On April 6, 2005,
I was thrilled to have the opportunity to speak with David X. Cohen, who
has a bachelor's degree in physics from Harvard University and
a master's degree in computer science from UC Berkeley.
A longtime writer for
The Simpsons, he left to develop Futurama with Matt Groening, where he was the executive producer and head writer. He has won Emmy Awards for his work on both shows.
An edited transcript of our conversation follows:
DXC: This is David X. Cohen. I'm just giving a sample of my voice.
So if you hear my voice and Sarah Greenwald's voice, you'll be able to
distinguish them.
Sarah: Thanks! But I think they'd be able to do that anyway!
From your past comments, it seems like you are really excited about math
and science, and that you like the math references but that you didn't
want them to outweigh the show. But it is hard for me to tell
how some of the other writers feel about the math references.
Do they mainly come from you, or other people too?
DXC: This is what I would say about my role in getting the math
references on Futurama. On
Futurama I was the head writer, so I could
set the tone about what kind of things were going to go in there.
Matt Groening could have theoretically overruled me, or the Fox studio,
but usually the mathematical references were more of a background joke
than the center of attention. It was basically the kind of thing
where any kind of background jokes that we wanted to do, we
were going to get away with. Because I was interested in the math,
it was pretty easy for me to wedge the things in there.
As far as where did the specific jokes come from, as you and your readers
know, there were several other people besides me who had a
math background:
Ken Keeler with a PhD in applied math and Stewart Burns who has a masters
in math from Berkeley. Jeff Westbrook also has a PhD in math.
Sarah: Isn't his PhD in computer science?
DXC: Computer science, you're right. I think his undergraduate
degree might be in math. Something to do with math [physics and history
of science]. Bill Odenkirk had
a PhD in chemistry, so certainly he studied his share of math. Everyone
else was a nerd of some kind or another –
again I use that term
in a loving fashion because it includes me and I love myself so much.
These are all people who as kids, even if they ended up being a history
major, many of them, I would not be surprised if they were on the math
team or whatever. These are people who are open minded to intellectual
subjects of any kind whether it is their area of expertise or not.
Math jokes are not the only kind of weird background jokes we put in, of
course. We have a lawyer on staff, and no doubt he snuck some law jokes
in that the rest of us didn't understand. The secret of these things
is to put them in the background or have them go over the heads of the
people who don't know about them, so that it is a treat for the people who
do know about them, but it doesn't derail the experience for the people that
don't. That was our goal and hopefully we succeeded in that.
Sarah:
In Mars University you had help with the
blackboard scene from David...
DXC: David Schiminovich.
I'll give him credit in a moment.
In fact, let me digress here to thank David Schiminovich.
I have an old friend from middle school/
high school named David Schiminovich, who is now an astrophysicist at
Columbia University in NY, and over the years he has provided numerous equations
and scientific references for The Simpsons and Futurama
so I just wanted to give him a shout out. A
simpsonsmath.com shout out
to David Schiminovich. Some specific things he provided, for example,
are Witten's Dog in the Mars University
[1ACV11]
episode of Futurama.
Sarah:
In the Lesser of Two Evils
[2ACV06] you have Bender and Flexo's serial numbers
expressible as the
sum of two cubes.
DXC:
I think that was my idea, although that might have been Stewart Burns.
That was discussed in the room in Futurama, so no credit whatsoever
to David Schiminovich for that. In fact, I'm taking away some credit for
other things for him not helping us on that one.
Sarah: And what about the episode with the
P and NP books
in the bookcases –
did you or someone else put that in?
DXC: The P and NP things are generally me
[loud car horn]. Oh, someone driving by
did not like the discussion of P and NP. Someone is not a fan of
P and NP. I had studied theoretical computer science at Berkeley, so
naturally the P and NP question is something that everybody is aware of
and nobody is actually working on because everyone is aware of it.
For my friends at Berkeley, I like to put in a theoretical computer science
reference once in a while. The joke there was that there were two binders.
If you are talking about the same episode. Did we have more than one
reference to that?
Sarah: I think just that one in Futurama
[Put your Head on my Shoulder
[2ACV07]].
DXC: There's two binders on the shelf and one is labeled
P and one is labeled NP, thereby indicating that they had found a way of
dividing up those problems and answering the question of whether they are
the same category or separate categories. That was me.
Sarah: Cool! The Escher
Relativity reference from I, Roommate
[1ACV03]
with the apartment
is actually quite interesting to me because it kind of relates to my
research. When
Bender is falling, is it the animators or writers
who decided which stairs he was going down and coming back on? Did you have
some global geometric structure in mind? My guess is probably not,
but it is actually quite interesting...
DXC: Your guess is quite correct. This is one of many things
where it is easier to write than to animate. Sometimes we put things
in the script like this and we say it's an apartment that looks like
the famous Escher drawing with the crazy perspective and stairways going
in all directions. We said something like
Bender falls down one and goes out a door and falls down the other
and we just assume that the animators can do this,
disregarding the difficulty of it, and they usually come through because
Rough Draft's animators are so good.
Sometimes we even realize what a challenge we are posing for them and
it doesn't stop us, but we just
write "good luck animators" when we give them the script.
Sarah: Like when he comes down
here there is a time delay
so I don't know if there were things that were planned out, or that is
happening when he is off the screen...
DXC: I would like to say we were discussing how far Bender
was flying into another dimension between reappearances, but it was
probably determined not by the math or the physics of space, but the
show had to be 22 minutes and 31.6 seconds long or something, so Bender had
to be off screen for exactly how long he was off screen.
Sarah: It's a great clip.
Are there other Futurama math moments you want to comment on?
The Heisenberg Uncertainty Principle
[Luck of the Fryish
[3ACV04]]
is something you mentioned in a
previous interview.
DXC: Yeah.
Sarah: I can't remember actually, I think maybe
Numb3rs referred to it now
[Uncertainty Principle [104]].
DXC: Referred to?
Sarah: Heisenberg Uncertainty...
DXC: Oh, they did!
Was my quote about the Heisenberg Uncertainty Principle that it was the
only reference to it on a TV show or that it was the only joke about it
on a sitcom? Because Numb3rs is a drama.
