With the recent assertion by SCO's chief counsel that `The GPL is invalid' based on an clearly absurd interpretation of copyright law, their case has completely severed what few strands of credibility it once possessed. Some people still argue that this is an important lawsuit, because of the possibility of related actions. This is to neglect the useful lawyer's maxim that bad cases make bad law. I don't think that significant precedents on IP will come from this farce, and the only non-prurient interest I see left is to understand why a well-regarded law firm like Boies, Schiller and Flexner has let its reputation be abused in this way.
Bram argued in his 13th August diary entry against the accuracy of electronic voting machines: in my last post, I tacitly made the assumption that if electronic voting systems are ever deployed, they will perform better than mechanical systems under normal circumstances. I realise that there are grounds to believe this an optimistic assumption; still it is important to bear in mind how bad mechanical systems are: apparently almost 1 in 30 votes is miscast or ignored. Also, there is no reason why electronic voting should not create a paper trail, although, I agree, most current proposals do not.
In Bram's 6th August entry Bram introduces a `game' played over ZFC: even in the simplified case of large cardinal axioms (LCAs), there may be no fact of the matter of which is stronger: if you look at the diagram of important LCAs in Kanamori's "The Higher Infinite", they form a partial order, not a linear order (I don't know whether this reflects known independence results or just ignorance). I do think as a kind of thought experiment, your exercise is illuminating; I like to think about how different mathematical pholosophy might be if results came to known in different order, might we regard a much weaker or stronger set theory as the default?
The Knight's Tour I
First in a series of posts on a combinatoric problem. A knights tour of an MxN chessboard is a sequence of squares of the board, where there is a valid knight's moves between each square and its successor, and where each square of the chessboard occurs exactly once. The tour is closed if its first square can be reached from its last. Can you prove that there are no solutions for 2x2, 3x3, and 4x4 boards, or closed solutions for the 5x5 board?
Erratum: The original version of this entry asked to prove there are no solutions to 5x5 boards, which is false: there are solutions, only no closed solutions.