Korolev on Norton’s Dome

This paper by Alexandre Korolev arguing that Norton’s Dome isn’t a kosher case of indeterminism in Newtonian physics appeared on my RSS reader recently. I was very curious about Korolev’s paper, but found it to be a letdown. In fact, Norton addresses most of Korolev’s objections in his 2006 update to the manuscript.

After some lengthy and (in my opinion) somewhat unnecessary refinements of the original thought experiment, Korolev gets to one of his main points, that the Dome fails to satisfy something called a Lipschitz condition. The significance of this is that failure to satisfy the Lipschitz condition violates the time reversibility of trajectories. It doesn’t strictly imply time irreversibility for any given trajectory; only that time irreversible solutions to the equations of motion exist. Korolev seems to think that because the Lipschitz condition allows for time-irreversible solutions, the Lipschitz condition must be an ‘implicit assumption within Newtonian mechanics’. Since Norton’s Dome violates the Lipschitz condition, it isn’t (by Korolev’s reasoning) really a Newtonian system, and hence it has ‘no serious metaphysical import’.

Korolev’s second main line of objection is that the Dome example works only if the dome is infinitely rigid, i.e. it’s shape is completely unchanged by the point mass. When I talked about the Dome to some physics undergrads I had the same complaint about idealizations — no real dome, made of molecules, can be perfectly rigid, etc. And there’s also quantum mechanics, which implies the point mass cannot be exactly poised at the top of the Dome. Well, we can ignore quantum mechanics because indeterminism simply isn’t an interesting find for a quantum mechanical system; we already know quantum mechanics is indeterministic. Norton deals with the point about the rigid idealization well (and Korolev doesn’t address it, even though his paper seems to have been published later than Norton’s update). There is no internal principle of Newtonian mechanics that would lead us to rule out such an idealization. Furthermore, it is acknowledged that we are talking about an idealized model and not a real system. (Otherwise, why even bother with Newtonian systems? Let’s go straight to quantum.) So it seems the only way we can think that this idealization is impermissible is by already having some external reason for not wanting to allow idealizations that violate time irreversibility and/or determinism. But then that would no longer be a reason to think that the Dome is not a Newtonian system, for nothing internal to Newtonian mechanics prohibits it.

I think Korolev’s first objection (that the failure to satisfy the Lipschitz condition allows for time irreversible trajectories) can be dealt with the same way — by seeing that his objection arises from an external demand put on Newtonian mechanics. If it so happens that Newton’s Laws allow time irreversible trajectories, then why should we declare such trajectories un-Newtonian, as opposed to simply accepting that there exist very special conditions under which Newtonian mechanics can be time irreversible? (Norton covers more ground in his 2006 update — pondering if we should add a ‘4th Law’ to Newton’s Laws in order to save Newtonian determinism from the Dome. I largely agree with his reasons for concluding that the Dome is a legit Newtonian system.)

Keep in mind that Norton originally intended the Dome to have the following ‘metaphysical import’:

Even quite simple Newtonian systems can harbor uncaused events and ones for which the theory cannot even supply probabilities. Because of such systems, ordinary Newtonian mechanics cannot license a principle or law of causality.

He just needed a simple Newtonian system. No extra assumptions of time reversibility or correspondence with real world systems. Seems to me the Dome can have the metaphysical import it was originally intended to have.

Korolev, A. (2007). Indeterminism, Asymptotic Reasoning, and Time Irreversibility in Classical Physics. Philosophy of Science, 74(5), 943-956. DOI: 10.1086/525635

Norton, John D. (2006). The Dome: An Unexpectedly Simple Failure of Determinism. In [2006] Philosophy of Science Assoc. 20th Biennial Mtg (Vancouver): PSA 2006 Symposia.

Norton, J. (2003). Causation as folk science. Philosopher’s Imprint 3 (4), 1-22.

Ubuntu + Philosophy Wallpapers

David Lewis, Roderick Chisholm, and Alvin Goldman.

I don’t like faces on my desktop, or I would have used the Lewis one.

