4 ms·

I've always found Knuth's views curious. Is it just that he's from a different generation, or am I too much of an amateur to understand his wisdom? I don't know

I've always found Knuth's views curious. Is it just that he's from a different generation, or am I too much of an amateur to understand his wisdom? I don't know. A couple of days ago he gave me a copy of his paper on Leaper graphs (On dead trees.. quaint :-) His office is a few doors from mine.) Along with a charming note about rewards for finding bugs. Anyway, Leaper graphs are the graphs that describe the moves of a generalized Knight on generalized chessboard. So I researched this some more, and found that Knuth was the first to enumerate all the Knight's tours that are invariant under 180° rotation. At this point I'm thinking, this sounds like it could be an ICFP problem, and a language like Haskell would be ideally suited for it. Nope, turns out he wrote the program in his C variant. http://sunburn.stanford.edu/~knuth/programs/sham.w http://sunburn.stanford.edu/~knuth/programs/sham.w I'm amazed you can write that in C and have it turn out as short as it was. It also looks like it has goto's. I really don't know what to take away from it.

mhansen 17y ago
The chessboard has rotational symmetry: if you turn it 180 degrees it is the same. Would not all tours be invariant under 180 degree rotation? EDIT: Sorry, I understand now. If the knight's tour ends directly opposite it's starting position, it is invariant under 180 degree rotation.
- randomwalker 17y ago
  This might help: http://www.mathpuzzle.com/leapers.htm http://www.mathpuzzle.com/leapers.htm As you can see from those examples, a symmetric tour is a rather regular-looking object; a random tour has an extremely low probability of being symmetric.
  - mhansen 17y ago
    Ah, thank you!
access_denied 17y ago
I take away from it that real programmers do not have an emotional attachment to one or other tool/ language. They are interested to solve a problem with maths and logic and the computer and his language are just the butler; a layer that has to be abstracted away. Obviously Knuth thinks that books as a medium are still valid. (I am with him on this one.) I have not read the book nor do I have any clue about Leaper graphs, but for some reason he thought it could help to research this. How can this research / knowledge help? Maybe it's just fun, I don't know.
- deleted 17y ago
  [deleted]
eru 17y ago
"I am more comfortable doing it with labels and goto statements than with while loops, but some day I may learn my lesson." (http://sunburn.stanford.edu/~knuth/programs/sham.w http://sunburn.stanford.edu/~knuth/programs/sham.w)

mhansen 17y ago

The chessboard has rotational symmetry: if you turn it 180 degrees it is the same. Would not all tours be invariant under 180 degree rotation? EDIT: Sorry, I understand now. If the knight's tour ends directly opposite it's starting position, it is invariant under 180 degree rotation.

randomwalker 17y ago
This might help: http://www.mathpuzzle.com/leapers.htm http://www.mathpuzzle.com/leapers.htm As you can see from those examples, a symmetric tour is a rather regular-looking object; a random tour has an extremely low probability of being symmetric.
- mhansen 17y ago
  Ah, thank you!

access_denied 17y ago

I take away from it that real programmers do not have an emotional attachment to one or other tool/ language. They are interested to solve a problem with maths and logic and the computer and his language are just the butler; a layer that has to be abstracted away. Obviously Knuth thinks that books as a medium are still valid. (I am with him on this one.) I have not read the book nor do I have any clue about Leaper graphs, but for some reason he thought it could help to research this. How can this research / knowledge help? Maybe it's just fun, I don't know.

deleted 17y ago
[deleted]

eru 17y ago

"I am more comfortable doing it with labels and goto statements than with while loops, but some day I may learn my lesson." (http://sunburn.stanford.edu/~knuth/programs/sham.w http://sunburn.stanford.edu/~knuth/programs/sham.w)