According to ancient complexity lore, at a saddle point high in the mountains of Oberwolfach lies buried a single flask of a mystical elixir known as Websbane, or the Hammer of Firefox. Some say that the productivity-enhancing potion was brewed from the sweat of Erdös and the toenail clippings of Euler; others that it was mixed, condensed, and extracted for the Prophesied One centuries hence who will derandomize BPP. Yet all agree on the tonic’s awesome efficacy: it is said that one drop would furnish lifelong protection against Slate and Salon; a teaspoonful would lift Wikipedia’s stranglehold on the soul. He who once imbibed would neither reread Onion articles from dusk till dawn, nor follow hyperlinks till scarcely a blue word remained amidst the purple, nor while away a Thursday googling a Montreal-born singer-songwriter mentioned in an email of de Wolf. Papers would get finished – books written – reimbursement forms turned in – blog entries posted without delay.

Today’s topic is what we can do until the Websbane is unearthed from its resting-ground. I offer four suggestions below; any additions are welcome.

  • Use the embryo strategy. Whenever you’re procrastinating on something, someone is bound to tell you “divvy it up into smaller chunks, then tackle ’em one at a time.” I’ve found that to be terrible advice. When I’m starting a project, I have no idea how to divvy it up. I might commit myself to writing chapters on A, B, and C, only to realize later that A and C are trivial and that everything worth saying pertains to B. Or I might start the introduction, then freeze for days because I can’t decide what belongs in the introduction and what belongs in the “meat” until I’ve already written them.What I’ve found to be more effective is what I’ll call the “embryo strategy.” Here you simplify your project so dramatically that you can finish the entire thing (more or less) in one afternoon. For example, if before your goal was to write a ten-page popular article about quantum computing, now your goal is to write two paragraphs. Then, once you’ve finished something, you progressively add layers to it. This seems to be the approach taken by most successful software projects, not to mention by Nature herself. The advantages are twofold: firstly, everything is built around one initial idea. This changes what the end product looks like, but I think for the better. And secondly — here’s the real beauty — at no point are you ever working on something that will take “unimaginably long,” compared to the amount of time you’ve already spent. (Give or take a small additive constant.)
  • Exploit the “quantum Zeno effect.” One to keep a quantum state from drifting uncontrollably is just to measure it over and over in some fixed basis. Roughly speaking, the mere fact that you’re looking means that the state “can’t try anything funny.” Similarly, I’ve taken to having my girlfriend spend the night with me when I need to finish a paper. What ensues is a long, romantic evening, wherein I sit at my computer and do my work, and Kelly sits at her computer and does her work. Interestingly, her mere presence often has the effect of projecting me onto a non-procrastinating subspace. (Kelly reports a similar effect on her as well.)
  • Don’t eat. When you’re trying to prove theorems about quantum complexity classes, hunger is your friend and linguini-induced sleepiness your enemy. As obvious as that sounds, it took me almost a decade fully to understand its importance. These days I usually eat only one meal per day — my “brinner” — and don’t even try to work till three or four hours after it. (Does anyone know the physiological reason why humans seem unable to multitask between brains and stomachs?)
  • Find yourself a “boss.” When I was at Berkeley, Umesh was my boss. That doesn’t mean he told me what to work on (he didn’t); it means that I got a warm fuzzy feeling from eliciting his opinion of what I had worked on. Since graduating, to stay productive I’ve had to seek out a succession of new “bosses” — from Avi Wigderson at IAS, to collaborators like Greg Kuperberg and Daniel Gottesman. Indeed, if you get a long, technical email from me, it’s not necessarily for your benefit. Mathematicians might be machines for turning coffee into theorems, but the fuel I run on is feedback.

Follow these rules, and you might someday become as disciplined and productive as I am.

24 Responses to “Websbane”

  1. scerir Says:

    Scott: Does anyone know the physiological reason why humans seem unable to multitask between brains and stomachs?

    Because there is a ‘second brain’ in the stomach. At least, this is what the German neurologist Leopold Auerbach discovered many years ago.
    ‘The Second Brain’, Michael Gershorn; American J. Medicine, 1999, 107:71s http://www.aikidoaus.com.au/dojo/docs/2nd_braina.htm

    One can also suppose that the level of serotonine in brains dealing with quantish problems falls down sharply, causing depression. Eating foods rich in carbohydrates (like those linguine, and specially those ‘linguine al pesto’) can relieve the symptoms of depression.
    But the effect is not at all instantaneous. 🙂

  2. anonymous Says:

    Here’s my tip that always, always works: turn off your computer, disconnect the monitor, turn off the powerbar. This makes it impossible for you to start internetting without remembering that you’re supposed to be working at your desk instead. This works. It’s kind of like how the likelihood of napping is reduced by going to the library instead of working in your room. If that doesn’t work, add more obstacles: disconnect your mouse and keyboard and put them in your closet, start using a login password, etc.

  3. Anonymous Says:

    Actually, I recommend eating only one meal per year, say on Christmas day.

    Any other Yule brinner fans out there?

  4. Scott Says:

    Actually, I recommend eating only one meal per year, say on Christmas day.

    Sounds good! I like Chinese food.

  5. Anonymous Says:

    Do I get the sense from your post that you’re working on a book…? Do tell!

  6. Scott Says:

    I wish.

  7. Nagesh Adluru Says:

    I reassert the Quantum Zeno effect though I did not have a girl friend for real, I had a crush and that itself motivated me to shape up my body and personality:D, really dramatically.