Experimental Philosophy Survey

Just helping to spread the word. Do your bit for experimental philosophy, if you have 15 minutes to spare.

Neutralizing the Reg

I’m not much of an architecture enthusiast, but the drawings for the new U of C library make me drool:

Organizing Yudkowsky’s Intro to QM

OK, there have been so many posts in Eliezer Yudowsky’s introduction to quantum mechanics for the layman that if I don’t visit Overcoming Bias for a few days, I lose track. And there isn’t an easy way to keep track of them over there. So I’m posting them all in order here. I’ll update when new ones come up. I might also attempt to organise them into a tree-like structure, since not every post is a prerequisite for the posts after it.

Quantum Explanations: Why he decided to write the series.
Configurations and Amplitude: A warm-up with mirrors and detectors.
Joint Configurations: More mirrors and detectors.
Distinct Configurations: Why QM leads people to say crazy things about the consciousness and the universe.
Where Philosophy Meets Science: Why scientists doing foundational work can’t avoid philosophizing.
Can You Prove Two Particles Are Identical?
Classical Configuration Spaces: No quantum in this. Background preparation for the next post.
The Quantum Arena: How it differs from the Classical Arena. Hint: Consciousness is not involved.
Feynman Paths
No Individual Particles
Identity Isn’t In Specific Atoms
Three Dialogues on Identity
Decoherence
The So-Called Heisenberg Uncertainty Principle
Which Basis Is More Fundamental?
Where Physics Meets Experience: Easing us into Many-Worlds with a fable.
Where Experience Confuses Physicists
Quantum Orthodoxy: Robin Hanson interjects with some comments on MWI.
On Being Decoherent: Why we can see a particle in one place at one time.
The Conscious Sorites Paradox: “When” decoherence happens.
Decoherence is Pointless: More on the continuity of decoherence.
Decoherent Essences: Why we shouldn’t ‘interpret’ the formalism.
The Born Probabilities: Problems with them.
Decoherence as Projection: Fun with polarizers.
Entangled Photons: Alice and Bob.
Bell’s Theorem: No EPR “Reality”: I really, really like this explanation of Bell’s Theorem.
Spooky Action at a Distance: The No-Communication Theorem
Decoherence is Simple: Why MWI does not violate Occam’s Razor.
Decoherence is Falsifiable and Testable: I think there are serious philosophical problems with this post and the next.
Quantum Non-Realism: Against it.
Collapse Postulates: “WHAT DOES THE GOD-DAMNED COLLAPSE POSTULATE HAVE TO DO FOR PHYSICISTS TO REJECT IT? KILL A GOD-DAMNED PUPPY?”
If Many-Worlds Had Come First: An alternate history of QM.
Many Worlds, One Best Guess
The Failures of Eld Science: Why MWI did not come first.
The Dilemma: Science or Bayes?
Science Doesn’t Trust Your Rationality: MWI and libertarianism. In response to Scott Aaronson.
When Science Can’t Help: More Bayes than QM in this.
Science Isn’t Strict Enough: Huge dose of Whig history of science in this.
Do Scientists Already Know This Stuff?: We’ve moved from QM into some rather flaky philosophy of science now.

Foldit

Now you can play a game to help scientists fold proteins. When I first saw this being linked I was sceptical that players were really folding proteins — I suspected that the game was just Rosetta@home with a small game tacked on that had nothing to do with the actual protein folding but would keep the computer user occupied while the Rosetta@home ran.

And it seems that Foldit players aren’t helping to fold proteins in the direct sense either:

Can humans really help computers fold proteins?

We’re collecting data to find out if humans’ pattern-recognition and puzzle-solving abilities make them more efficient than existing computer programs at pattern-folding tasks. If this turns out to be true, we can then teach human strategies to computers and fold proteins faster than ever!

So they intend to collect data from the game to help them spot heuristics humans use that can then be implemented in computer programs. They aren’t going to take the results of human protein folding as the ‘correct’ structures.

