## The Future of Computer Science, and Why Every Other Major Sucks By Comparison

Does this post finally herald my return to regular blogging after a months-long absence?

I don’t know. For me, writing a *Shtetl-Optimized* entry always followed the same process: I’d get an idea and start typing, furiously rocking back and forth in my chair. Then the voices in my head would pipe up: no, I can’t *say* that—what will everyone think?—judging from past experience, they’ll probably take offense—I can already see the commenters boiling me alive—maybe if I rephrased it, or, y’know, provided some context—but to explain the *real* context, I’d need a whole book—and who has the time for that?—better wait till after tenure—meantime, maybe I could blog about something light and uncontroversial instead—but then what’s the point?—we already have *one* GASARCH—well, I could always put off a decision till later—

Back in the blog’s heyday, I’d win these fights about 40% the time and the voices would win about 60%. (In other words: if you’ve ever taken offense at an entry of mine, rest assured that you haven’t even seen the half of my drafts folder.) But now that I have an actual stake in this shabby world—students to advise and look after, a tenure case to build, *conceivably* even a family to start—the voices win more like 98% of the time. And that’s why my blogging fell off.

Occasionally, though, something comes along so uncomplicatedly joyous that I feel no reservations about sharing it with the world. Such was the case this weekend, when I was somehow called upon to represent MIT’s EECS Department in the annual “Professor Talent Show” at Campus Preview Weekend. This is an event where six faculty members square off, taking eight minutes each to

(1) explain why their department is the coolest,

(2) crack jokes, and

(3) possibly demonstrate a musical or athletic talent.

Then, using electronic clickers, the several hundred prefrosh in attendence vote for which major carried the day. Though I had no absolutely no talent of any kind to demonstrate, and was up against a banjo-player, violinist, and basketball-spinner among other tough competitors, for some reason **EECS won!** You can see my PowerPoint slides here:

**The Future of Computer Science, and Why Every Other Major Sucks By Comparison**

http://www.scottaaronson.com/

(You can read the jokes that go along with each slide in the slide notes at the bottom.)

**Update (4/15):** I hadn’t realized at all that there’s actually a video of me giving the talk! (Click on “Part 2.”)

Comment #1 April 12th, 2010 at 6:36 pm

Who represented the math department?

Comment #2 April 12th, 2010 at 6:41 pm

I enjoyed the whole talk, but slide 12 is especially enjoyable. Many disciplines see themselves as the center of the Universe this way. Certainly I can think of physicists, economists and mathematicians who view absolutely everything through the lens of their subject, and so, it’s natural to see (say) computer science as subject to physics. Indeed, one might say that’s the point of view that gave rise to quantum computing.

Comment #3 April 12th, 2010 at 8:20 pm

Qiaochu: The math department wasn’t represented this year.

Comment #4 April 12th, 2010 at 8:34 pm

I’ve had a wee question for a while, and maybe it’s a really dumb question, but it seems to fit with this presentation so I’ll ask…

Computer science seems to be inherently digital. It all comes down to bits which are either there or not. At least superficially math and physics seem to deal with continuities which appear to be analog in nature. Is this true? Are these subjects “larger” than computer science as a result?

Comment #5 April 12th, 2010 at 8:54 pm

Hey Scott, your talk went down well with my 8-year old daughter.

Comment #6 April 12th, 2010 at 9:10 pm

I’d just like to note how the use of Powerpoint slides meshes really well with the whole killer robots / matrix / evil overlords theme. Good going.

Comment #7 April 12th, 2010 at 9:48 pm

Aww, I’m sorry I didn’t get to go now! I’d totally would have gone if I knew you were defending CS.

Comment #8 April 12th, 2010 at 11:12 pm

At least superficially math and physics seem to deal with continuities which appear to be analog in nature. Is this true? Are these subjects “larger” than computer science as a result?Vladimir: Interesting questions!