Sarah: I'm sorry, but I don't remember.
DXC:
Then I may have to back up and say that
we made the only
joke about the Heisenberg Uncertainty Principle. That's
one of my favorites because we actually violated our own rule. The joke
is out loud about the Heisenberg Uncertainty Principle. We liked it so
much that we said it only takes two seconds and if it derailed anybody, they
could get back on track a second later.
Here's one more, and credit to David
Schiminovich again. One of the points that I docked him is coming back,
because one of my favorite math and science things from Futurama
is the question of how they can travel around the universe even though
you can't go faster than the speed of light. Before the show went on the
air, I was very worried about this –
unnecessarily it turns out, because nobody
cares. So I talked to my physicist friend
David
Schiminovich, and we talked about a few possible reasons why they could
go faster than the speed of light. The ultimate one we settled on,
which I'm very proud of, is that they are not going faster than the speed
of light, but that they have increased the speed of light in the future.
We never got around to showing the back story of how that happened exactly,
but in my mind, some reaction was set off on Earth or somewhere nearby, and
there's an expanding bubble moving out through the universe – and within
that bubble the speed of light is now faster, and outside of it, it is
still what is was before. People actually study this in physics – that
there may be regions of the universe where there is a boundary where the
laws of physics change on one side or the other. Kind of interesting...
Sarah: Speed of light being constant is not so clear anymore,
anyway.
DXC: That's right! I just read about that too. That's
another of my favorites.
Sarah: There are a number of scenes on blackboards
where, for example, the one that you mentioned in
Mars University you
can actually see, but there are others where it is just blurry.
Is that because...
Did you as writers say what was going to go on the blackboard,
and if so why is it blurry on both the DVD and on TV, or did you just say,
"Put some symbols on a blackboard and make it blurry," to the animators?
And I'll show you some examples if you want...
DXC: I'd have to see the exact ones you are talking about.
There are two possibilities that spring to mind. The most likely, by
far, is that we didn't even know that a blackboard was going to be in the
scene, but it ended up there, and the animators put something in later on...
Sarah: I don't know if we are going to be able to see
this at all [in this bright light]... I might have to show you later on.
DXC: It's the Globetrotter's physics team
[Time Keeps on Slipping [3ACV14]].
Sarah: And you can see...
Well I can't see right now, but in better lighting
you can see
part of the blackboard
and read what is there, but the rest
of it is just blurry in other shots [shot 1,
shot 2].
DXC: That blackboard –
I'm trying to remember –
I would have to look at it [in better light]. I don't remember the answer
to that. That is a particularly complicated blackboard. I think we
worked on that blackboard. You're saying you can't read it?
Sarah: No –
not on the DVD.
DXC:
Here's what I'm going to do in honor of this
simpsonsmath.com
extravaganza. Wait I keep saying Simpsons, but it's
all Futurama.
Sarah: Yes, but both Simpsons
and Futurama for tonight's talk.
DXC: I am going to call up Rough Draft studio, the
animation studio, and find the original drawing of that and see if it's
legible.
Sarah: Wow!
DXC: I am almost positive that we worked to make that legible,
because I remember when we were editing, we requested moving somebody
aside to see the blackboard better, but I can't actually remember if that
was just because we wanted to show that there were some crazy equations
on the blackboard. That might be. We maybe just wanted to say there is
some complicated stuff on the blackboard.
Even if it was gibberish, just to make the joke that they used
basketball players for physicists.
[Update from DXC:
Hmm. I have no recollection whatsoever of that 360-degree-slamdunk
equation. I feel pretty confident in classifying this blackboard as being
otherwise composed of gibberish.]
Sarah: Is it you or the animators who would do those kinds of
things, you being the writers?
DXC:
This is how I would break it down. If the equations mean anything...
If they are funny, then it was me, particularly.
Sarah: I'm sure the other writers will be happy to hear
that!
DXC: If they are actual math, then it was the writing
staff probably who provided them, and if it was some crazy thing, like
here the joke may have just been there were basketballs in the equations,
and we decided that was enough of a joke, and we were too lazy to also
make it a real math reference, but I have to look at it to be sure. [See
the above Update from DXC.]
Sarah: Here's another example where Fry is having this
nightmare about...
DXC: Ancient Egyptian Algebra
[A Fishful of Dollars
[1ACV06]]...
Sarah: And you can see the ancient Egyptian algebra
blackboard, but on the final exam, it looks like there are some symbols on
there, but I don't know if that was just "draw some symbols!" or if somebody
planned out what they were.
DXC: I don't think we planned it. A lot of times
what happens is that when we are writing it,
we are first concentrating on if it makes sense and is funny, and then
when we see the rough animation coming in, we realize – oh, there
is a blackboard in the background, let's now provide something for that
blackboard.
These things can come in at the beginning, they can come in
at a later stage when
the animation is partly done, or they might never come in if we didn't
realize there was an opportunity.
Sarah: From The Farnsworth Parabox
[4ACV15],
this is universe XVII.
There are a bunch of Roman numerals you can almost
make out and guess, but not really. Did you just say to animators, "Put
some Roman numerals on a board?"
DXC: I think you are right.
In the case of this Roman numeral universe and in the case of the ancient
Egyptian algebra, we probably said,
"There is an equation with a lot of Roman numerals on the board," or "There
is an equation with Egyptian symbols on the board,"
and we didn't specify it further. I'm sorry! We blew an opportunity
there. We were busy!
Sarah: What kind of responses did you get to your challenge to
mathematicians to analyze Fry's DNA?
DXC: For those of you who have listened to the DVD commentary of
Season 3, Roswell that Ends Well [3ACV19], I "wisely" gave
out my email address to everyone in the world, although luckily it wasn't my
real email address. But even giving out my "fake" email address that I give
out when pressed may have been a mistake, because the amount of mail I got
about the question of who Fry's parents and grandparents are in this strange
time travel scenario was overwhelming. I got literally hundreds, maybe 500
responses from around the world. The interesting thing is that the DVDs
were released
on different schedules in different parts of the world. We recorded that
commentary, and I
said that Fry was his own grandfather in this episode. I said, "That's an
interesting question. Where did his genes came from? What percent of each
of his grandparents' genes does he have?" And then I gave my email
address and said that if you can figure it out, then email me. I forgot
about this because after
we recorded the commentary, a year went by when they were just putting
the DVD together. I forgot all about it.
