A piece up at the Guardian blog which probably belonged over here at CT but I didn’t have my CT login to hand. Basically, Harry Collins, a sociology professor, has been doing the Dian Fossey bit with a subcommunity of physicists. He has been accepted among them to the extent that he can have perfectly sensible conversations with physicists, and even teach them a few new things about physics on occasion (since he puts a lot more effort into networking than they do, he’s usually got some new bits of information from the bleeding edge of research).

The question that interests me is, in what sense can one say that Harry Collins doesn’t “really” understand gravity waves? What is that thing which he is missing, if anything? A lot of people on the Guardian blog seem to want to argue that the particular mathematical manipulations carried out by gravity waves researchers are in some way constitutive of what it is to “understand the physics”, but this seems to me to be obviously wrong. “The current state of research about gravity waves” clearly names a different entity from “gravity waves”, and what I’m interested in is the existence of any sense in which the physicists understand gravity waves and Collins doesn’t. (It’s a common belief among physicists, probably derived from Quine, that there is a particular correspondence between mathematics and physics which might serve to hold a special relation together. Not so, as we’ve known ever since Hartry Field‘s work, managing to derive Newtonian mechanics using only logic).

We don’t want to make “understanding the subject” mean “being able to do calculations about the subject”, unless we have some reason to believe that this is a necessary condition rather than a sufficient one (and to be frank, I don’t believe it’s a sufficient condition; I’ve spent enough time with economists to know that ability to do the maths does not mean that someone understands the economics). Is there anything? Or is Collins’ concept of “interactive expertise” really all there is, in terms of understanding?

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A. Random Physicist 10.10.06 at 3:28 pm

I guess my first thought is: can he apply his knowledge to new and unfamiliar situations and correctly predict the results of experiments done in those situations? This doesn’t necessarily require mathematics (although it might, in certain situations), but it would require the correct application of the principles involved. I think that would be required to say that someone really understood a subject.

engels 10.10.06 at 3:43 pm

I don’t understand why you say in your Guardian post that Collins can’t possibly make an original contribution to the field. Couldn’t he make a claim, and perhaps provide an informal argument for it, which the nerds find original and persuasive, and which some of them later prove to be true, by expressing it in technical language and developing mathematical proofs based on his reasoning (or conducting experiments). Can’t we give Collins (any of) the credit for such a discovery?

Daniel 10.10.06 at 3:55 pm

1:

I guess my first thought is: can he apply his knowledge to new and unfamiliar situations and correctly predict the results of experiments done in those situations?Apparently yes; in the linked paper, one or two of the questions involved things that he hadn’t seen before and he had to figure it out.

2: In principle this would be possible, but Collins’ own assessment is that he doesn’t think he could (he also gave up on a project on the sociology of amorphous semiconductor researchers because he thought he wasn’t making enough progress toward establishing interactional expertise.)

Bryan 10.10.06 at 3:57 pm

Let us imagine that the field of gravity waves is entirely an extremely elaborate hoax designed to fool Harry Collins. The entire idea of ‘gravity waves’, in this hypothesis is akin to the made-up physics of science-fiction, say, Star Trek, and the mathematics is all, basically, gibberish and only superficially systematic.

Now, of course, this is a thought experiment and I’m sure Harry Collins has many extremely good reasons to believe this isn’t true, and no reasons to think it is. However, it is my inclination to say that he cannot be sure it isn’t the case as it stands. If he really

understoodthe mathematics, however, hewouldbe in the position toknowthat it wasn’t the case.Jim Harrison 10.10.06 at 4:02 pm

In the days when I was in the textbook business, I would regularly pass important information from one scientist to another. I was amazed at how isolated researchers could be. In one case, two guys with labs on the same corridor had separate grants to study the same problem but didn’t know that the competition was across the hall. I expect that non-scientists with more intimate connections to researchers–the salesmen who deal in lab animals, for example–routinely serve as vectors of vital news and, in all probability, also raise critical questions and make important suggestions. Of course, if the grad students can’t get credit, the Purina Rat Chow guy is probably out of luck. I assume a sociology professor has middling chances.

Gdr 10.10.06 at 4:13 pm

Bluffing is a skill that most people pick up a working knowledge of, and some people become experts at it. There are lots of everyday situations where a bit of bluffing is useful: job interviews, tutorials, oral examinations, presentations, arguments, debates.

Any teacher will recognize the phenomenon: clever but lazy students develop all sorts of techniques for faking a greater understanding of the material than they really possess. The way to expose someone’s bluffing is to test his understanding deeply on a few key points, to keep on pushing for clarity and detail, and reject waffle, shallow generalities, smokescreens, and irrelevence. (That’s why PhD vivas take, or should take, this form.) However, if social nicieties prevent you giving the bluffer a thorough Socratic going-over then his bluff will likely succeed.

The test in the experiment consisted of wide-ranging and shallow questions, with no opportunity for the judges to probe to see what kind of understanding lies behind the words in the answers. It’s exactly the kind of test you’d design if you wanted to give the bluffer the best chance of success.

J. Ellenberg 10.10.06 at 4:15 pm

We don’t want to make “understanding the subject” mean “being able to do calculations about the subject”, unless we have some reason to believe that this is a necessary condition rather than a sufficient one.In mathematics, I would certainly say that “being able to do calculations about X” is a necessary (but perhaps not sufficient) condition for “understanding X.” For most of us, there are lots of areas outside our primary expertise about which we could converse intelligently, even suggest ideas — but in which we could not actually

doanything.Walt 10.10.06 at 4:17 pm

I’m only going on what the Wikipedia article says, but I don’t see how the Hartrey Field example proves what you say. When Hilbert axiomitized geometry, he wasn’t playing sudoku. He was doing mathematics.

Daniel 10.10.06 at 4:17 pm

I had a horrible feeling that the phrase “become experts at it” was going to be linked to this page.

I think you’re misunderstanding Collins’ situation, though. He is a fixture at gravity waves conferences and has been talking to the physicists in detail for 30 years. Lots of them do, in fact, believe that he understands gravity waves.

RJO 10.10.06 at 4:18 pm

In the 1970s and 1980s the philosopher David Hull started to study the field of systematic biology in the context of his philosophical interests in evolutionary epistemology. Hull became involved to the extent of making many important contributions to the field, even though he had no real background in biology, and he eventually became president of the field’s leading professional society. His sociological work was brought together in Science as a Process.

Was Hull “really” a philosopher or “really” a systematic biologist? He became both of course. Did he ever do the sort of emiprical work that many systematists do? No, but his talents lay elsewhere: he made important contributions to the history and theory of the field, which fed back into practice. Not all practicioners in any field have exactly the same talents or interests; some are experimental, some theoretical, some mathematical, some comparative, some visual, some verbal. Collins has clearly trained himself to be a physicist, and it makes no difference whether he has every particular skill that many others in the field possess. Scientific disciplines don’t have essences any more than species do.

Tracy W 10.10.06 at 4:35 pm

You state in the article that he can’t design and carry out an experiment. If he’s been spending so much time around physicists I find this hard to believe.

And, if it is true, I wonder if he also can’t design an experiment, leaving aside the “carry it out” bit, which may require a fair bit of manual skill, bug-detection, etc.

If Collins can’t design an experiment (which I find hard to believe), then this does imply a gap in his understanding since he can’t take the principles further.

Which I guess is the same point “a random physicst” makes.

Why though is it surprising that Collins has picked up all this knowledge? Don’t physics students pick up a lot of knowledge from hanging around physics professors? Okay, presumably Mr Collins goes away sometimes and writes up his sociological results, but there’s many a physics student who goes away sometimes and does other things like raise kids.

In my experience, maths is about the only thing I need to sit down and explicitly study to make sense of it, other things can be roughly picked up by conversation and observation (though for those things where getting it wrong can be deadly, eg scuba diving or arc welding, I go for formal study, teaching and practice every time).

Matt Kuzma 10.10.06 at 4:38 pm

During the course of studing physics in college, there are a few things I can definitely recall really only understanding after going through a long process of rigorous mathematical dirivation.

You’re certainly right that the math is not the physics, and I would add that sometimes physicists forget this. I remember at one point in a class I was taking a student went up to the professor after the lecture and asked “Is this really what’s happening, or is this just math that predicts the outcome reliably?” and to my surprise the professor told the student that, no, this is actually what’s happening. I think in many cases the models are so good that researchers can forget that they’re still just models for the real thing.

But I can say that, if you haven’t done the manipulations in relativistic math of speed and mass and acceleration, you don’t understand relativity. If you haven’t derived those equations, you don’t really understand the theory. Likewise, if you haven’t studied enough electricity and magnetism to be able to derive the electromagnetic wave, then you probably don’t really understand light, even in a classical sense. If you haven’t computed potentials with the shroedinger equation, you have no hope of understanding quantum mechanics. These are things for which analogies and axioms just don’t cut it. There are too many variables and their relationships are too complex to be expressed in anything less the math they use.

And I can also say that I have first-hand experience faking the physics, as there are a few more esoteric classes from my last year that I never reached true understanding of. I passed those classes, but plasma physics is still a complete mystery to me.

Off the top of my head, however, I would say newtonian mechanics and thermodynamics probably need almost no mathematical work to understand. Some of the more complex phenomena, like unstable axes of rotation, might elude you, but you could get by.

I don’t know where the study of gravity waves falls in terms of its math-heaviness.

Andrew Edwards 10.10.06 at 4:39 pm

Let us imagine that the field of gravity waves is entirely an extremely elaborate hoax designed to fool Harry Collins. The entire idea of ‘gravity waves’, in this hypothesis is akin to the made-up physics of science-fiction, say, Star Trek, and the mathematics is all, basically, gibberish and only superficially systematic.Now, of course, this is a thought experiment and I’m sure Harry Collins has many extremely good reasons to believe this isn’t true, and no reasons to think it is. However, it is my inclination to say that he cannot be sure it isn’t the case as it stands. If he really understood the mathematics, however, he would be in the position to know that it wasn’t the case.This is quite clever and I was initially persuaded, but here’s the rub.

Let’s say that fine art does not actually exist and is all an elaborate hoax designed to fool me, Andrew Edwards, into believing that people enjoy looking at various paintings, some of which have big ideas behind them. The entire world of fine art in this example is akin to the famous Sokal paper, and its productions are randomly generated then semi-plausibly justified ex-post. Actors are hired to portray people in art galleries.

I have many reasons to believe that this is not the case, but I cannot – it is impossible – formally prove or disprove the hypothesis. Does this mean that I cannot possibly understand fine art? Jokes about the inscrutability of fine art aside.

Or replace ‘fine art’ in the above with anything without an underlying mathematics. Wine tasting. Literature. Football. My girlfriend’s emotions.

If mathematical / logical proof that X is not a hoax is a requirement for understanding of X, I think you end up saying that nothing without a mathematical structure can possibly be understood.

Matt Kuzma 10.10.06 at 4:46 pm

I would also like to point out that the questions of the turing test Collins passed were written by Collins himself. A more rigorous test would be for seven questions to be written by gravity-wave researchers.

Jim Harrison 10.10.06 at 4:50 pm

To be a bona fide scientist, you not only need to know how to arrive at valuable results, you need to know how to get credit for your work. Harry Collins may well be able to do the former, even if it involves getting mathematical about the subject; but he’ll have a devil of a time satsifying the second requirement. Ergo, he can’t do physics.

Ali Soleimani 10.10.06 at 4:51 pm

Speaking as a physicist, if Harry doesn’t understand any of the mathematics then he doesn’t understand *why* any of these facts about gravity waves he’s heard are true. He must take them solely on faith, without any ability to derive them or understand why they’re true — let alone be able to correct them or create a new fact. While physicists do take some things on faith, the scope is relatively limited (in a subject they understand well.) I might take someone’s else word that there is a certain result to a calculation, but if I understand the field I *will* understand how to do the calculation, and I could repeat it if needed.

Furthermore, where physics (and mathematics) are concerned, there is a real necessity for this type of understanding. While the simple-to-understand results we talk about in plain language might

seemsufficient to explain what’s really going on, they’re not. As anyone who’s learned any physics can attest, it’s very easy to hear or read explanations of a topic and think you understand it quite well… only to quickly find you can’t answer the simplest questions or apply your “knowledge” to a slightly different situation. It takes practice and experience before you gain insight into what’s going on and become able to apply it, ie, really understand it. Beginning students always learn this the hard way, when they discover working problems is necessary to learning any new piece of physics.This I think is the key distinction between what Harry has and what real physicists have. Harry probably has a decent understanding (on some level) of

facts known to be true about gravitational waves.But he has no understanding ofwhythose facts are true, and his knowledge ends at what he’s heard explicitly. If someone hit him with a simple question he’d never talked about before, he’d have no idea how to answer it. Someone with a real understanding of gravitational waves could.So your final question, Daniel, is a little perverse. If you don’t understand how to “do calculations” — ie, answer questions — in a subject of physics,

you don’t understand the subject.That’s not a triviality, it’s what physics is about: answering questions and making predictions about the physical world. If you don’t have that, you just have a set of just-so stories.—-

While I’m not familiar with Henry Fields’ work in particular, from the description you linked to it seems obviously false that he rederived Newtonian mechanics “without mathematics.” He may have done it without the standard machinery of vector analysis in R^3, but he accomplished that by developing a simpler form mathematical system. Anyone who’s done axiomatic logic, set theory, group theory, etc should recognize that this is no less mathematics than the R^3 folks are used to.