First answer: I strongly believe that, once you get down a small enough scale (namely the Planck scale, of 10

^{-43}seconds or 10^{-33}centimeters), the apparent continuity of space and time will break down—in much the same way that the apparent continuity of water breaks down once you get to the molecular scale. In other words, Nature is revealed will be fundamentally digital, at least for the right definition of “digital”!(The issue is subtle, because I

don’texpect the continuity of quantum-mechanical amplitudes to go away. But because amplitudes evolve linearly, I don’t think that the continuity of amplitudes poses any more problem to a “digital” view of the universe than the continuity of classical probabilities.)Support for my view comes from, e.g., the “holographic principle” in quantum gravity, which places a finite upper bound on the amount of information that can be stored in any finite region of space (namely, ~1.4*10

^{69}bits per square meter of surface area).A second answer is that, even if you think the laws of physics include a “genuine” continuous element, the tools of theoretical computer science are well-equipped to handle computation over continuous fields. Indeed, since the 1960s,

algebraic complexity theory(which studies the number of field operations needed to effect a given transformation over the reals or complex numbers) has been a major research area in theoretical computer science, with lots of beautiful results as well as exchange of ideas with standard “digital” TCS.Comment #9 April 13th, 2010 at 12:05 am

Scott, I uploaded this to slideshare[1] because I don’t like any powerpoint viewers but I don’t mind their viewer. If you mind me having done so, I’ll take it right down.

[1]: http://www.slideshare.net/llimllib/the-future-of-computer-science-and-why-every-other-major-sucks-by-comparison-3705322

Comment #10 April 13th, 2010 at 12:10 am

Thanks Scott! Could you make any further comments vis. axiomization, such as the famous ZF? Does that question even make sense? If so, how does quantum computing fit in as compared to normal non-quantum computing we all learn in school?

Comment #11 April 13th, 2010 at 1:27 am

Embellishing Scott’s reply to Vladimir, Continuous versus Discrete is a lot more subtle than generally realized. Theorems in math about continuity are proven in the context of the real numbers (or similar topological constructions). But the real numbers are only a construction created so you can prove theorems and try to reason about things like a solution to x^2 = 2. The reals are “pretty good” because the two main ways of trying to deal with the continuous: order theoretic (dedekind cuts) and metric (cauchy sequences) lead to the reals, but there is no reason to think they are real.

I admire Scott’s confidence in his “strong belief” about what happens at the Planck scale. At scales we can see Right Now things are getting pretty messy. In zipping out papers, cosmologists like to act as they understand (going from bad to worse) dark matter, dark energy, inflation, etc. A lot of people aren’t in on the joke.

Permit me a sacrilegious thought: Will P vs. NP come to regarded at the 20/21 century version of “how many angles can dance on the head of a pin”? The fact that widely different NP-C problems are all equivalent should suggest that this tool is way too blunt to be useful for any actual programs.

Comment #12 April 13th, 2010 at 5:52 am

Hey Scott, great that you’ve posted again. About those voices, well, how mad people get would depend on what kind of material you post. I think everyone likes Terry Tao’s blog, for example. Just the small fraction that I can even remotely understand is enough to make it one of my favorites.

I watched a video lecture by Umesh Vazirani where he mentioned that the exponentially long vectors in quantum computing come from the multiplication of dimension that happens when you compute tensor products. I’d be interested to know the meaning of the tensor product in this context, if you want something to write about that would probably interest quite a few readers.

Comment #13 April 13th, 2010 at 7:01 am

Bill: Thanks! No, I don’t mind at all.

Comment #14 April 13th, 2010 at 7:03 am

Vladimir: Comments about axiomatization? Uh, I’m all for it? Sorry, maybe you could sharpen your questions a bit?

Comment #15 April 13th, 2010 at 7:30 am

asdf: Unfortunately, along with ~(6.5*10

^{9}) – 1 people on this planet, I have to deal with the limitation of not being Terry Tao.But if you want to know the “meaning of the tensor product”: well, I always thought of it as just the mathematically straightforward way to put together two systems A and B into a composite system A*B, in such a way that you can still act on A without affecting B and vice versa. When you do that, the dimension of your state space

multiplies—that is,dim(A*B) = dim(A)dim(B)

—basically because you now need to account for all possible

correlationsbetween A and B. In other words, if A is found inthisstate,thenwhat’s the state of B? If A is found inthatstate, … etc.To build intuition, it’s helpful to think about classical probability theory, where you also use the tensor product (even if you don’t call it that) to combine two distributions into one larger one. E.g., if you have a bit x with distribution (p

_{1},p_{2}), and another bit y with independent distribution (q_{1},q_{2}), then the joint distribution over xy is just(p

