Author Archives: Robin Houston

Revisiting “On editing text”

This document is an incomplete draft. About two years ago I wrote about a category-theoretic treatment of collaborative text editing. That post is unique in the history of Bosker Blog in having been cited – twice so far that I know … Continue reading

Posted in algorithms, category theory, Mathematics | 2 Comments

Decoding the mysterious symmetry of the bicycle lock numbers

Suppose you have a lock of this sort that has n dials and k numbers on each dial. Let m(n, k) be the minimum number of turns that always suffice to open the lock from any starting position, where a turn … Continue reading

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The bicycle lock problem

Don’t lock your bicycle with a combination lock. Someone will steal it: I learnt this the hard way. It’s quite easy to open a combination lock by feel, without knowing the combination. Try it: with a bit of practice, you … Continue reading

Posted in algorithms, Mathematics | 4 Comments

Beyond Bézier curves

There is a new feature of Pages and Keynote, not mentioned in any of Apple’s publicity nor in any press coverage I’ve seen, that is really very interesting. Perhaps it will even one day prove to have been revolutionary, in … Continue reading

Posted in algorithms, Mathematics | Tagged , , | 8 Comments

I hate the Pumping Lemma

I hate the Pumping Lemma for regular languages. It’s a complicated way to express an idea that is fundamentally very simple, and it isn’t even a very good way to prove that a language is not regular. Here it is, … Continue reading

Posted in chatter | 45 Comments

The algebra of Unix command substitution

Shadab Ahmed raised an interesting question. Open a Unix command shell, type : ‘!!’ and press return. Then type : “!!” ‘!!’ and press return. Now repeat the following a few times: press the up arrow, and press return.

Posted in Mathematics | 6 Comments

“Venn diagram” partitioning

Paddy3118 wrote about partitioning elements in the same way a Venn diagram does. So, if we have sets A, B and C, the partitions are

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