When you get right down to it, mathematics really is ‘only logic.’ Just a special type of logic, with precise relationships between the various entities, giving rise to complicated abstract structures.

It’s obvious to anyone that’s worked with physics that ‘understanding the mathematics’ is indeed integral to understanding the physical theory. It really *is* understanding the physical theory, since the math is just the actual way of expressing the theory.

Now you don’t need to understand a certain mathematical formalism to understand the theory. There are generally many equivalent formalisms describing a theory, and any one will do (though some are better than others.) Indeed, usually the more formalisms you understand, the better you truly understand the underlying physical theory. Different formalisms give you ‘different angles,’ so to speak, on what’s going on, elucidating certain aspects at the price of complicating others. This is the reason, as Feynman famously said, that every physicist worth his salt knows how to solve a given problem in at least three or four different ways.

Daniel 10.10.06 at 4:53 pm

14: no, they did it both ways, didn’t they?

Scott Martens 10.10.06 at 4:55 pm

Hmm. I see two possible lines of argument here:

1 – Yes, Collins is a real physicist.

Imagine the physicists had publicists, of a sort. People whose job was to understand their work well enough to go around and distribute their ideas and results, as well a collect those of other research teams. Would this be any less legitimate a science that, say, being an experimental physicist, in contrast to a theoretician or a phenomenologist? Physics is complicated business, and labour is divided between different kinds of physicists. On what basis should we consider one type of contributor to physics different from another in their right to claim the title of physicist?

If there were “physics publicists”, obviously Collins would be qualified for the job.

2 – No, Collins is not a real physicist, or even a fake one.

The Turing test was always a bad idea because it deemed a program to be human-equivalent if it could pass itself off as a human. Instead, the test should have been: Can the computer do what a person does? Can you interact with it the way you interact with a person? Does treating the machine as a person get you somewhere that treating it as a machine wouldn’t?

The proof is in the pudding. Does Collins do what physicists do? Is he capable of doing what physicists do? Would treating him like a physicist advance physics? Obviously not. That he can pass himself off as a physicist is as beside the point as the fact that a very good Madonna impersonator might be able to pass herself off as Madonna in some context. Unless she has record execs at her beck and call and can sleep with Guy Ritchie when she wants to, she’s not Madonna.

Gdr 10.10.06 at 5:05 pm

I don’t think that any test involving short discursive answers to a handful of questions can distinguish shallow from deep understanding of a subject. It doesn’t really matter who writes the questions.

As Collins et al write in their paper, “Some of the judges, and all of the judges in respect of some of the answers, did not feel that the technical differences in the answers allowed them to make a judgement. In these cases they fell back on style”. And of course, you cannot tell how well someone understands a subject from their writing style.

I think it’s a very interesting paper.

Daniel 10.10.06 at 5:09 pm

18: Scott, I think the question is not “is Collins a physicist”, which he says he’s not, but “despite not being a physicist and not being able to do the maths, does Collins understand gravity waves?”

John Quiggin 10.10.06 at 5:11 pm

Feynmann, in QED, takes pretty much the opposite line to most commenters above. He says the math of quantum electrodynamics is needed to solve problems in an efficient fashion, but that it’s possible to understand (most of) what’s really going on without it. He certainly succeeded in convincing me that I understood what he was talking about, but then I never got around to trying the math.

armando 10.10.06 at 5:11 pm

Echoing comment 16, I also find the contention (from wikipedia) that you can do physics without math quite bizzarre. That you can use (mathematical) logic in place of vector calculus is somehow supposed to separate math and physics? If so, then an awful lot of mathematicians dont do math, publish in math journals which dont contain math and read and write math textbooks which have nothing to do with math.

Very odd.

Walt 10.10.06 at 5:13 pm

I don’t think it’s

crazyto call Collins a physicist, but he is a very limited one: while not every physicist can do everything that physicists do, the list of physicist activities that Collins can do is unusually limited. He clearly understands the field in some sense that most of us do not, and apparently can even make contributions at seminar talks, which are all activities of real physicists. But he can’t design an experiment. He can’t check theoretical calculations. He can’t write numerical simulations. So in a small way heisa physicist, but only in a small way.Daniel, I think you’re being misled by the economics example. Economists use mathematics to make qualitative predictions; in many instances you could have made these predictions with no mathematics at all. Physicists use mathematics to make quantitative predictions. If those quantitative predictions aren’t borne out, it’s a major issue for the field.

dearieme 10.10.06 at 5:14 pm

There are lots of people who style themselves physicists who don’t design or perform experiments. Don’t, and perhaps can’t.

Jonathan Dursi 10.10.06 at 5:16 pm

I think that what it means to `understand’ the gravitational waves, `do’ the GW physics, and the role of the mathematics in all of this all needs to be clarified a bit.

I think it’s entirely possible that Collins does understand gravitational waves to a strong degree. Generally it takes a while to develop a `physical intuition’ of these things which can guide one, right or wrong, in coming up with new ideas. After discussing things with as many people as he has, and for as long as he has, he probably does have an excellent physical intuition for these problems, and that’s a nontrivial accomplishment — it’s something that takes practitioners some time to develop.

The question I guess is w/rt the depth, scope, and nature of his understanding. ARP in comment #1 comes up with one good measure, as to whether or not he can apply his understanding to new (to him) situtations and come up with the right answer. That’s a very good measure of understanding for a student, and I think one would say that a student taking a GR course for non-physicists who achived that measure of understanding would be properly said to understand the course material.

On the other hand, to function as a practicing physicist one has to apply one’s knowledge to

entirely newsituations and come up with an answer, and that requires a deeper level of knowledge. It also generally requires mathematics, butnotfor mathematics sake! It requires the mathematics for a very simple reason — in any interesting situation there are generally competing physical effects, and to see which ones `win’, one must actually compare numbers. The more complicated the physical situation, the more quantitative you have to be to make interesting predictions. And if you can’t make predictions or measurements which are interesting and compelling to other physicsists, you aren’t `doing’ physics.Daniel 10.10.06 at 5:19 pm

That you can use (mathematical) logic in place of vector calculus is somehow supposed to separate math and physics?Yes. The point being that you can get to Newtonian mechanics without having any concept of number or asserting that there is such a thing as a set. Quine believed that the ubiquity of mathematics in physics meant that physics was ontologically committed to asserting the existence of the fundamental mathematical entities; Field argues that it isn’t.

Walt: sorry, I must have phrased this badly, as everyone is treating this as a demarcation dispute, “is Collins a physicist?”. It’s not that. The question is “is there anything to the physicists’ understanding of gravity waves over and above Collins’ understanding of gravity waves”? My contention is that there isn’t; having a means of making calculations is not a necessary or sufficient condition for understanding anything.

Daniel 10.10.06 at 5:23 pm

But he has no understanding of why those facts are true, and his knowledge ends at what he’s heard explicitly. If someone hit him with a simple question he’d never talked about before, he’d have no idea how to answer it.No. Not true. This is discussed in the paper. One of the questions asked in the test was one that he hadn’t come across and seven out of nine physicists picked his answer as the physicist’s one.

Panda 10.10.06 at 5:24 pm

We don’t want to make “understanding the subject” mean “being able to do calculations about the subject”, unless we have some reason to believe that this is a necessary condition rather than a sufficient one.It depends on what society wants of its experts. Several people above mentioned the phenomena ( familiar to anyone whose ever taught a math based subject to undergrads – or been an undergrad in such a subject) of students who feel like they understand the material presented in class but then find that they can’t do the homework problems.

Its true that understanding the examples presented in class well enough to discuss them intelligently is one way of “knowing” the subject. But consensus is that only the ability to apply that knowledge to new situations makes you an expert.

The practical reason is that, at least with technical subjects, we want our experts to be able to do things, produce effects, invent the laser or whatever. If I seek out an expert in auto mechanics, it generally isn’t because I’m looking for someone with a broad understanding of automobile function and design with whom I can have an interesting conversation. Its because I want someone who can fix my car.

So you can imagine a different definition of expert that doesn’t include the “able to do the calculations” clause, but for practical reasons society has decided that that’s not the definition it wants.

I also agree with Matt Kuzma above. There are definitely subjects (especially quantum mechanics in my experience) that you really can’t understand unless you’ve spent some time manipulating the mathematical apparatus and seeing how it behaves.

Ginger Yellow 10.10.06 at 5:25 pm

I don’t know if it’s deliberate, but I’m picking up massive echoes of Searle’s Chinese room here. The funny thing, though, is that the positions seem to have been reversed. Like Searle, Daniel doesn’t “want to make “understanding the subject” mean “being able to do calculations about the subject””, but surely Searle would say that the physicists (who can do the calculations) understand physics and Collins (who can’t) doesn’t.

As for myself, I don’t get what the fuss is about. As Jason Rosenhouse points out, the guy’s been studying the physics of gravity waves as a dilletante for 30 years. If having done that I wasn’t able to pass myself off as a physicist

in my own area of study answering questions I chose myselfI’d consider my life an abject failure.Bryan 10.10.06 at 5:34 pm

Well, you can’t be sure that other people enjoy fine art, expensive bottles of wine, football or literature, but you can be sure you enjoy them. Or perhaps not, I’m sure people have convinced themselves they’ve enjoyed things only because they were convinced they ought to have enjoyed it. And you can, of course, understand the rules of football, which aren’t mathematical and are just formally agreed-upon.

What would it mean to say you “understand” fine art? You can be aware of what you enjoy. You can make predictions about what other people will claim to enjoy that might be accurate. You can be aware of the explanations that other people give when claiming they enjoy such-and-such a piece. You can understand the mechanics and techniques of painting or sculpting. You can learn a technical vocabulary for describing formal properties of a piece. Surely, if you could do all these things you ought to be able to say you “understand” fine art. And, arguably, those might be all there could be to such an understanding.

But would we really want to say that Collins is a connoisseur of gravity waves? I think not.

armando 10.10.06 at 5:34 pm

Yes. The point being that you can get to Newtonian mechanics without having any concept of number or asserting that there is such a thing as a set. Quine believed that the ubiquity of mathematics in physics meant that physics was ontologically committed to asserting the existence of the fundamental mathematical entities; Field argues that it isn’t.Oh, I see now. Still, its a very weak point since the same argument shows that mathematics is separated from mathematics – you don’t *need* to base everything on set theory.

Walt 10.10.06 at 5:35 pm

Maybe I’m not understanding what you mean by “understanding”, since the answer to me seems trivially yes. I can tell you that general relativity predicts that a different orbit of Mercury than Newtonian mechanics. A physicist can tell you the actual predicted orbit, one that matches experiment. I find it hard to see how it can be anything other than that the physicist understands it better than I do.

Rob St. Amant 10.10.06 at 5:40 pm

There’s something you’ll hear pretty often among young academics, at least the kind I hang out with: “I didn’t

reallyunderstand this topic until I taught a class on it.” This is a pragmatic approach to the question of whether Collins understands the physics of gravity waves or not, but I think it’s a reasonable one. Most people who can be said to understand a topic can communicate their understanding not only to people who already understand it, but also to people who don’t yet understand it. Another possibility: If I were running a physics conference or workshop, could I trust Collins to review papers for it? If I’m a physicist specializing in gravity waves, do I consider Collins one of my peers or just a talented outsider? (I don’t know the answers to these questions, by the way.)Tracy W 10.10.06 at 5:43 pm

Likewise, if you haven’t studied enough electricity and magnetism to be able to derive the electromagnetic wave, then you probably don’t really understand light, even in a classical sense.I’ve done this, albiet as part of an engineering degree rather than a physics one, and I still didn’t feel like I understood light (I assume you’re using light here in the sense of electromagnetic waves).

soru 10.10.06 at 6:11 pm

The question is “is there anything to the physicists’ understanding of gravity waves over and above Collins’ understanding of gravity waves”? My contention is that there isn’t; having a means of making calculations is not a necessary or sufficient condition for understanding anything.I suspect 30 years of study and discussion of music scores would enable a profoundly deaf person to answer simple written questions about classical music better than the average conductor.

Nevertheless, you could devise questions he couldn’t answer adequately, e.g. ‘what symphony is playing now on the radio?’.