Ignoring the Environment

A few chapters later and I’m still not impressed with Material Beings. I am especially unconvinced by van Inwagen’s argument, in the chapter “Artifacts”, for why organisms are objects but the aggregations of particles that appear to us as houses and galaxies are not. He is driven to concede that like organisms, some apparently persisting objects (like houses and galaxies and machines) might have ‘homeodynamic’ characteristics akin to those of living things. The obvious move, for those who want houses and galaxies in their ontology, is to exploit this similarity and say that lives and houses and galaxies and machines exist. (Recall from my previous post that the thesis of the book is that the only non-simple objects that exist are lives.) Van Inwagen had earlier argued that apparent objects like houses have organism-like homeodynamic characteristics in virtue of their having a “history of maintenance” by intelligent beings. I don’t find this persuasive because it seems to me that galaxies, for example, appear to be persisting objects despite not having a history of maintenance by intelligent beings. But never mind. My main target is his objection to the possibly reply of his critics that there exists an object y composed by simples {x_i} iff the activity of the x_is constitutes a life or the x_is are the current objects of a history of maintenance. This definition would allow his critics to assert that tables, chairs, houses, etc. exist. But van Inwagen objects that this definition “goes against all [his] deepest instincts. The question whether certain things constitute a life is a question about the relations they bear to one another and about nothing else.“

The sentence I bolded I find particularly astonishing, and not in a good way. It’s astonishing because I can’t fathom why anyone would have such an instinct. Surely what constitutes a life depends on the ‘fit’ between the aggregate of simples in question and the environment. That is, certain aggregates of simples may form a life in this universe, on this particular planet, but may simply be a collection of lifeless particles in different (most, in fact) environmental conditions. And doubtless there are many aggregates of simples for which there exists possible environments that they can be lives in, but which are not lives on this planet in this universe. How could anyone consider it a deep instinct to ignore the influence of the environment in this matter? Isn’t it obvious that whether an aggregate of particles is alive is a function of at least two variables — the aggregate of particles, and the environment surrounding that aggregate? And isn’t it particularly odd for a someone who leans towards a functionalist definition of life to ignore environmental factors? After all, without the environment, what could the aggregate of particles interact with; in what could it [appear to] play a role?

An obvious reply by van Inwagen would be that in an inhospitable environment, a cat (say) would be dead, and when it is dead, its parts bear different relations to one another compared to when it’s alive. For example, its heart muscles no longer move relative to its chest cavity, etc. All right then. But the route is open for his critics who think houses exist to have an internal “homeodynamic” account of why an evolving galaxy, say, is a persisting object. Then the scoreline would be equal again — we would have no more reason to consider lives more privileged than artifacts on the ontological front. And while it may be implausible that one could define a persisting galaxy solely in terms of its internal relations, surely it’s no more implausible than defining a live cat solely in terms of its internal relations. Frankly, it doesn’t seem likely to me that either van Inwagen or the critics I imagine here could come up with such accounts. It seems far more plausible to me that it is simply not true that whether an aggregate of particles composes a life is a question about the internal relations of that aggregate. Here’s a quick and dirty argument for that last statement. I think any functionalist definition of life (of the kind van Inwagen seems to be expecting the biologists to provide) would have to include some requirement of material or energetic exchanges of a certain nature between the organism and its environment. After all, we do not know of any organism that does not rely on such exchanges for its sustenance. And, if we want to do the whole intuition-pump thing, it is difficult to think of an entity that is completely isolated from the rest of the universe as a life. Even if it doesn’t need to renew its parts like us carbon-based Earthlings do, surely some sort of exchange of information, in the form of photons or whatever, is essential to its nature as a living thing. Such exchanges can’t occur with just any environment. They certainly can’t occur in a matter-less, energy-less void. So the definition of an organism would put restrictions on the external relations between an organism and its environment. Ergo, it can’t just be a function of the internal relations between parts of the organism.