    It’s nice that the weird effect has a name now:)

  8. Nagesh Adluru Says:

    I would say “Don’t eat” is not a good idea. Instead “Eat smart” is. Eat smart means schedule your eating, eat according to nutrition facts. high protein, high fibre, low fat etc.

    I say this because being productive is as important as being healthy and producing for longer time:) “Don’t eat” might work in the short run but definitely not in long run.

  9. Mike Taylor Says:

    I think the “don’t eat” rule works better as “don’t snack”. One of the most effective time-wasting tactics I have when I am supposed to be working on something is reated trips to the kitchen make a sandwich or brew some tea or get a biscuit or defrost some chicken or …

  10. Anonymous Says:

    Use the embryo strategy.

    This is called “incremental development” and has proven to be the best way to write a software project. Write code that compiles and executes at all points in time. Initially most of the functionality is grayed out. As the project develops functionality becomes available. This creates the right combination of high level design and hands-on experience to take the project to completion. It also keeps the bug count low, since you are running, and hence testing your code all the time.

    Lastly, the feedback of seeing the thing work, if only partially is a great psychological incentive to carry on.

    Now, the quantum Zeno effect just sounds like a good excuse to have Kelly spend spend the night with you. You should try wine and a good dinner. Works all the same and is more enjoyable that late night quantum paper writing, unless you are into quirky (quarky?) stuff.

  11. Sudhir Kumar Singh Says:

    “….but the fuel I run on is feedback.”

    This reminds me of the model of quantum computation with linear optics; without feedback it is not even universal for classical computation but with feedback it is as powerful as the standard model.

    I think it is true for most of us (particularly as a student).


  12. Greg Kuperberg Says:

    Scott: I’ve had to seek out a succession of new “bosses” … like Greg Kuperberg

    Whoosh-CRACK! Get to work!

    Since you were dwelling on obvious inclusions, do you know the smallest class in the Zoo that “obviously” contains QMIP?

  13. Scott Says:

    Oof — the best “obvious” upper bound on QMIP is far from obvious! 🙂

    Certainly it’s in NEEXP. But maybe one could improve that to EEXP, by searching for the optimal prover strategies using SDP.

    For what it’s worth, my conjecture is that QMIP=NEXP — i.e., that there exist protocols for which the provers might as well just ignore their ebits. Hirotada Kobayashi, Keiji Matsumoto, and Stephanie Wehner have all thought about this question more than I have.

  14. Ben T Says:


    How do we see that QMIP is in NEEXP?

  15. Scott Says:

    Here’s what I was thinking:

    Any superoperator the provers might want to implement on the poly(n)-qubit registers they share with the verifier, they can implement in exponential time.

    This means, in particular, that they should never need more than exponentially many ebits.

    Now that I think about it, this should give an upper bound of EEXP. There are doubly-exponentially many prover strategies to test, and testing each one takes (classical) doubly-exponential time.

    Of course I’m handwaving, and I might be totally wrong.

  16. Ben T Says:


    I’m missing something.

    Since the provers can’t communicate, they can do some superoperators, but not others (e.g. SWAP). So take some superoperator they can implement without communication. It’s obvious that with communication they can implement it in exponential time. How do you implement it without communication in exponential time?

  17. Scott Says:

    Hmm. Is it true that any superoperator on an N-by-N dimensional Hilbert space that can be applied using no communication, can be applied using at most O(log(N)) ebits? (This should just be a linear algebra question.)

    If so, then we can split the superoperator into Alice’s half and Bob’s half, and do exhaustive search over both.

  18. ben t Says:


    I don’t think that’s true, but only for a reason that’s unimportant: in the absence of communication, you can’t make an arbitrary state from ebits, you want an embezzling state or something like that.

    So if we change “can be applied using at most O(log(N)) ebits” to “can be approximately applied using an entangled state on an O(poly(N))-by-O(poly(N)) dimensional Hilbert space” then it might be true. But I don’t know how to prove it.

  19. Aaron Says:

    Scott: Does anyone know the physiological reason why humans seem unable to multitask between brains and stomachs?

    I’m pretty sure it’s a blood-related issue. That is, there’s only so much blood in the body, and when there’s food to be digested, the body decreases the blood-flow to the brain while increasing it to the gastro-intestinal areas. The net effect is the familiar post-meal lethargy.

  20. Scott Says:

    That’s the observation I was looking for. Thanks, Aaron!

  21. Miss HT Psych Says:

    Scott: Does anyone know the physiological reason why humans seem unable to multitask between brains and stomachs?

    When we eat high-glycemic-index foods (such as carbs like pasta, bread and potatoes) we cause something called “sugar spikes”. Our blood glucose levels rise very high very quickly, and crash very low just as quickly. Our brains need glucose… it’s literally food for your brain. So, your better option for eating when exercising your brain is food that is low on the glycemic index (i.e. cereal, fruit and lentils). So maybe snacking isn’t the enemy… it’s yummy tasting meals. 🙂

    (Wow… years of track training, and working in research out of my area just paid off! LOL!)

  22. Anonymous Says:

    My problem isn’t so much slate and canadian singer/songwriters as it is reading Scott Aaronson and Michael Nielsen’s blogs….

  23. john Says:

    Scott, as an addendum to miss ht psych’s suggestions on what to munch on while creating the long lines of abstraction that are quantum theorems, you may want to try protein bars of some sort. They have a low glycaemic index, releasing their energy slowly; hence, they do not cause the insulin induced dive in blood sugar levels and the associated lethargy that comes while digesting other types of foods.

    They may also have the added effect of adding a “sports jock” aspect to your diet and personal image, although the desirability of this is most definitely debatable.

  24. Scott Says:

    Thanks for the suggestion!