Jack 10.10.06 at 6:26 pm

What is understanding gravity waves supposed to be good for if not making calculations about them? Surfing on them?

Put another way, does Sir Alan Sugar understand computers? Did he when he was good at selling them? Who understands cars better, Michael Schumacher, Carlos Ghosn, a Toyota engineer or an environmental campaigner?

In one job my fax number differed from a trade journal’s by a single digit. A client accidentally sent a confirmation of a very mundane transaction to the journal which described it in excruciating detail on the front page. Inside were league tables of far more complex business. If the writers had really understood the business it would have been a diary piece but I still learned stuff reading the journal.

As far as what Field may have done I don’t think it’s relevant. If Field has an alternative way of presenting Newtonian mechanics without sets or numbers and someone else could come up with a more elaborate version that worked for general relativity, Collins would still not be able to use it. By the same token you would be able to do a lot of maths with Field’s set-up. I think the word calculus might be more helpful here.

Why on earth didn’t Collins learn the maths anyway? Does he think that he wouldn’t understand more if he did?

“In mathematics you don’t understand things, you get used to them.” J. von Neumann

bza 10.10.06 at 6:28 pm

Daniel, you’re overselling Field’s work. Firstly, as Ali Soleimani pointed out in 16, what Field was (arguably) able to do was *not* reformulate Newtonian gravitation without the use of math. He was able to reformulate it in a mathematical framework that did not mention numbers or other so-called abstract objects; it had instead only terms for space-time points and other physical entities. But it’s still a highly mathematical theory. Indeed, it crucially depends on the use of full second-order logic. So Field’s work is just irrelevant to the question whether physical concepts can be understood in purely qualitative terms: his reformulation of gravitation is in terms of an unusual kind of math, but it’s still formulated mathematically.

Second, very few people think Field’s result is generalizable to other areas of physics. See David Malament’s review for details. (That’s a jstor link, so you’ll need to access it through a research institution.)

Thirdly, it’s far from clear that Field’s work is successful even on its own terms. There are several respects in which a Field-style reformulation of a physical theory is expressively weaker than standard formulations (see Malament’s review again), so it’s problematic at the least to say that he’s shown that we can do science without the numbers. In addition, there are good arguments that Field’s formulations *do* actually encode a very strong theory of cardinal numbers. (See Ken Mander’s review; jstor again)

Neel Krishnaswami 10.10.06 at 6:35 pm

engels wrote:

I don’t understand why you say in your Guardian post that Collins can’t possibly make an original contribution to the field. Couldn’t he make a claim, and perhaps provide an informal argument for it, which the nerds find original and persuasive, and which some of them later prove to be true, by expressing it in technical language and developing mathematical proofs based on his reasoning (or conducting experiments). Can’t we give Collins (any of) the credit for such a discovery?In my field (type theory, which is an offshoot of mathematical logic), I’d say no, you couldn’t give him any of the credit. There are numerous plausible-sounding logical systems with very convincing informal justifications that simply aren’t true at all. The list of logicians who have seriously proposed inconsistent systems likely includes a majority of the great logicians. We just don’t know whether a particular system is consistent or not until someone does a consistency proof.

morinao 10.10.06 at 6:43 pm

the guy’s been studying the physics of gravity waves as a dilletante for 30 years. If having done that I wasn’t able to pass myself off as a physicist in my own area of study answering questions I chose myself I’d consider my life an abject failure.Never mind the dilettante, how would you feel if you were the expert who fielded questions in his own area of study and still couldn’t convince his peers that he was the real physicist?

harry b 10.10.06 at 7:01 pm

Field’s aim is to refute Quine’s view that since you have to assume the existence of numbers to do physics, numbers exist (putting it crudely). If you can do physics without assuming the existence of numbers, then numbers needn’t exist; we can be conventionalists about numbers (and don’t have to be platonists about them). Much disputed; and I’m not sure if he still holds that view. The book, btw, was widely stocked in stupid bookstores on the assumption that it was a “Science for Dummies” book (or so the story goes).

ginger yellow (#30) — I think that’s right about the Chinese room argument, and this conversation just reminds me why I found Searle’s conclusion from that argument so unconvincing!

will u. 10.10.06 at 7:13 pm

“I don’t know if it’s deliberate, but I’m picking up massive echoes of Searle’s Chinese room here. The funny thing, though, is that the positions seem to have been reversed.”

Likewise, I recently had a conversation with a mathematics major who claimed that, since

of coursephysics is just applied mathematics, surely mathematicians understand physics better than physicists do.engels 10.10.06 at 7:22 pm

Neel – Yes, but you’re talking about the conditions for knowing that a statement is true, whereas I was wondering about when it would be right to credit someone with making “an original contribution to the field”. I could concede that Collins didn’t know his statement was true until it was proved but still hold that he made an important contribution by formulating it (informally) and giving an intuitive argument for it.

Even leaving aside the assumption that Collins gives an intuitive proof of his assertion, I think it’s possible that making a conjecture can be a contribution to a field, in mathematics at least.

Jack 10.10.06 at 7:36 pm

Ed Witten might be the most influential mathematician of the moment but in many cases he has guessed results that have only later been proved by other mathematicians shown where to look. Mathematicians gave him a Fields medal so I guess they think he counts. Of course many thesis advisers have done similar things on a smaller scale. I’m sure that it is even stronger in physics.

agm 10.10.06 at 7:48 pm

Bah, I’ve partially written a long tedious answer. In short, if Collins can’t make contributions to the field based on however much he understands, e.g., he can’t take a shift at LIGO and see what’s going wrong at the moment based on monitoring equipment (i.e., experimental contribution), if he can’t analyze the data to see what it looks like, how to remove noise, how to select and calculate and interpret the appropriate statistics (numerical/empirical/phenomenological contribution), if he can’t do theoretical modeling (guess what type this would be), than it’s a really simple question. Physics is an empirical subject, and appropriately enough, the way to check is simple and empirical: if Collins can’t do gravity wave physics, then it’s trivially easy to see that yes, there’s a whole world of understanding beyond his. A layman can even make contributions, it happens all the time (such as experimental astronomy), and not have a professional’s understanding.

Really, what the fQ#$ is so hard about accepting that a science whose project is describing the world emprically inescapably requires that you can do some sort of math? It’s really arrogant to assume that when we physicists tell you that the ability to do math is indeed a necessary condition to do physics that we don’t mean it; more to the point, if you make such a claim, YOU ARE WRONG. (Yes, I’m testy today and don’t care what you think.)

————————————–

Daniel,

I am very confused to your question, and to its point. Agreed, your post initially doesn’t ask whether Harry Collins is a physicist, which is good. That question would have the very simple anser, “If he does physics, he is a physicist of some sort.” If Collins is contributing to the field, conferences, papers, seminars, something we can credit him for, that gives him a stake in the field, this is quite different from whether he understands gravity waves. Hell, I’ve thoroughly been confused and confused acknowledged scientists who didn’t even know that the term “gravity waves” refers to phenomena in two different fields (one being the gravitational analogue of electricty and magnetism, the other being a phenomena in fluid dynamics applied to atmospheric/ionospheric research). But I think this question, about figuring out what Collins understands, is irrelevant to the second point you raise: if a physicist is one who does physics, what does it mean to do physics?

I would say that if Collins cannot do the math (or cannot do experimental and/or numerical work)

in the research area he can claim knowledge of, then he is at most an interested non-physicist. Physics without math is what Aristotle showed us cannot be done — you cannot describe the physical world in the manner such that credibility of your claims can be tested, you cannot compare the implications of your model with what is measured empirically, without the math. Some people claim that Faraday, the celebrated British experimentalist of the 1800s, couldn’t necessarily do the math, but that would be irrelevant, for he jumped from apprentice bookbinder to experimental inquiry, leaving it for Maxwell to formalize his field model. In other words, the most famous example of doing physics without formal training was demonstrably showing his understanding day in and day out by doing physics.Your quote, about not wanting to make [“understanding the subject” mean “being able to do calculations about the subject”], is amazingly and alarmingly wrong. For physics and other quantitative inquiries, “being able to do calculations about the subject”

ISinescapable. We rarely see something that is simple enough to just think about it and get a good prediction anymore. Without math there simply is no way of comparing your prediction to an observation and being able to tell that your explanation of the behavior is close enough to what is actually happening to be at least partly correctagm 10.10.06 at 8:11 pm

You know, f#$% it. arp’s post in #1 here gave a better and clearer answer (to both this post and the one DD has in the Guadian) than what I said.

vivian 10.10.06 at 10:01 pm

Look, physics has this penumbra of “realest, hardest boot-camp of all human knowledge”. I’ve known tenured physicists who cheerfully admitted that they didn’t really understand something, or a paper, in their field. Also knew one who announced that since Physics was only for the Best students, anyone who scored average or below on a test should find a new major… especially the females in the class. Speaking of which, history (barely) records women and others, who couldn’t be real physicists yet were treated as such by a key colleague.

It’s a great blog post (or two) but in real life, do we care about club membership or about gravity waves and colleagues who can help one learn about them?

Dan Simon 10.10.06 at 10:25 pm

It’s sad how much damage Alan Turing did to the world of science by misleading so many people about the (lack of) connection between externally measurable states and “internal” states such as “understanding”.

In a typical experiment, one takes one or more “subjects” whose properties one doesn’t understand, and makes them interact with an “apparatus” with well-understood properties, in the hope of learning about the properties of the subjects. In the case of the Turing test, it’s clear that both the human and computer answerers are fairly well-understood–their common goal and strategy is to “seem human”, one by responding naturally and the other by following a fixed, understood algorithm–whereas the interrogators’ strategies are unknown in advance and completely lacking any

a priorimodel. It follows that the Turing test is an experiment on the interrogators–presumably to determine their ability to make certain distinctions under certain conditions.Apparently, gravity wave physicists are incapable of distinguishing Harry Collins from a “proper physicist” by asking them both a small number of general questions and requiring them both to answer off the tops of their heads. Big deal.

anon 10.10.06 at 10:33 pm

I don’t have time to read the paper at the moment, but by the time I do this thread will have passed by, so here are some long-winded thoughts in passing:

1) There are plenty of physicists who can’t design experiments. They are called theoretical physicists, or mathematical physicists. As the joke goes, they are physicists who can’t do physics. This isn’t crucial to any of the arguments above, but it should be pointed out. In particular, complicated experiments involving gravity waves (cosmological kind) involve teams of people, all of whom have expertise concerning some

partof the puzzle.2) I support the distinction Collins makes (according to your article) between “interactional expertise” (conversing with an expert) and “contributory expertise” (contributing to the field). To answer your initial question, it is clear that Collins understands gravity waves well enough to have the former but probably not well enough to have the latter. Collins seems to agree.

I support your contention that there should be no qualifiers on this statement. The notion that Collins doesn’t “really” understand, or that he is “simulating” understanding doesn’t seem to apply in this case (unlike, say, Searle’s thought experiments).

3) But I think you treat Collins’ taxonomy too rigidly. The line between interactive and contributory expertise is

nota sharp one — the notion that “if you can do the math, you understand the field” is mostly the type of argument you hear from those mathematicians who think every field is just mathematics (like economics, right, Daniel?) and from physicists who think every field is physics (like economics, right, Daniel?). You do not generally hear this argument from chemists and biologists, for example, both of whom tend to get shafted in these sorts of arguments.All of those people making the argument that you

haveto understand the mathematics are being imprecise, I think. It would be more accurate to say that it is extremely difficult —but I would argue not impossible— to display contributory expertise in this particular field without being able to perform some calculations. One mayconjecturethat it is impossible, but there is no proof of that fact (that I know of). This simply makes Collins’ a limited physicist. Lord knows there are plenty of those.4) “Not understanding the math” is also imprecise, and I’m curious to read what Collins’ writes about his level of understanding. For example, it might be possible to manipulate mathematical terms without being able to perform the final calculation. Though it is removed from my field of interest, I always thought this was what one did with Feynman diagrams: You perform a bunch of computations symbolically, following simple rules on symbols alone. At the end the result may be “re-translated” back into an integral you may or may not be able to evaluate. But I have always assumed Feynman saw his diagrams as a convenient tool, one he used so that he didn’t have to slog through a lot of mathematical details. Understanding would come from the

useof the tool to generate results, not from the (literal) manipulation of symbols.The experimental analogue would be that one does not have to understand how every piece of equipment in a lab works in order to conduct an experiment; you only need some degree of understanding of how to manipulate the tools (“This device heats the water”, “This device splits the light into two beams”, etc.). Once again, as an old joke goes, an experimental physicists is a bad plumber, a bad carpenter, a bad mechanic, etc.

