Prof. Sacks was the prof for Math 141 (Mathematical Logic) at Harvard last
year. The class was so laid back it sounds like something out of Hitchhikers.
Sacks also provided us with a few great quotes. It started when he was
summing up what we'd learned about first order logic, and he said
"Now we've seen that you can take the Peano axioms, and make a standard
model for them... you start with one, then you tack on two, and three,
and four, and..." and as he says this, he moves over one step with each
number, `placing' them next to each other, until about ten, at which point
he's reached the door. So he walks out the door and turns the corner,
counting faintly... after a few seconds we hear a "seventeen" wafting down
the hallway, and then a door slam shut. The whole class is cracking up,
and about 20 seconds later he walks back in to the room with "...but we
also know that you can construct a model with numbers bigger than all of
Other various quotes from his more inspired lectures:
Somehow, the price of clarity is complexity. ...Wait, are there any
philosophy students in the room?
Now this theorem I actually am going to prove. You should know that not
one in a hundred logic professors can prove this theorem without preparation.
Now the interesting thing here is that I have not prepared...
(In all fairness, he did in fact prove the theorem...)
This makes sense. This over here, this does *not* make sense. That's
why I called it algebra.
I brought this book today... a wonderful book. Because I wrote it.
...How much do you think this book costs? $60? $70? Nah. $90.
And $130 in Japan.
The depth is the significant aspect of the length.
By "recursion" I mean "defined by recursion".
It goes without saying, but I'm going to say it anyway... I like to
say things that go without saying.
I was going to say "topology", but I wasn't sure what I meant by that.
Theorem. I'll attribute this to Myhill; I can't imagine who else
would have proven it.
So this element is a smashing witness to the fact that cC is not We.
Set theory. Yaaay, set theory! ...Set theory, as you might guess,
is about sets.
[This satisfies] every axiom which I can think of, and a few more
I'll tell you about next time.
Sacks: Today we're going to do comprehension. What is comprehension?
Student: I dunno
Existence is a cute proof. I don't know what word to use. Neat? Cool?...
Anyway, existence is not obvious.
Of course, we could have introduced recursion theory that way, by
teaching set theory and then restricting ourselves to the finite
ordinals... that would have been insane.
Who knows, maybe this will work.
I hate rigor.
An obscure proof which I managed to present in an obscure way.
Mustowski was always annoyed at me that I misspelled various Polish
names-- his was easy, but some of his friends' were impossible.
By induction...no, not by induction...by nothing, we have that...
Absolute. Absolutely absolute. Absolutely positively definitely absolute!
Good question. Why *do* I want to show they're equal?... I'm
Student: Are we in the middle of a proof?
Sacks: No, this is just another digression.