Aug 2, 2006

Cubes 2

I know, this sequence of titles looks like that terrible movies Cube and Cube 2: Hypercube (I apologize to those who liked them...), but Prof. Caticha answered my email and, as I predicted, there is a more elegant formula for expressing the n-cubes algebraically. It is not to much different from the one I posted, but I will describe it anyway. Instead of initiating with the representation of the 1-cube as I showed in the last post, you can initiate it by representing the 1-cube as the Pauli matrix

Also, changing the notation of the unity matrices such that I_n is the (n+1)x(n+1) unity matrix just to make the final formula prettier and following exactly the same procedure as before, the expression for the n-cube becomes

Well, I have nothing specific to speak this week, but I was browsing the arXiv and found some odd papers. What I mean is that they have curious titles, but I really still haven't read them to say something about their contents. I'm listing them here if someone wants to check. :)
  1. Football: a naive approximation to the effect of increasing goal size on the number of goals - J. Mira (physics/0607183)
  2. A fixed point in Coptic Chronology: the solar eclipse of 10 March, 601 - John Ray, Gerry Gilmore (astro-ph/0607520)
I have found some interesting links this week:
  1. California and Carnegie Planet Search
  2. Wave Packets Animations
  3. Find a Postdoc
and also some news:
  1. Mysterious quasar casts doubt on black holes
  2. Shadowy T-rays: Hunting Tumors and Exploring the Universe
  3. Medical 'Miracles' Not Supported by Evidence

Picture: Hypercube, by Shem Booth-Spain

1 comment:

mac_davis said...

What does the little sigma mean?