The purpose of physics graduate classes

I’m taking a graduate statistical mechanics course this semester. My first physics course in more than two years, and my first graduate physics course.

One reason I started disliking physics courses when I was an undergraduate was that class time was spent almost entirely on going through the details of the derivations in the textbook. If there’s anything guaranteed to send me to sleep, especially if it’s a 9.30am class, it’s someone at the board moving symbols here and there and reciting the arithmetical rules he’s using to move those symbols. Furthermore, the vast majority of derivations are mathematically straightforward and can be understood from a close reading of the textbook. I don’t need someone to go through what I can glean from reading the textbook on my own.

For whatever reason, I thought that graduate classes in physics would be better. Well, this one isn’t. The professor is going through nearly every single line in Pathria’s text. What’s more, he actually tells us to read the textbook beforehand because he doesn’t want us to be looking at the textbook figuring out the math while he’s “teaching”. But if I read the textbook beforehand (which I do), I understand the derivation, so I get bored when he comes to class and goes through the exact same derivation, except more slowly and in more painful detail. So far I’ve always ended up working on my problem sets during class instead, which I find a much more productive use of my time.

One point that Eriz Mazur makes in this excellent talk on science education is that in a humanities class, it’s standard to expect students to do the assigned reading. The class then proceeds with the assumption that students have done the reading. The instructor does not hold your hand and lead you through every line of the reading. It is also understood that if you don’t do the readings, it pointless to go to class because the class is going to assume you’ve at least grappled with them, and start off on that higher level.

The opposite happens in science classes. In the vast majority of physics classes I had, even if the professor recommends that you read certain parts of the textbook or lecture notes, s/he still leads you by the hand through the very material that you’ve just read. You could not read any of it and still get the contents of what you were supposed to have read through the lecture alone. (The one class I had that did not follow this mould, which was also my favourite class in any subject ever, was taught by someone who would receive negative feedback from most students about his more Socratic teaching style. People complained that he did not follow a textbook, but for me, it is exactly when someone follows a textbook that his lectures fail to add value.) The learning style encouraged by such teaching seems to be passive rather than active, compared to humanities classes.

All this may be excusable as a sop to undergraduates who are either too stupid or lazy to read textbooks on their own, but firstly, the same undergraduates are not treated as such by their humanities instructors, and secondly, why is this still going on in graduate classes? Why do graduate students have to be hand-held through a textbook? If you can’t read a textbook like Pathria on your own, should you even be in a physics PhD programme?

A useful contrast is with my philosophy graduate seminars. There, as with undergraduate humanities classes, you’re expected to do the readings before class. Discussions in class proceed on the assumption that you have done your readings. Students are typically asked to present some of the readings, and the presentations will have some sort of summary of the contents of the readings, but it’s nothing to the extent of the presenter going through step by step of the arguments in the readings, the way physics teachers go through the textbook derivations step by step. And of course, there is much discussion of the readings.

I discussed this with someone before, and the response was that in science, there is typically a definite “right answer” to questions, whereas in the humanities, most of the important answers are still unknown. The implication is that if there is a “right answer”, then this should be told to the students. In contrast, if the right answer is not known, then discussion might somehow bring one closer to it.

I suspect many people think of science education this way, and I think they’re deeply mistaken. The objective of science education as I see it is not to tell people the right answers. The objective is understanding. People may know the right answers without understanding why they are right. In physics, the analogue would be if a student could do all the problems set by her instructor by the simple expedient of applying certain formulaic rules, but does not understand why those rules hold. This was my situation for most of my physics classes, and was a huge contributor to why I became frustrated with physics. Of course, I did go to my professors outside of class to try to get a deeper understanding, but most of the time they could not answer my “conceptual” questions. They seemed to be prepared only to tell students how to apply certain rules, without being able to justify those rules themselves.

The peer discussions that Mazur and an increasing number of people who study science education are advocating go some way to helping students get to the answer on their own and, on the way, gaining a deeper understanding of why the answer is what it is. It makes science education more like humanities education.