_{1}q_{1},p_{1}q_{2},p_{2}q_{1},p_{2}q_{2}).Notice that the number of probabilities we have to write down is now the

productof the numbers of probabilities in the two individual distributions — the same as with quantum mechanics. I hope that makes tensor product seem a little less mysterious.Still, I should tell you that some people claim to be uneasy about the status of tensor product in QM—what is it? is it a separate axiom? or just a formalization of what we

meanwhen we talk about a “composite system”?Likewise, the same way some people ask whether quantum mechanics would still make sense with (e.g.) the real numbers in place of the complex numbers, or the L

_{3}norm in place of the L_{2}norm, other people ask whether there’s any alternative to the tensor product that would also make sense. Personally, I don’t know of one. Sure, there are other ways to combine two Hilbert spaces into one—like thedirect sumand thesymmetric product—but it’s easy to see that they don’t capture what we want here. At the same time, I also don’t know of any nontrivial “uniqueness theorem” for tensor product (does anyone else?)Comment #16 April 13th, 2010 at 10:18 am

As no one pointed out the obvious, I’ll do it. Scott, that is an awfully hilarious piece of presentation you did there! And damn, I’m looking forward to your STOC presentation(s) to see if you can get this twist in virtually any talk you give.

Plus, if it’s a matter of believing, I’m also one of those thinking that Plank constants imply the discreteness of nature (and uselessness of continuous math, but that’s going too far :)).

Comment #17 April 13th, 2010 at 11:32 am

The tensor product is uniquely defined by its “universal property” (see http://en.wikipedia.org/wiki/Tensor_product , though the category theory is a bit difficult to unwind if one has never seen it before). Specifically, if we have vector spaces V and W, then the tensor product V \otimes W is the “universal object” that is bilinear with respect to V and W. That is, for any space U where there is a bilinear map V x W -> U, then we have that there is a (unique) homomorphism V \otimes W -> U.

So in some sense the composite system requirement is exactly that of bilinearity (as we want linear maps on V and W to extend to the composite system in natural way), and so given this, it sort of makes sense to take the “maximal”/”universal” bilinear object in the sense that we don’t loose any information by doing so.

Comment #18 April 13th, 2010 at 2:15 pm

Scott asks:

At the same time, I also don’t know of any nontrivial “uniqueness theorem” for tensor product (does anyone else?)Hmmm … there are some purely geometric theorems that govern the reverse process … which is to say … the pullback of metric and symplectic dynamics (both classical and quantum) onto lower (or higher!) dimension manifolds … it turns out that both dimension-decreasing and dimension-increasing pullbacks are much-used already, in both classical and quantum simulations.

However, pullback methods do require the replacement of Scott’s axiomatic assertion “amplitudes evolve linearly” with the slightly weaker axiom “amplitudes evolve symplectically”.

Fortunately, pretty much all of the dynamic, thermostatic, and informatic goodness of mechanics—both classical and quantum—remains intact after pullback.

This is good news for simulationists (whether classical and quantum) regardless of whether the state-space of Nature (whether classical or quantum) turns out to be linear or not.

Gosh, if only we knew how to formulate field theory so that its goodness—particularly causality and relativity—survived pullback, then we could drop the QM linearity axiom entirely!

The above are some of the reasons why Alice and Bob have been looking to Scott’s promised manuscript

The Computational Complexity of Linear Optics… Scott, is there any prospect that this work will appear pretty soon?I’m hoping that this will be one of very few articles—pretty much zero AFAICT—that will tackle head-on these issues of linear versus symplectic dynamical flow on Hilbert versus product state-spaces.

Comment #19 April 13th, 2010 at 5:51 pm

After my definite retirement as a commenter I could not resist to comment again (this time and only this time) and just now, not just in order to appear just bellow John, not because the praise of (¿boring?) political correctness, not because the appearance of multicore parallelism in the Moore law´s slide, not because of the use of the four levels in another slide (yes, four since isn´t CS the discrete restricted version of mathematics, or conversely mathematics the extended continuous version of CS ?), not because the great discussion about the Lipton´s WID hypothesis, etc…

But because i´ve been thinking lately about human like intelligent robots, and about what would happen when we would be able to make them…and one of the slides depicts one of the possible scenarios. Possible, but fortunately highly unlikely !

Comment #20 April 13th, 2010 at 7:41 pm

“along with ~(6.5*10^9) – 1 people…”

Good to see that your blogging hiatus hasn’t diminished your dry wit and/or utter disregard for significant-figure convention.

