Yule Heibel's Library tagged math →  View Popular, Search in Google

Make my head explode - while the honeybee dances...
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Mathematicians like to examine different manifolds the way antiques dealers browse through curio shops--always exploring, always looking for unusual characteristics that expand their understanding of numbers or geometry. The difficult part about exploring a manifold, however, is that mathematicians don’t always confine them to the three dimensions of ordinary experience. A manifold can have two dimensions like the surface of a screen, three dimensions like the inside of an empty box, four dimensions like the space-time of our Einsteinian universe, or even ten or a hundred dimensions. The flag manifold (which got its name because some imaginative mathematician thought it had a shape like a flag on a pole) happens to have six dimensions, which means mathematicians can’t visualize all the two-dimensional objects that can live there. That does not mean, though, that they cannot see the objects’ shadows.

One of the more effective tricks for visualizing objects with more than three dimensions is to project or map them onto a space that has fewer dimensions (usually two or three). A topographic map, in which three-dimensional mountains get squashed onto a two-dimensional page, is a type of projection. Likewise, the shadow of your hand on the wall is a two- dimensional projection of your three-dimensional hand.
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barbara_shipman math bees quantum_physics geometry

Thought-provoking post about "random matrix theory."

mit_techreview math statistics random_matrix_theory petr_seba