5) I think you mislead when, later in this thread, you ask “is there anything to the physicists’ understanding of gravity waves over and above Collins’ understanding of gravity waves?” This posits a monotonicity to “understanding” — as if being a physicist necessarily implies a “deeper” or “fuller” understanding. But why can’t being a physicist simply imply one who is oriented towards demonstrating “contributory expertise”? This distinction is made within physics (and many other fields) using such terms as “active.” A professor who has moved on to managerial posts at a university may no longer be an “active physicist,” with the implication that the professor is no longer oriented towards making a contribution to the field. This does not mean that the dean of students nee professor might not have a sudden insight demanding publication, or even that the retired dean might not return to teaching and “active” research. It is a statement about the current priorities of an individual, not some sort of inherent property the individual has come to possess.

This is why I am curious about how, operationally, Collins distinguishes “interactive expertise” from “contributory expertise.” One does behave differently if one’s goal is to make a contribution to a field — Collins, for example, would have learned the math — and I imagine there is much for a sociologist to say about how educational institutions shape/define/routinize the development of “contributory experise.” And maybe someone would argue the strong case that the mathematics is not necessary at all, but simply a barrier imposed by those in power to safeguard their position — how some of my executive friends describe MBA degrees, for example. But that’s not the only argument that could be made; only the most incendiary one.

Anon

Jack 10.10.06 at 11:09 pm

Speaking as a graduate student in a related field, I know plenty of folks who can whip up a storm of mathematical manipulation and get quantitative answers to all manner of problems, but who don’t seem to understand the fundamental physics very clearly. I mean “fundamental physics” pretty literally: they don’t have a very clear physical model in their heads. There are many types of question where, if you do have a clear model in your head, the answer is trivial, whereas if not, you can get the answer by doing the math, but when you end up with N=3, you might say “huh, that’s surprisingly simple” but you won’t know *why*. I think one can go a long way on such physical models (Feynmann was famous for it, though of course he knew the math too).

Of course, a long way is not all the way, or even close, and generally the physical models would not have been created or communicable without the mathematics, but given that they now exist, there’s a lot of room for parasitic physics that can possess itself of track-2 understanding (physical, not mathematical, models) and even make new predictions and insights. But track-2 certainly isn’t the same as track-1 (being able to do the formal manipulations) nor is it the same as tracks-1&2 — what “real” physicists must have.

Jack 10.10.06 at 11:13 pm

Whoops, it should be n=2.

Jonathan Dursi 10.10.06 at 11:25 pm

There’s a bit of nonsense in the comments, presumably largely posted by people in non-science disciplines who would like to believe that science, too, is solely an issue of making convincing-sounding arguments.

Science is an iterative process of examining observations and generating experimental results, creating theories to understand them, and testing the theories’ predictions against new experimental and observational results. Which part of this process does Collins claim to be able to perform? If none, what possible sense can it make to ask “is there anything to the physicists’ understanding of gravity waves over and above Collins’ understanding of gravity waves”? Yes, there is something over and above; it’s the depth of knowledge wihch gives the ability to do all of the above. You know, the science.

The apparently serious argument that it’s possible to do the science without the math is clearly nonsense. Let’s continue to take gravitational waves as an example. There’s a natural system, the double pulsar system PSR J0737-3039A and B, which are spiralling inwards. Is the observed rate of inspiralling consistant with the predictions of General Relativity, or are modifications to the theory necessary, or is an entirely new theory of gravity necessary? Quick, do the comparison without the introducing the concept of numbers. Or the measurement, for that matter.

Bryan 10.11.06 at 12:49 am

I take it that I was trying to argue (#4) something similar to what Jonathan Dursi (#51) is arguing, although from a very different angle. I think there’s been some confusion in the answers overall because there’s a certain imprecision regarding the concept of “understanding” something. Clearly, realistically, Collins “understands” gravity waves on

somelevel (vastly more than I do, for example). I could read some popular science article on the subject and “understand” it better than I do now. What my proposed thought experiment was attempting to do was to distinguish between second-hand (the physicists who can do the math) and third-hand (Collins) understanding (obviously gravity waves don’t understand themselves!). Assuming the accuracy of the datum they are using, those that can do the math are in a position toknowhow well their theories fit the datum, while Collins is reliant on their word in this regard.Daniel 10.11.06 at 1:21 am

It’s really arrogant to assume that when we physicists tell you that the ability to do math is indeed a necessary condition to do physics that we don’t mean it; more to the point, if you make such a claim, YOU ARE WRONG.As John Q points out above, Richard Feynman thought it was possible to understand physics without being able to do the mathematics (although in fairness, he was really arrogant).

In general, I still think a lot of people are trying to say that “understanding the physics of gravity waves”, (which is a physical thing) means “being able to take part in the activity of physics as it is practised”, which is a sociological phenomenon. I would warn everyone taking this view that you are opening up a door through which I (and even more so, the sociology of scientific knowledge school) will certainly be driving a coach-and-four at some point in the future.

I agree that this does resemble the Chinese Room argument (which I personally do find very convincing). A lot of the responses look very much like the Robot Reply in Searle’s paper; the idea being that “understanding gravity waves” means “being able to do the manipulations, plus being able to enter into various kinds of causal interaction with gravity waves”. I don’t think the Robot Response is convincing in either case.

Here’s two thought experiments:

1. Say tomorrow, Harry Collins gets a bump on the head and wakes up with mathematical abilities like those of the Dustin Hoffman character in “Rain Man”. He can now look at any calculation or equation in a physics textbook, and the answer just pops into his head. He doesn’t understand the process and it doesn’t pass through his conscious mind at all, but he can now “do” the maths. Does he

stillnot understand the physics of gravity waves?2. Say that in a million years’ time, the hard labour of mathematics has been completely delegated to computers. Physics and philosophy of physics are completely merged, and physicists just spend their time sitting around, discussing models in general terms, while their pocket computers make all the calculations for them and answer the quantitative questions above. So much so that the ability to do the maths that is done today is about as relevant for a future physicist as the ability to calculate the cosine of something by hand today.

Now say that in this million-years-in-the-future, gravity waves have still not been discovered and the gravity waves research community is still going strong (on current evidence, not that unlikely). Will it be the case that nobody alive understands gravity waves? Or, since everyboday alive will be talking about gravity waves in exactly the way that Harry Collins does today, will we have to posthumously recruit him to the ranks of those who understand gravity waves?

I very much liked Bryan’s “massive hoax” thought experiment, but I think the refined version shows how it’s too strong:

Assuming the accuracy of the datum they are using, those that can do the math are in a position to know how well their theories fit the datumBut the majority of them are only in a position to do this with their own data and their own theory (simply because until the magic computers are invented, there aren’t enough hours in the day). For the majority of their understanding of gravity waves, the physicists are actually in the same position of relying on others as Harry Collins, and I’m not persuaded that something special is added to their understanding by the fact that they could, if they wanted to, do the calculations themselves. After all, Harry Collins

coulddo the calculations himself; he’d just have to learn maths first.Walt 10.11.06 at 1:24 am

I realize that the internet doesn’t have enough of intemperate rants (#44) or invocations of authority (#51), but up until recently we were trying an exotic new argument technique: making points without insulting anyone.

Jonathan Dursi 10.11.06 at 1:52 am

Re comment 53:

Your points 1 and 2 misrepresent the role of mathematics in the process. Mathematics isn’t a mystical ability that one does or doesn’t have, breaking the world neatly up into physicists/mathematicians and muggles — if you are born with The Math, or have it plonked into you by a a bump to the head you can Understand, and if you are born Without you can’t…

The math here isn’t the understanding itself, nor does Having Math make you Understand; the mathematics just

codifies(and is necessary to codify) the detailed understanding of the relevant physics. That’s why several posters here have acted very confused when others try to separate `the understanding’ from `the mathematics’; it makes no sense. Thedetailsof the understanding are, in fact, written in the very quantitative language of mathematics. One can abstract a great deal from those details and still have a working knowledge of some parts of the problem; you can have a glossy-pamphlet level understanding of what’s going on without any math at all, and you can have a more nuanced but still simplified understanding with a simplified version of the math, but to really know what’s going on you need to be able to speak the language that the details are written in, and wrest from that language the quantitative predictions.This isn’t an arbitrary thing; the world is a quantitative place. Apples dropped from trees don’t qualitatively fall downwards; they fall with a very specific set of forces acting on them which result in predictable velocities and accelerations. Pulsars orbiting each other don’t qualitatively emit waveforms, they quantitatively lose energy to infinity in the form of gravitational waves and fall into each other at quantitatively predictable rates.

Someone who admittedly does not have a quantitative understanding of the physics of gravitational radiation is necessarily lacking something in their understanding of the physics of gravitational radiation. That this is controversial is something of a surprise to me.

Jonathan Dursi 10.11.06 at 2:01 am

Which is to say, the magic-math-doing-computer doesn’t alleviate the problem. A quick google finds a few java applets (here’s one) for calculating gravitational waveforms for given orbits. That these have existed the whole time doesn’t improve the understanding of gravitational waves by any of us here one iota, even if they can grind the numbers for any particular situation — if that were true then a 3 year old with a calculator would understands multiplication.

There are in fact computer packages that do some of the grunt work for general relativity maths (such as GRTensor) but they are labour-saving devices for people who already understand the theory, not math-replacement (or understanding-replacement!) tools.

Scott Martens 10.11.06 at 2:05 am

I think the question is not “is Collins a physicist”, which he says he’s not, but “despite not being a physicist and not being able to do the maths, does Collins understand gravity waves?”I think the other more interesting and more closely parallels Searle, because the answer to whether Collins understands gravity waves seems obvious to me.

The vast majority of humanity has no understanding of Newtonian mechanics, but it seems silly to say they don’t understand gravity. Very few certified electricians have seriously studied electromagnetism, but it would be very weird to say they don’t understand electricity. Car buffs are routinely quite ignorant of organic chemistry and materials science, as well as basic mechanics, but no one would say they don’t understand cars. So, why is it odd to say that Collins understands gravity waves?

True, the ordinary person couldn’t calculate a missile trajectory; nor could most electricians design a microchip; and few car buffs have the expertise to design a car. But this only suggests that their understanding is different from that of scientists and engineers – people’s understanding is generally limited by their conditions and expectations. In the same way, Collins’ understanding is different because he doesn’t expect to do the same things with his knowledge as a physicist.

But, I like the thought experiment in #53 about future physicists using computers to do all the math is interesting. But I’d take it in a different direction. If the computer does the math, does it really mean that the physicist isn’t doing it? Consider, instead, if the computer the does all the physics math is a chip inside the physicists brain the only does math for that one physicist? Does that change whether or not it’s the physicist doing the math?

Now consider a physicist who has a terrible accident and is brain damaged. Imagine that in the future, doctors install a chip in his brain as a prosthetic to make up for the parts of his brain that have been damaged. So, the chip is already doing much of the math the physicist would have been doing himself. Is this different from having a computer – located either inside or outside the skull of the physicists – so the math for him. In any of these cases, has the physicist stopped doing the math himself because he uses a device to grind through the actual calculations?

For the majority of their understanding of gravity waves, the physicists are actually in the same position of relying on others as Harry Collins, and I’m not persuaded that something special is added to their understanding by the fact that they could, if they wanted to, do the calculations themselves.Daniel, it seems to me that you’re suggesting that if Collins were to set up a gravity wave research group of his own and hire a bunch of physicists to do all the real work, while he was simply the boss, he could then be as much a physicist as anybody who has slogged through all those years of math in school. I’m not sure that makes sense.

Hodgepodge 10.11.06 at 3:05 am

I find this whole conversation very odd.

We have no trouble accepting that someone who has never painted a masterpeice (or anything at all) might not only understand, but actually be an expert on fine art. We can accept that someone who can’t form a single artful sentence or convincingly act one scene might be an expert on literature or drama. We can accept that someone who has never been to 18th century Britain can in fact be an expert on it. We can accept that someone who couldn’t even dream holding public office or winning an election might be a notable expert on politics.

What we cannot and should not accept is that these people are painters, writers, actors, or politicians. But that is not what they are claiming to be. They claim to have the understanding of their fields to provide valueable insight into them, but explicitly do

notclaim to possess the insight necessary to practice in that field or to teach the practice of that field at more than a basic level.Plenty of scientists understand this distinction. Sagan and Hawking didn’t write for the layman to prove that non-scientists weren’t members of the Scientist’s Club (TM)(R) and could therefor never

reallyunderstand science. They wrote for the layman because they realized that there is a level of understanding of science that is sufficient to provide input into the field but not practice in it that is valueable for every human being to have.Bryan 10.11.06 at 3:22 am

How is it that a certain relationship between neurons, chemicals and whatever other stuff there is in one’s brain be said to ‘mirror’, ‘correspond’ to, or express an ‘understanding’ of, some external phenomena? If we agree that somehow the property of ‘understanding’ can somehow inhere in this relationship between things inside our brain, it is not clear why this property of ‘understanding’ cannot also inhere in the relationship of things not all located in one skull. Or perhaps the whole idea of ‘understanding’ is only a convenient, or fruitful (in some sense) fiction.

