Nuts and Bolts

notebook workingYes, part of my job is to sit and think about how the universe works. People hear this, and they wonder exactly what that entails. Well, it entails a lot of things – sometimes there’s the grand thoughts and the thought experiments and the like that you hear of from documentaries and books about Einstein and other famous scientists – but more often that not it is grungy nuts and bolts.

Take yesterday for example. After a week of working on various calculations and chipping away at improving my understanding of how to approach a certain problem, I decided to take Saturday and be outdoors a bit more…see what it was like outside. You know…. Have an actual Saturday Saturday. (I did not end up being booked to do that TV shoot, by the way, so I had a nice clear day ahead of me.)

What actually transpired was this:

I sat around puzzling over factors of two and minus signs. Essentially the whole day. There were a few stops here and there to do a few things, like a quick blog post in the morning over breakfast, think about what I might do during the day, get some laundry started, and so forth, but eventually I got completely pulled back into the matters that had been on my mind all week.

It all started in the shower, where I began to find that rather than thinking idle thoughts, I was coming up with new interpretations of the aspect of a simpler version of the computation that I did understand and then wondering if those new interpretations could help me understand what the source of my puzzlement was in the current computations. (This is often how we work…. you try to understand a correct and completed computation in as many different ways as you can (the underlying physical interpretation sometimes, or a geometrical one, or sometimes purely from a mathematical standpoint) and then one or more of those ways helps guide you to make progress with new questions or computations.)

So I emerged from the shower and wandered downstairs to the board and stared for a while. Then I wandered into the kitchen to find the tiny notebook that I’d scribbled in on my way on the walk yesterday afternoon to get some things from the supermarket. I’d sketched out some thoughts there which I thought I’d got to work, but my new thoughts called into question a factor of two. I’d put aside my worries about a relative minus sign in the other part of the computation. The two was now more important.

Eventually, I could not let it go. I could not work out what the source of the two was. Was it physics? Did I mis-transcribe an expression at some point and lose it somewhere? Did I lose a two in computation somewhere in the notebook? These can be hard to isolate. I flipped to earlier parts of the big notebook from early in the week and found that I’d somehow multiplied at some point where I should have divided. It was a general expression, but it turned out that when specific cases were inserted those factors boiled down to lots of factors of two as well. So this meant going over that computation again and seeing if it filtered into my later computations…. Yes and no. I’d evidently already caught this error some several pages (=two days) later, but had not made a big deal of it in the narrative that I sometimes leave in my notebooks as warnings to my future self….. More puzzling over conventions. Then I realized that I’d been extrapolating a part of the computation based on a marvelous numerical coincidence (where all the puzzling factors of two miraculously cancel just in one special case – I later understood the physical reason for this…. something called supersymmetry, which you’ve heard me talk about here before perhaps) when I had no right to. So I had to re-think a sort of ad hoc rule I’d made up….

Mid-afternoon came. Still had not gone out. But there was always this sense that I was on a verge of a breakthrough in my understanding of everything since I really liked my new interpretation that I’d thought of in the shower… I was now trying to re-cast everything in that light. Then the minus sign began to make sense. All of a sudden I properly understood it physically (or at least I thought I did….I had to modify things slightly later, but the essence fell into place in a flash…). The factors of two kept me going well into the afternoon. Every time I re-did aspects of the computation I understood things better, until eventually… The very last factor of two fell into place. It was not me at all. I was working using conventions from a 1999 paper in one part of my notebook, and a separate 2003 paper in another part of my notebook. Guess what? The unit of energy used in one paper was precisely twice that of the later paper. As soon as I realized this, there was that flash/click of global internal resolution (I’ve discussed that feeling here before) and I felt great. I’d understood Stage Two of my computation.

It was time to celebrate by finally leaving the house. Looking at the time, I saw that it was six pm and I’d not had lunch yet. Decided to go and see a movie and hang out with actual human beings. Cinespia was showing Rebel Without A Cause in the Hollywood Forever cemetery in a couple of hours. I could get a tasty burrito, a drink, a blanket, and go along and hang out at what would no doubt be a packed and fun viewing. Sounded like a plan. So I had a few crackers and another cup of tea and decided to write up my results in a blog post (on the other blog) for my young apprentices to enjoy.

An hour and a half later I had not left yet. I’d got into the writing of the post, and then got sort of sucked in. Posted it after a while (having now abandoned the nice movie idea…perhaps I’d go see a late night showing of something later on) and decided to make some dinner. While starting dinner I realized that while I’d concluded that one of the papers I was working from had to have made a mistake in its conventions (because of my brilliant new way of thinking, of course) there were still some puzzling things that did not fit with the as yet to be done Stage Three of the computation.

