2015-Apr-19
The first intellectual operation in which I arrived at any proficiency, was
dissecting a bad argument, and finding in what part the fallacy lay; and though
whatever capacity of this sort I attained was due to the fact that it was an
intellectual exercise in which I was most perseveringly drilled by my father,
yet it is also true that the school logic, and the mental habits acquired in
studying it, were among the principal instruments of this drilling. I am
persuaded that nothing, in modern education, tends so much, when properly used,
to form exact thinkers, who attach a precise meaning to words and propositions,
and are not imposed on by vague, loose, or ambiguous terms. The boasted
influence of mathematical studies is nothing to it; for in mathematical
processes, none of the real difficulties of correct ratiocination occur.
-J.S. Mill, Autobiography
I believe “school logic” is a.k.a. scholastic
logic and is something along the lines of “philosophical” logic and what Mill
covered in his A System of Logic.
Sometimes I found combinatorics problems to require careful thinking in order
to avoid plausible-looking mistakes.
At Art of Problem Solving,
instructors suggest “counting in two ways”, i.e. using two different counting
strategies and comparing the results.
2014-Oct-14
Programming wisdom:
Someone wrote to me once suggesting that JSLint should give a warning when a
case
falls through into another case.
He pointed out that this is a very common source of errors, and it is a
difficult error to see in the code.
I answered that that was all true, but that the benefit of compactness
obtained by falling through more than compensating for the chance of error.
The next day, he reported that there was an error in JSLint.
…
I investigated, and it turned out that I had a case that was falling through.
…
I no longer use intentional fall throughs.
-Douglas Crockford
2014-Aug-18
This reminds me of a story from the time when Queen Mary and Westfield College,
University of London decided to change its name to Queen Mary, University of
London.
My colleague Wilfrid Hodges was giving a lecture in Germany, and put up his
first slide, giving his name and affiliation as “Wilfrid Hodges, Queen Mary,
University of London”.
Somebody asked, “Is that a joint publication?”
-Peter Cameron
2014-Jun-29
An interesting comparison of the cultures of the US and Germany:
http://math-www.uni-paderborn.de/~axel/us-d.html
When I travel internationally, I wish I could absorb this level of detail about
a culture, but of course it’s impossible without living there for an extended
period of time.
2014-May-26
(This is an old list from when I was studying it
in around 2009.)
2014-May-25
From Modern Computer Algebra:
“We start by using [Newton iteration] to find a custom-Taylored division
algorithm that is as fast as multiplication…”
