johnkemeny.com

Τomas Rokicki is a man of many algorithms.  He co-authored Golly, a Life simulator that is super fast due to its unique hashlife algorithm.  Last month he proved that 25 face moves (where face move = a quarter or half turn) are suffficient to solve any Rubik’s cube, and he did it using a computer (similar to the solution to the famous Four Color Problem) – specifically, he used Herbert Kociemba’s Cube Solver, which you can download for free.

In 1995 Michael Reid showed that 20 moves were necessary to solve the superflip (pictured).  Kociemba ran his cube solver over 1 million random configurations, and not one needed more than 20 moves to solve.  He then ran 1000 optimal random configurations (at ~2 minutes per solution with 3 GHz processors and 8 GB memory) and found the “average” cube can be optimally solved in ~18 moves.  It clearly appears that 20 moves should suffice to solve any Rubik’s cube.  But can that be proven?

Initially, solution algorithms could take up to 75 moves.  In 1995 Reid showed Kociemba’s algorithm could reduce the maximum to 29 moves, still quite a ways from 20.  In 2006 this was improved to 27, and in 2007 to 26.  Now, thanks to Tom Rokicki, it stands at 25 - and he is on to 24.

Update: As of June, Rokicki cut it to 23 using a Sony/Spiderman render farm.

Update: As of August, Rokicki cut it to 22 using the same Sony/Spiderman render farm.

As described by the inimitable Ze Frank, Color Wars 2008 are coming. I have been assignated<sic> to Team Clear(wiki). Ironic given my rainbow-colored twitter backdrop, no?

David Bau has written a Sudoku Generator with output in PDF, Postscript, plaintext, and HTML.  Nice thing to do.  Difficult ones, requiring lots of guesses, have ratings above 3.00, while a rating of 0.00 means no guesses required.  Enjoy!

If you stare at the dot for 30 seconds without moving your eyes you will be shocked at the colors you see. 

Here’s how it works.  The first image is a constant brightness image with the hues (colors) reversed- it is not just a negative.  The constant brightness makes the rods in the eye perceive the b&w image accurately.  But the cones are fatigued by the colors.  Therefore when they see white, which is a full spectrum, in the b&w image they don’t respond to the fatigued colors, and thus perceive the opposite ‘true’ colors.  

This is a very interesting demonstration that color is not merely physics, i.e., the color of an object is not merely the colors that are not absorbed.  Color depends on what the neurons tell the brain, and how the brain interprets it.

Birds and reptiles have 4 types of cones that detect 4 different frequencies.  Along the way mammals lost 2 of these cones.  So dogs have very poor color vision (seeing eye dogs distinguish traffic lights by position!).  Fortunately for primates, a duplicated cone gene came into use, so we humans have 3 types of cones (long, medium, short or RGB, though ‘R’ is closer to yellow at its peak sensitivity).  But 2 of the 3 cones (both attached to the X chromosome – which males have only one of, hence the prevalence of colorblindness in males) are very close in peak frequency, unlike the widely separated 4 cones in birds and reptiles.  So not only can birds and reptiles see in more colors than humans , such as “invisible” ultraviolet, they can outsee us in colors.  At least, except for owls, we have them beat in 3D with binocular vision.

Do you see a 2 or a 5?

Just deciphered the UPC code in the 42 Puzzle.  PANIC!

In 1862 President Benito Juarez ordered Mexico‘s army, under General Ignacio Zaragoza, to defend the nation against French invaders.  The army, consisting of ill-equiped soldier-indians, met and defeated Napolian’s powerful European army at the Battle of Puebla.  May five – Cinco de Mayo – is a celebration of the great victory.  Alan and Lia party and parade to mark the holiday.  They are cooking traditional Mexican tripe soup, menudo.

Jana Tylova beat the  odds, and, as the only woman finalist, solved the puzzle below (after many others) in under 15 minutes to win the first ever Sudoku Championship in Lucca Italy.

 

Hint: you need to guess to solve this final puzzle.

I don’t seem to fit with any crew very highly.  Guess I need my own craft & crew.