Those “Light-Bulb” Moments..

Last week I read a piece in the October edition of Physics World (which you can read here, but only if you have a subscription) about whether breakthroughs in physics occur through sudden “light-bulb moments”, or are more often the result of solid hard graft? The piece includes some interesting comments from distinguished scientists about their own “Eureka” moments, which I’m sure will resonate with many researchers, not only physicists. Incidentally, the article refers to such moments as “claritons”, a word I’ve never heard before, presumably a soliton of clarity…

I’m pretty sure that everyone who works in science – even the eminent individuals interviewed for the Physics World piece – has spent a large part of their time “stuck”. I know I have. In the long run it’s probably good to go through such periods as I think they’re essential for intellectual development, but they’re undoubtedly extremely frustrating at the time. How you get “unstuck” is a very mysterious process. I’m not a neuroscientist, but it seems to me that when you get really immersed in, say, a research problem, your subconscious brain gets drawn into what you think is a fully conscious process, to the extent that even when you’re apparently not thinking about something you really are. I’ve had ideas come to me in all kinds of weird situations: watching ducks paddling on a pond, listening to music, walking in a park, and even pushing a trolley around a supermarket. Often it seems that it’s precisely when you’re not thinking that you have your best ideas. It’s not always clear what acted as the trigger, but and when it is it is often something quite abstract. In the case I mentioned of the ducks on the pond it was just a question of thinking about reference frames. It was a nudge in the right direction, but I still had to do quite a lot of work to finish the calculation. Come to think of it, it’s usually at that conceptual level that such things happen rather than in the detailed working, at least in my case.

The Physics World piece also talks about ideas coming through dreams. That has happened to me too, but I think it’s basically the same phenomenon that I’ve just discussed. It seems to me that dreams are a product of your brain sorting through recent events or experiences and trying to make sense of them in terms of others it has filed away. This can help with a research problem by flagging up a connection with something else hidden away. I can remember at least two occasions when I’ve woken up from a dream with an exact understanding of what I’d been doing wrong and how I could fix it. It’s great to wake up in the morning with that kind of feeling!

I know it’s wrong to draw inferences about other people from one’s own particular experiences, but I do feel that there are general lessons. One is that if you are going to be successful at research you have to have a sense of determination that borders on obsession. You have to immerse yourself in it and be prepared to put long hours in. When things are going well you will be so excited that you will find it as hard to stop as it is when you’re struggling. I’m writing as a physicist, but I imagine it is the just same for other disciplines.

The other, equally important, lesson to be learned is that it is essential to do other things as well as doing science. Being “stuck” on a problem is an essential part of mathematics or physics research, but sometimes battering your head against the same thing for days on end just makes it less and less likely you will crack it. The human brain is a wonderful thing, but it can get stuck in a rut. One way to avoid this happening is to have more than one thing to think about.

I’ve lost count of the number of times I’ve been stuck on the last clue in a crossword. What I always do in that situation is put it down and do something else for a bit. It could even be something as trivial as making a cup of tea, just as long as I don’t think about the clue at all while I’m doing it. Nearly always when I come back to it and look at it afresh I can solve it. I have a large stack of prize dictionaries to prove that this works!

It can be difficult to force yourself to pause in this way. I’m sure that I’m not the only physicist who has been unable to sleep for thinking about their research. I do think however that it is essential to learn how to effect your own mental reboot. In the context of my research this involved simply turning to a different research problem, but I think the same purpose can be served in many other ways: taking a break, going for a walk, playing sport, listening to or playing music, reading poetry, doing a crossword, or even just taking time out to socialize with your friends. Time spent sitting at your desk isn’t guaranteed to be productive, and you should never feel guilty about taking a thinking break.

I’d be interested to receive examples of other “light-bulb” moments through the comments box. I’d also welcome comments from neuroscientists on my extremely naïve comments about how the brain works in such situations.

P.S. It’s interesting how the light-bulb has become so strongly associated with the sort of brainwave discussed in this piece. Here’s a short discussion.

14 Responses to “Those “Light-Bulb” Moments..”

  1. Anton Garrett Says:

    I’ve lost count of the number of times I’ve been stuck on the last clue in a crossword

    But that’s not surprising. It’s the last clue because it’s the one you have kept putting to one side because it’s harder.

