On Good Ideas

A commenter, slim potato, implicitly asked a really good question earlier. It was a working in a notebook comment on a post I did yesterday about my struggles with a computation I was working on. I gave an answer, but since I know that a lot of readers don’t read the comments, and because one of the missions of this blog is to give a window on what scientists such as myself do and (importantly) how we do it, I thought I’d elevate the comment and my response into a post. Feel free to add your own thoughts to it in the comments, either as a non-scientist, a scientist, a specialist from another field, or other.

slim wrote:

I would have assumed that most of your time when working on a paper was involved on catching good ideas, not getting muddled with conventions and calculations.

cvj wrote:

Hi,

Thanks. That’s a common misunderstanding of what we do. What makes a field of physical science like physics work is computations – all of that business with calculations (including checking that your computations conventions are internally consistent) is vital to the field.

Frankly, “Good Ideas” are a dime a dozen. Anyone in my field ought to be able to think of at least six of them before breakfast. What makes a good idea go from a good idea to an idea that actually is useful and relevant is those several hours of muddling away with computations and calculations, testing out the idea and seeing how it fits into the scheme of things, and how it fits into the larger tapestry which is all the calculations that have ever been done in physics for generations. You can’t just make up stuff out of whole cloth, you see. Sitting around dreaming or talking is important to do too, but it is all utterly worthless (as science) without calculation. This is vital to what makes what I do science, at the end of the day. Finally, if I were working on an aspect of the subject that was directly related to a physical phenomenon “out there” in the world (this project is not so directly related, as far as I know, it is more about what’s going on “under the hood” of string theory), then the value of the good idea and the computation is also tested by comparison to a well-designed experiment, which has its own sequence of stages of ideas and computations (and worrying about conventions) to go through to bring it to fruition.

Thanks,

-cvj

Thanks, slim potato!

There’s a lot more that could be said, but I’ll leave it at that for now. For more snapshots of the sort of things that I (and several others) do in our day to day work in (theoretical) physics, I’ve collected together some of my earlier posts of the same sort as yesterday’s, and you can find it on the page “Notes From the Day”.

Enjoy!

-cvj

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13 Responses to On Good Ideas

  1. Tommy says:

    Well said. The amount of time I spend checking factors and conventions is much more than most laymen would ever believe. I’ve spent an entire week worrying about a single minus sign once.

    I also spend a lot of time checking or redoing many of my calculations. When you get a result you wanted there’s a temptation to simply declare the calculation correct which is quite dangerous. I often force myself to take out some fresh scrap paper and redo the whole thing just to check. That’s also what good collaborators are for.

  2. Also true, as I’m discovering, in my branch of science (she says, soldiering on with her maths in pursuit of a paper, in the face of…well, maths). I like how you worded this explanation — nice one.

    Cheers,
    IP

  3. slim potato says:

    Thank you very much, Clifford.

    Actually, I’m a first year Physics student so that I know how time-consuming calculations can be.
    In order not to turn into a mere “machine for turning coffee into equations” I also toy with ideas.
    Yet when checking on the arXiv it always happen that someone came before and tamed that idea ; I find this most depressing.

    So I was surprised when you wrote that “anyone in [your] field ought to be able to think of at least six of them before breakfast”.
    I guess it’s due to my lack of knowledge and I’m working hard to catch up with the field.
    I’ll hurry and go through your book, then. (I’ve already read the first part: you did a great job !)

  4. Tommy says:

    slim,

    Random bit of advice for someone just starting out. It helps to have a good advisor of course, talking with him and especially postdocs working on things you are interested in. They often have a bit more perspective on things and can tell you about things people find interesting currently. This can be done in a casual way, say over lunch or after work beers.

    Another thing that is good when first starting out is to take a recent paper you find interesting and try to think of a way to extend it, just a little bit. Maybe they didn’t include charge. Maybe they only worked something out for a certain gauge group. It seems trivial, but its a good place to start (especially for someone new) and you’ll often find a lot of interesting stuff arises as you proceed. I recall getting two whole papers out of literally trying to add rotation to someone else’s work early in my graduate career.

