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May 19, 2009

Where is the Philosophy of Physics?

Posted by David Corfield

As the subtitle of this blog says, we run ‘A group blog on math, physics and philosophy’. To what extent, though, do we cover all the interfaces of this triad? Well, we do some philosophy of mathematics here, and we certainly do some mathematical physics. But the question I’ve been wondering about recently is whether we should be doing more philosophy of physics.

If we followed the position that physics is the search for more and more adequate mathematical structures to describe the world, perhaps we needn’t take the philosophy of physics to be anything more than a philosophy of mathematics along with an account of how the structures which are most promising for physics are chosen. But this view of physics would be controversial.

Philosophy of physics is a large field asking questions about the interpretation of quantum mechanics (a table comparing thirteen), about the direction of time in statistical mechanics, about the relation between space, time and motion, and about much more. That such work is necessary for physics to progress is a thesis of the philosopher Michael Friedman, who has featured here before. I was reminded of his argument while reading this paper comparing Cassirer and Kuhn.

For Cassirer, says Friedman, in mathematical physics

We can…conceive all the theories in our sequence as continuously converging, as it were, on a final or limit theory, such that all previous theories in the sequence are approximate special cases of this final theory. This final theory is only a regulative ideal in the Kantian sense – it is only progressively approximated but never in fact actually realized. Nevertheless, the idea of such a continuous progression toward an ideal limit constitutes the characteristic “general serial form” of our mathematical-physical theorizing, and, at the same time, it bestows on this theorizing its characteristic form of objectivity. (p. 241)

and

…thought does not require a “substantialistic” or “ontological” identity over time of permanent “things” but merely a purely mathematical continuity over time formulated in successively articulated mathematical structures. (p. 245)

Kuhn, on the other hand,

…consistently gives the question an ontological (“substantialistic”) rather than a mathematical (“functional”) interpretation. Thus, for example, when Kuhn famously considers the relationship between relativistic and Newtonian mechanics, he rejects the notion of a fundamental continuity between the two theories on the grounds that the “physical referents” of their terms are essentially different, and he nowhere considers the contrasting idea, characteristic of Cassirer’s work, that continuity of purely mathematical structures is sufficient. Moreover, Kuhn consistently gives an ontological rather than a mathematical interpretation to the question of theoretical convergence over time: The question is always whether our theories can be said to converge to an independently existing “truth” about reality, to a theory-independent external world. (pp. 245-246)

Friedman goes on to explain how

…with Kuhn – and with the logical empiricists – that Einstein’s general theory of relativity is in an important sense incommensurable or nonintertranslatable with the Newtonian theory of universal gravitation it replaced. Whereas Newtonian theory represents the action of gravity as an external “impressed force” causing gravitationally affected bodies to deviate from straight inertial trajectories (moving with uniform or constant speed), Einstein’s theory depicts gravitation as a curving or bending of the underlying fabric of space-time itself. In this new framework, in particular, there are no inertial trajectories in the sense of the geometry of Euclid and the mechanics of Newton, and gravity is not an “impressed force” causing deviations from such trajectories. (p. 248)

So

…even after the mathematics required for Einstein’s theory was developed, it still remained fundamentally unclear what it could mean actually to apply such a geometry to our sensible experience of nature in a real physical theory. One still needed to show, in other words, that Einstein’s new theory is empirically or physically possible as well, and this, in turn, only became clear with Einstein’s own work on what he called the principle of equivalence in the years 1907–12. (p. 249)

What is needed is something Friedman calls scientific philosophy and elsewhere meta-scientific work:

in addition to the necessary mathematical developments (the evolution of non-Euclidean geometries, as unified and completed in Riemann’s work) and the necessary physical developments (the discovery of the constancy and invariance of the velocity of light, the numerical equality of inertial and gravitational mass underlying the principle of equivalence), we still need a set of parallel developments in contemporaneous scientific philosophy to tie together the relevant innovations in mathematics and physics and thereby effect the necessary expansion in our physical or empirical possibilities. (pp. 249-250)

In the case of general relativity, some of this meta-scientific work was done by Mach, Helmholtz and Poincaré, before Einstein.

If Friedman is right, we would expect the need for some of this meta-scientific work to allow the n-categorical physics revolution. I wonder what form it should take. The Café discussion which struck me as being most like contemporary philosophy of physics was that concerning Spitter, Heunen and Landsman’s work on topos theory in physics. But what of the mathematical physics we talk about mostly here?

You can see me trying to urge you knowledgeable people in this direction here. In On Unitary Representations of the Inhomogeneous Lorentz Group, Wigner discusses how observations made by different observers ought to be related in terms of a group acting on frames of reference, so I wondered whether a similar story existed for 2-groups.

Urs says

the Lawvere-ification of the proper center of modern theoretical physics is still to be done.

Do we need a new Mach, Helmholtz and Poincaré?

Posted at May 19, 2009 2:01 PM UTC

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Re: Where is the Philosophy of Physics?

we still need a set of parallel developments in contemporaneous scientific philosophy to tie together the relevant innovations in mathematics and physics

It seems to me that we are getting quite a bit closer to that gooal, as of late. Not that there is nothing left to do, but signs are more hopeful than they used to be.