Then a year goes by and suddenly I get 100 email messages from Australia
because it came out there. I forget the exact order. Australia, England.
It came geographically first. 100 from Australia. 300 from
England. And then I was thinking, "Oh god,
now it is coming out in the United States," 1000
from the United States. I apologize to anyone who sent something to me that
I didn't answer. I would say that I answered about 100 of them at
random. Some of the ones that I could see were very long
files I purposely looked at.
Sarah: You realize
you are encouraging people to send you long files to look at...
DXC: Most of the email that comes to that address that I gave I cannot look at because of a matter of time. So I apologize to everyone who sends
it. On rare occasions I respond at random just
so that I can feel good about myself. I'll break them down for you.
Tell me if I'm talking too much here, by the way.
Sarah: Not at all – it's great!
DXC: I'm going to break them down for you. I would say that
70% of the responses, of however many responses there were,
said, "I don't know much about math or genetics,
but I just want to say Futurama
rocks," or maybe about 2% said, "I just want to say Futurama is
OK, and my grandmother gave me this DVD, and I just wanted to see if it was
you."
I would say about half of the remaining ones took our position that he was
one third each
of his three other grandparents. There were a few that said that
his grandfather (the person who he thought was his grandfather) really was his
grandfather and his grandmother was already pregnant when he got killed, but
that was not our intent because that's not as crazy and interesting.
The remaining people brought up this issue that is possibly the most
interesting, which is that nothing really makes sense because of this well
known science fiction paradox about his Y chromosome.
And if he had no paternal grandfather, as he was his own paternal
grandfather, and the Y chromosome comes down the line of male ancestors,
then the Y chromosome could only come from himself so you are always stuck
with this loop, unless you allow for some mutation.
Sarah: Or you allow something like his grandfather was his
grandfather to begin with, but then after time step 1, Fry was his own
grandfather. That hurts my brain –
I don't know what you do with that one,
but...
DXC: Suggesting that there could have been some asymptotic behavior
so that Enis was his actual grandfather originally, but as you go through
the loop repeatedly in time, his DNA gets watered down, but he just keeps his
Y chromosome from Enis. That seems... Again no offense to the thousands of
pieces of email that came in, but what you just expressed was much
more to the point than the great majority. But some of them were really
good. A few of them were actually laid out with integral signs and really
nice looking math, and those I actually forwarded to Matt Groening and the
mathematicians on staff. So the people who really put effort into it –
some
of your work did make the rounds to the Futurama
mathematicians. So thank you, and I
appreciated your efforts, and I'm sorry if I didn't get to your contribution
to fake science.
Sarah: Other math or science moments
that you want to comment on?
DXC: I'm sure there are, but we may have to resume this
after I think about it for a while, since I didn't prepare well for this
interview. I like all of the computer science references in there.
This one still makes me laugh. Can this be a PG-13/R rated commentary?
Sarah: Sure.
DXC: In the DVD commentary I had to tell a cleaned up
version of this story.
There was an episode that had a lot of Star Trek parodies.
It was the first episode of Futurama season four,
Kif Gets Knocked Up a Notch
[4ACV01]. The character of
Kif Kroker gets pregnant. There is a scene which is a parody
of Star Trek: The Next Generation where they have the
holoshed, which is not a very clever take on the holodeck. You go in there
and it can create a holographic version of anything, basically.
I was a huge Star Trek fan, so this is not a knock on Star Trek
at all, but basically anybody who
knows anything about computer programming in computer science,
when they see the holodeck, they say, "Well
the amount of time it would take to program up this scenario, which can
take everything into account... It could take 10 million programmers
10 million years, or whatever, to just do this one scenario where
they are having a picnic in central park in 1835," or whatever it is.
Yet they can call up anything at any time. We had a joke in this
episode where Kif wants to have a romantic day with his fiance Amy
and he takes her to this
and he says "I programmed it myself –
4 million lines of BASIC."
That is another case where we actually did the joke out loud instead of
putting it in the background.
I thought that was very funny. It may have only been me that thought
it was very funny. We were discussing this in the rewrite room.
One of the writers said, "4 million lines of BASIC, 99% of the audience is
not going to get that." Eric Kaplan said, "Fuck them!"
Sarah: But don't you think a lot of Futurama's
audience is exactly that target audience?
Not just one percent, although I don't know how many..
DXC:
You are right that Futurama's audience is not the regular
TV audience. We may have misestimated the percentage, but I suspect
that the majority of people watching would not get it. For example,
a lot of people watching are kids, and BASIC programming
is not as big now as it was when computers could only do what you told
them to do. I'm sure the percentage of people who got it was not
high, but it was probably higher than one percent, I'll admit.
But anyway, that was our discussion, and
lack of concern for 99% of our audience or 93% or whatever, as the case
may be.
I just want to make a statement by the way,
if I didn't say this already. When we put these
references in, a lot of the time we really don't know if a single
person on earth is going to see them. After people started to notice them,
we realized that nothing is going to slip by, but at first we really did not
know if it was for our own amusement or not. You don't realize
how happy you make the writers of the staff when we actually
see these things,
because there aren't that many people that appreciate these references.
In reality...
Sarah: Oh you would be surprised...
DXC:
That's the thing –
we don't know when we put them in if anyone is going to
appreciate them.
Sarah:
Well, you don't realize how happy you make me and my students,
and it's because they are really great ways to get them excited about the math.
Lots of people are very interested and amused, so thank you!
DXC:
Here's one more point for David Schiminovich. He
provided a joke for The Simpsons
about transforming the torus into a sphere, which is a donut with a bite out
of it.
Sarah: What about in that same blackboard scene, in the
episode where Homer is emulating Thomas Edison
[The Wizard of Evergreen Terrace [5F21]], there is also a power of
twelve equation
in there.
