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P-Value Extravaganza

This is the best video about frequentist statistics I’ve ever seen. Watch and enjoy:

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by Jesse Kelly Productions.

Found on youtube’s math blog. If that blog really is automatically generated, I think we need to reject the null hypothesis that Google hasn’t invented strong AI. Am I doing it right? brb, going to watch the video again.

Flat tori in three-dimensional space and convex integration

French researchers Vincent Borrelli, Saïd Jabrane, Francis Lazarus and Boris Thibert have described an isometric embedding of the flat torus in 3D space, using the convex integration theory developed by Gromov in the 1970s. That means they’ve produced a surface which is topologically a torus – it has a single hole — which preserves distances between points in the 4D flat torus. Interestingly, the tangent plane is defined everywhere — the surface is in a sense smooth — but the normal vector is not defined, so it’s also a fractal. This is impossible in higher dimensions

© Borrelli et al / PNAS

I’ve recorded a short video explaining in a handwavey fashion, with a few props made from things I had lying around, just what has been done.

Life imitates Life

A while ago somebody created a simulation of Conway’s Game of Life inside a bigger version of the Game of Life. Now, YouTube user Phillip Bradbury has created a very simple — and aurally pleasing — video showing it in action.

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Apparently this is made possible by the Outer Totalistic Cellular Automata Meta-Pixel (OTCAMP), a “two state programmable unit cell which allows Conway’s Life to simulate any outer totalistic rule. OTCAMP is a meta-cell which is also a meta-pixel. OTCAMP meta-pixels display evolving meta-patterns on-screen in meta-realtime.”

An outer totalistic rule is a rule for a cellular automaton which defines the transitions between cell states based on the total number of switched-on surrounding cells surrounding them. The Game of Life is one such rule.

Source: Richard Elwes on Google+.

Top N Facts about the Klein Bottle

In honour of Felix Klein’s birthday, Matt Parker and Katie Steckles investigate the amazing surface which bears his name.

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