248 dimension puzzle solved
By Hannah Isom
If you’ve ever found yourself baffled by maths homework, then spare a thought for the poor scientists who have spent four years doing their sums! A group of 19 mathematicians from the US and Europe have finally solved a 248-dimentional puzzle, producing an answer that, if written on paper, would cover an area the size of Manhattan.
The team have managed to map the structure of an extremely complex ‘Lie group’, named E8. The precise structure of E8 has baffled scientists since the beginning of the 19th Century. Lie groups are basically a way of investigating the symmetry of objects. Any object that is symmetrical, for example a sphere, has an underlying Lie group.
E8 is a particularly complicated version of a Lie group*. In fact, the mapping of its structure required more data than the human genome project. Even after the brainiacs had grappled with the theory of the problem, it still took two years to implement the experiment on the Sage supercomputer, and 77 hours to run.
The findings of this ambitious project, which is part of the Atlas of Lie and Representations project have only scratched the surface in terms of understanding the complex implications. One application is thought to be helping physicists understand their own conundrums, including string theory (which I am sure is more complicated than figuring out how long a piece of the stuff is).
David Vogan from the Massachusetts Institute of Technology (MIT) is particularly excited about E8. He will be presenting the findings of the study at a lecture entitled ‘The Character Table for E8, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness.’
*What's sobering is that even the easy versions of Lie groups are completely baffling. You can try understanding them here, but if you'll take our advice you'll go to Hannah's other articles and enjoy more top science.
The team have managed to map the structure of an extremely complex ‘Lie group’, named E8. The precise structure of E8 has baffled scientists since the beginning of the 19th Century. Lie groups are basically a way of investigating the symmetry of objects. Any object that is symmetrical, for example a sphere, has an underlying Lie group.
E8 is a particularly complicated version of a Lie group*. In fact, the mapping of its structure required more data than the human genome project. Even after the brainiacs had grappled with the theory of the problem, it still took two years to implement the experiment on the Sage supercomputer, and 77 hours to run.
The findings of this ambitious project, which is part of the Atlas of Lie and Representations project have only scratched the surface in terms of understanding the complex implications. One application is thought to be helping physicists understand their own conundrums, including string theory (which I am sure is more complicated than figuring out how long a piece of the stuff is).
David Vogan from the Massachusetts Institute of Technology (MIT) is particularly excited about E8. He will be presenting the findings of the study at a lecture entitled ‘The Character Table for E8, or How We Wrote Down a 453,060 x 453,060 Matrix and Found Happiness.’
*What's sobering is that even the easy versions of Lie groups are completely baffling. You can try understanding them here, but if you'll take our advice you'll go to Hannah's other articles and enjoy more top science.
 |
| The E8 root system consists of 240 vectors in an eight-dimensional space. Those vectors are the vertices (corners) of an eight-dimensional object called the Gosset polytope 421. In the 1960s, Peter McMullen drew (by hand) a 2-dimensional representation of the Gosset polytope 421. This image was computer-generated by John Stembridge, based on McMullen's drawing. All clear now? |
Share this