DXC: Is that the Fermat's equation?
Sarah: Yes, there is one in the segment you wrote,
Homer3
[Treehouse of Horror VI [3F04]],
and one in this episode too.
DXC: They're both from me.
Sarah: Cool!
DXC: Here's the story behind that. I take full credit for
those. One more point from
David Schiminovich.
The Fermat's Last Theorem joke first appeared in the 3-D Halloween
episode Homer3, and I got the idea that I could come
up with a near-counterexample to Fermat's Last Theorem that is accurate enough
that if you test it on a bad calculator, it would appear to be true, and
it would drive people crazy.
DXC:
And the power of twelve one that came later is better. So here is what
happened. I wrote a little program in C which I'm going to try and
dig out –
I'm going to try and see if I can find this and provide this
for the website –
the actual program. It is on a really old
computer somewhere. I am going to have to see if the computer still starts
up. It is on a circa 1995 Powerbook somewhere. I wrote a little C
program somewhat cleverly, I think, it was a little better than the
dumbest possible thing, but not much better. It would churn through
all kinds of combinations of a, b, and c, and the exponent n, and
try to find a near-counterexample to Fermat's Last Theorem, and it would
just keep track of the best one. I was running it on an old Powerbook or
something, so I couldn't really try every combination in the universe
–
but I found some that were pretty good, and I put it in that Halloween
episode. But I was thinking about it and I kept running it and I found
some better ones, so then I found an excuse to put it in again.
The first one, you know, I had one calculator that it worked on,
which had 8 digits, and one that had 10 digits you would see, so I think
the other one might be right to 10 digits, or I forget exactly how many.
Sarah: It's 9 and the later one is 10.
DXC: 9 and 10. It was kind of for my own amusement,
but I wanted to have one that would work on my best bad crummy calculator.
So I put it in again. I apologize for using the same joke or reference
twice, but...
Sarah: Oh, no –
we'll talk about it tonight, but
the cool thing is that 178212 + 184112
=192212...
DXC: Wow! You've memorized the equation?
Sarah:
I use it in class all the time.
That's the one in Homer3,
and you can use an even/odd argument on
it –
so my liberal arts students understand it without knowing Fermat, and
it is a great introduction to Fermat.
DXC:
Right.
Sarah:
But the other one you put in, both sides are even, so you can't use that
argument.
DXC:
I can't remember –
I may have used some feedback. I forget how far apart
those occurred on the show.
Sarah:
A number of years.
DXC:
So then I know I did use some feedback from the fans, with them not knowing
it, by just monitoring the discussion group alt.tv.simpsons.
When these episodes run and there is some obscure reference,
I will often lurk on these things and just see if people
notice them, so it was very exciting to me when I saw the first message –
"What's going on, he seems to have disproved Fermat's Last Theorem."
That was exactly what I was hoping to see and I saw it. Yes!
Sarah:
Fermat wasn't completely resolved by Wiles at the time you
were working on the
first reference.
DXC:
That's right.
Sarah:
You didn't actually need that –
going back to Euler who showed that
the power of 3...
DXC:
Hadn't it been proved up to some exponent also?
Sarah:
Yes [for all exponents up to 4x106 (Cipra, 1993)],
but the power of 3 was enough because if you can't have powers of 3,
then you also can't have powers of 12.
DXC:
Someone could have always made a mistake. That Euler –
you can never be
sure, he's not that trustworthy.
Sarah:
Oh, don't knock Euler!
DXC:
Someone pointed out the even/odd argument about the first one.
I have a few of these postings that I saved. And in fact, just today
I was looking to see whether I could find the program, but I couldn't yet,
so that is why I know I have to go back. But I know I found
some even/odd email that I had saved, so I would say that I did refer
to that. So thank you to the fans who pointed out the shortcomings of the
first one. I am 99% positive that the second time around I looked for one
that would satisfy that parity.
[Update from DXC: The programs are
extremely similar,
but the improved version DOES do a parity check, so that definitively answers the question of whether I was looking out for that!]
Sarah:
I think it is the right side
of the second one that is not divisible by 9, but the left side is.
DXC:
I may have looked for some other of those tricks to see as many as I could
satisfy, but
it is less fun if the numbers are so big that you can't do it on the
calculator.
Sarah:
Did you ever have any contact with Noam Elkies about these equations?
DXC: No. That name sounds familiar, but I can't remember
why.
Sarah:
There are people who are interested in what he calls Fermat near-misses, that
is, numbers that are almost solutions to Fermat. He does some stuff with
algebraic number theory and cubic curves related to Hall's Conjecture, which
relates to the ABC Conjecture. Both those examples are in
there
[Rational points near curves and small nonzero
|x3-y2| via lattice reduction,
2000],
so I just didn't know if you'd had any contact with him.
DXC:
No, but I had actually sat in on a number theory class at Berkeley one year
when I was a student there [taught by Ken Ribet].
Sarah: Cool!
In Homer3, I'm told that the equation
rho(m0) > 3(H0)2 / 8 (pi) G
is a formula for the universe collapsing back in on itself -
was that put in by you or David Schiminovich intentionally as a nod to
Homer's collapsing "3-D" universe?
DXC:
Yes, that's an equation for the critical density of the universe,
at least as it was understood 20+ years ago when my college
astrophysics textbook was
written. I decided to claim the universe WOULD collapse on itself,
since that is basically what we see illustrated in the 3-D segment.
(Similarly, I chose P = NP to suggest that doing all this computer work
for the episode wasn't so hard after all!)
Sarah:
Also, in that blackboard scene for Simpsons Wizard of Evergreen Terrace - where
you put the other Fermat Near-Miss, the top of the board has the
equation M(H0) = pi (1/137)8 sqrt(hc/G).
While I recognize parts in this equation, including the 1/137, it seems like
this equation just ties them together randomly - or am I missing a connection
to something meaningful?