Stage Three started trundling along on its own in my head, of course, and then I realized that I’d been stupid in part of Stage Two! There was of course nothing wrong with that paper after all. I’d been silly. I had to change the blog post to update my thoughts there so as not to mislead any of the guys reading it…. Another hour later, having done that, Stage Three just completed itself in my head.

So I decided I might as well do a blog post on Stage Three and get it over with. Sigh. 11:15pm I finally finish and now I decide to make dinner. I decided I’ll just got for some comfort food and so make some tasty cornmeal porridge and went and sat on the sofa. I looked over the blog posts, pleased. The voices in my head were finally quiet. Everything was resolved, and my quest for the last two weeks was actually fulfilled. I can move on to the really really new stuff now…. but I was happy to do that later.

I ended up treating myself to a viewing of “Team America: World Police” (IMDB) by the South Park people. It was just as gasping-for-air funny as I remember it from that great showing of it I went to when it came out in the cinema. It was the perfect audience for seeing that sort of film and I cried streams of real tears of mirth and we were all virtually rolling on the floor with laughter right from the opening titles. (Not sure it would be that funny if you saw it on television or DVD on your own…. it’s definitely an audience movie for the first viewing…. although once you’ve done it with a good audience, then the memory of the laughs really helps out the later viewings.)

So after an hour and a half or more of laughing out loud long and hard at many and various points (oh, goodness…. the appearance of Kim Jong-Il’s fearsome pumas…. got me laughing all over again just typing it on a Sunday morning) I went to bed.

Today, after a few slow Sunday morning activities (like coffee, picking up off the clothes line all the washing I did yesterday between scribblings, sending some emails), I’m determined to get outside for real today. So (what was supposed to be) a quick hello to you via this blog post is all I will do before heading out to the Hollywood Farmer’s market, and then perhaps I’ll tackle a nearby mountainside later in the afternoon.

-cvj

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16 Responses to Nuts and Bolts

  1. Pingback: How science is done: the nuts-and-bolts edition « Entertaining Research

  2. Cecil Kirksey says:

    Dr. Johnson:

    You are a confessed theoritical physicist of the HEP-quantum gravity area I believe. I have been trying to obtain a definition of a successful career for such a physicist. I mean IF you are suppose to be identifying NEW theories that are capable of describing our universe, how can you measure success if any of your (not you personally a generic theoritical physicist) ideas NEVER are confirmed or are in fact in conflict with existing data or new data?

    You (again generic) obtain tenure. Is teaching considered a success? You train more smart people to do the same thing. Maybe you write a book based on the current SOA. Of course you write papers and maybe some are published in a peer review journal of high note. Is success judged by your peers? Your published papers require peer review; your tenured position requires peer approval. But once tenured you do what you want consistent with any contract obligations for your tenured position. Is this success?

    But the above paragraph could describe almost anyone with a PhD and doing “research”, i.e., 12th century Germanic literature. Now I know research, particular pure research, is for knowledge only, but a theoritical physicist is suppose to produce theories that correctly describe our universe.

    There have been only a few notable theoritical physicists. (I have read autobios or bios about most, still need to read about Dirac though). But these books are about successful theortical physicists in the highest sense. What about the run of the mill theoritical physicist? What’s his/her claim to fame.

    Sorry for the rambling, but just curious how a theoritical physicist views success. Maybe it is just being accepted by your peers and an earning a decide wage.

    Thanks for your time. BTW I really enjoy you flower pics. What type of camera? I do alot of bird shots and some flowers too. I am just a retired engineer who would have loved to have been smart enough to be called a theoritical physicist successful or not.