It’s funny that you posted this particular entry within four minutes of that conference report entry. Maybe the two are not only close in posting time.

Posted by: Urs Schreiber on May 19, 2009 2:41 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

My question is whether what’s being discussed at that conference is the equivalent of what Friedman says was needed to allow general relativity to become an empirical possibility. Is it just that we no longer need to go about wondering what it would be like to ride on a beam of light?

Posted by: David Corfield on May 19, 2009 2:57 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

David wrote:

My question is whether what’s being discussed at that conference is the equivalent of what Friedman says was needed to allow general relativity to become an empirical possibility. Is it just that we no longer need to go about wondering what it would be like to ride on a beam of light?

That conference is being run by mathematicians, most of whom are not primarily interested in using topological quantum field theory as a testing ground for ideas in physics. (There may be a few exceptions.) So, you won’t find many people there pondering simple thought experiments like Mach or Einstein did. Instead, we can hope some people at this conference are the 21st-century analogues of Riemann or Hilbert. That’s good too.

But we still may need our Machs and Einsteins.

Posted by: John Baez on May 22, 2009 3:40 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

It seems to me (as a non-physicist, of course) that another issue in the philosophy of physics is the situation where misapprehension of the scope of mathematical “ideas” limits one’s belief about what’s possible physically and what should be investigated experimentally and how experimental results should be interpreted. This seems particularly relevent in physics which isn’t looking at the elemental building blocks of the universe and their behaviour.

Taking two examples (that I’m by no means expert in): five-fold symmetric “crystals” (and other general “quasi-crystals”) appear to have been “explained away or simply denied” for about a decade because the mathematics describing “crystalline things” was believed to be complete and inconsistent such objects (at least according to a wikipedia page that’s said to need expert attention):

http://en.wikipedia.org/wiki/Quasicrystal

(It looks like the story is more complex in that the mathematics of non-periodic tilings existed but wasn’t known to those studying the physics of crystals.)

Likewise, I’m sure there are other examples where a misapprehension about the scope of a “mathematical understanding” for a physical “system” delayed recognition of some physical phenonmenon in that system. What, if anything, can be done to avoid simply not seeing possibilities because they don’t fit within the “currently being developed” mathematical framework when that framework clearly isn’t finished yet, so by definition its extent can’t be precisely known?

Posted by: bane on May 19, 2009 5:11 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

I notice that there are 13 alternative quantum theories listed.
Each apparently has an insufficient interpretation or the right
one would have a lot more agreement. I take this as a breakdown
in the underlying philosophical criteria, the scientific method
though perhaps that isn’t the usual view of its status. Penrose
has stated that something is missing from quantum theory, so I
think the most likely circumstance is that none of the 13 is
right. The problem with QT interpretations is no falsifiability.

“Falsifiability (or refutability) is the logical possibility
that an assertion can be shown false by an observation or a
physical experiment. Falsifiability is an important concept
in science and the philosophy of science. Some philosophers
and scientists, most notably Karl Popper, have asserted that
a hypothesis, proposition, or theory is scientific only if
it is falsifiable.”

Posted by: Stephen Harris on May 20, 2009 3:13 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Friedman makes a distinction between the quality of the scientific philosophy which led to general relativity and that which led to quantum mechanics. He reckons that in the latter case philosophical interventions have not been “timely”.

Posted by: David Corfield on May 20, 2009 9:16 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Thanks for the hint, DC. I was able to discover your excellently written review and why JB switched from quantum gravity to category theory (which I hadn’t read but wondered about).

“(See Baez forthcoming* about the possibility that “…quantum theory will make more sense when regarded as part of a theory of spacetime” and his claim that “…we can only see this from a category-theoretic perspective - in particular, one that de-emphasizes the primary role of the category of sets and functions.”).

* John Baez, Quantum quandaries: a category-theoretic perspective.

Posted by: Stephen Harris on May 21, 2009 8:16 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

This may be true about interpretations of QT. (I was also staying away from “physics of elementary things” because as a non-physicst mathematician it’s difficult for me to see what work is “mathematizing the physical world” and what is “mathematizing a mathematization”). I was making a slightly different point (slightly provocatively):

One theme in the post was how additional physical conceptions can be required to make a new mathematical conception into physics. I was interested in the opposite case, where one has mathematics which is not wrong but is not “the whole story”. Ie, there framework is clearly falsifiable in theory, and probably in practice, as an experimenter could imagine seeing phenomena not covered by the theory, but if one believes the mathematical theory is the COMPLETE description of the system why would one look out for phenomena beyond its range?

In my original post I mentioned two examples, which was left over from something I thought about mentioning but decided against on the grounds that I didn’t understand much about it. There’s apparently another piece of evidence that N=8 supergravity’s perturbation theory might be ultarivolet-finite at all orders ( http://arxiv.org/abs/0905.2326 ); it was apparently believed that as a mathematical structure this couldn’t be UV-finite, and this belief appears to have been one motivation for creation of various new physical ideas to provide physical counterparts for new mathematical structures designed to yield appropriately finite expansions. So it’s possible misunderstanding of the scope of a mathematical object has led to a mis-step on the physics side. (Or maybe not; I gather the evidence on both sides is still very, very preliminary.)

