense.

"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. 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."

...
Continued on Webwire.

 

[ark]

E8 is closely related to 4D Platonic solids, Clifford algebras and Hamilton's "Icosians":

http://www.cassiopaea.org/forum/index.php?topic=2870&p=1

See also:

http://www.cassiopaea.org/forum/index.php?topic=2870&p=1

and

http://www.valdostamuseum.org/hamsmith/D4.html

http://www.valdostamuseum.org/hamsmith/pwtile.html

for some more pretty pictures.

 

[dant]

A curious question I have is:

Wasn't all of this information [about E8] known in antiquity, was lost,
and is being 'rediscovered' again? After all, why is E8 referred to as
a platonic solid - as if in reference to Plato, who supposedly got his
information from another source, of antiquity, supposedly obtained
from the history of the Atlanteans?

 

[John G]

A curious question I have is:

Wasn't all of this information [about E8] known in antiquity, was lost,
and is being 'rediscovered' again? After all, why is E8 referred to as
a platonic solid - as if in reference to Plato, who supposedly got his
information from another source, of antiquity, supposedly obtained
from the history of the Atlanteans?

Given all the Cs said about the Atlanteans, I'm sure they knew E8. The Sri Yantra could be a remnant of that E8 knowledge.

http://www.valdostamuseum.org/hamsmith/PDS3.html#sriyantra

Every 2-dim projection on my website (actually webpage) comes from E8. I wrote a little C program to rotate the E8 coordinates. The D4 projection has the outside shape of the Sri Yantra. There's a D3 projection that forms the Star of David, it's in one of my papers linked to from my webpage. E8 is really cool and has different uses. It can tile a spacetime as Ark mentioned. It can house physics degrees of freedom, for example the D3 of the D3 projection has the conformal degrees of freedom Ark talks about alot. The relationship to Clifford Algebras Ark mentioned is also interesting. Getting E8 from Clifford Algebra is like getting "it" from "bit". Another use of E8 at Tony's website is to describe the three generations of matter/antimatter. My use of E8 was to describe Jungian and Enneagram personality theory. Tony actually mentions Jungian personality theory in relation to Clifford Algebra at his site. My first paper before finding Tony was really doing E8 root vector geometry without knowing it though personality theory really only goes up to E6. E7 and E8 using the physics analogy would kind of create a many universe version of a single E6 personality universe.

 

[ark]

A curious question I have is:

Wasn't all of this information [about E8] known in antiquity, was lost,
and is being 'rediscovered' again? After all, why is E8 referred to as
a platonic solid - as if in reference to Plato, who supposedly got his
information from another source, of antiquity, supposedly obtained
from the history of the Atlanteans?

Plato was talking about solids in our 3D reality. E8 is related to (but it is NOT) a Platonic solid in 4D reality. E8 itself has neither 3 nor 4 but 248 dimensions. But its "structure" (its mathematical "code" or "skeleton") fits well into 4D.

I doubt that anything about E8 was known in antiquity. Unless unconsciously.

 

[John G]

I doubt that anything about E8 was known in antiquity. Unless unconsciously.

yeah I probably should have mentioned that even if sacred geometry can capture the bivector and triality aspects of E8's polytope, that's still quite far from 60 gig of matrix data or even the 248 sets of coordinates. One really doesn't need to know E8 to get to Mars or move big rocks.