DXC:
David Schiminovich reminded me that M(H0) is actually the
(currently
unresolved) mass of the HIGGS PARTICLE. Here's his explanation:
"The H0 stands for the Higgs particle. The equation gives the
mass of
the Higgs boson in terms of various physical quantities including (a
close approximation of) the fine structure constant (1/137) and the
Planck mass (the term in the square root). The value comes out to
something like 0.5-1 TeV/c2 which was higher than the lower limit on
the mass (though I believe now it is below the upper limit).
The "joke"--if you can call it one--is including the Planck mass, tying
in G."
Sarah: Thanks!
DXC:
On The Simpsons I was never the head writer, so there were
some specific scripts I worked on, like the 3-D Halloween episode, where
they came more from me specifically and survived the process of the people
above me. But again there you have people who are pretty open to putting
in obscure references as long as they don't make it an unpleasant experience
for people who don't know about it.
Sarah:
You mentioned references surviving the people above...
I've noticed some of the
Simpsons math references get cut out in syndication, so I was
wondering how did Fox or other people feel about some of these references.
Did they try and edit them out before they showed up to begin with?
DXC: Editing shows down for syndication is actually a very difficult
task because these shows are often high speed shows to begin with when
they occupy 22 minutes. When you have to cut them down to 20 minutes
it is often very difficult to find any 2 minutes you can cut out without
ruining the whole show. I would often say there is often not a lot of choice
in terms of what comes out. I don't think there is a conspiracy against
the math jokes, but if you think about what I was saying before, that these
jokes are not the focus of the episode, well, a lot of things that are
not the focus of the episode are going to have to come out when they
edit for syndication, so that it still makes sense. Unfortunately,
a lot of the spice of the episode has to come out to get those 2 minutes out.
Sarah: As far as the math or science
references, did anyone at Fox ever ask you to cut one out?
DXC:
As far as the editing process from the Fox network, they are not too concerned
–
the censors that is, not the creative executives –
the censors are only really looking at it in terms of how many times did we use the word ass, or hell, or whatever...
Sarah: They are not looking at the content?
DXC: Occasionally the censor would attempt to make a point about the
science. For example, I can remember a couple of these...
There was one episode where we had an x-ray device called the
f-ray
[Fry and the Slurm Factory
[1ACV13]],
which could see through anything, even metal, and for some reason,
that time the censor, instead of sticking to the hells and asses,
said, "Well technically there are x-rays that can see through metal."
Once in a while they just took issue with these strange scientific things.
Or my favorite one of all along these lines...
I think it was in the same episode
[Fry and the Slurm Factory
[1ACV13]], so the censor must have been in a mood,
where they went to the Slurm planet where Slurm is manufactured from the
excretions of a giant queen worm and she is defending the use of worm
excretions as a beverage by explaining that we eat lots of things like that
–
honey comes from a bee's behind, and then she says milk comes from a cow's behind... The censor took it upon himself to say: "Note: milk does not come from a cow's behind."
Once in a while they take issue. I broadly categorize that as
a scientific reference that they took issue with.
The math went by them unnoticed, I think, so never a problem there.
As far as the content of the show with the executives at Fox,
Futurama and The Simpsons (especially
The Simpsons) don't really work by the rules of
pretty much any other show on TV in that Matt Groening and James Brooks have
a special deal where they have the ultimate authority, aside from matters
of indecency. But as far as content they have the final say,
and their deal says that they are not required to listen to the
opinions of the executives. So on many shows they might
have said, "
Oh, you can't have the Friends discussing calculus,"
but on Simpsons and Futurama that wouldn't be an issue,
luckily for us.
Sarah: Do you think you'll try and throw in some more math
references into whatever your next series will be?
DXC: Of course!
Sarah: Which might have nothing to do with math, like
rap music or whatever...
DXC: Right, well I'm working on a pilot right now
about a rap group, which is called Grandmaster Freak and the Furious
Fifteen, tentatively... So I'll put in a plug here. Ice Cube
would be one of the stars and producers. God knows whether it will ever
appear on the air. I hope so, but these things are always a crap shoot.
Right off the bat, we are working with fifteen members of the group plus
the leader, Grandmaster Freak, the sixteenth. Already I thought those
were good, interesting numbers. I could have picked any number, but
I like the image of the fifteen of them marching in a triangle, so that's
one of the reasons.
Sarah: That's great.
DXC: And when you add the leader in, I like the fact that
you can make it into a nice grid on screen, kind of like the
Brady Bunch, but with sixteen instead of nine. That's one reason that
there are those numbers of people in the group. So I'm thinking about it
already that those are interesting numbers. I'm sure I'll find more
uses for them down the line.
Sarah:
In my liberal arts class, which is a course for non-majors,
I created a segment on What is a Mathematician?
where we combine sociology and philosophy and look at the questions:
What is math? How do people succeed in math? Why is it useful?
So I was wondering if I could ask you some questions about your math
background, with some of these big picture ideas in mind.
DXC: Go ahead... If I can inspire people to study math and
then give it up, and move on to something else, I'm happy to do so.
Sarah: What influences led you to study math/physics/cs, because
you studied all of those, right?
DXC: For my whole life, starting when I was a kid, I was
fully intending to be a scientist of some kind.
If I had to say what is the number one influence on me wanting to
study science, let's say more broadly, it would be that
both of my parents
were biologists, and I grew up seeing them doing interesting things.
I think obviously what goes on in your family is a huge
influence on whether you find these kind of things interesting or not.
I personally always
found myself more interested in the physical sciences
and math and computers and that kind of thing than biology specifically,
so I didn't follow exactly in their footsteps, but I always envisioned myself
as being a scientist of some kind.
I grew up in New Jersey
where careers in entertainment are not the number one thing on people's
minds either. I always liked writing, but I thought it was just a hobby.
It didn't even occur to me that it was something you could do for a living.
So I would write the humor column for my high school newspaper,
but it never popped into my mind that that would someday derail me
from my original plans.
I also had a couple of good teachers: Mrs. Cardine, in 8th grade,
Dr. Meckler I had for calculus in high school –
a great teacher.
Having teachers who are enthusiastic...
Some of these teachers I think were viewed by some of the students
in the school as teaching at a little too high of a level,
especially Dr. Meckler. His class was quite small, actually.
He taught calculus, and he wasn't willing to compromise.