  5. Clifford says:

    Hey slim,

    Did not mean to be overly glib about the ideas business, but there is some truth to what I said about breakfast and so forth, but it does take a while to get to that stage. It comes from being around long enough to learn enough bits of the field to see how things connect to each other and so forth. There comes a point then where if someone tells you that they have uncovered fact A about a given system, a whole host of things to do (some of them simple but important extensions along the lines of what Tommy was saying, but others more involved) occur to you immediately. Many of them are good ideas, and really good things to explore. The trick is being able to bring computational concrete to those ideas (not always possible), and/or having the skill and insight to know which of them are worth exploring. A good advisor is someone who can help you navigate this sort of minefield of ideas. She will show you how to start with small computations, and build up to huge really involved ones that can take months in some cases… all glued together with a guiding intuition about what the central idea is. I guess the point is really to find good balance between ideas and computation…. each guides the other. It takes experience to get the balance.

    All the best with the new stage of your career! It is a fun time…!

    Best,

    -cvj

  6. Paul Clapham says:

    Having been a teaching assistant for undergraduate math courses, I know how easy it is to do something small like getting a sign wrong early on in a calculation. As a marker, you correct that sign with a red mark. Then on the next line there are two red marks. And on the line after that there are three or four red marks, and by the time you get to the end, the whole equation is just a sea of red marks and the answer is totally wrong.

    When you’re writing a paper, you don’t want this to happen to you. Either the reviewers will catch it (rather embarrassing) or they won’t, but one of the journal readers will (horribly embarrassing). So yeah, you do spend a lot of time checking the details.

  7. Clifford says:

    Hi Paul C,… That is all certainly true, although I’ll mention here that for me at this stage of what I’m doing, all of this is well before anything like a paper is being written. It is just the issue of trying to figure out what’s going on in the physics. (I took “paper” in slim p’s original comment to really mean “project”.)

    Cheers,

    -cvj

  8. WC says:

    I would be interested in knowing how many of a normal physicist’s good ideas make it to the published world.

    Suppose you get a idea, and you do some checks on it, and find that it does not work in the original great way, that you thought. However it might still be mildly interesting. But to type it up as a paper you still need to do a lot of calculations — so is it worth the effort of doing this extra work and getting it published? Or should you start working on something else? What if you are a graduate student and the checks that you did on it took some time?

  9. slim potato says:

    Thank you so much, Clifford and Tommy.

    That sounds ridiculous but nobody did ever bother to give me such reassuring tips. I come from a country where there is a concrete wall that separates students from professors and research workers.

    Regards,

    SP

  10. nigel says:

    ‘Anyone in my field ought to be able to think of at least six [good ideas] before breakfast. What makes a good idea go from a good idea to an idea that actually is useful and relevant is those several hours of muddling away with computations and calculations, testing out the idea and seeing how it fits into the scheme of things, and how it fits into the larger tapestry which is all the calculations that have ever been done in physics for generations.’ – Clifford

    Popularization of physics often tries to avoid discussion of calculations and to focus on the ideas. It’s nice that you’ve put the facts straight in this post.

  11. Clifford says:

    WC: – It really depends upon the idea, and it is something you should discuss with your advisor. If your result is solid, even though not what you expected, and you ended up showing something else, that fact may well be useful to someone and so sometimes can be publishable. That is something your advisor should be able to help you with.

    Generally speaking, I find that no calculation is a total waste. You got the practice, for a start…. Further, even if the idea that you were working on did not work out and you got a null result, or just no result at all, document your computation in a notebook so that you can reconstruct it later and save it. Chances are it might well feed into something else later on in your career.

    Good luck.

    -cvj

  12. David says:

    Absolutely, couldn’t agree more. Without the calculations how would we really know a “good” idea from “bad”. The good ones are the ones that survive the furnace of calculation. I often have ideas that just don’t work though in an arm chair with a whiskey they might sound very persuasive. The most interesting ideas are often those that nobody would believe were it not for the calculational evidence. I once spent three months getting some factors right because it mattered. Fortunately it doesn’t always matter and knowing when it does is something I hope we pick up through experience.

  13. wloop says:

    Hello every one. Some years ago in my old University I was chatting with one of my Professors and he asked me about my future plans and what I wanted to do when I grow up. I answered: I want to be like you
    and then he said to me that I should made a lot of sacrifices so as to reach my goal , and that’s where our conversation ended. I am sure he didn’t mean to discourage me but to advise me to work hard. Because I get strongly influenced by people who admire, from that time and until now I am waiting for these ‘sacrifices’ to come. I think that I work hard but never feel like making a sacrifice because I like what I do, which makes me think that at the end I don’t work really hard. I don’t know if I made myself clear. It is not that I am sad or something, I am really happy !! These are some thoughts that I have from time to time ! So I would like to ask you what is your opinion on that and what ‘sacrifices’ you made so as to become who you are .