Still, the contrarian in me wonders about if there is any systematic issue in 21st century physics, particularly NOT elementary particle/gravity physics, where missaprehensions about the scope of some mathematization has clouded enquiry. (I like being a mathematician so this isn’t “anti-math”, I’m just curious the philosophy of physics in relation to mathematics.)

Posted by: bane on May 21, 2009 10:04 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

As a crassly self-interested scientist, I’m mainly interested in philosophy of mathematics that can actually help me as a mathematician, and philosophy of physics that can actually help me as a physicist.

If we restrict attention to this sort of philosophy — ‘philosophy as handmaiden to the sciences’ — I think the philosophy of physics is currently much more important, and harder, than philosophy of mathematics.

Why? Because mathematicians already know lots of good things to do — lots of philosophically interesting things, too — and they’re busy doing them. Fundamental physics, however, is in a discouraged and frustrated state. It could really use some help.

I don’t mean to paint too bleak a picture. Various people like Urs Schreiber are happily working on programs that could eventually lead to revolutions in fundamental physics. Unfortunately, it’s not yet clear how. For example, I don’t see yet how the beautiful mathematics of nn-categorical field theory will make progress on tough problems like the cosmological constant problem, or indeed any detailed aspects of the particles and forces we see around us.

Maybe experimental results at the Large Hadron Collider will change the story in a year or two. But we may need to be patient. We may need years of deep mathematical work and a couple of brilliant ideas based on pondering the experimental data.

In the meantime, here’s a nice study of the difficulties physicists find themselves in:

This is the first of a collection of essays that Zapata plans to put on his blog.

Posted by: John Baez on May 20, 2009 3:30 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

There is no Dark Energy. Look at the published literature on this, if you like.

Posted by: Kea on May 20, 2009 8:51 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Fundamental physics, however, is in a discouraged and frustrated state. It could really use some help.

I’m wondering what the right kind of help could be. Is there anything to be gained for you physicists by attending conferences such as Philosophy of Gauge Theory? Are you all rushing out to buy Gauging the Real? Do you regret missing the Everett@50 conference?

Posted by: David Corfield on May 20, 2009 9:10 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Yeah, you tell ‘em, David.

Posted by: Kea on May 20, 2009 9:30 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

David wrote:

I’m wondering what the right kind of help could be. Is there anything to be gained for you physicists by attending conferences such as Philosophy of Gauge Theory? Are you all rushing out to buy Gauging the Real? Do you regret missing the Everett@50 conference?

It sounds like you’re fishing for the answer no. I’m looking for philosophers who understand the math and physics of today roughly as well as Leibniz understood the math and physics of his day. So, I’m almost bound to be disappointed. But you keep suggesting interesting projects and connections here on the nn-Café, and I find that very helpful — so it’s certainly possible for philosophers to push science forward, even today.

Posted by: John Baez on May 20, 2009 5:15 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

In his reply to that paper by Friedman I was discussing, Andrew Chignell writes

…although the “peculiar role” that Friedman reserves for his brand of transcendental philosophy might in fact be qualitatively different from the normal practices of scientific investigation, it is noteworthy that all of the 20th-century figures that he credits with having done the sort of thing he recommends are what we would think of as scientists and not, or not primarily, as philosophers. These are the sort of people who “tie together the relevant innovations in mathematics and physics and thereby effect the necessary expansion in our physical or empirical possibilities” (p. 250). Helmholtz, Poincaré, Mach, and Einstein are not extensively studied in your average philosophy department, and of these four only Einstein made it into the Library of Living Philosophers. So my worry is that Friedman’s recommendations about what kind of philosophy remains viable will end up saving philosophy from the sciences but still hand it over to the scientists. In other words, the only people with the expertise that is required to do the kind of philosophy that Friedman is recommending will be, like Einstein, highly trained scientists in their own right.

[Perhaps ‘19th-century figures’ was meant.]

This is a result “many would-be Kantian philosophers will find rather gloomy”.

Posted by: David Corfield on May 21, 2009 10:52 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

First of all, sorry because this will be another superficial post written on the fly. I wonder if it’s appropriate to formulate David’s question in the context of ‘applications’ vs. ‘influence.’ That is, it seems that the question has been often posed here of whether there are applications of philosophy to physics. Of course the notion of application is notoriously hard to define, and I won’t attempt to do so here. But I think we can agree that there are applications of mathematics to physics. The belief seems widespread that there are applications of physics to mathematics, but the sense of this may be somewhat different from the other direction. That is, these supposed applications usually take the form ‘a mathematical structure that was developed to solve a problem of physics ends up being applied to pure mathematics.’ I won’t be able to say now how, I’m sure someone else has a better understanding of this issue, but it seems different from how physics looks for mathematical objects that more or less directly correspond to physical entities.

Now, do people know of some examples in which philosophy was applied to physics in a somewhat narrow sense? Once again, I certainly don’t doubt that there has been tremendous *influence* at many stages. I realize the question is very vague, but perhaps not entirely empty.