If people were in there who had just made it through the previous
ones and who were padding their resume, they didn't pan out.
I think that doesn't go over as well in schools now,
and even at the time didn't make him the most popular teacher.
But for the people who were really interested in math, on the
other hand, it was great.
This is a dilemma, I guess, in teaching, and I don't have the answer to it,
but how do you cater to the people who are really interested,
and at the same time to the other people?
Maybe they shouldn't be in the same class at the same time, honestly.
I like the idea of exposing everyone to math, but you do have to cater
to the people who are especially interested if they are going to go on
and become math professors or whatever.
Maybe the class should have been divided into two classes, but
the school may have not had the money. I'm sure these problems
all still exist today.
But anyway, I do want to give credit to a couple of great teachers
I had in high school and middle school who got me fired up about it.
Sarah: And it sounds like the answer to this is already
yes, but did you have support from both family and society?
DXC: Yes. Definitely my family, of course.
Science was highly valued in our house.
As far as our school, I went to a very unusual school. I went to
public school in New Jersey. It was just a really interesting school.
It was very integrated –
people from all over the world, people
of every race, and nerds were not picked on in my school.
We did not have these standard high school cliques that you think of,
like the cool kids and the nerds, but instead there were
hundreds of different kinds of people. It seemed like everyone was
free to do their own thing, basically. If you liked math,
that was cool with everyone else. If you liked rap music, that was
good, and if you liked both of those things, that was good.
I'm happy to say that you could play Dungeons and Dragons and
study math and not be really picked on at our school. So that
definitely helped.
Sarah: What kind of barriers did you face? In reference to
math/science-type studies...
DXC:
The barriers I faced were internal conflict. That is pretty much the
only thing. My nature is that I wish I could do everything in my
lifetime, and I can't. Whenever I'm doing something I'm always thinking,
"Well but..." If I was doing math and I found out, "Oh wait you can have
a career in writing," and I was thinking "Maybe I should be writing"...
And of course when you're writing, you're thinking, "Oh! If I had
been a math professor, I might have solved Fermat's Last Theorem
before that other jerk!" The grass is always greener, I guess.
The main hurdles I faced were my own worries that maybe I should be
doing something else that I would also enjoy doing.
I can't really blame anyone else for the fact that I'm not
still a computer science or physics professor. It was just me.
So, sorry me! No –
I love math and physics, and if I could have two lifetimes
I would like to go through one doing that.
Sarah: I have some questions related to your mathematical
style... What were or are your favorite mathematically related
experiences?
DXC:
I can tell you some of my favorite classes that I took
when I was in college
and then some of the favorite things I just like to do.
I'm going to back up even further, back to school.
My favorite thing of all time, of course, is being on the math team
in high school.
Sarah: That DVD Easter Egg
[2ACV06]
that shows you as math team
– I don't know it by heart –
president or whatever.
DXC: Yes. That was not far from the truth. That little
Easter Egg on the DVD that showed me as president and king and tsar,
or whatever,
of the math team.
We had a great math team in my high school, which surprised people
because there were all these fancy private schools in the area, and
much wealthier suburbs, but we were the math team champions.
It was very satisfying to us as the underdogs.
So math team was my favorite. We were in three different leagues:
the county league, the state league, and the national league.
My greatest achievement was one year going to
ARML,
the American Regions Math League.
It was very exiting, and
I was very impressed by this guy...
I'm really rambling now, but memories are coming back.
Sarah: No –
it's great!
DXC:
The national individual champion of the year was
Mike Reid, who was a very distinctive looking guy with like two foot
long blond hair who was on the New York City A team.
There was a final championship round at this math meet for the
individuals who had gotten a perfect score on everything up to that point,
which I assure you was not me.
Although I was good,
I was not a standout in the national arena, I'm afraid to
say.
There were twelve people who had gotten everything right up to that point.
So they had them for a tie breaker in the front row of this auditorium
with hundreds of people in it and the idea was that they would
put up a slide of the problem and also hand it to these guys on paper –
guys and girls, sorry...
I'm already harming the future math chances of
women everywhere by providing lack of inspiration.
So the guys and girls who had gotten a perfect score up to that point
got this problem on paper,
and they
projected it for everyone else in the auditorium to see –
and the idea is that not only did they have to get it right, but
the first person to get it right would be the national champion.
So they project this extremely complicated
geometry problem on the screen which has all these circles
and lines and it's like, "How long is such and such line segment?"
or something like that. So I get out a piece of paper, and everyone else
is going to do it just for their own amusement to see if
they can do it, and I drew one circle on my paper –
and this guy,
Mike Reid, handed in his answer
while I was drawing this circle. Literally, it may have been five seconds.
He handed in the answer, and it was correct, and he won.
And then I got to know this guy, because it turned out he went to college
with me the next year.
We would amuse ourselves at lunch and dinner, sitting in the dining hall.
We would give him fractions like
13/17, and he would instantaneously write them out to as many decimal
places as he wanted to. He was
later in Berkeley, so I would see him around. But I have not
seen him in a few years.
Hi, Mike, if you're seeing this.
Math team was kind of number one
in terms of something that made math really exciting.
I'm very competitive. Talking about inspirations,
making it into a game made it fun for me.
That's one thing.
Things I enjoyed in college...
I think my favorite math class was
complex analysis with the sum of the residues.
That was my favorite. It was just
so elegant and so simple, which is always good.
I loved that.
I also loved the hands-on kind of hacking. I took an electronics class where
we just wired up circuits and put wires in breadboards and sat there and
skinned
wires and built things, and I just found that very
relaxing and enjoyable, to actually build some things.
I am kind of a hacker at heart. I spent years of high school programming
our Apple II computer in the wee hours of the morning, and making
video games,
which did not sell. You've never seen them, but my dad and I played them
a lot.
I enjoy anything that is kind of hacking related
–
an artificial intelligence
class I took in college where we wrote Othello programs that played
each other in a tournament –
again the competition aspect for me
made it fun.
And then graduate school, moving along...
