Life in higher dimensions

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

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My favorite facts from high school
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1. Higher dimensional geometry

• The real number line
• The Cartesian plane
• The 3d world
• Just add dimensions P(w,x,y,z)
• Mathematician arent afraid
• Not physics, not time, just four (or more)
  geometrical dimensions

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Regular Polytopes
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How many?
2d regular polygons ? infinitely 3d regular
polyhedra ? 5 4d regular polytopes ? 6 5d
regular 5d polytopes ? 3
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2. The Mercator World Map
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Social Studies Teacher Myth
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The truth
Designed for constant compass directions See
Wikipedia
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Stereographic Projection
Project P to sphere along the line to the north
pole.
Mercator Map
Ster Proj
Log z
Not cylindicrical projection!
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3. Worlds fastest computers

• top500

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Performance Trends
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Extrapolations
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Earth Simulator
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Earth Simulator
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Beowulf Clusters
Our Experience
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Beowulfs
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The First Beowulf
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Enjoy Mathematics