Incidentally, while physics and mathematics have been also very influential in philosophy (I think), I’m not aware of much in the way of applications there either. But perhaps there are philosophers who have tried to construct rather comprehensive mathematical models of philosophy in the manner of, say, mathematical models in cognitive science?

Posted by: Minhyong Kim on May 23, 2009 11:19 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

I don’t see yet how the beautiful mathematics of n-categorical field theory will make progress on tough problems [in theoretical physics]

Sure it’s not clear. Just as once upon a time it was not clear

- what differential geometry has to add to Maxwell theory;

- what group and representation theory has to add to Quantum Mechanics;

- what symplectic geometry has to add to Hamiltonian mechanics;

- etc.

In each case the point was and is that some structure just happens to be the right natural language for some phenomenon. At first this is always just a reformulation of what is known, usually of less than what is known. But without it, all further progress is blocked. Concerning the current frustration in theoretical physics in this light, let me make the point that there are indications that it is precisely formal math that is needed to alleviate this frustration, much more than the usual semi-anything fiddling around:

one of the more frustrating aspects in one part of the community is that it is very hard to classify 2-dimensional CFTs. This was clear for decades, but was largely ignored. Now currently it is regarded as one of the outstanding issues. In any case, when you look at the large literature on this problem (called the landscape problem) you notice that there is only a tiny minimum of technical understanding of the problem. One knows virtually nothing about how to classify non-rational 2dCFT. In fact, one hardly knows how to define them (though that has gotten much better, it seems). Now, on the formal side, the math side, we see huge progress with the understanding of classification of TFTs. And we know exactly how the mathematical machinery used to handle these generalizes to the case of CFTs: we just switch from the n-category of diffeomorphism classes of cobordisms to that of conformal classes.

So it’s already kind of clear that in the end there will be a conformal Baez-Dolan hypothesis which tells us that 2dCFTs are classified precisely by certain objects in certain categories. In fact, for the rational case this is already established: where you have Frobenius algebra objects in Vect for 2dTFTs you have Frobenius algebra objects in modular tensor categories for CFTs.

What is needed is the generalization of this structure theorem to the non-rational 2dCFT case. It’s a problem in n-categorical math at the verge of being tractable. And it is of huge interest in theoretical physics. Just up to now few people are crossing this border.

Posted by: Urs Schreiber on May 20, 2009 11:40 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

…there will be a conformal Baez-Dolan hypothesis which tells us that 2dCFTs are classified precisely by certain objects in certain categories.

What’s a best guess as to what replacements for those two ‘certain’s might look like?

Posted by: David Corfield on May 20, 2009 11:58 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

…there will be a conformal Baez-Dolan hypothesis…

And there’s also that result of Kevin Costello’s:

A topological conformal field theory is the same thing as a Calabi-Yau A A_\infty category.

Posted by: Bruce Bartlett on May 20, 2009 6:12 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Something for nLab – explaining the difference between:

  • conformal field theory
  • topological field theory
  • topological conformal field theory
  • functorial quantum field theory
  • algebraic quantum field theory

And then, where the qualifiers ‘rational’ and ‘non-rational’ can be added.

Posted by: David Corfield on May 21, 2009 9:58 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

John Baez wrote:

I don’t see yet how the beautiful mathematics of n-categorical field theory will make progress on tough problems [in theoretical physics].

Urs replied:

Sure it’s not clear. Just as once upon a time it was not clear

- what differential geometry has to add to Maxwell theory;

- what group and representation theory has to add to Quantum Mechanics; - what symplectic geometry has to add to Hamiltonian mechanics;

- etc.

In each case the point was and is that some structure just happens to be the right natural language for some phenomenon. At first this is always just a reformulation of what is known, usually of less than what is known. But without it, all further progress is blocked.

I hope everyone knows that I agree with Urs here. I’m basically betting my career that he’s right! This is why I quit focusing on quantum gravity and switched to full-time work on mathematical infrastructure like nn-categories, higher gauge theory, categorified symplectic geometry, groupoidification and so forth.

It’s not clear how any of this infrastructure will solve the tough problems of fundamental physics. I keep wishing it were clear. But, I think it’s the best strategy for making progress at this time — at least for me, that is.

Posted by: John Baez on May 22, 2009 4:00 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

`As a crassly self-interested scientist, I’m mainly interested… ‘

Heh. As someone who’s known John Baez for over 20 years, I don’t buy this.


Posted by: Minhyong Kim on May 22, 2009 1:55 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

What I personally perceive as intriguing is a potential change in the scientific method. The reason is that astrophysical observations steadily gain importance, say in particle physics, and naturally in cosmology. However, we only have one universe to observe, and e.g. inferring the topology of the universe from missing fluctuations does not produce hypotheses that can be tested at will on an arbitrarily large ensemble of universes… Does anyone else perceive this change in the scientific method? Is it related to the discussion about the landscape and the anthropic principle (I’m too ignorant to tell)?

Posted by: Tobias Fritz on May 20, 2009 9:42 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

I doubt it’s a change in the “scientific method” as much as it is that we are more and more doing what Feynman predicted in The Character of Physical Law (1965): physics, or parts of it, are becoming a “historical science” like archaeology or palaeontology.

