Monday, April 30, 2007


Mathematical landscape

Mathematical landscape is a term that describes the objects one finds in higher dimensions. It is also used in connection with mathematician's attempts to find unifying principles in physics and mathematics. Some believe that the link between them is an as yet undiscovered symmetry that will be the same symmetry under which the laws of nature behave. A particular example of this is the Monstrous moonshine conjecture, which linked the Monster group with modular functions and string theory. Another example is the appearance of the largest exceptional lie group, E8, as the gauge group of heterotic superstring theory.

196883 dimensions: The Monster group is the largest sporadic simple group and this is the smallest number of dimensions it acts in. It is the largest finite sporadic group. The monster group is linked with continuous objects like the J-invariant and modular forms by the Monstrous moonshine conjecture. It is conjectured to be the symmetry group of the constraint polynomial in invariance mechanics.

256 dimensions: The number of dimensions (excluding space and time) to represent all the degrees of freedom from supergravity (128 bosons + 128 fermions), which is the same as the lowest order of superstring theory. This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Mathematical landscape". This entry is a fragment of a larger work. Link may die if entry is finally removed or merged.

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