Fall 2003 QG Seminar Errata

John Baez

• On page 15 it's remarked that JB doesn't know how many 3-element rigs there are. Nick Hay wrote a program to find out, and he found two: Z/2 with its usual + and x, and another one, which I believe must be isomorphic to the set {0,1,2} equipped with the operations

  (x + y) min 2
  

  and

  xy min 2
  

  That is: normal + and x, followed by replacing any number greater than 2 by 2.
• On page 22, the condition (sum j) |A_ij|² = 1 is not sufficient to guarantee that the matrix A is unitary; we need (sum j) A_ij A*_jk = delta_jk.
• On page 26, there's a reference to "JB's CM notes". These classical mechanics notes are not yet available online, but they should be someday!
• Near the top of page 36 it should read:

  Ha* psi = (a* H + [H,a*]) psi
          = (a*H + a*) psi
          = (a*E + a*) psi
  

  We left out the "psi" on the third line.
• On page 46, it should read "where |i,psi>|² is the prob. of system in state psi to be found in state e_i."
• On page 49, the first chain of equations should begin with

  Delta2psi(A + C) 
  

  and end with

  Delta2psi A
  

  We left out the squares.
• On page 58 it should say "we use the fact that psi_n form an orthogonal basis...", not "orthonormal".
• On page 65 we left out the label "t = 3pi/2" on the bottom graph, where the corkscrew is going the other way.
• On page 66 the 4 diagrams at the bottom right should be labelled t = 0, t = pi/2, t = pi, and t = 3pi/2. We have some of the times wrong. This rather cryptic diagram is meant to show the four most interesting points of the swinging of a pendulum with period 2pi, corresponding to 4 points on the graph above.
• At the very end of the notes we should include a handout giving the proof that B⁷ is isomorphic to B. This can be found in Figure 1 of a paper by Marcelo Fiore, Isomorphisms of generic recursive polynomial types, in 31st Symposium on Principles of Programming Languages (POPL 2004), ACM Press, 2004, pp. 77-88.

home