See subject.
Lot of questions buried in that.
Can he be practicing, creative physicist, as opposed to a teacher or commentator on other people’s work?
How much do mathematicians need their muscular control to “work,” ie, think many-valued constructions through? Eye muscles not included, as well as such speech synthesis as he has.
Other questions I’ll raise if I see a cue…
As a theoretical physicist (which he is), yes, of course. In any case, the distinction between being a creative, original thinker and a “commentator on other people’s work” is a lot more blurry, even in science, than is commonly assumed. In science and scholarship, all creative theoretical work is ipso facto, in some sense a commentary on, and dependent upon, work that has gone before.
Yes, as I think you are implying, there is much evidence that the muscles play a much larger role in thought than is commonly believed. Einstein talked about the early stages of his thinking about relativity as experienced in terms of muscular feelings. Thought does not all happen inside the brain, including thought about physics, the body is involved too. However, in this respect the eye muscles are by far the most important aspect of musculature, so otherwise paralyzed people who retain eye muscle control are not significantly impaired in their thinking. (And most paralyzed people do retain eye movement control, since the eye muscles are controlled by their own dedicated cranial nerve, rather than via the spinal cord, through which most other movement control must go, and where the relevant lesions are normally located.) Most human voluntary movements are eye movements anyway, the eyes just move so quickly and frequently.
Funny (not ha-ha), I never thought of that. Fascinating issue.
I was more in the sense of using a pencil for symbol manipulation. For conceptual diagramming, yet another level.
But both different than your idea, which I hope we get to.
I would guess that Hawking has developed his powers of visualization to a high level (like Sheldon Cooper writing on his imaginary whiteboard). Presumably he can also “write” on his computer screen, even if that is a bit more laborious than using a pencil or a dry-erase marker wold be.
I don’t know whether this is relevant to your question or not, but Leonhard Euler didn’t need his eyesight (and thus presumably his need to use a pencil for symbol manipulation) in order to work. Then again, few people have a memory as good as Euler’s.
I had a blind math professor at one point. He had a graduate student working for him to put things on the board when necessary, but the professor still had better visualization skills without the board than the grad student did with it.
And Hawking’s work has been declining significantly in quality of late, but that often happens to academics in their later years, disability or no (if nothing else, just from reversion to the mean). He still came up with some very groundbreaking work after losing the use of most of his body, though.
I will just mention two data points. First one. After Steve Smale proved that it is possible to turn a sphere inside out with any creases (although it was allowed to intersect itself, Klein bottle style, but the intersections had to be transverse, meaning tangents to the two parts of the surface not allowed to be parallel at a point of intersection–it gets fairly technical and there is at least one 4-way intersection point), it was a blind mathematician, I have forgotten his name, to actually describe an explicit construction. What Smale had done was show that the “obstruction” (a very technical idea) to such a construction vanished.
Second one. As a result of a torn retina, I had to spend three weeks lying of my stomach (most of the time) last January. But I was supposed to give a talk on a certain subject in March. One place in the construction was a rather detailed computation, which I hadn’t memorized. I spent part of the three weeks going over it in my head until I could have dictated if needed. So I would have said I needed a pencil and paper, but I didn’t. Remember Hawking doesn’t have to take out the trash, wash the dishes, change a light bulb, all the 1001 time wasters that bug me. I am certainly not saying I would prefer having all that leisure time, heave forfend, but he does have a lot of spare time to do these computations in his head and has had a lot of practice at it.
Bolding mine. What about all of the simple tasks that he does which surely take him a lot longer than a fully able bodied person (getting dressed, eating, using the bathroom)? I don’t think you can safely assume that Stephen Hawking has a lot of free time cuz he doesn’t have chores.:rolleyes:
In regards to the OP, he is a brilliant man that undoubtedly has superior powers of visualization (better than average) that most likely have only been strengthened by his reliance on them. And I’m sure he has developed some sort of workaround that allows him to manipulate symbols via a computer screen when that visualization is not adequate to the task at hand.
I always figured his vocoder had a floating point unit.
Last I heard, he was controlling his voice software with his cheek muscles and there’s real concern about him being locked-in. While he’s been compensating for decades, it may be advancing disability and age are both a factor in his declining work.
Even so, his ability to visualize and do things entirely within his head are exceptional.
I remember reading an anecdotal account by (or about) a grad student of Hawking’s, who worked with him on the AdS/CFT correspondence, trying to understand whether information is lost in black holes, which Hawking had famously betted on, but has since conceded defeat. IIRC, it was commented that Hawking no longer did most of the calculations himself, the necessary manipulations being too cumbersome to carry out. But I can’t seem to find the story.