Another reply I imagined van Inwagen giving is that an aggregate of simples is a life iff there exists a possible environment in which it fulfills the functional role of an organism. But, as I mentioned earlier, there are probably many aggregates in our world that we would be reluctant to call lives, but which are lives in some possible environment. Allowing for alternative environments would seem to qualify too many things as lives.

So, I still don’t see what’s so special about lives, other than the grammar we use in talking about them, that would imply that they exist and tables and chairs don’t. Van Inwagen wants to avoid answering the question of what a life is, and I was prepared to grant him that liberty until he started making assertions that would probably contradict the kind of definition of life that he was gesturing towards. It seems to me that the stark contrasts he insists exist between lifeforms and non-lifeforms are apparent contrasts stemming from our language, while the real contrasts, if they exist, remain out of his reach because he has shied away from giving an explicit definition of life. And why should I care that we have one grammar for lives and another for non-lives? Why should I think that this difference in grammar points to a difference in ontology? Show me the difference first, then we’ll talk.

Intuitions about life

I’m finding Peter van Inwagen’s Material Beings annoying so far. It annoys me because it evinces an unhealthy respect for common intuitions, sometimes to the extent of declaring conflicts of said intuitions with facts to be philosophical problems. I tend to be only too ready to jettison the intuitions in such cases, but some philosophers go on to derive some outrageous conclusion or other by way of solving the apparent problem.

I don’t intend to attack van Inwagen’s argument for his outrageous conclusion that “there are no tables or chairs or any other visible objects except living organisms”. I’m only 1/3 through the book so the argument hasn’t been fully laid out yet. But the book got on my nerves early on with some heavy intuition-reliance on several probably minor issues. And I’m blogging this now because I’ve just read a particularly irritating passage that relies on some rather naive biology. Again, this reliance might turn out to be incidental to his main argument; I don’t know. But it’s certainly not incidental in the context of van Inwagen’s methodology in this book.

The offending passage comes in the context of van Inwagen’s explanation of how ‘lives’, the spatial-temporal processes that are biological organisms, are fundamentally different from non-living events:

…there is an interesting and important feature of lives that is not shared by waves. Consider two waves… which are moving in opposite directions and which pass through each other. A still photograph taken at the moment the waves coincide spatially will show what seems to be one wave whose amplitude is the sum of the amplitudes of the two coincident waves. I think we must say… that both the waves exist at the moment of superposition and that each is at that moment constituted by the activities of the same water molecules. We may describe this possibility — the possibility of two waves’ being simultaneously constituted by the activities of the same objects — by saying that a wave is not a jealous event. Lives, however, are jealous. It cannot be that the activities of the xs constitute at one and the same time two lives. Lives are, in fact, so jealous that only in certain special cases can two lives overlap… The only clear case, in fact, is the case in which one of the lives is subordinate to the other, as the life of one of my cells is subordinate to my life. (…the only possible case… I think, would be the case in which the activity of the ys constitutes the life of a cell and the activity of the xs constitutes the life of a multicellular organism. I doubt whether there could possibly be xs and ys such that the activity of the xs constitutes a life, the ys are properly among the xs, and the activity of the ys constitutes the life of, say, a hamster.)

Here’s an example of non-jealous lives that is not a case of small units of life being ’subordinate’ to a larger unit: the bacteria in human guts. I claim that they are not subordinate, because although they are useful to humans, they are also ‘free’ to serve their own [reproductive] interests; it is arguable that they are not really ‘our’ cells — they don’t share their host’s genetic material, for one. It would be surprising if, among the microorganisms in our gut, there aren’t any that are mere free-riders who don’t add to our [evolutionary] fitness. Yet, I claim, that the processes constituting these bacteria are part of the overall process constituting a human life. Given that the bacteria outnumber cells containing human DNA in a given human body, and given the importance of the bacteria to normal human digestive functions, it does not seem appropriate to exclude these bacteria from the overall process of a human life. (If you need one, and even more spectacular example of dependence on bacteria is that of the Siboglinid tube worms, which are completely dependent on bacteria for their nutrition.) To put it in van Inwagen’s vocabulary, if we let ys = gut bacteria, then it seems like his ‘hamster’ example has been found, except we have bacteria instead of a hamster. Isn’t it correct to say, in some sense, that “the activities of commensal gut bacteria constitute at one and the same time the lives of humans and bacteria”?