    • telescoper Says:

      Also because you can always hope for some additional checked lights* until you reach the last clue.

      *light=place in the grid where a letter of the solution is to be written.

  2. Anton Garrett Says:

    I can tell two such testimonies. One was when, in the early 1980s, I was labouring to prove a mathematical conjecture relating to the Boltzmann equation. (Specifically, to the spatially homogeneous equation in the absence of external fields for a single particle species, in which case the equation is integrodifferential and quadratically nonlinear.) The conjecture, for what it is worth, is that successive derivatives of Boltzmann’s H-function, the velocity-space integral of f log f where f is the one-particle distribution function, alternate in sign. That dH/dt is never positive was proved by Boltzmann himself, on which (questionable!) basis he called -H the entropy. Numerical evidence in the early 1980s suggested that higher derivatives did satisfy the conjecture. So I spent a few weeks trying everything I could think of to prove the conjecture, but got nowhere. Then after one fruitless morning I thought, “What if it’s not true – what if the failure lies beyond the regime that has been investigated numerically?” I realised immediately that the Laplace transform of a non-negative-definite function has the alternating derivatives property, and it was easy to show that the inverse Laplace transform of the H-function used in the numerical studies changed sign. So, if a mathematical theorem existed that it is not only sufficient but necessary for derivatives to alternate that the function be writable as the Laplace transform of a function that never changes sign, I would be hope: the conjecture would be proved false. A trip to the library found me such a theorem, in Widder’s book on the Laplace transform. In fact the resulting short paper of mine was one of three to be submitted before the first disproof was published. One of the others pushed the computer harder and found a breakdown numerically. The AHA moment in this story was “What if it ISN’T true…?”

    That example involved merely a True/False conjecture rather than open-ended insight. I remember when I had my best idea – how to eliminate an axiom in deriving the laws of probability, by using RT Cox’s strategy to derive the single law for p(A-NAND-B|C), from which the sum and product rules both follow becaues you can construct any logic operation from NAND. I can only describe it as like an occasion years earlier when, playing that solo card game in which the aim is to get four aces remaining on the table but no other cards, I suddenly ‘knew’ after looking at the cards that on this deal it was going to be possible, without having the faintest idea how.

    • telescoper Says:

      “The art of discovering the causes of phenomena, or true hypothesis, is like the art of decyphering, in which an ingenious conjecture greatly shortens the road.” G. Leibniz

    • telescoper Says:

      It seems quite often these moments consist of a realization that one is looking at the problem from the wrong end, or at least that there is another way of approaching it that might be more profitable.

      Another class seems to be related to the difficulty of recovering things from memory, which gets worse as one gets older and is very frustrating to endure. Sometimes things seem to refuse to be recalled unless and until one stops trying.

      • Anton Garrett Says:

        I like your phrasing that “things seem to refuse to be recalled”. Ed Jaynes once called this sort of thing the “mind projection fallacy”. Partway through his lecture about it (in probability theory – I’m sure you can see the relevance) the overhead projector bulb blew, and he couldn’t get the reserve bulb working – he actually said “it doesn’t want to go on”…

      • telescoper Says:

        One case when the mind projection fallacy is hard to avoid is when you’re talking about your own mind!

    • Anton Garrett Says:

      Oops, that should be “I would be home” rather than “I would be hope”.

  3. “It seems quite often these moments consist of a realization that one is looking at the problem from the wrong end, or at least that there is another way of approaching it that might be more profitable.”

    I have yet to see any problem, however complicated, which, when you looked at it in the right way, did not become still more complicated.

    —Poul Anderson

  4. Let’s be happy that they are light-bulb moments and not light bulb moments. 🙂

    • telescoper Says:

      Isn’t it strange that “Light Bulb” is not hyphenated (as a noun) whereas “Lamp-post” is?

      • Both forms are acceptable in both cases, as well as “lightbulb” and “lamppost”. The usual order, as terms become more familiar, is to move from two words to a hyphen, then from a hyphenated term to one with no hyphen (e.g. e-mail to email).

        I note that the WordPress spell-checker (note the hyphen!) knows about “lamppost” but not “lightbulb”. People might prefer to avoid “lamppost” since the successive “p”s make it look a bit strange.

    • Anton Garrett Says:

      A light beam is not the same as a beam of light…

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