Posted by: Blake Stacey on May 20, 2009 5:56 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Philosophy can definitely help physics, especially in the areas where one reaches the boundary of the domain of science, like the question of the theory of everything or the question of the nature of reality which is compatible with quantum mechanics. Somebody here said that we need a philosopher who would know math and physics like Leibniz in his time, and this is true, since when I as a physicist try to read some of the philosophy of physics papers written by philosophers, I am quickly turned off by a strange jargon and esoteric topics. The next best thing would be a physicist who is ready to address the interesting philosophical questions. There are very few such people, and a couple of years ago, Max Tegmark, a cosmologist from MIT, published a paper “The Mathematical Universe” in Foundation of Physics, arXiv:0704.0646, where he tried to answer some of the deep questions about the nature of ultimate reality, from a physicist perspective. This paper was so inspirational for me that I wrote a paper “Temporal Platonic Metaphysics”, arXiv:0903.1800, which generalizes the ideas of Tegmark. In a nutshell, Tegmark’s idea, he calls it a hypothesis, is that the reality is the same as the ultimate mathematical structure which describes it. This idea is philosophically a sort of extreme platonism, and it immediately resolves various puzzles and paradoxes one encounters when trying to formulate a theory of everything, like the problem of initial conditions or the meaning of the landscape of vacua in string theory. However, the part which I find unsatisfactory, is the explanation of the passage of time, which according to Tegmark is an emergent feature, and I disagree. For me, the time is the fundamental feature, and the difference between a mathematical theory and the corresponding universe is that the universe is this theory immersed in time.

Posted by: Aleksandar Mikovic on May 20, 2009 6:53 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Aleksandar,

What is the precise definition of the expression “emergent feature” as used by physicists?

Posted by: Richard on May 21, 2009 3:29 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

As far as I know, the sense of “emergent feature” used by physicist is that it is a feature of a complex system which arises from the elementary constituents and their interactions, but it is not known exactly how this happens. In other words, an emergent feature is a property of your system which you believe that can be derived from the postulates of the theory that describes the system and this is because the explicit derivation is too complex or not known. An example is a turbulence in a moving fluid.

Posted by: Aleksandar Mikovic on May 21, 2009 10:26 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

The physicists I know who talk about “emergent properties” use the term to refer to aspects of a phenomenon due to interacting components, even when the origin of the “emergent properties” are understood. Temperature and pressure would be considered emergent properties of a gas, for example; the proton mass would be an emergent feature of the dynamics of quarks and gluons. An “emergent property”, as I hear the phrase being used, is a property of a macrostate which is useful in making empirical predictions. Typically, the connotation is that one doesn’t have to know all the details of the microstate, only the coarse-grained variables which specify the macrostate (to make predictions about a traffic jam, we don’t have to know the odometer reading of every car involved).

Posted by: Blake Stacey on May 21, 2009 6:36 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Hmmm … perhaps a related word is “artifact”?

Posted by: Richard on May 22, 2009 3:43 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

for some alternate views of the philosophy of science more generally, see

www.fermentmagazine.org/philsci.html

I would be interested in any reactions

jim

Posted by: jim stasheff on May 23, 2009 6:43 PM | Permalink | Reply to this

Keats and Wordsworth; and Re: Where is the Philosophy of Physics?

“Philosophy will clip an Angel’s wings,
Conquer all mysteries by rule and line,
Empty the haunted air, and gnomed mine -
Unweave a rainbow….”
John Keats, Lamia

This seems to be a natural transformation of:

“Sweet is the lore which Nature brings;

Our meddling intellect

Mis-shapes the beauteous forms of things:–

We murder to dissect.

Enough of Science and of Art…”

William Wordsworth, AN EVENING SCENE ON THE SAME SUBJECT, 1798

Posted by: Jonathan Vos Post on May 23, 2009 10:32 PM | Permalink | Reply to this

Emily Dickinson; Re: Keats and Wordsworth; and Re: Where is the Philosophy of Physics?

The rainbow never tells me

That gust and storm are by,

Yet is she more convincing

Than Philosophy.

– Emily Dickinson - The rainbow never tells me

Posted by: Jonathan Vos Post on May 23, 2009 11:14 PM | Permalink | Reply to this

Time is on My Side (Rolling Stones); Re: Where is the Philosophy of Physics?

I’m trying to read the following, in the context of the question of whether Time is continuum of discretum:

Topological Paradoxes of Time Measurement

Lisker, Roy (2001) Topological Paradoxes of Time Measurement.

Abstract

This paper applies the ideas presented in “Time, Euclidean Geometry and Relativity” ID 1290 , to a specific problem in temporal measurement. It is shown that, under very natural assumptions, that if there is a minimum time interval T in ones collection of clocks, it is impossible to measure an interval of time 1/2T save by the accidental construction of a clock which pulses in that interval. This situation is contrasted to that for length, in which either the Euclidean Algorithm or a ruler and compass construction can be used to construct a leng[t]h 1/2L from a length Lo

Posted by: Jonathan Vos Post on May 24, 2009 12:01 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

13 interpretations? There are hundreds of variations on the basics. There’s a pervasive sense that something is wrong, which plays out in an enormous number of new ideas, many of which obviously fail some test or another. Different individuals and groups focus on different ideas of what are important themes and principles. It’s foolhardy at this point in time to declare too definitely that one particular approach is definitely the way to go. Of course one has to believe something to have the courage to try to approach what is a very hard problem, but humility about one’s own approach is most probably wise.