I’m intrigued by the “furiously rocking back and forth” thing, though, because I do exactly the same thing when I’m thinking/excited/listening to music/whatever. Thing is, I’m diagnosed as borderline-Asperger’s, about which diagnosis I’m sort of skeptical — but I’ve always thought the rocking was some of the more compelling evidence in favor, since it’s stereotyped and I’ve been doing it to some degree since childhood. But I don’t think I’ve ever known anyone, autistic or neurotypical, with the same behavior pattern, so it’s a lone data point.

So: I apologize in advance if this is way too personal a question, and I totally understand if you’d prefer not to answer it (I mean, I’m asking it anonymously), but you’ve never been diagnosed as anywhere on the autism spectrum, have you?

P.S. The talk looked hilarious and awesome! Almost makes me wish I were a couple years younger, just so I could have voted for it.

Comment #21 April 13th, 2010 at 8:15 pm

Sorry Scott I don’t really know what ZF does very well. I have some vague idea that even though ZF is “discrete” it somehow covers all the concepts of “continuous” stuff like calculus. So I thought maybe it was germane.

Comment #22 April 13th, 2010 at 8:40 pm

Scott, thanks! What I meant about Terry Tao’s blog is that he posts quite a few in-depth technical articles, some about his ongoing research, some lecture notes from his classes, and some fairly low level and expository (those are the ones I have the best luck with). I’d expect that his uniqueness as a mathematician comes through the most in the highly advanced articles which I can’t understand anyway. Of course the other thing that amazes me is the amount of writing he does. Mathematical writing is incredibly hard for me even when I know exactly what I’m trying to say. It takes me hours to get a sentence or paragraph right, not that I’m so good at math, but I think some very good mathematicians are the same way. Tao just tosses it off.

Comment #23 April 13th, 2010 at 9:34 pm

With regards to whether the continuity of the reals makes math bigger than computer science, it is a well-known fact that the

realreal numbers are those expressible as a 64-bit IEEE 754 floating point value. Everything else is hypothetical mumbo-jumbo with no application to the real world. I bet that when the continuity of the universe quantizes at small scales, it quantizes into floats.Comment #24 April 14th, 2010 at 1:20 am

asdf, I completely agree with you about your second comment (comment 22) about Terry’s blog.

Comment #25 April 14th, 2010 at 1:36 am

We can zoom in an arbitrary amount by first moving away a correspondingly large distance. If the universe is arbitrarily large then it must also be arbitrarily small, or neither. That’s my daily wisdom.

Comment #26 April 14th, 2010 at 2:03 am

Maybe after zooming in a sufficient amount we would see stars that are very far away, alongside bodies that are just really very small. And then we wouldn’t know, is this a really small particle on my microscope or just a really big star?

Comment #27 April 14th, 2010 at 5:28 am

Prof.Aaronson,

Delightful presentation Its just sad that Richard Feynman isn’t alive to counter with a talk on why Physics is Cool

Comment #28 April 14th, 2010 at 6:36 am

>> counter with a talk on why physics is cool

I guess you noticed that all the cool stuff (quantum computers, relativity computers, time travel computers etc.) is really about physics.

Comment #29 April 14th, 2010 at 1:38 pm

Does this post finally herald my return to regular blogging after a months-long absence?I suspect that you are getting bored with blogging, and if so, that’s a good thing. It’s been a very good blog, but it’s still a good thing.

Comment #30 April 14th, 2010 at 4:36 pm

and that’s why Scott’s presentation won

http://tech.mit.edu/V130/N19/graphics/postcpw-5.html

Comment #31 April 15th, 2010 at 6:16 am

I agree with you to some degree ..not completely

Comment #32 April 15th, 2010 at 9:51 am

If you have controversial things to blog about, why not do it pseudonymously?

Comment #33 April 15th, 2010 at 1:35 pm

pkbek: For better or worse, I hate the idea of splitting my identity into several parts, and then having to worry about which part is speaking at a given moment. I yam what I yam.