These might seem like the sorts of questions that annoying students intoxicated with philosophy 101 like to ask, but I can’t help but suspect they are sort of a brick wall that inquiries of this nature will eventually run into.

agm 10.11.06 at 3:27 am

“being able to take part in the activity of physics as it is practised”, which is a sociological phenomenonPhysics, as it is practiced, is indeed something that can be seen as a sociological phenomenon. However, to imply that this is all there is, as could be read in this statement if I were still in a horrible mood, is at best an incomplete understanding. Simply put, this is not economics, not sociology, not gender studies, not even mathematics. In fact, traditional lore holds all sorts of stories about how mathematicians as a group used to, maybe still do, love to hate on physicists for improbable things like treating derivatives as a ratio of derivatives, and then getting experimental results that are close enough to reality to consider it justified. This is exactly what causes the trouble between some string theorists and other people in the field — without contact with reality in an experimental way,

it ain’t physics. If Collins, or anybody else, is providing part of that contact, then you can say that yes, the person has an understanding of gravity waves comparable to that of a “real” physicist, for that person IS a real physicist.Regarding the gedanken experiment about computer in the far future, we aren’t discussing the future, we’re discussing now. And as things are done now, you have to tell the computer what numbers to crunch and how to do so. And what will happen in the future is that you will have to decide what to tell these computers to decide about, where to spend cycles. Physics cannot be reduced to math, so we must seek the answer elsewhere. And again the answer is to be able to explore new things, to make a contribution to the field. I repeat, the measure of whether Collins, or any layman, or really any person at all, has an understanding on par with professional, active, publishing physicists is whether or not that person is contributing to a field of research or has demonstrably contributed to the field.

About Feynman diagrams, still math. Formalizing things behind pretty symbols (e.g., the penguin diagram) is still math. The creation of a form of vector calculus made electromagnetism no less mathematical, but it made it quite more tractable. I’ve leafed through printings of Maxwell’s books, and everything is done in sets of scalar equations. Not as easy to handle as the equivalent in vector notation. And still inseperable from a need for physical understanding — how do you think Maxwell realized that there was a need for displacement current? Not just from making equations prettier, more symmetrical, which is a standard sort of problem in Jackson; he was seeking energy conservation, a guiding empirical principle of classical physics. Maxwell was demonstrating his physical understanding in a novel situation and making a contribution to the field. If Collins can do this, or even a fraction of this, then his understanding is clearly as good as your typical trained monkey with a PhD attached, and much better than that of many grad students still struggling to realize how conservation principles are related to symmetries (or other understandings of the physical world).

Re the pulsars:

Goddamn it, walt, it’s not an argument from authority, it’s an argument of “Show me that you know what you’re talking about.”

agm 10.11.06 at 3:29 am

for improbable things like treating derivatives as a ratio of derivativesSorry, that should read “for improbable things like treating derivatives as a ratio of differentials”.

Daniel 10.11.06 at 3:38 am

This isn’t an arbitrary thing; the world is a quantitative place. Apples dropped from trees don’t qualitatively fall downwards; they fall with a very specific set of forces acting on them which result in predictable velocities and accelerationsJonathan, you seem to be getting dangerously close here to an argument which would imply that non-physicists don’t really understand what an

appleis, which I would certainly take as a reductio.Daniel 10.11.06 at 3:47 am

Daniel, it seems to me that you’re suggesting that if Collins were to set up a gravity wave research group of his own and hire a bunch of physicists to do all the real work, while he was simply the boss, he could then be as much a physicist as anybody who has slogged through all those years of math in school. I’m not sure that makes sense.But this is the actual set-up of most big labs these days; it’s a known controversy within physics that a lot of Big Science papers have primary authors who can’t necessarily reproduce the calculations. I’m sure this is a terrible scandal and all, but I similarly wouldn’t want to claim that the top man literally doesn’t understand the paper with his name on it.

moving on …

without contact with reality in an experimental way, it ain’t physicsBut you clearly here mean

potentialcontact with reality and thepossibilityof future experiments; otherwise you’re ruling out lots of physics (including some canonical examples) where people didn’t know at the time how to verify or falsify their theories experimentally. In any case, you go on to say:I repeat, the measure of whether Collins, or any layman, or really any person at all, has an understanding on par with professional, active, publishing physicists is whether or not that person is contributing to a field of research or has demonstrably contributed to the field.which is a definitively sociological test, and a rather more radical one than most sociologists of science would be comfortable with.

Formalizing things behind pretty symbols (e.g., the penguin diagram) is still math.But if understanding isn’t dependent on any

particularformalisation, why do we think it’s dependent on any mathematical model at all?ksii 10.11.06 at 3:57 am

How much mathematics do you really need in order to understand some subfield of physics anyway? A condensed matter physicist doing computational work doesn’t necessarily need to know much about the elegant mathematical formulation of QM using rigged Hilbert spaces. And if you aren’t a mathematical physicist you probably do not need to know a thing about measure theory but just be content and assume that your integrals mostly converge. It seems to me that an understanding at some appropriately approximate level could be reached with a rather small amount of math at least in some subfields of physics. Doing so

completelywithout math seems a bit improbable. I think there’s a Feynman quote (inThe Character of Physical Law) that directly contradicts the one in 21.agm 10.11.06 at 4:39 am

Showing that multiple formalisms are equivalent, or being conversant in them, is an asset, and indeed, that’s what got Feynman his PhD (his dissertation work was creating the Feynman diagram formalism and showing that it was equivalent to the other two major quantum mechanics formalisms, IIRC). We tend to take it as prima facie proof of real understanding to be adroit in multiple formalisms, because we know that mastering a single one usually does not get you the same grasp of subtle implications as just knowing one. “If all you have is a hammer” is not a complement in physics any more than it is in economics. However, competence with multiple formalisms automatically means competence with at least one, and without at least one you have no concrete model that can make predictions in subtle circumstances where mere analogy doesn’t hack it. Take for example length contraction in special relativity. For quite some time it was thought that when viewing an object passing by you, you saw a length-contracted object, say instead of a cube you saw a box whose face was shorter in the direction it travels. Eventually it was realized that no, you don’t see that at all. James Terrell (and apparently Roger Penrose also) showed that what you see is essentially a chunk of the backside of the object as if it had been rotated, because what you see is not all the photons that leave the object at the same instant but rather all the photons that arrive at your camera/eye/detector at the same time. The ability to make this sort of deduction is the understanding we are talking about when we talk about having an understanding like a “real” physicist has, it is what I mean when I say something about the importance of understanding a formalism. If light has a finite speed, as we know it has, then there are implications for that, and the formalism is a tool we can use to get at them. The little details, which are all too often the ones that are more important (say, is light emitted continuously or all at once as a photon) are testable or have testable implications, but you have to have to formalism to predict, interpret, analyze, discuss in any sort of coherent manner.

So, saying that physics is a sociological endeavor makes mathematics and formalisms MORE important, because then a) you need a way to communicate your work to others and b) your ass is on the line as to whether or not you can be trusted to show good judgment in assessing reality in a way anyone else might care about. That’s why papers are refereed instead of just thrown on the winds these days, since it’s much harder to establish credibility. You only strengthen my argument by pointing out the social nature of physics.

And frankly, with regards to what actually is and isn’t physics, I don’t give a f#$% what sociologists think it is — I’ve been trained in physics, so I expect empirical evidence or at least the possibility of such. I know what I’ve been doing for the last few years, and I know that very shortly indeed judgment will be rendered as to whether I should be changing fields or not. I know that while other people have other opinions, that it’s both nice and useful to respect those in many situations. However, this is not one of those situations. Just cause salespeople and speakers and other assorted interesting characters show up at scientific conferences year after year doesn’t make them a practitioner of the field anymore than my going to every neurosurgeons’ conference ever held for 30 years would make me competent to crack your head open and start fiddling with your brain. No, training and practicing and convincingly demonstrating that I know what I am doing, say by not doing things that are known to generally kill or maim and also doing things that are currently genreally regarded to help is what demonstrates a proper understanding. Being able to bullshit on what is essentially a rigged test tells me nothing about whether Collins is contributing to the field, it provides no evidence of any kind that would allow me to reliably asses where he falls on the spectrum between

“gravity wave groupie”

and

“Wow, that’s an awesome question? But what about …?” “Well, let’s see … if we know XXX, then YYY. And YYY could mean that ZZZ. Well, wait, ZZZ would mean XYZ, which you couldn’t possibly have because ASD would then be false, and this principle/axiom/symmetry with decades of strong support from a variety of experiments on different systems would be violated, and then …”

soru 10.11.06 at 4:52 am

But if understanding isn’t dependent on any particular formalisation, why do we think it’s dependent on any mathematical model at all?I suspect that it somewhat depends on whether the thing being understood exists, and if it does exist, corresponds exactly 1:1 with one or more simple mathematical descriptions.

Lots of things don’t exist, or don’t have that kind of knowable mathematical description. Gravity waves could well be such a thing.

It would be strange if something’s existence and simplicity didn’t lead to an increase in the degree to which it was understandable when compared to a non-existent complex thing, such as a free market.

If you were not in a position to take advantage of that increase in understandablity, you will understand it less than someone who is, all things being equal.

agm 10.11.06 at 4:58 am

Sorry about that part about light being emitted continuously or as quanta. I switched examples, didn’t properly clean it up. Though it’s another great example of needing the formalism, since its s great story, because although Planck solved the ultraviolet catastrophe by postulating that light was emitted and absorbed in chunks, it was Einstein who showed that photons live their whole lives as chunks of light, including propagation — the story goes that Planck never accepted quantization as much more than getting a single relation that reconciled the behaviors observed by Wien for high frequencies and Rayleigh’s observations for low frequencies. Again showing that a proper formalism is needed, even if others turn out to be equivalent (this was indeed the sort of argument that Schroedinger resolved between the wave and matrix versions of early quantum mechanics). You may have equivalent ways of doing things, but one them had better be close enough to correct to be useful, or none of them are.

Ginger Yellow 10.11.06 at 5:06 am

Morinao:

Never mind the dilettante, how would you feel if you were the expert who fielded questions in his own area of study and still couldn’t convince his peers that he was the real physicist?

A bit bemused, maybe, but no more. Put it this way, if you were the human comparator in a successful Turing test would you think you’d failed as a human being?

Alex 10.11.06 at 5:54 am

Probably not. Which is, of course, another point towards the inadequacy of the Turing test. It don’t cut it. Read the transcripts from this year’s Loebner winner – it’s frankly indistinguishable from a toy chatbot’s output, but certainly distinguishable from a human’s. It’s too easy to simulate conversation – all you really need are the help strategies and a list of acceptable but content-free replies to induce the human participant to keep talking.

It’s as if you programmed a computer to respond to ICMP packets and TCP connection requests, but nothing else – an Internet router connected to it would see something equivalent to normal functioning, but the packets would just be dropped.

More broadly, I think there’s an important question of implicit skill here. If we define “physicist” as being capable of carrying out physics experiments, quite a lot of that requirement isn’t specific to physics — for example, being able to use the lab instruments effectively. There’s probably more similarity in that skill between a research chemist and an experimental physicist, both of whom can deal competently with new tools, than there is between two physicists, one of whom is an experimentalist and one a theoretician.

Experimental design and methodology aren’t trade secrets, either. Even sociologists are meant to use the scientific method and evaluate quantitative results.

In the example of the neurologist above, most of the things that would make you incompetent to fiddle with somebody’s brain wouldn’t actually be neurology. They would be general surgery, and in a non-trivial measure, manual dexterity.

Z 10.11.06 at 6:10 am

I disagree strongly with the point of view that the situation would have been different in mathematics. Indeed, had a sociologist spent the last 30 years doing heavy networking activities in the community of-say-mathematicians working on modular representations, I would expect him to be perfectly able to sustain a discussion with experts in the fields and to answer even hard and new (to him) questions about the subject.

However, Collins would, presumably, have no capacity whatsoever to judge if a new result was sound or not (especially if this result was somewhat surprising). I would say that the ability to find mistakes is as important (in fact much more important) as the capacity to correctly answer questions. The relevant question to distinguish between the understanding of the physicist and that of the informed layman is not “Could the result of a radio-wave incident on the interferometer be the same as that of a gravitational wave?” but “Find the mistake in the following reasoning…” “Is this prediction correct:…”

If Collins can do that, and he may be able to do so after so many years, then I would say he understands gravity waves in a manner comparable to a trained physicist, even though he doesn’t master the technical paraphernalia. If he can’t, then their understandings are intrinsically different.