Some principles that other people think absolutely central, I think peripheral, and vice versa. Outright cranks of course think Physicists are almost totally wrong about almost everything, but pontifications about what is and is not in the canon are sometimes as ludicrous as a crank’s ideas. Our choices of course define our research. Personally, I had to do some wildly cranky work on Quaternions to realize how ridiculous one’s claims might look to other people, and that a little humility about one’s current obsession might be wise. The Wild Things are out there, some of which will be tamed over time.

Getting papers published on relatively peripheral ideas is challenging, but there is enough commitment in the community that it happens, and out of somewhere we can hope for an epiphany. The focus on category theory (on the n-Category Café? ridiculous!) seems to me too abstract, but the nice thing about category theory is that if someone constructs a relatively concrete empirically successful model, we can have fun categorifying it. It’s a win-win, whether a category theorist does the heavy lifting or someone else does. As I say, Category theory seems too abstract to me, but there’s enough interest to follow its abstract progress. Anyway, I follow anything that Klaas Landsman does with interest, and John Baez, … .

One principle that I cherish is that to make progress in reconceptualizing Physics at this point in time needs a sophisticated eye on Philosophy of Physics. The methodology of Physics has been turned upside down by the post-positivist critique, which has been absorbed into the Physics community in slightly absurd, twisted ways, enough so that ideas like Falsifiability are strongly modified from their mid-twentieth Century status (though the rampant Platonism in some quarters rather belies my claim that Mathematical Physics has understood the post-positivist critique at all).

Theory-ladenness, incommensurability, underdetermination, the pessimistic meta-induction, the trade off between formalism and pragmatism, and a healthy self-criticism are a minimum for anyone who seriously wants to do groundbreaking research. I think understanding both the Philosophy of Physics and the ways in which the ideas have been taken up by Physicists is essential to get any potent new idea published (a peer reviewer has to understand at least partially why I think my new approach might be interesting to someone other than me).

Sorry this is so long. Anyone ever noticed that about Philosophy of Physics papers?

Posted by: Peter Morgan on May 20, 2009 10:26 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

There’s a range of rather different activity which gets called ‘philosophy of science’ from probing for tensions and incompletenesses in specific contemporary theories, to reflecting generally on theory-world relations, e.g., underdetermination and realism.

I’m surprised to hear that “the post-positivist critique…has been absorbed into the Physics community”, even if “in slightly absurd, twisted ways”. Perhaps this reflects that physics has reached a further stage beyond that observed by Alasdair MacIntyre (Tasks of Philosophy, p. 10)

Instrumentalism, like attempts to refute skepticism, is characteristically a sign of a tradition in crisis.

If something remains reasonably constant through the centuries it’s human nature, so some thought on how our virtues should best be deployed and our vices best curbed to organise a creative research community may have better shelf life.

Posted by: David Corfield on May 21, 2009 3:38 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

”(…)from probing for tensions and incompletenesses in specific contemporary theories, to reflecting generally on theory-world relations, e.g., underdetermination and realism.”

Are there specific/well-defined techniques/criteria available for the practising physicist in order to test for those concepts in his/her research? A guide for physicists…

Thanks,
Christine

Posted by: Christine Dantas on May 21, 2009 4:11 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Unfortunately no rule book will help here.

I suppose what philosophy teaches you is to treat language very carefully. This might make your more likely to pick up on awkwardnesses that are being smoothed over. But then again this is a fairly common intellectual ability, and domain knowledge is indispensable, so it’s more likely, e.g., that a string theorist locates the gap between claimed and actual achievement in the case of the AdS/CFT correspondence.

On the other hand, if you have both the critical faculty and you immerse yourself in a subject, then you may be able to come up something like the philosopher Laurence Sklar’s treatment of statistical mechanics in Physics and Chance.

Perhaps it’s no bad thing to have people who aren’t paid to produce the standard kind of result in a field to pose a few questions to it.

Réné Thom said something apposite:

Je voudrais dire mon étonnement que la collectivité scientifique ne possède pas en son sein des critiques, à la manière des critiques littéraires ou artistiques. Sans doute les barrières à la publication (la “peer review”) jouent-elles – partiellement – ce rôle. Mais dès qu’un groupe – un “paradigme Kuhnien” – a conquis sociologiquement une position dominante, ces barrières tendent à perdre leur pouvoir de discrimination; bénignes pour les tenants du paradigmes, féroces pour les étrangers. Je suis convaincu qu’il y aurait, dans l’appréciation globale de la production scientifique, place pour un type d’esprit indépendant, non exempt de préjugés, mais soucieux en tout premier lieu de rigueur intellectuelle. Si la philosophie n’avait pas divorcé d’avec la science depuis longtemps, on aurait dû trouver chez les philosophes des sciences, les épistemologues, des individualités capables de tenir ce rôles. (‘Vertus et Dangers de l’Interdisciplinarité’: 636-643).

