Archive for March, 2010

The Socolar-Taylor aperiodic tiling

March 25, 2010

Yesterday on the arXiv appeared a preprint by Socolar and Taylor presenting an aperiodic tiling of the plane with one tile. I haven’t had time to check in any depth yet but that certainly looks interesting indeed, it had been a bit of a holy grail for a long time.

This subject of aperiodic tilings is fascinating: some tilings are aperiodic such that any finite patch will not be enough to say so. Even worse: others are aperiodic but it is impossible to actually prove it (undecidability of the domino problem).

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Free AMS back issues

March 25, 2010

A great news is that very recently many free digital back issues of  Proc. AMSof Trans. AMS and of JAMS have been made available!

About 100MY

March 7, 2010

The fastest man-made spacecraft so far are the Helios probes, which reached 0.000234c. Let’s say one manages to build probes about 4 times faster, reaching 0.001c (that’s still well within the bound where impact by interstellar dust would damage or even wipe out the probe).

The Milky Way being 100,000 Light-Years in diameter, that puts a contraint of about 100 Million Years to travel accross it all. Respectable, but not daunting, by evolutionnary standards.

Yet, as far far as close  neighborhood goes, that speed would put the 32 closest stars to the Sun within 16,000 Years of travel. That, on the other hand, is a little bit frustrating, our best shot at landing on an inhabitable place being quite further away still…