At last, I am done at the Universiteit van Amsterdam. This week I turned
in my last project for the semester, an enormous programming
project (and also re-submitted a paper that got lost in email, nearly
giving me a failing grade in another course). Amsterdam was a
fantastic experience; I wish I’d had more time to spend in the city
and the Netherlands. We’ll just have to go back some time…
However, taking masters courses at the UvA/ILLC I did also learn so
much more than I expected to. Below are some of the more useful things
I learnt and wrote in my note books, in direct quotation from my
lecturers:
All of these [infinite numbers] have their own personality. Aleph-one
is sort of dull, stubborn; aleph-two is more liberal. Of course,
aleph-zero is countable–a joyful character.
These days, we think of singular ordinals as more friendly objects,
and the regular ordinals are… not so friendly.
You can make enormous leaps in a proof just by saying ‘Similarly,’ and
hoping for the best.
Every initial segment [of a set of numbers] is like made of cheese or
whatever.
This proof is better understood in the darkness. [Turns off the light
in the classroom.] Some proofs have that property.
And now..! The great invention of… somebody… hmm.
I am already two minutes overtime and someone up there has a birthday
and I was promised some cake, so I will take cake down and prove this.
Simple things should have simple proofs. This is not entirely true.
Arabic and Chinese are the most interesting machine translation
languages to the US now. Farsi might become part of that group soon if
the Iranians stick their heads far enough out.
If the last element of this list did not exist… Something terrible
would happen.
If I were cruel, I would exchange the regular symbols with ones like
0, or 1, or even Ω or ∆; but I’m not. But there are people
out there…
I will wash my hands before dealing with this holy subject of the
axioms.
Counting on your fingers is not enough [with infinite numbers]. Well,
it depends on your fingers I guess.
This deadline is more fair, since everyone will have the same ‘no
time’ to work on the homework.
There are no miracles in mathematics, nothing comes from thin
air. Except… the empty set comes from thin air.
The reason they call them heuristic methods is that you can do
whatever you want.
[There is one exception to the product of probabilities being lower
than each individually]; the chance of a series of unfortunate events
is always higher than each unfortunate event happening individually.
Discovering Amsterdam 