There is nothing to stop the indignant metaphysician from just insisting that the objects constituting the life of a human are the tiny minority of cells that contain human DNA, and everything else is other lives. But I would gently suggest that the biologically messy notion of a “life”, at least going by van Inwagen’s choice of functional individuation, may not be the best starting point from which to build a complex metaphysical thesis. Is there perhaps a better way that he could have defined a “life”? Well, there isn’t one that’s obvious to me. If he chooses to define it my similarity of genetic material, he runs into the problem of having to say that a pair of genetically identical twins constitutes the “same life”.

I did not mention the long, elaborate analogy he had used to sketch his functional definition of life. This right after saying that “it is the business of biology to answer this question [of what a life is]“. I just don’t see the analogy as enlightening everything. It seems instead to expose the weaknesses of his reliance on an assumed clear notion of what a life is.

Another strike against van Inwagen’s claim that a life is a “reasonably well-individuated event” comes from an example that he uses to demonstrate what are not reasonably well-individuated events. The example is that of a flame that spreads into several spatially separated fires. These, he claims, are not well-individuated. But it’s difficult to see how, if we consider only their level of individualization, a kind of unicellular organism that reproduces by simple binary division could be said to have members that are any better individuated. Since the binary division requirement implies that the ‘event’ that begins with the very first cell of this kind of organism is spatially and temporally continuous with all the descendants of that cell, what’s stopping us from calling saying that every cell thus reproduced is a part of a larger mega-organism? How are the individual cells any better individuated than the flame which splits into seven flames?

Now, maybe that is a clear biological definition of a life to be had after all. But on current knowledge, I wouldn’t base my entire metaphysical project on anything as uncertain as the individual nature of lives. I suspect there is significant potential of us altering our ontological terms as we learn more biology, so our current usage of the word “life” need not necessarily reflect any fundamental fact about actual lives, if such even exist.

Brought to you by Nostalgia

The worry that I might be mistakenly wanting to go to grad school because of nostalgia for college has crossed my mind, but I’ve never taken it seriously. Like Miss Self-Important, I’ve always assumed that the bits of college I liked the most are heavily featured in grad school. As Jacob Levy puts it:

Neither, however, is the warning generically for Chicago undergrads. If you find yourself nostalgic for your Chicago undergrad experience (particularly, say, midterms-through-finals of winter quarter when it feels like your work stretches out forever into both the past and the future) you’re probably doomed to grad school.

For some reason, my most memorable courses were almost all in winter quarter. So I was generally pumped up, work-wise, in winter. I think most of my best work was done during that midterms-through-finals period. And at that stage a one week break at the end of it all sounds heavenly. The real ‘oh shit’ period for me was generally at the end of spring break, when I would realise that one week of rest is simply not enough and there’s eleven more weeks of what just hit me to come. Now I’m not nostalgic for that feeling. But it only lasted for a short while, as the first week of the quarter would quickly descend, with the attendant adrenaline rush from the prospect of novelty.*

In college I used to be pathetically easily distracted from exhaustion. In my current situation, it’s a perpetual struggle to bar exhaustion from my conscious thoughts. This despite sleeping about twice as much as I did in college.

*It’s quite likely that I’ve written this paragraph, nay, the whole blog post, out of pure nostalgia.

A Different Introduction to Quantum Mechanics

Eliezer Yudkowsky is putting up a series of posts introducing quantum mechanics in a clear, intuitive, and (needless to say) non-conventional way. Despite already having a long list of quantum thingies to read, I decided to read it because he prefaces the series with a criticism of the conventional tactic of discussing the classical wave/particle duality — a criticism the best physics teacher I’ve ever had shares. I agree with them that that pseudo-classical approach is one of the main reasons why students don’t understand quantum mechanics even after significant instruction.