  3. Clifford says:

    I would say that the measures of success are more or less the same that they have ever been. As scientists (theorists or experimentalists) we are part of a large community constructing a body of knowledge that is analogous to building a large and intricate structure, like a bridge. No particular tiny part of the structure that I or anyone else (with a few exceptions) build might be considered great work, but it is an important part of the whole, or the bridge won’t work. As theorists we are developing tools and ideas that often have a wide range of applicability. It is never clear at any one point in time what all of those avenues of exploration will produce, or to what use the knowledge may ultimately be put. But that’s ok. In fact, it is part of the wonder of it all… you just never know. You strive to establish the facts about what you’re doing as carefully as you can, with the existing knowledge as your guide and standard by which you measure the value of what you uncover, and you keep moving forward. What defines “forward”? That is not always clear, but you do the best that you can at the time, and follow the questions that seem best to you. For my own work, a lot of what I am interested in focuses on (1) the nature of the physics of spacetime when you include quantum mechanics, (2) better understanding of how to describe the various forces of nature in various extreme regimes. These lead me to questions about black holes, cosmology, the nature of spacetime itself, the description of physics when the usual things we hold dear about spacetime (smoothness, dimensionality, etc) are not neccessarily behaving in familiar ways…. the strong interactions and quark confinement, the various exotic forms of matter that arise when strongly interacting matter is put into extremes…. and so forth. As a theoretical physicist I actually love applying myself to any interesting physics problem when I think I can make a contribution, and so I would say that my interests are not limited to the above. Measures of success are therefore built around making progress in finding better descriptions of the things I mentioned… sharpening our understanding of the various phenomena that can arise, narrowing down which aspects of the tools being developed can be honed into tools that can help us make contact with experiments that can establish what nature’s really doing. I’m under no illusions that I’ll singlehandedly write down some theory that nobody has thought of that will describe some profound aspect of nature…it is possible, but extremely rare… and but I’m confident that as part of the community I’ve made highly significant contributions to the body of work that may one day help us understand various profound aspects of nature. If that body of work turns out to not be the best for describing nature, that’s fine too. The work needed to be done in order to establish that one way or another, so the endeavour was worthwhile. Furthermore, the history of science has taught us that time and again, well defined and rich theoretical tool often end up having useful applications in unexpected domains.

    Cheers,

    -cvj

  4. Clifford says:

    And yes, teaching is a big part of the measure of success too. (I missed that part of your question on first reading) …It is a vital part of academia, and a major means by which society ensures continuity, and ultimately learns how to feed and support itself better. I’m proud of every single student (at whatever level) I’ve had the pleasure and privilege to teach, over the last 20 years and more.

    Best,

    -cvj

  5. Carl Brannen says:

    When I took a QFT class at U. Cal., Irvine, a homework assignment was to calculate the lifetime of the neutron, a “simple calculation”. For me it needed about 10 pages of tedious calculation, far more than I ever would have guessed. I slaved over it but could not get rid of some factors of 2 pi. When I got my homework back, I was shocked to get a grade of “A”, and a note from the instructor that it was normal to lose factors of 2 pi. It’s been 25 years and it’s not at all unlikely that my memory of this event has diverged from reality somewhat.

    The reason the calculation was difficult for me, was the integration over phase space. My suspicion is that the foundations of QFT, (the calculations in God’s notebook that derive the angles and coupling constants), should be simpler than this.

    Now that I’m interested in density matrices, I’m sort of tempted to redo the calculation in that formalism. It turns out that the propagators for virtual particles are natural in density matrix theory.

  6. Blake Stacey says:

    And yes, teaching is a big part of the measure of success too. (I missed that part of your question on first reading) …It is a vital part of academia, and a major means by which society ensures continuity, and ultimately learns how to feed and support itself better.

    Having just spent the evening teaching a motley assortment of academics from different fields how to model cellular automata and simulate network growth by preferential attachment, I was very happy to read this!

    If that body of work turns out to not be the best for describing nature, that’s fine too. The work needed to be done in order to establish that one way or another, so the endeavour was worthwhile. Furthermore, the history of science has taught us that time and again, well defined and rich theoretical tool often end up having useful applications in unexpected domains.

    I think this is a difficult point to appreciate if you haven’t had some experience actually doing math. That’s unfortunate, because it really is an important point.

    (By the way, who says string theory isn’t falsifiable?)

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  8. Pyracantha says:

    I’ve always wanted to know how you get the pictures of your hand (sometimes both of them) doing something. Do you mount your camera on a headlamp and use an auto-timer? Or do you simply have another person photograph you?

  9. Clifford says:

    No… it’s all me.

    Usually I just use the free hand, like in the one here.

    In the past, there’ve been some cooking posts where you’ve seen both hands. In those cases, I’ve done a detailed photo-realistic painting of the scene from memory later on.

    Thanks for asking.

    -cvj

  10. Clifford says:

    Sorry… just kidding. I have my “third arm”….. a thing I can mount a camera on that can clamp onto things, like a kitchen cabinet door, etc.

    -cvj

  11. pedant says:

    An entertaining tale, that reassures me that it can happen to anyone. I recall, years ago, doing some calculations with a colleague – two very different fomulations, expected to lead to the same answers. Which they did, reproducing results in the literature. Application to the uncharted problem in hand gave, after a lot of paper had been scribbled on, answers that were identical, save for one term. This plagued us all week. Come Saturday my colleague was left to man the fort while his wife went shopping (perhaps he should have gone in her stead, given your experiences). She returned to find him locked away, as the kids rummaged round the house, moaning and bellowing like wounded beasts. “And what do you think you’re doing?” “Helping Daddy look for his factor of two”. Which he found in the end, of course.

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