Of partial relevance, I’m currently reading God Created the Integers, which is a compendium of historic mathematical texts that Hawking edited. While the texts themselves are other people’s work (even the translations and notes), he does provide a brief introductory essay for each author represented.
In at least one case he works through one of the problems. Granted, it’s mainly commentary and not the same as doing the higher math for physics, but if nothing else it shows that he is interested in doing the math.
It should also be noted that doing calculations is a very small part of the actual work in physics. Computers can do calculations just fine. The real trick is in knowing which calculations to do, and in how to interpret them.
I don’t think you can doubt his interest in maths and his mathematical ability. Historically, when Hawking and Penrose first made a splash in theoretical physics they represented a wave of young physicists who were much mathematically sophisticated than their predecessors.
If you want to look at how math heavy Hawking’s recent papers have been, arXiv is a good place to start:
http://arxiv.org/find/hep-th/1/au:+Hawking_S/0/1/0/all/0/1?skip=0&query_id=1004cf90c5fba9f2
If this isn’t too [absurd|impractical|personal] a question, could you, or some of the other practicing physicists here, give some notes on how you “use math” or “calculate” when you’re in that mode (ie not filling out expense reports).
My closest image is when asking composers what they “do” when composing (when, in this case, you’re physics-ing). You can use a piano every now and then, jot down ideas and work out in notes (representing sound or other), or go full-tilt-boogie using your mind’s ear only–up to a point where you lose track of where everything is structurally.
Late Beethoven obviously comes to mind, but of course he had his pen.
(Less well known, but far more puzzling, are the towering polyphonic works of the Renaissance. Hardly a single shred of manuscript or evidence has been found of any sketches.)
ETA: of course I understand the brunt of your post, when it comes time for the spinning of numbers by brute force at some point in the thought-feedback cycle.
He does not dress or toilet himself, he has body tenders who deal with that. They get him up in the morning and put him to bed, and during the day he simply indicates to them what his needs are [or they are done on a schedule, no idea how much sensation he has remaining to him.]
A large but difficult to quantify part of the work is figuring out what questions to ask in the first place. It’s difficult to quantify because it tends to be done in “aha” moments-- You’ll get great ideas at lunch (especially if you’re eating with colleagues), or as you’re falling asleep, or on the toilet, or whatever.
Then you need to set up the problem in such a way that it’s calculable. This often involves drawing diagrams on a whiteboard, carefully labeling all of the measurable quantities on it, and recording the mathematical relationships between the quantities. Massage those relationships enough, and you end up with the equations you need to solve to answer your question.
Now, sometimes, the equations you get will be just plain unsolvable: There simply isn’t enough information. At this point you need to figure out how to get the additional information you need. Sometimes this means setting up or designing a new experiment, sometimes it means heuristic guesses or approximations, and sometimes it just means that you publish what you’ve got, and let others try to find more information.
Even if there’s enough information for the equations to be in principle solvable, sometimes the calculations will be too hard for the calculation to be remotely practical (even with computers). In this case, you need to figure out what approximations you can do (usually this involves concluding that some effects are negligible compared to others, and leaving those out of the calculations). How much you can get away with here depends on how much precision you want: Sometimes, just getting an order of magnitude is good enough, and sometimes, other calculations have already been done and your whole goal is to get them more precise than others have, by considering some of the things they neglected.
Then, once you’ve got the problem set up mathematically in this way, you put it in a computer, let it run over your lunch hour, or overnight, or over the weekend, or whatever, and get your results. Or, if the problem is big enough that just putting it in the computer will take a while, you tell one of your grad students to do it.
Of course, once you have the results, you’re still not done “physics-ing”. You also need to share those results. This, too, has many steps, ranging from telling your lunch partners about the interesting results that seem to have cropped up, to telling the other members of your group at your weekly meeting, to preparing a Powerpoint to show at a seminar to the department, to making a poster for a conference, to publishing the paper (not all of the steps always occur, of course). And there’s also some overlap between the “physicsing” and the “filling out expense reports”, since the expense reports are usually for grants, and you get grants by pointing out the interesting work you’ve done, and telling the grant agency about all the great ideas you have for new work, as soon as you have the funding.
Chronos, what field do you work in? Also, do you have an account on giantitp?
I’ve heard Hawking say (in his own words, if not his own voice) that he views his disability as an asset for his work, since it allows him long periods without distraction. Yeah, he’s a bit of an optimist.
You also have to remember Hawking’s results have never really been numerical. He is more a physicist who formulates the equations that others use or proves a general fact about the equations.