A Futurama Math Conversation with David X. Cohen

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:

Mathematical Moments in Futurama (Mars University, Lesser of Two Evils, Put your Head on my Shoulder, I, Roommate, and Luck of the Fryish)
Blackboard Scenes in Futurama (Mars University, Time Keeps on Slipping, A Fishful of Dollars, and The Farnsworth Parabox)
Mathematical Analysis of Fry's DNA (Roswell that Ends Well)
Appreciating the References in Futurama (Kif Gets Knocked Up a Notch)
Mathematical Moments in The Simpsons (The Wizard of Evergreen Terrace and Treehouse of Horror VI)
Syndication Cuts & Censoring Scientific References (Fry and the Slurm Factory)
Mathematical Moments in Grandmaster Freak and the Furious Fifteen
DXC's Mathematical Background

Mathematical Moments in Futurama

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.

Blackboard Scenes in Futurama

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!

Mathematical Analysis of Fry's DNA

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.

Appreciating the References in Futurama

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: Our pleasure.

Mathematical Moments in The Simpsons

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.

Sarah: Yes, it makes the best classroom worksheet ever – thank you!

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.

Syndication Cuts & Censoring Scientific References

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.

Mathematical Moments in Grandmaster Freak and the Furious Fifteen

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.

DXC's Mathematical Background

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: Are there any diversity issues in your experiences?

DXC: Yes, there are – serious ones. The most obvious one, which I know is something you're interested in, is male/female balance in these fields, especially in physical science. It seems like all of the careers I've been in have a bad imbalance. My hobbies too. In studying physics in college, undergraduate, a major male/female imbalance, with more male, in case anybody is not aware of that. Studying computer science at Berkeley, the same deal. Although, I have to say in the theoretical computer science subsection of the department, there was actually a reasonably even balance. To my surprise, the kind of more mathematical computer science, at least at Berkeley at that time, had a relatively even balance. It may not have been 50/50, but it might have been 60/40 or 55/45. I think that some of the more hardcore programming kind of areas were more male. So the department as a whole was definitely much more male than female.
          In comedy writing, same deal. Many more men than women, who you work with and who are employed. This does not explain it, but one thing leading to this definitely, at least from the writing where I'm hiring people, is that there are many more men than women trying for these jobs. That is not a good excuse necessarily, because why is that? People may be getting discouraged at an earlier point.
          I'm guessing it may be a similar thing, you could tell me better than I would know, as far as who is applying to graduate school. Is it more men than women applying to graduate school in math/physics? I don't know. Do you know the answer?

Sarah: Proportionally more women drop out at every stage than do men. Even so, in graduate school, in mathematics, it's about a third of graduating PhDs that are women at this stage, but that does not translate into the number of tenure track and full time professors at a bunch of the institutions. So actually the percentages are pretty good in math, but especially at the top institutions in mathematics, they are nowhere near that in terms of people there.

DXC: In some other areas, it's different. Like, a friend of mine who is a biochemist was out here, and I was talking to him a couple of days ago. He said his department is majority female – the students. But I don't know about the professors. That didn't come up. But the PhD students were majority female, so it is obviously not across the board in science. I don't know how it breaks down from one science to another, and I'm sure it may have even changed in the twelve years since I've been doing it. Obviously, I think everybody would be happier if it was more even.
          Now, as far as other diversity issues. The racial breakdown – again, serious problems in all these areas, I would say. Not that there's no diversity. There's certainly a lot of international diversity. That's not exactly the same thing, but, for example, studying at Berkeley, a lot of students were from India, from China, so you have some racial diversity, but I would say, definitely underrepresented were African Americans, Latinos. Not that there weren't any. There were some. Just as there are women in comedy writing and computer science, but not represented to the same level as they are in the general population. I don't have the answer to how to do this, but I will agree that the problem exists.

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.

Sarah: Any other comments?

DXC: I think I've said my peace...

Sarah: Cool. Well thank you very much!

For more information, check out Futurama πk - Mathematics in the Year 3000,   simpsonsmath.com, and a summary of Math-Club, whose audience included a number of Simpsons and Futurama writers.

Dr. Sarah J. Greenwald, Appalachian State University
Legal Notice: The Simpsons and Futurama TM and copyright Twentieth Century Fox and its related companies. This web site is for educational use only. To view these pages, you must agree to these terms. We do not benefit financially in any way from this web site. Images on these pages were taken from episodes that are copyrighted by Twentieth Century Fox. We will not distribute audio, video or image files.
Disclaimer: This web site, its operators, and any content contained on this site relating to The Simpsons or Futurama are not specifically authorized by Fox.