Andrew Brown 10.11.06 at 6:17 am

I find this professionally interesting, in that as various sorts of specialist journalist, I would like to think that I understood the fields that I was writing about, or that I understood them more at the end than at the beginning.

Of course this implies that understanding is not a binary quality, but that has to be true. Yet at the same time it seems like that complete understanding of some bits of science is possible. There has to be a distinction between understanding some chunk of science (where in principle complete undersatnding is possible) and understanding all the ways in which that chunk of modelled behaviour can interact with the rest of the world, or even with other chunks of well-modelled behaviour.

Ginger Yellow 10.11.06 at 6:20 am

“Read the transcripts from this year’s Loebner winner – it’s frankly indistinguishable from a toy chatbot’s output, but certainly distinguishable from a human’s. It’s too easy to simulate conversation…”

Leaving aside the broader question about the Turing test’s suitability, isn’t this specific example support for it? Nobody confused the Loebner winner for a human, let alone better than chance. Surely this and the long history of failed attempts to teach computers (and animals) language, in fact demonstrate that it’s very hard to simulate conversation convincingly.

Daniel 10.11.06 at 6:26 am

Agm:

We tend to take it as prima facie proof of real understanding to be adroit in multiple formalisms, because we know that mastering a single one usually does not get you the same grasp of subtle implications as just knowing oneBut here, as far as I can see, you mean “understanding of the mathematics” and “the subtle implications of the mathematics”. This is surely by the by.

I also don’t really see either of your examples as particularly convincing with regard to formalism. In the first, you actually stated the important principle without any formalism, and in the second, the problem (the ultraviolet catastrophe) only existed as a problem of the mathematical formalism in the first place; there’s no physical phenomenon to be understood.

I also think that your hostility to sociology of science makes no sense, particularly when (as all the other physicists seem to be unable to help themselves from doing) you immediately follow it with a sociological definition of what a physicist is (“I’ve been trained as one”).

Z: Collins’ entire field is the study of how physicists go about deciding whether a new result is valid or not, so I wouldn’t be so sure that a Turing Test would pick him out on that criterion either.

Alex 10.11.06 at 6:34 am

72: No. The problem is that the most plausible route to a Turing pass is one that certainly would not lead to an intelligent machine, just a conversation simulator. Once the understanding from linguistics that much of conversation is the formal mechanism of taking turns and responding to errors – the signalling rather than the traffic – comes in, the validity of the test goes.

Z 10.11.06 at 7:19 am

Daniel: Sociologists of science study the

sociologicalcomponents of the process through which a result is accepted or not (reputation, circulation of idea, shifts of paradigm, Matthew effect…). But prior to this work, there is a strictly scientific process, generally conducted by very few people (but not always so, see how it went for the works of Perelman) and generally entirely devoid of social interactions. Any trained scientist can accomplish this work, at least in his very specific field. I can (probably) decide whether this new article on Euler system is correct or not. I am not sure that Collins is unable to do this work-thirty years is a long time-but I would say his understanding is akin to that of a more classicaly trained physicist only if he can. That he can has certainly not been tested by the questions asked in the report.If he can’t, then

that thing which he is missing, if anything?is exactly that. Put in a down to earth way, if he can’t, he would be a very lousy lab director, because while no-one expects the lab director co-signing the article to understand each and every part of it, scientists do expect him to be able to say where a faulty article is faulty.Iain Coleman 10.11.06 at 7:58 am

A lot of the physicists commenting here seem perplexed by the original question, and as a former physicist myself I can understand their perplexity. I imagine that anyone who’s studied physics has had the experience of coming to understand some topic in much greater depth once they grasp the mathematical structures involved. It’s an “Aha!” moment. You can have a pretty good understanding of something (wave motion, say) through verbal descriptions, analogies, and examples, but once you see how all the mathematical structures fit together, suddenly you understand it on a whole new level. At least part of this is because a given mathematical description isn’t just some isolated formalism: it connects up with all sorts of other mathematical structure which might be familiar from other applications, and so you can see deep connections between apparently disparate phenomena that would have remained hidden if you hadn’t understood the mathematics.

Compared to this, the ability to use the mathematical formulas to crank out quantitative predictions is of secondary importance – though it is essential if you want to be considered a physicist (rather than just somebody who understands some physics). But even if you never do a calculation in your life, you do need to understand the mathematical structure of a physical theory if you want to have a physicist’s level of understanding. I seem to remember Feynman arguing along much these lines in

The Character of Physical Law.The main evidence for this statement is the self-reports of physicists concerning their mental states before and after achieving such mathematicl understanding. Daniel can choose to believe these or not, but I can’t see where he’s going to get better evidence.

Martin Bento 10.11.06 at 8:50 am

Perhaps another way to look at this question is this: will AI take us to the point where computers can handle the math, including evaluating it, and therefore Collins will be able to do what physicists do? I think those who believe in strong AI – the notion that it is possible for computers to be intelligent and conscious in the same senses that humans are – are committed to the view that computers are in principle capable of being physicists. However, the technical ability to manipulate the math seems more suited to a computer than the conceptual understanding that Collins has, and therefore seems likely to be automated first, and possibly is automatable even if the conceptual understanding is not. After all, on the level of pure calculation, computers already surpass human beings as mathematicians. As far as comparing experimental to projected results and judging the significance of divergencies, it sounds tractable, maybe not perfectly, but the judgement of humans is such matters is also imperfect. Even such things as intuition from experience – in math, such things would seem to be more precisely specifiable than in most areas. If experience can be so specified – if it can be represented as pattern recognition, for example – computers instantly gain the advantage of being able to draw on the “experience” of everyone represented in their databases. Human cannot simply “add more RAM” or grow their knowledge base arbitrarily large, and are therefore more limited to the capabilities of their specific heads. Maybe I’m being naive here, but what is there about the math itself that requires a human touch?

In fact, it is interesting to me that we’ve seen AI efforts at such things as writing stories, although it seems like computers, lacking a human experience of the world but being superb at calculation and manipulation of precisely-defined models, would be more likely to produce a Gell-Mann than a Proust.

If Collins could using computers do all the math that the physicists can do, and evaluate it, would his understanding then be equivalent? His understanding under that stipulation need not be different than the understanding he has now, does it? Does some of the understanding reside in the computer since that’s where the math is? If so, does a calculator “understand”, in part, accounting?

Cranky Observer 10.11.06 at 9:11 am

> I don’t understand why you say in your Guardian

> post that Collins can’t possibly make an original

> contribution to the field. Couldn’t he make a

> claim, and perhaps provide an informal argument

> for it, which the nerds find original and

> persuasive, and which some of them later prove to

> be true, by expressing it in technical language

> and developing mathematical proofs based on his

> reasoning (or conducting experiments).

When you have time look up the history of spread spectrum radio technology and who the two original co-patent holders are. You might be surprised.

Cranky

Jonathan Dursi 10.11.06 at 9:55 am

Your statement is not a reductio, but it certainly is absurdum.

It is completely true that someone like me does in fact

nothave as complete an understanding of apples as a biologist who can quantitatively model the growth of the apple from a bud and can predict how the growth of the apple might be effected by natural or artificial environmental factors. Do you really doubt that?Collins may well have a pretty decent partial understanding of gravitational waves, but his understanding is lacking compared to that of actual GW physicsists. I can demonstrate this — the LIGO team for instance can make use of their added understanding make predictions and attempt measurements of GWs that Collins cannot.

I’m still waiting for an answer to my pulsar question. How does someone who doesn’t understand the theory of general relativity quantitatively take a suprising new observation and use it to test the theory — a fundamental part of doing the science? And if you can’t figure out whether a new observation confirms or contradicts a theory, how well do you

reallyunderstand the theory?Martin Bento 10.11.06 at 10:16 am

Jonathan, is there any fundamental reason a computer program could not be written that would check experimental results against a variety of currently competing theories, and see which theories are most consistent with that result? Yes, the program would be “doing the math”, but would it be understanding the physics. I guess this is where we get into the Chinese room, but in the specific domain of math, it seems pretty applicable, regardless of whether it is more broadly. Is there any fundamental reason computers could not do all the math humans can do (and more probably) regarding gravity waves, including meta operations like evaluating the math? If Collins does not truly understand gravity waves because he cannot do the math, but could do the math using a computer with no further understanding of the math (though with an understanding of how to interact with the computer program, not itself an intrinsic feature of gravity waves) then is the math essential to understanding? Perhaps the next revoultion in science will come when the field is open to those mathematically ungifted, mathematical aptitude being a pretty specific brain function.

Jonathan Dursi 10.11.06 at 10:31 am

If one doesn’t understand the theory quantitatively, then one doesn’t understand it well enough to know

themost basic thing about the theory — does it describe reality, or not?Martin:

What and whether a computer could do the work is irrelevant to the question of Does Collins Understand Gravitational Waves As Well As Practicing Physicists. Collins, manifestly, does not, because the practicing physicists can use their understanding to do things that Collins can’t. Can Collins still be said to have a deeply incomplete understanding of gravitational waves? Sure, why not. Hell, until a real theory of quantum gravity is developed and extensively tested, no one has a

completeunderstanding of gravity…But again, the role of mathematics is being misunderstood. The role of maths here is not one of some inate ability that once you have, suddenly the understanding happens — if you are strong you automatically can lift things, if you Have Math you can automatically Understand Gravity Waves. The quantitative understanding of the theory is necessarily encoded in a quantitative language. If you don’t understand the theory quantitatively then you don’t understand it well enough to know THE most basic thing about the theory — does it describe reality or not.

Could, in principle, some computer `do’ the science by making unexpected observations, figuring out what the relevant theories predict in those cases, and comparing the observations to those predictions? Yes; those computers are called `scientists’. And they understand the theories well enough to quantitatively figure out what it predicts in unexpected situations, and quantitatively compare it to the world. Collins does not.

Could a computer someday be a scientist in its own right, unattended? Sure, why not, who cares.

Daniel 10.11.06 at 10:33 am

76: I’d actually be quite amenable to a theory of scientific truth where “understanding” something referred to a subjective, first-person experience had by the scientist. But I warn you that if we agree on this, I am going to take the wheel and drive it to some places which the (self-identified) “hard” scientists are not going to find congenial after all.

I am already working on a thought experiment in which you can get the exact same subjective experience of understanding a physical theory by eating a couple of mushrooms, and suspect that I might not be that far off on the science of that one :-)

Daniel 10.11.06 at 10:41 am

It is completely true that someone like me does in fact not have as complete an understanding of apples as a biologist who can quantitatively model the growth of the apple from a bud and can predict how the growth of the apple might be effected by natural or artificial environmental factors. Do you really doubt that?Yes, of course I do. A biologist (or for that matter a gardener; let’s not be precious here), knows a lot more facts about apples than you or me, but it’s mysticism to say that he

trulyunderstands what an applereallyis and we don’t. It’s an apple.I’m still waiting for an answer to my pulsar question.You will continue to wait until either someone comes across this blog who has interactional expertise in discussing general relativity, or you rephrase it to be a bit more relevant. Harry Collins did, in fact, apply his knowledge to a new question in the original Turing Test.

If one doesn’t understand the theory quantitatively, then one doesn’t understand it well enough to know the most basic thing about the theory—does it describe reality, or not?This is not something which demarcates Collins (or you or me or my gardener) from gravity wave physicists).

I understand really quite a lot about maximum likelihood estimators, by the way, but I have never calculated one in my life, never expect to and indeed couldn’t. I can use statistical packages to do all of the above, but I think it is quite important to your case that this isn’t the same thing.

Jonathan Dursi 10.11.06 at 10:51 am

This is not something which demarcates Collins (or you or me or my gardener) from gravity wave physicists).

It in fact is. People with quantitative understanding of gravitational waves and general relativity used their understanding to determine whether or not an unexpected observation was or was not consistant with the theory of gravitational waves. They tested their understanding against reality. They can do that because of the detailed nature of their understanding. Those that can talk a good game but can’t make such comparisons lack a depth of understanding that these physicists have.

Perhaps you could provide a definition for `understanding’ a phenomenon so that it makes sense that people who can predict what the phenomenon will do or how it will be manifest have, in fact, no additional understanding than those who can’t.

Jonathan Dursi 10.11.06 at 11:20 am

And this:

is an intentional misrepresentation of what I’ve said. In fact, I’ve said that current researchers still don’t have a complete understanding of gravity, so this nonsense about

trulyunderstanding apples is a red herring.Gardiners and biologists who study apples do in fact understand apples more completely than I; so may a pastry chef who specializes in apple deserts. Both can make predictions about what will happen (to their apples, or deserts) under different conditions. Those that can make reliable quantitative predictions have an even deeper level of understanding. I know what an apple is, and can distinguish some varieties, but have very little understanding of apples, how they come to be, how they come to be deserts, or how best to grow them to achieve some result.