Comment #34 April 15th, 2010 at 7:16 pm

Vladimir #21: Yeah, you can develop the whole theory of real numbers—calculus, analysis, etc.—starting from set theory. The core ideas of how to do that were invented by Cauchy and friends in the 19

^{th}century (e.g., defining a real number as an equivalence class of convergent sequences of rational numbers). That’s the stuff you’d learn about in an undergrad real analysis course, where they deluge you with ε’s and δ’s.But then as Cantor noticed, certain “metaquestions” about the real numbers—like whether there’s a subset of them that’s larger than the integers but smaller than the set of real numbers itself—turn out to be rather hard. Since the work of Gödel and Cohen, we now know that the reason the Continuum Hypothesis is hard is that it’s independent of ZF set theory!

Fortunately, the independence of CH and related statements doesn’t have “practical” consequences, for quantum mechanics or anything else. In my opinion, there’s a fairly compelling reason for that: it’s because anytime you use real numbers for any “practical” purpose, you could just as well have used a countable subset of the reals (e.g., the computable real numbers, or maybe even IEEE floating points, as a previous commenter said). So for example, in quantum mechanics and quantum information, we know that it suffices to represent amplitudes to some finite precision, to predict the outcomes of any feasible experiment.

Comment #35 April 16th, 2010 at 12:01 am

You’re starting a family?

Comment #36 April 16th, 2010 at 12:05 am

No, it’s just the first time that the possibility no longer seems like science fiction.

Comment #37 April 16th, 2010 at 3:01 am

Thanks for the answer Scott! On one hand I wouldn’t want you to get too distracted from your work by this blog and specifically questions like mine, but on the other hand it’s lovely to have such a nice concise answer. I find when one is ignorant about such things trying to get traction even with all the info available online these days is hard because the information that one can find just isn’t very accessible. I for example find myself in a position where I am not prepared to do the work to really study this stuff but I am very curious about the generalities in just the way you explained them. I’ve even read a few books about math for laymen but none of them gave me a clear birds eye view like your succinct answer. So thanks very much indeed! Oooh good luck with the relationship stuff too!

Comment #38 April 17th, 2010 at 4:54 am

Wow! The slides look really great and are highly informative. Is there any way I can borrow it? I mean, if you allow it, of course. This file is so big that I’m guessing you are probably using an external hard drive. Anyway, I love the Professor Talent Show!

Comment #39 April 20th, 2010 at 10:04 pm

Actually some time before you gave this talk I wrote an essay (quoting you a great deal!) in kind of the same format.

http://procrast-nation.com/?p=3704

To be honest I think the topic deserves more words than I gave it.

Comment #40 April 22nd, 2010 at 1:36 pm

Hi Scott,

Just a word of encouragement; your blog is one of the most accessible ways for the quantum semi-literate to stay connected to what is going on in the world. Please keep on writing!

Cheers,

Paul

Comment #41 May 6th, 2010 at 4:45 pm

Scott wrote: “I yam what I yam.”

To which I cannot resist replying: I Fink, therefore I yam!

Comment #42 May 8th, 2010 at 12:01 am

“At least superficially math and physics seem to deal with continuities which appear to be analog in nature. Is this true? Are these subjects “larger” than computer science as a result?”

Well continuity = computability!

Here is a nice accessible paper on such matters:

http://www.cs.bham.ac.uk/~mhe/papers/entcs87.pdf

Comment #43 May 10th, 2010 at 3:22 pm

Thnaks, Scott I watched a video lecture by Umesh Vazirani where he mentioned that the exponentially long vectors in quantum computing come from the multiplication of dimension. http://www.bookmarkdofollow.com

The Future of Computer Science, and Why Every Other Major Sucks By Comparison

http://www.scottaaronson.com/talks/futurecs.ppt

Good for share.

Comment #44 May 12th, 2010 at 1:39 pm

Congratulations, and I’m tickled because that’s exactly the reason I don’t blog. I thought maybe I was the only one with the aggressive internal editor.

Comment #45 May 12th, 2010 at 1:41 pm

P.S. You only won because MIT doesn’t offer an entomology major.

Comment #46 May 30th, 2010 at 7:07 pm

Given the URL of the PPT, you can get a PDF version at http://www.freepdfconvert.com

This is the copy they produced for me; it disolves in 24 hours:

http://www5.freepdfconvert.com/export/490262211/result/futurecs.zip (which unzips to a pdf).

The layout looks good (so far). The notes seem to have come across as a little yellow page icons you can click to see popups.

Comment #47 May 31st, 2010 at 8:38 pm

Prof. Aaronson,

I second comment #32. Put out your controversial stuff anonymously. It’s good for the world.