Life in higher dimensions Mapping the World Roadtrip: most powerful computer in Japan Alan Edelman June 13, 2006.

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Presentation transcript:

Life in higher dimensions Mapping the World Roadtrip: most powerful computer in Japan Alan Edelman June 13, 2006

My favorite facts from high school

1. Higher dimensional geometry The real number line The Cartesian plane The 3d world Just add dimensions: P=(w,x,y,z) –Mathematician aren’t afraid –Not physics, not time, just four (or more) geometrical dimensions

Regular Polytopes

How many? 2d: regular polygons  infinitely 3d: regular polyhedra  5 4d: regular polytopes  6 5d: regular 5d polytopes  3 …

2. The Mercator World Map

Social Studies Teacher Myth

The truth Designed for constant compass directions See Wikipedia

Stereographic Projection Project P to sphere along the line to the north pole. Mercator Map Ster Proj Log z Not cylindicrical projection! N S P RdRd

3. World’s fastest computers top500

Performance Trends

Extrapolations

Earth Simulator

Beowulf Clusters Our Experience

Beowulfs

The First Beowulf

Enjoy Mathematics