Jack 10.11.06 at 11:22 am

Asking whether or not Collins “understands” gravity waves is a bit like asking whether or not the slides at the Tate are art. “Understands” is too nebulous so the question comes across as a bait and switch, hence the heated response. Like intelligent design it’s the next move that is interesting, worrisome and unarticulated.

I’d be more interested if he had spent 30 years hanging out with actuaries or geneticists. Somewhere where there are large external pressures for the supposedly characteristic processes to respond to.

If Collins did have an idea he liked, would he be able to check it or develop it by himself? If not there is something that might be called understanding that he doesn’t have. If so, in what sense is he not a physicist? That is not to say that what he has might not also be called understanding, it’s a flexible word.

Are gravity waves the new oranges? Lots of people use apples, only physicists and the occasional undercover sociologist makes any use of gravity waves so there are fewer places to plant the goalposts.

armando 10.11.06 at 11:37 am

I don’t think there is any inherent problem in calling him a physicist and though the test is poor evidence of this, his contribution to physics is something else.

However, one should note that if all physicists had his skills, then we wouldn’t have physics any more, in a rather strong sense. That is, not only would the subject change, it would also cease to function. That isn’t a huge problem, since the same can be said of other specialist roles. However, in this sort of discussion it is worth making explicit. Collins is essentially occupying a new role which isn’t that of the traditional physicist, and his “understanding” isn’t the same. Networking and producing original research are related, sure, but they aren’t the same thing.

jenna 10.11.06 at 11:37 am

Not that I expect anyone is still perusing this thread, but my first thought was: economics seems to me (admittedly not my forte; i stuck to theoretical math) an attempt to rigorize and illuminate complex relationships btwn entities that are not necessarily purely mathematical. there’s always that step where you try to explain what is happening in terms of human action.

not so in physics. physics and mathematics seem almost indistinguishable at some point b/c, well, they are: mathematics is the fundamental language we use to describe the physical world. can’t get around it. so yes, i think mathematical fluency is absolutely fundamental to a deep understanding of physics – otherwise it’s not clear how you would distinguish btwn acutal theory and a bunch of buzzwords.

A. Random Physicist 10.11.06 at 11:43 am

A think that this has been a pretty interesting discussion, and I’m actually pretty sympathetic to daniel’s point of view. But I think a couple things are getting lost/confused in the discussion.

The first is that sometimes “understanding” has been used in an absolute sense (does Collins “understand” gravity waves) when it shouldn’t be. For a large subject like gravity waves or physics, I think it only makes sense to talk about relative understanding and that any line between “understands” or “doesn’t understand” is a bit arbitrary. So we should really be talking about Collins’ understanding relative to other peoples’. I’m sure Collins’ understanding of gravity waves isn’t as good as some physicists, but I wouldn’t be surprised if it’s better than mine.

The second is the role that math plays within physics. I’ll have to disagree with some of the other physicists who have posted here claiming that “doing” the math is fundamental to physics. To my mind, math is merely a language for expressing certain ideas. The power of math is that it allows us to express these ideas extremely consistently and precisely, so that we all know exactly what we are talking about (or at least we think we do :-)). The question then becomes whether one can adequately express those ideas in some other language. I’m not even going to try to answer that one.

It’s the underlying concepts that are fundamental, and an experte should be able to precisely define them, manipulate them, and use them to make predictions and answer questions. Does this require “doing” the math? Maybe. But I’ve been in enough arguments with mathematicians about how much rigor is needed in a calculus class before a student can “understand” the derivative to know that there’s always someone who thinks that more mathematical rigor will automatically lead to a better understanding of the concepts, and that is certainly not true, at least in my experience.

So the question is, how accurate and precise is Collins’ conception of gravity waves? Is it good enough to call him a true expert? My gut says no, but I’m not completely convinced that’s the case.

Walt 10.11.06 at 11:49 am

I don’t see how there can be a definition of “understanding” that doesn’t include the ability to deduce additional facts about the object.

Daniel, what do you mean by “understanding”?

Martin Bento 10.11.06 at 11:56 am

A lot here does seem to circle around what we mean by “understanding”. Also, some commenters seem to treat understanding as binary (either Collins understands or he does not), whereas others recognize degress or “depths” of understanding. I would say this: the ability to do the math does not in itself constitute understanding of the physics, as the math is a rigorous logical system independent of real-world referents. There are likely mathematicians who understand the math applied to gravity waves better than any physicist, but this does not mean they understand gravity waves at any level; they may not even have neard of them. Therefore, the mastery of the math itself does not constitute understanding.

A “gravity wave” is a conceptual model we apply to describe an aspect of reality: to see its relationship to other aspects, and to predict its behavior. This model is specified by applying math to real-world events, but it is the mapping, not the math itself, that constitues gravity waves as a model. Can the model be specified without the math? Probably not fully. However, manipulation of the math does not require any understanding of the model, and the math itself can be conceptually described without requiring competence of performance. One could say what differential equations or, for that matter, division are without necessarily being able to perform them. So if the performance requirements of the math could be shunted off onto a computer (in the literal sense, not the metaphorical one where the mind is a computer), what would be required for “understanding” would be the ability to map correctly the mathematical results to the real-world phenomenon. This is what makes the model a model.

It may be possible that computers will someday be able to perform all functions of the human brain. However, even if that is not possible, it may be that computers may be able to perform all the mathematics humans can. That is a much more modest claim, as math is rather the computer forte. However, being able to do math in itself implies no understanding of real-world phenomena, since math is independent of such.

john c. halasz 10.11.06 at 12:14 pm

Physics aside, isn’t this all just Robert Brandom territory? To understand something is to be able to handle the nexus of inferences and implications, consequences and antecedents, in socially interactive practices of raising and substantiating claims, whether implicit or explicit, including the appropriate or reliable points or moves of entry and exit, (such as perceptions or proofs), with participants reflexively and mutually monitoring one another through processes of “deontic scorekeeping”. The degree to which any given participant can be said to understand a matter depends on the density of cross-implications and further inferential moves that he or she can handle. But what would characterize the understanding of advanced scientific researchers is not just the density of their understanding, but also that it is applied at the “cutting edge” of the matter, where further inferences and implications are unknown or uncertain. Mathematics is the science of formal operations, without regard to anything other than its own formal rules of implicature. But when any such formalization is deployed in scientific research,- and a threshold of formalization is one of the criteria of actual productive scientific research,- it is *applied* in specific ways that implicate, at least implicitly, substantive conceptions characterizing the “object domain” of that field. Now it may be exceedingly difficult, well-nigh impossible to articulate those substantive conceptions at the “cutting edge” in anything other than formalized mathematical terms, (partly because scientists themselves acquire those understandings implicitly through lengthy formalized training), and their explicitation would be an entirely extraneous philosophical task. But I think the basic issue here is not so much one of understanding “pure” knowledge, as of understanding the role of application internal to cognitive practices, (as opposed to applying achieved knowledge externally to some other matter).

Jonathan Dursi 10.11.06 at 12:51 pm

Martin Bento makes clear what I’ve been apparently quite poorly trying to say about the relationship of the math to the understanding of the science.

To the extent that I can understand what John C. Halasz has written, I’ll choose to believe that he’s saying what I’ve been trying to say about the procedural aspects of the science, and that `understanding’, if it is to have any meaning in this context, must include the ability to do something with that understanding.

In both cases, I think crucial to the discussion is that understanding is something which one can have more or less of, deeply or shallowly, and broadly or narrowly.

bryan 10.11.06 at 1:02 pm

Time for another thought experiment. The actual details of this one are probably totally nonsensical (I still haven’t the faintest inkling of what a gravity wave is), but perhaps the

structureof it can still be appreciated.Advanced aliens attack our planet with gravity wave guns. First off, they kill all the gravity wave physicists, but spare Collins, the mere sociology professor. The leader of the human military resistance goes to Collins for advice on how to fight these gravity wave guns. Is it possible Collins might have some useful advice to give–more useful than anyone else (save, of course, the now slaughtered gravity wave physicists) would be able to give?

Jake 10.11.06 at 1:58 pm

94: Useful? Sure. More useful than anyone else? Probably not, unless you arbitrarily define “gravity wave physicist” to include anyone who knows more about them than Collins. But there are probably physicists who think about black holes, or other aspects of GR, who with possibly as little as a month’s time would be able make much more meaningful statements.

The confusion over whether Collins can be said to understand gravity wave physics is also a bit confusing to me – does anyone doubt that if the physicists who were reviewing the answers also got to pick the questions, it would be clear who was the physicist and who wasn’t?

jon 10.11.06 at 2:53 pm

I’ve in fact done the experiment involved, tried to be a physicist without understanding math. It can’t be done.

A physicist’s job is to advance the state of physics. Advanced math is, in practice, such an vital tool, you’re pretty much useless without it.

Therefore, yes, there’s a real sense in which the physicists understand gravity waves and Collins doesn’t. He can understand alot, but can’t toy with the ideas. Imagine trying to do Econ without being able to test theories.

It’s true that physicists often make guesses, but the first thing they try with each guess is to try doing some math to see if it works out.

pdf23ds 10.11.06 at 3:53 pm

A. random physicist:

“To my mind, math is merely a language for expressing certain ideas. The power of math is that it allows us to express these ideas extremely consistently and precisely”

It’s about time someone made this point. Wow.

I’m going to take it a bit further, though. I believe that the kind of intuitive, thorough, “A ha!” type of understanding that the physicists here have said only comes with an understanding of the mathematics, is not primarily a mathematical understanding. That’s because humans don’t natively understand things with math. They understand them with metaphors–visual, spatial, intentional. (For evidence of the last, observe how often scientists anthropomorphize things when explaining them casually.) Deep intuitive understanding *is* metaphorical understanding.

Mathematical notation is not absolutely necessary. But it is practically necessary (as others have said) because it offers a way for people communicate their metaphorical understanding in terms precise enough to be useful. There is no other way to communicate physical laws between humans that comes anywhere near to the precision and concision of mathematical notation.

But math notation isn’t tied to mathematical understanding–there is no such thing. It still has to be translated, by anyone who uses it, into metaphor–into understanding. And I imagine that with the right vocabulary and enough practice, people could learn to speak directly about the metaphors they use in their intuitive understanding, and this could provide another notation that provides just as deep an understanding of the principles. (It would just be more inconvenient to work with, being less terse and less oriented towards calculation.)

pdf23ds 10.11.06 at 3:58 pm

“and this could provide another notation that provides just as deep an understanding of the principles.”

I mean to say, “that can be used to communicate just as deep …”

Alex 10.11.06 at 5:46 pm

A couple of points – both here and on CIF, various posters have yelled that Collins probably couldn’t debug a gravity wave simulation’s source code. Wildly irrelevant. How many physicists can code well? A few. How many coders are physicists? Very few. Given the equations – i.e. the Sacred Math – but without knowing what the values meant, any competent programmer (in a wide range of different languages) could do the job. But they wouldn’t understand a thing about gravity waves. All they would know is that the grey machine was happy with some solutions and not others.

I propose another test. Given Collins, could a mathematician, or a physicist with no knowledge of gravity waves, work out what he was talking about?

agm 10.11.06 at 7:04 pm

Daniel,

With regard to what you quite correctly describe as something that looks like hostility, I apologize for being and sounding intemperate. Personally it’s been a really, really horrible month. However, physics simply does not reduce to a sociological phenomenon; physics studies physical phenomena, and it is an empirical science. The beam inside the accelerator at Fermilab, where a magnet is currently being replaced, the plasma escaping the magnetic fields set up to attempt fusion, the observation and characterization of the cosmic microwave background (which got the physics Nobel last week), these are NOT socioogical things. They are physical investigtions that get embedded into a sociological framework so that we can talk about them with other people. Abstract away the physical meaning, remove the phenomena, and you lose the essence of what is physics. The appearance of removing our work from the need for physical confirmation/explanation is precisely why many non-string theorists get upset when some of the string theorists have made claims that the mathematics is so beautiful that it must be right, or that it is the only game in town. Physics is a phenominological science and thus cannot be reduced to ONLY a sociological endeavor.

agm 10.11.06 at 7:46 pm

a random physicist,

I agree with you in theory. In practice lies the rub. Language is ambiguous, so to communicate physics to each other we use mathematics. It almost verges on the Whorfian(?) hypothesis, but in order to communicate clearly we have to use math. Using plain ol spoken language, as thousands of people doing pedagogical research in technical fields have shown, just isn’t clear enough.

——————————–

I’m going to give a much more concrete example of how you have to have a complete understanding of a formalism to be competent, to have a fuller understanding than where we’ve wrongly been pegging Collins, and how the mathematics is simply and utterly inseparable from a prodessional’s level of understanding.

