## 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) |Aij|2 = 1 is not sufficient to guarantee that the matrix A is unitary; we need (sum j) Aij A*jk = deltajk.
• 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 ei."
• 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 psin 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.
Thanks go to Squark and Nick Hay for spotting some of these errors. If you discover any more, please let me know, and we'll note them here. Eventually we'll correct them (the old fashioned way, using correction fluid) and rescan the pages.

baez@math.removethis.ucr.andthis.edu
© 2003 John Baez and Derek Wise