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Computers beat humans at Computation, Enumeration and even (though most people don’t realise this) Deduction. However, a central feature of most mathematics is relating to the literature, which in practise is gathering together results (and concepts) to be used for … Continue reading
Many years ago I spent several months obsessed with a marvellous theorem of Lohkamp, without any new theorems of my own resulting. I have learnt both mathematical and moral lessons from this, which I explore in this posting (and possible … Continue reading
The entropy of a set is the logarithm of the number of elements in . Gromov’s remarkable insight (which he elaborated on in a course I attended a decade ago) by taking the logarithm we can ensure additivity: . Perhaps one should also … Continue reading
People enjoy solving puzzles. In real life, solving puzzles is useful, for instance recognising a camouflaged predator. But this is not a sufficient reason to be rewarded (emotionally) for solving the puzzle, rather than just for the outcome. In a … Continue reading
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