Posted by: David Corfield on May 21, 2009 5:24 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Thanks for the reference to Laurence Sklar’s book and Réné Thom’s quotation.

Surely, not something to find in a rule book, but a lifetime study and refinement of one’s intellectual capacity.

In order to improve my reading of philosophical texts, I have recently studied this book:

Méthodologie philosophique (Portuguese edition; I’m not certain there exists an English translation…) by Dominique Folscheid and Jean-Jacques Wunenburger

That book is aimed at students of philosophy; I’m just an enthusiast. I thought that was an excellent book. It presents some techniques for reading, interpreting and writting philosophical texts. So I was thinking along that line: some similar book aimed specifically towards the philosophy of science, specially for scientists, in order to help them improve their intellectual rigor concerning their research activities from a philosophically-oriented approach.

Christine

Posted by: Christine Dantas on May 21, 2009 6:53 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

Such a book is a great idea! I read some of Sartre’s Being and Nothingness when I was in high school, and it was a little rough going because I did not know the precise definitions of many technical words. I had to guess and constantly refine my guesses as I proceeded through the text. That was an excellent intellectual exercise, but it would have been preferable to have a quick guide to terminology.

Posted by: Richard on May 22, 2009 3:51 AM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

David, you’re surely right that it’s only in a limited way that the Physics community has absorbed the post-positivist critique.

What I think physical scientists are generally conscious of is that post-modernist Po-Mo has somehow taken hold in some of society, and physical scientists generally think such an attitude is bunk, beneath contempt, ludicrous, incomprehensible, etc. The part of society that takes Po-Mo seriously is just stupid. I think, however, that Physicists’ general failure to engage with the critique of modernism was the cause of the SSC calamity, for example, now almost 20 years ago, which I would say was decided by non-scientists who had been educated in the immediate context of Kuhn, Feyerabend, and the rest, and who held the purse strings.

I take it that post-positivism is dangerous ground for scientific methodology, because it is fundamentally a critique, it is rarely a constructive approach. That fact, however, does not lessen the force of the critique. Nor does saying that it doesn’t do anything for us help much. Structural realism is one attempt to accommodate the post-positivist critique, but it falls quite a way short, to my mind. I somewhat prefer a model-building approach, which I think of loosely as an attempt to make Nancy Cartwright constructive, but it seems a somewhat immature and slow-moving literature, and what I have seen pays too little attention to the algebraic-empiricist approach that QM was founded on.

I think the general Physicists’ response to the situation is to carry on with modernist business as usual even while acknowledging that “there are problems, but it’s just not constructive to think about them”. Let people who want to waste their time on abstractions do it somewhere else, while we get on with productively building mathematics or apparatus that may have no meaning, but it is a deliverable.

If someone who has spent 20 years of their life producing almost no deliverables and worrying at pointless abstractions should come up with a new constructive idea that people suddenly notice might be a useful new mousetrap, the goal-oriented crowd will use it, but there’s probably no use wishing that those people otherwise will take the plunge into Philosophy.

If you’re selling Physics, to admit that the product is built on sand would undermine the brand, but that doesn’t mean that you don’t have internal doubts. The desire to deny that a threat to your livelihood is significant is strong and reaches into the subconscious. The true R&D people of course will go there, and make a mess most of the time in the hope that they’ll think of something spectacular just one time.

Now I’m sounding crank-y instead of philosopher-y, which is both a subtle and not-so-subtle difference, but I’m not going to spend the time editing a blog comment to perfection. Thank you for introducing the topic in a way that I have found productive to explore.

I like your MacIntyre quote, even though the quote itself is somewhat glib.

Your final comment, recommending “…thought on how our virtues should best be deployed and our vices best curbed to organise a creative research community…”, reaches some way into the subconscious motivations that I allude to above. It is awesome to see the shifts of passions in the community over decades in ways that are rarely articulated well, but which move mountains while we wonder what to call them.

Posted by: Peter Morgan on May 22, 2009 5:26 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

It is true that physics finds itself in a bit of a mess. I think an interesting research program will be to compare the various problems faced in string theory, twistor theory, category theory, etc. I’m somewhat embarking on that myself.
I think messy areas are good, because the definitions are available, and lots of interesting problems can be solved. Looking for a messy area in physics, I think is the key to success.
The ambitions of a 22 year old!

Posted by: Peadar Coyle on May 23, 2009 1:28 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

I work in data analysis, pattern recognition, forecasting in complex domains of biomedicine and healthcare - and in these domains there are dual problems:

1. HETEROGENEITY of input patterns (objects?) - think of the difference between drawing colored balls out of urns - where colors in textbooks are limited to 2 or 3, versus drawing human iris patterns in biometrics, where it’s not clear what aspects of the patterns you need for successful pattern recognition task.