My favorite things... That was my first exposure to theoretical computer
science, which I didn't know anything about. I actually went into
graduate school thinking I was going to study neural networks and
do more kind of hacking stuff, but I just found these theoretical
computer science proofs so elegant –
and stuff about algorithms
and bounds and all of those kinds of proofs –
that I switched into
that area, which possibly was a mistake.
This is kind of my dilemma, which maybe is partially responsible for
the fact that I'm a writer now. The thing I kind of enjoy doing the
most is hacking at a computer and hacking at AI programs and that
kind of thing, and building circuits or whatever. And the thing
I find the most elegant and intellectually satisfying is theoretical
stuff and proofs, which in reality I enjoy understanding, but
I don't enjoy working on as much. So I kind of work myself into a corner
a little bit.
I've never given this interview in such detail before –
I've talked
about this stuff, but this is the venue, I guess, to get this stuff off
my chest.
Sarah: So, building on what you just said,
describe the process of how you did or do mathematics.
Lots of people have different styles of how they do mathematics, so
what was the style that worked for you?
DXC:
I like to have a physical picture of what is going on.
I can tell you a big breakthrough in my mind, in terms of math.
My freshman year of college... I had taken calculus in high school.
I even took a third semester of calculus at a local college with some
of my other friends, because in our school, at that time, it was not uncommon
to take calculus your junior year. They had high hopes for us.
So they had this thing where you could take a third semester calculus
at Fairleigh Dickinson University nearby.
I had taken a bunch of calculus, but then I took physics my freshman year,
which was kind of a serious physics for physics majors.
It involved a lot of calculus, and I found a lot of it difficult –
the
multivariable calculus and 3-D integrations that were required.
I was kind of looking at each problem from scratch, just trying to figure
out how do I set up this variable. I didn't have a good physical
understanding intuitively about what was going on. I could do these
equations that I had learned in high school, but I didn't really
understand what was going on
–
and then one day in this electromagnetism
class, I suddenly realized and understood that all it is, is just
adding up the volume of these spheres or cubes or whatever integral you
are setting up.
As soon as I suddenly realized, "Oh, you can just picture it in terms of this
shape," it became trivial to do these integrations, and I didn't have to
think about what's going on in the x-coordinate, the y-coordinate,
the z-coordinate. "Oh, it's just the area of a sphere times this tiny
thickness of the sphere," and then adding those up or whatever.
As soon as I had a physical understanding of what was going on, then
the class became very easy for me.
But up to that point I thought, "Oh I'm not going to cut it as a physics
major," and it was just like one moment of one day and after that it seems
trivial, and you don't realize why you didn't understand it.
So that's one thing about teaching which I'd recommend to any teachers,
is that for me, the more physical reality you can put on it, the better.
Similarly, in graduate school, the one paper I published is about flipping
pancakes, which is a very physical thing. You can actually
get this baby toy which is these stacks of cylinders that sit on a stick,
and flip them around, and you can actually look at this picture.
The question was how do you sort these disks
to get the biggest pancake on the bottom and the
smallest pancake on top if they start in an arbitrary disordered
state, and the only thing you're allowed to do is put a spatula somewhere
in the middle, pick up the ones above it, flip them over, and put them
down, as a group. Doing that repeatedly, putting a spatula in different
places, you want to sort this out.
So a very physical thing, that got me excited when I found out that no
one knew the answer in general for how many flips it takes to sort
this thing. So, here, my approach, which is what I enjoy doing again,
is that this is a theoretical problem, but what did I do?
I wrote computer programs that would do massive searches and try
everything and the best way to sort 6 stacks of pancakes, 7, 8.
It seemed very clear to me empirically that if it's n pancakes,
it takes 2n flips to do it.
By the way, I have to back up. These are burnt pancakes. I'm sorry.
So not only do you have to sort them, but you have to get
a certain burnt side of pancake down when you are finished.
Initially they can be either way. This is way too complicated rambling,
but...
The answer seemed very clear from these computer searches that it
was 2n, but I couldn't prove it. I could prove that you could do it in
2n, but I couldn't prove that it always took at least 2n.
It could have been easier. So I tried these searches and it said for
4 pancakes, the computer said yes, it takes 8. It always takes at least
8 and at most 8. For 5 pancakes it took 10,
6 pancakes, 12, and 7 pancakes, 14.
At the time computer power wasn't as great as it is now, and this is
12 years ago.
I was using a huge bank of computers and I was running them all night
when no one cared.
But then suddenly 8 pancakes, it only took
15. "Oh, something interesting is going on here." After much work,
it seems more likely that the answer is
3n/2. I never proved that, but I found some
strong evidence and other people may have proved it now. I don't know.
[It looks like this is still an open problem:
The Pancake
Problems.]
So that is my approach. I like it to be a physical thing and, if
I can, apply computers to guide me at least.
The computer didn't solve anything, but it said,
"Oh there is something worth looking at here." So that made it more fun
for me.
Sarah: And I can already infer some of the answer to this,
based on what you just said, but how did you get the flashes of insight
you needed to do problem solving?
DXC: Looking at computer searches, for that particular
problem, gave me a flash of insight that the answer wasn't what it seemed
to be, the obvious answer.
Sarah: In general, if you think back in general, how
did you do math/physics/cs... You are working on problems and you needed
to get some flashes of insight, how would you generally get them?
DXC: I don't know the answer. Is there a good answer to
that question?
Sarah: Well... I mean I could tell you what I do...
DXC: OK, tell me, and then I'll see if that sounds
familiar to me and I'll go, "Oh, me too."
Sarah: So I look at lots of examples, ask
different questions, and I talk to lots of different people.
I try and piece a lot of different things from different places together.
There are other people that work alone and
go walk around a lake, let it settle, and things come to them. Lots of
people have different ways of doing that kind of stuff, right?
DXC: I don't feel like I have a clear answer to that.
Maybe that's why I'm not a star physicist now. But
sometimes people ask me if there is anything in common between writing
and physics or math, or anything like that. Usually I give this
straightforward answer of "No!" because I don't think there is that much,
but there is one thing and it relates to this specifically...