My research requires calculating the distance to reflection of an extraordinary mode radio frequency wave from the transmitting instrument. This requires knowing how fast the wave is traveling at any given point between being transmitted and being reflected, because it changes depending on the properties of the medium that the wave is traveling in. The original version of the code was written by one of my advisor’s previous graduate students, and when I started working for, she took the project and tossed it at me, saying “Here, go make this ready for publication”. I looked through everything, made the IT people dig out everything he had ever put on a computer here, still couldn’t figure out what he had done and why what I had been given did not work. Thousands of lines of code, all of it spaghetti code — only a few comments explaining what he had the code doing, and the only useful one was a reference to a single equation on a certain page of Stix’s book on waves. So I go to the library, find the book, and spend two weeks trying to recreate the equation that he had programmed. Eventually I decided to take a different tack and rederived the equation for the X-mode group and phase refractive indices without any reference to what he had done. In less than an hour I found the error, something very easy to make — while treating everything else correctly, my predecessor had programmed in the formula for the square of phase refractive index in the longitudinal approximation. However, the quantity necessary to calculate the group refractive index (which tells you how fast the wave is traveling) is not the square but the first power of the phase index. This is bad because if you use the square instead of the first power, then the code says that the wave reflects significantly further that it actually would in reality.

It only took one night to fix the code and start spewing out results to do statistics on, but without the ability to do the math, and as arp has wisely pointed out, without the ability to see the meaning of the math, I would not have been able to do this. At no point was there any sociology in this beyond a handful of emails to ask this researcher or that about how their code works, or how they calculated this quantity for a paper and why it mattered to them. Aside from the emails, at no point was another person involved in this work between the point where my boss tossed the project at me and the point where I started stalking my advisor about revising the draft of the paper I had written. What sociology thereis would lie in how my advisor and I relate, in the network I built in contacting these other researchers, in the ethos or sharing knowledge/tools/experience, but the fundamental result is the description of the physical behavior. So to speak, you don’t get credit for anything but the results, because that is what matters in physics.

agm 10.11.06 at 8:09 pm

I also don’t really see either of your examples as particularly convincing with regard to formalism. In the first, you actually stated the important principle without any formalism, and in the second, the problem (the ultraviolet catastrophe) only existed as a problem of the mathematical formalism in the first place; there’s no physical phenomenon to be understood.I almost forgot something. It is not naive, it is wrong to say the ultraviolet catastrophe was not a physical problem. The Rayleigh-Jeans law, derived from observation of blackbodies, implied that you would get an energy density going to infinity as the frequency of light emitted by a blackbody increases. This has energy conservation implications. However, we also have a couple of centuries of experimental evidence that energy gets conserved in closed systems, so something that looks like a violation of an established principle is exciting and important, simply wonderful. This means there is a place we can improve our description of the world and make it look more like reality. In this case, Planck made an ad hoc hypothesis about the atoms in the walls of blackbodies and their energy levels, thus starting the development of one of the most important and exciting developments in all of human understanding ever, quantum mechanics.

Alden 10.11.06 at 8:13 pm

Given the equations – i.e. the Sacred Math – but without knowing what the values meant, any competent programmer (in a wide range of different languages) could do the jobThat’s me! I program hydraulic models used in civil engineering and I understand neither the physics nor the math. I just know how to write a program that will produce the numbers my customers are expecting ;)

Jack 10.11.06 at 10:42 pm

Agm makes a good point: being a physicist, unlike being many other things, consists of passing a turing test administered not by men but by God–or to put it less Einsteinishly, administered by pure physical stuff. If you don’t have the “interactional expertise” with the stuff, no matter of interpersonal interactional expertise will make up for it.

robotslave 10.12.06 at 4:21 am

A big part of the problem in this debate is that in the particular field in question, physicists have not yet designed and run experiments that have yielded results confirming any of several theories of gravitational radiation.

There is

indirectevidence in the form of astronomical observations; i.e. “the observed system appears to be losing energy at a rate consistent with all viable theories of gravitational radiation.”There have been several experiments designed to observe gravitational waves directly. None have succeeded to date.

If a person must confirm (or be able to confirm) theories with predictions and experiments and direct observation and all the rest of the scientific method before that person can be said to “understand” a scientific theory, then no physicist today can be said to “understand” gravitational radiation very well.

Daniel’s question does not stem from any lack of understanding of the scientific method.

Personally, I think this whole debate is rooted in a lack of distinction between a scientific theory and a mathematical model based on that theory. In physics, of course, this distinction is rarely made— compare with, say, evolutionary biology, where you have theories (e.g., punctuated equilibrium) with little or partial or even no accompanying mathematics at all (or mathematical models that arrive long after the underlying ideas).

In a typical scientific situation, I would say that a person understands a mathematical model when one understands how it can be derived from the non-mathematical ideas underlying the theory, and I would accept such an understanding of any model involved as a necessary condition for a “real” and “scientific” understanding of the theory. Whether or not said theory is itself “real” (or, if you prefer, “confirmed”) I would treat as a separate question entirely. I may differ with Daniel on that last one, I’m not sure.

The problem with the specific case of gravitational radiation is that even if we stipulate that there is a single mathematical model to “understand,” (that model being general relativity, and so ignoring viable alternate gravitaional models), there is, as yet, no widely accepted or experimentally confirmed derivation of that model starting from fundamental, non-mathematical principles. There are, in fact many different theories of gravitational radiation, none of them sufficiently compelling or problem-free to produce consensus in the rarified community Harry Collins studies.

Now, back to Daniel’s question. I must assume that he is asking us about Harry Collins’ understanding of actual gravitational waves, if they do in fact exist, rather than about Harry Collins’ understanding of any particular

theoryof gravitational waves, which is trivially inferior to that of a physicist working on that particular theory.We can answer Daniel’s question using numerical methods. Let there be i working theories in the gravity-waves community and k physicists in that community. Let ct(n) denote Collins’ degree of familiarity with theory n, where 0 as a whole has a better understanding of actual real gravity waves than Harry Collins does. Two heads are better than one, indeed.

The interesting question, however, is whether the statistically average gravitational wave physicist has a better understanding than Harry Collins. To resolve this, we…

[earnest calculation, reasonable assumptions, margins of error estimated, etc]…and thus we can see that while the average gravitational physicist does indeed have a better understanding of actual real gravity waves than Harry Collins, the advantage doesn’t seem all that impressive, what with both scores being so low.

Jake 10.12.06 at 12:23 pm

There have been several experiments designed to observe gravitational waves directly. None have succeeded to date.None have observed gravity waves to date. Whether this is because the experiments were not sensitive enough or because theories of how gravity waves are generated is incorrect is a question that is fundamental to understanding gravity wave physics to answer, requires math to answer, and (I suspect, but am not certain) Collins would not have been able to answer.

john 10.12.06 at 3:54 pm

As John Q points out above, Richard Feynman thought it was possible to understand physics without being able to do the mathematics (although in fairness, he was really arrogant).Feynman was a great popularizer of physics, but he knew that you had to understand the math to do physics. He told his physics students that they didn’t understand particle physics until they could get all of the factors of 2 pi (in computing the integral from a feynman diagram) right. While he thought everyone could gain some understanding of physics and knew that there’s more to physics than math, he certainly didn’t confuse the level of understanding of a physics practitioner who could do the math with a layman who couldn’t.

john 10.12.06 at 4:20 pm

But math notation isn’t tied to mathematical understanding—there is no such thing. It still has to be translated, by anyone who uses it, into metaphor—into understanding. And I imagine that with the right vocabulary and enough practice, people could learn to speak directly about the metaphors they use in their intuitive understanding, and this could provide another notation that provides just as deep an understanding of the principles. (It would just be more inconvenient to work with, being less terse and less oriented towards calculation.)You’re right that mathematics is more than notation. After all, algebra predates modern algebraic notation by thousands of years. However, “more inconvenient” is a staggering understatement. Even using a poor notation can make problems orders of magnitude more difficult (expand the tensor calculus of Einstein’s gravity equation into the many equivalent linear equations, then try to work with them for one example). English is going to be much more verbose and complex than the linear equations.

For many problems, the additional memory required to hold the expanded information exceeds the capacity of the brain and calculations take longer than a human lifetime to complete. To look at another mathematical notation, look at software. MS Windows is already 50 million lines of code. Translating it to machine language (a less abstract notation, like the linear equations in place of tensor calculus in Einstein’s equation) would require about 500 million lines. It would be much longer in English. Could anyone understand it well enough to produce the next version?

agm 10.12.06 at 7:02 pm

Oh god, robot slave, I am very glad I’d finished my coffee before reading that. I tip my hat.

Kenny Easwaran 10.12.06 at 8:07 pm

106.

None have observed gravity waves to date. Whether this is because the experiments were not sensitive enough or because theories of how gravity waves are generated is incorrect is a question that is fundamental to understanding gravity wave physics to answer, requires math to answer, and (I suspect, but am not certain) Collins would not have been able to answer.Has anyone been able to answer this question? I’m sure many people have come up with answers to this question (some saying the experiments weren’t sensitive enough and some saying the theories were wrong, and some saying we were testing the wrong theories), but does anyone have really good reason to believe that one of them (rather than one of the others) is the right answer? Some day I’m sure we will, and Collins probably won’t be the one to do it, but as Daniel pointed out, the fact that he hasn’t yet doesn’t distinguish him from most (or perhaps even any) gravity wave researchers. We don’t expect every researcher to be able to have achieved every breakthrough in the field.

robotslave 10.12.06 at 10:56 pm

Hmm, it seems part of my post was clipped out somehow, but fortunately it was in the bit where I went way too far in semi-facetiously detailing a numerical method to answer Daniel’s question, so I doubt anyone even noticed there was anything missing.

robotslave 10.13.06 at 9:07 pm

jake:

The question of why experiments to measure gravity waves have not in fact measured gravity waves is one that no current gravity wave theorist can answer, no matter how much mathematics they deploy in the effort.

Are gravity waves simply not strong enough to be measured with the apparatus? Are gravity waves strong enough to be detected by the apparatus simply very infrequent, or very infrequent in our local neighborhood, or damped somehow? Do they not exist at all?

A single unambiguous detection of a gravity wave would eliminate the “they don’t exist” option without using any math.

And that single reading plus piles and piles of math wouldn’t help at all in deciding which of many alternate gravitaional wave theories is correct, due to the sort of non-mathematical possible explanations for low readings that I just mentioned.

I think what you’re saying is that it will take lots of math to build more sensitive experimental apparatus.

I’d agree, of course, but I’d also point out that most of the math deployed in that effort would be for the engineering involved, and not at all related to the kind of math used by purely theoretical gravitational radiation physicists (and perhaps entirely unknown to them).

It will also take quite a lot of money to build more sensitive experimental apparatus, but I don’t think anyone is suggesting one needs a degree in finance to understand gravity waves.

Johan Richter 10.15.06 at 11:34 am

What I find strange is that he has not learned the math in all those years. A paper in a physical journal has lots of math in it. Aren’t you likely to do a worse job as a sociologist of physics if you can’t understand it?

As to Daniel’s question. Collins obviously has some understanding of gravitational waves. The formulation of the question seams to require a binary definition of understanding which I reject. However a physicist working in the area would have a deeper understanding. I find that obvious.

A physicist would be able to make quantative predictions from the theories of gravitational waves. Making quantative predictions shows a deeper understanding than making qualitive predictions, since a qualitive prediction is really just quantative prediction where you’ve only kept the sign of the answer.

A mathematician on the other hand would have gaps in her understanding because she would not neccessarily know how to translate a fact about the mathematical framework into something you expect to see in the real world. So she would not be able either to make any quantative predictions about the real world. Thus, knowing the math is neccessary but not sufficient for a full understanding of physics.

Johan Richter 10.15.06 at 3:19 pm

Also, what did you mean with your statement about economics? Did you mean that they did not understand economic theory or did you mean that they did not understand how the economy really works?

Raven 10.15.06 at 9:00 pm

“… you seem to be getting dangerously close here to an argument which would imply that non-physicists don’t really understand what an

appleis….”— Daniel in #62.

The apple falls; but particle or wave?

To grasp and taste might seem the way to tell,

Yet Heisenberg gives us a warning grave:

We’d just obscure where

orhow fast it fell;And, harder news, to watch also does that.

We who can’t touch, nor see, must speculate.

Thus it partakes, with Ernst’s endangered cat,

Of plural, mixed, or undetermined state.

In many worlds, perhaps all needs are met,

One apple falls to all our waiting hands;

But in this world, the much more likely bet

Is falling once. We wait for where it lands.

At last it hits upon diffraction’s cause —

But what comes through the grate is merely sauce.

(C.M. Joserlin, 10/15/2006. Thanks, Daniel!)

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