2. CO-HETEROGENEITY of data analysis pathways. In other words, starting with a given dataset (eg, excel spreadsheet / schema) there is no unique algorithm to follow but rather a combinatorial explosion. Further, quantitative validation of the accuracy of a pattern recognition task (eg, classification, clustering, forecasting) is a /distinct/ algorithm which again is not unique.

I say the problems are dual because if the patterns are simple, then simple algorithms suffice and there is no problem. But in complex domains (eg, biomedicine, healthcare, econometrics, finance) you’re typically looking at hard
inverse problems.

Under limited quantitative evidence there are many “predictions” that fit the data (and validation is yet another sort of “prediction” about the underlying algorithm)

There is lacking a philosophy of physics to deal with heterogeneity in complex systems, for example, what’s the intrinsic geometry if you’re just given data?

To give a typical example, if you switch from L2-norm (least squares) to L1-norm (“robust” or quantile-based) framework already breaks symmetry in that the algorithms tend to be unrelated (in L2, optimization is obtained by setting derivatives equal to 0 and solving for kernel, whereas in L1 you’re usually solving a linear program.

look at the difference between Singular Value Decomposition versus Robust SVD - they’re totally different approaches)

Mathematics cannot tell you which to choose: L1 or L2? - if you say “choose the more accurate one” it depends on how important outliers are and in the presence of noise you have the same problem when validating the algorithm (ie, must fix such criteria).

Therefore is it not a /philosophy of physics/ issue?

When algorithms to carry out pattern recognition are implemented as pages and pages of Mathematica code (a functional language, thus related to category theory), you can begin to see the problem: there is a combinatorial explosion of potential analysis pathways that don’t necessarily yield the same answers. (Mathematica’s built-in Quantile[ ] function has 6 options to choose from!)

Another issue is that many data analysis operations are projective. For example, standard nonparametric measures for classification is based on (Shannon) mutual information between random variables. That measure is just a scalar, not injective. You cannot recover the input histogram/distribution for example (Shannon’s communication theory is not topological in nature, nor semantic)


To summarize, the more noisy and heterogeneous the application domain and input datasets (patterns of stock market crashes, unemployment time series, gene-expression datasets, clinical outcome measurements), the more highly co-heterogeneous are the computational methods brought to bear.

My question is, can’t category theory be applied to organize these “cones” and to help search for limits and to characterize the adjoints to see what structure is lost in projective stages?


most important statistical ideas as well as those in many other fields are centered in vague concepts
their expression in precise terms is always to be tested against their vague expression with any discrepancy to be resolved by redefining the precise version

j tukey / “spectrum analysis in the presence of noise”

Posted by: Alan Calvitti on May 27, 2009 3:06 PM | Permalink | Reply to this

Re: Where is the Philosophy of Stats?

anyone seen

THE SEARCH FOR CERTAINTY
On the Clash of Science and Philosophy of Probability
by Krzysztof Burdzy (University of Washington, USA)

Your Price (Hardcover): US$55 / �45 US$41.25 / �33.75

This volume represents a radical departure from the current philosophical duopoly in the area of foundations of probability, that is, the frequency and subjective theories. One of the main new ideas is a set of scientific laws of probability. The new laws are simple, intuitive and, last but not least, they agree well with the contents of current textbooks on probability. Another major new claim is that the “frequency statistics” has nothing in common with the “frequency philosophy of probability,” contrary to popular belief. Similarly, contrary to the general perception, the “Bayesian statistics” shares nothing in common with the “subjective philosophy of probability.”

The book is non-partisan on the scientific side – it is supportive of both frequency statistics and Bayesian statistics. On the other hand, it contains well-documented and thoroughly-explained criticisms of the frequency and subjective philosophies of probability. Short reviews of other philosophical theories of probability and basic mathematical methods of probability and statistics are incorporated. The book includes substantial chapters on decision theory and teaching probability, and it is easily accessible to the general audience.

Contents:

* Main Philosophies of Probability
* The Science of Probability
* Decision Making
* The Frequency Philosophy of Probability
* Classical Statistics
* The Subjective Philosophy of Probability
* Bayesian Statistics
* Teaching Probability
* Abuse of Language
* What is Science?
* What is Philosophy?
* Concluding Remarks
* Mathematical Methods of Probability and Statistics
* Literature Review

Posted by: jim stasheff on June 2, 2009 7:43 PM | Permalink | Reply to this

Re: Where is the Philosophy of Stats?

THE SEARCH FOR CERTAINTY

No I haven't seen it, but it looks interesting! I hope that somebody (maybe me, but probably only if I find it in a library) looks at it and tells us about it. (I assume from the capital letters, jim, that you didn't write that review.)

Posted by: Toby Bartels on June 2, 2009 11:23 PM | Permalink | Reply to this

Re: Where is the Philosophy of Stats?

Indeed, it’s the publisher’s ad

Posted by: jim stasheff on June 3, 2009 2:22 PM | Permalink | Reply to this

Re: Where is the Philosophy of Physics?

I’d forgotten about the philosophy of physics going on in the blog discussions connected to John’s Quantization and Cohomology course. There was even talk of temperature living on a Riemann sphere.

Posted by: David Corfield on June 4, 2009 11:21 AM | Permalink | Reply to this

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