If you are writing, especially comedy, there is not a formula where you
can generate the next joke –
or if you are using one anyway, then
it is not going to be a very good joke –
and I think it is kind of the
same if you are trying to prove something. If it was obvious where to
go, then it would have already been proven. So the one thing I think
they have in common is that these are professions where
you are flying blind a little bit, and you might have gotten into an
area where you are not going to get the answer, or you are not going to
get the joke, and you are just working from your own self-confidence,
that it is a fruitful area to work in or there might be something
funny happening here.
Sarah: What do you do when you get stuck?
Do you keep plugging away, do you relax and go get coffee, in
writing or in...
DXC: I guess this is what I would say. I might have a
rule of about three days. If sleeping on it, talking to people,
thinking about it, and writing...
And I think after a few days, if I feel like it is not leading to anything
fruitful, again same thing for writing, and that is primarily maybe
what I'm talking about now. I just feel like if this is not turning
out to be funny, then we have to back it up a step and look at
the broader picture and go in a different but related direction
and see if some other area is fruitful. And once in a while, that's
not either, and you just throw the whole thing out, and you have to
bite the bullet and start on something new.
Sarah: And how does your mathematical mind work?
Do you have a photographic memory, are you really good with numbers,
visualization?
DXC: I have a bad memory. That puts me at somewhat of a
disadvantage.
So this is how my mind works for math and maybe for everything in
life. I think I have a good mind for logic, and if I know something,
what I can deduce from that.
Often I can remember the process of doing something but I cannot
remember –
if you ask me specific numbers –
like you just remembered
the specific numbers that are in that Fermat's Last Theorem joke.
I would never remember that.
Sarah: I see that equation all the time.
DXC: You see it all the time?
Sarah: So that's a little different.
DXC:
I don't have a good memory, but I have a good memory for how to do
something –
how to deduce things I think from a fact that I know.
I like to write things down, I guess, also and just look at it.
I find everything easier to think about when
it is on paper –
writing too.
If I'm talking about a story and trying to make it make sense, I find that
fairly difficult, but obviously, at the initial stages,
you have to do that. But once
something's on paper, I find it much easier to say,
"No, cross this out." I think kind of the same for math.
And it is not just the process of... It is not reading it but writing it
which helps for me.
Writing the equations down puts them in my mind.
And studying for tests and things, I found that just writing stuff
over and over again would put it in my brain somehow.
Not reading it 10 times, but writing it.
So there is something going through the writing center of my brain.
Sarah:
Do you have any general comments about what math is or where
you think math comes from, philosophically?
DXC:
To me, maybe it is because of the thing I just said, about how my
mind works... The interesting thing to me about math
is not what's often taught, which is just how do you add,
or how do you multiply, but what is the underlying logic or
truth to how things fit together. For example,
I think if you teach people numbers in different bases, like
base 2 or base 10 or something like that, how is base 2 like base 10
–
that gives people more insight into what is the basic reason why
things work out the way they do.
What are the different digits –
this is at a very simple level for
middle school or whatever, but that kind of stuff is much more
interesting than teaching people the rules of doing long
division by carrying numbers or whatever. Again, maybe going back to the
idea that for me,
once I could picture things physically or what was going on,
then I could understand and do it again.
But if you had said I had to memorize something
which didn't intrinsically have a logical meaning to me, I couldn't
do it. I can't commit those things to memory.
I have to understand what is the underlying logic of things.
This is kind of a general answer...
Sarah: Any words of advice to undergraduate
math or science majors?
DXC:
Based on my experience I guess, if it is something you want to do for
your career,
I think I would say stick with the thing which is fun for you to do
because if you are going to do it for decades, it's got to be fun.
You can get into this frame of mind of, "Oh
I've studied it in high school, I've studied it in college, in graduate
school," and you get into this frame of mind of, "Oh
I'm doing it for these degrees."
But just be careful that you're thinking about what is the
thing which is fun for you to do. And by the way, a lot of other
careers are not that much fun either, and even writing, which I find...
Here's another thing that writing has in common with math for me.
When you are finished with it – it's great!
When you look back, it's like I wrote this or
I wrote that paper, I discovered this thing, I understood
this thing. That's great.
For neither one of them is the process honestly that much fun for me.
I can't claim that I've ever found the thing that is fun for me all the
time. I think if I had then I wouldn't have
switched careers or something.
I love the moment of understanding or having accomplished something.
Sometimes I enjoy the process and sometimes I don't. And maybe that
is how every career is.
The more you can stick with the area which you find fun
and not just elegant or satisfying, I think is the area you're likely
to achieve in.
Sarah:
It seems clear that you would have been a great teacher. Did you do any
teaching at Berkeley? TA or anything like that? Or was it all research?
DXC: I did not do any teaching of an actual class unfortunately,
when I was there, because I actually agree with you
–
I think I would have
been a reasonably good teacher. I wanted to do that, but I had a research
assistant position which was just fine. And you know how lucrative it
is to be a graduate research assistant.
Sarah: Oh yeah...
DXC: I was rolling in the dough. I did give some seminars, which I
basically enjoyed doing. That's what makes me think I might have enjoyed
teaching. Unfortunately for the world of math students, perhaps, I
bailed out before I got the chance.
Maybe that's why I'm in this math club now, so I can get up and lecture
once in a while to unwilling participants.
Sarah: Do you have any interest in going to math conventions?
DXC:
If it was a math conference that had some stuff for the educated
armchair mathematician, then yes. But if it was going to be all cutting
edge stuff, then I'm afraid I may have passed the point where I could either
follow it or contribute.
Sarah: The Mathematical Association of America will often
have conferences that students go to and teachers go to
and a lot of things aimed at both those groups.
DXC:
Yeah. Or if it was some recreational thing, that would be fun. Or sometimes
I think about our local Math-Club we have here in LA, which has a
bunch of writers and non-mathematicians and former mathematicians, and
we meet and talk about math on very irregular occasions.
Sometimes we think, "Oh we should form a math team since that was all of
our favorite thing." And challenge the local high schools or maybe
middle schools since we've forgotten...
So maybe that could be my return to math –
competing on an even footing with
8th graders.
Dr. Sarah J. Greenwald,
Appalachian State University
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