Faking da funk and faking the physics

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.

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.

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 do anything.

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).

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.

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.

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.

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.

I don’t think it’s crazy to 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 he is a 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.

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 new situations and come up with an answer, and that requires a deeper level of knowledge. It also generally requires mathematics, but not for 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.

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 myself I’d consider my life an abject failure.

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.

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

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?’.

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)

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?

“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 course physics is just applied mathematics, surely mathematicians understand physics better than physicists do.

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.

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.

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 priori model. 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.

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.

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.

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. The details of 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.

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.

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.

for improbable things like treating derivatives as a ratio of derivatives

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

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 …”

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.

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.

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.

Daniel: Sociologists of science study the sociological components 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.

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?

Jonathan, you seem to be getting dangerously close here to an argument which would imply that non-physicists don’t really understand what an apple is, which I would certainly take as a reductio.

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

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?

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 really understand the theory?

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?

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 complete understanding 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.

And this:

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 truly understands what an apple really is and we don’t. It’s an apple.

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 truly understanding 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.

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.

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.

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.

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.

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?

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.)

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?

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.

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

That’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 ;)

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 indirect evidence 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 theory of 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.

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.

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

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.

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.

“… you seem to be getting dangerously close here to an argument which would imply that non-physicists don’t really understand what an apple is….”
     — 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 or how 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!)