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
those."
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
completely confused.
Student: Are we in the middle of a proof?
Sacks: No, this is just another digression.
---
I am taking a statistical physics course right now, and have compiled
the funniest quotes from this class. All quotes are from John Thorstensen,
the professor. He likes to keep the class lively...
"Manually operated analog scribing device" (description of chalk)
"In fact, entire math departments have been known to go off the
deep end" (on infinite real numbers)
"Yup, you're losing your marbles." (on a statistical problem involving
marbles in a jar)
"This, incidently, works great if you're color blind." (probabability
of picking a red or green marble)
"Uh, that's the same equation."
"Now you have to pound the table, and jump up and down."
"Good day to get a little extra sleep."
"You use little itty bitty nails, and nail the atoms down." (on how
to measure the number of states they can be in)
"We can throw out constant factors as we want."
"I didn't know Maxwell had thermodynamic relations...I guess he got around."
Avogadro's number..avocado's?"
"Factorials of Avogadro's number become intractable."
"And what is this? Can you say ENTROPY?"
"It's just a..it's just a word."
"Then they have to come out, and cut you off with a blowtorch."
(on the hazards of licking a cold flag pole)
"Which in decimals is 1.66666...which is the mark of the devil."
"Enthalpy, which in Greek stands for E+pV."
"This will become unclear in time."
"George Q. Enthalpy, little known physicist."
"cross derivatives? angry derivatives!...perturbed..."
"You all are probably wondering what all this stuff is good for."
"I'm tenured, there's almost nothing you can do about it."
(after making a mistake in sign convention)
"The Joule-Thompson Throttling. Now you can't throttle them,
they're dead." (an experiment)
(
geocities.com/hanson_c)