Pushing the idea further, I see no reason why a graduate class in physics cannot be run like a graduate class in philosophy. Have the students read the relevant section of the textbook beforehand. This should be just as obligatory as doing the readings for humanities classes is. In class, ask if anyone has had any problems understanding the assigned readings. If someone has, try to straighten her out. Do not go through every step of the proofs in class, since it could (and should) well be the case that most students understand the proofs already. Class time should be used instead to discuss interesting implications of the proofs, setting the context for them, considering the assumptions they use and what implications those assumptions have, and so on. In fact, I also see no reason why the model of having students present on the assigned readings cannot be applied. Do physics professors have such low expectations of their students that they think they cannot learn on their own and have to be spoonfed just like undergraduates? Or is it I who has overly high expectations of physics graduate students?

Reductivism, simulations and materiality

One of Jerry Fodor’s arguments against reductivism in his 1974 paper is that bridge laws reducing, say, economics to physics are undermined by the possibility of simulations of economic systems that instantiate the same economic ‘laws’ but have a very different physical basis from economic systems that are composed of interacting humans. It’s difficult to imagine what bridge laws would carry out the reduction successfully for both the simulated economy and the real human economy.

Someone in class pointed out that this would seem to be more of a problem for economics than for something like chemistry. After all, it seems like the physical basis for chemical systems has to be electrons, protons, and so on — the ontology of quantum mechanics, the science to which it allegedly reduces. What other physical basis could there be?

But then there are such things as simulations of chemical systems. If we take these to be parallel to the case with simulated economic systems, then bridge laws relating chemistry to quantum mechanics would have to cover not only the cases where the physical properties are instantiated in an actual physical system, but also those where they aren’t actually instantiated but represented in a computer simulation.

I take it that it would be an unacceptable move to say that the laws of chemistry don’t apply to simulated chemical systems, and in any case it’s difficult to see why one should be allowed to say that and not allowed to say that the laws of economics don’t apply to economic systems that aren’t composed of humans.

The only other way at present I can think of to get out of this bind is to say we should somehow regard the chemical simulation as instantiating the physical properties it represents. But the awkwardness in that phrase (what does it matter how we regard it — it either instantiates them or it doesn’t, regardless of our regard) suggests that I can’t find a way to make this sound like a good move. And in any case we run into the same problem: why should we do this for the chemistry case but not for the economics case?

Still, I have this intuition that somehow chemistry is essentially about actual atoms and molecules, while economics is more removed from the material nature of the systems it is applied to. But I can’t think of a way to justify it.

Taking baby physics too seriously

I don’t know if this objection to the Dowe/Salmon causal processes account of causation has been raised in the literature. It’s on hindsight fairly obvious, so I would be surprised if it hasn’t.

The notion of a causal interaction is crucial to the causal processes view. In Dowe’s account, a causal interaction is an intersection of two world-lines of causal processes that involve an exchange of a conserved quantity (e.g. energy-momentum).

Part of the motivation of requiring the exchange of a conserved quantity is that that is a requirement that seems to rule out pseudo-processes and that seems to be grounded in physics. But Salmon’s and Dowe’s writings on causal processes are littered with baby physics examples like a ball hitting a window and billiard balls colliding. And it wasn’t until yet another class on causal processes this morning that it struck me that in none of those examples of collisions is there an intersection of world-lines of objects. If you want to talk about particles, none of the world-lines of the constituents of the balls intersect: the ‘collision’ is simply a matter of the electrostatic forces between those constituents preventing them from getting too close! This seems obvious, but somehow the use of such homely examples hoodwinked me until I’d had to sit through a summary of the causal processes framework for the fourth or fifth time in the last 8 weeks.

Relaxing the requirement to “approximate” intersections (i.e. close approaches) doesn’t work either. It’d merely open a larger can of worms about what the threshold for when a near approach should be considered an “intersection”. You would need to consider scattering cross-sections and so on, which obviously differ depending on the forces and particles involved.

Seems to me that if you really want to talk about intersections of world-lines, then you need to use the field-theoretic conception of physics. But that brings along a whole other suite of problems like how to individuate objects and processes on that conception, and how, if you call a set of points on a manifold a ‘process’, that may be said to ‘possess’ a ‘conserved quantity’.

A metric over possible worlds?

In order to ground counterfactuals (among other things), David Lewis proposed a notion of distance between possible worlds. The natural thing to do would be to suppose that this distance function, like most of our distance functions, satisfies the metric axioms.

It’s easy to see why the distance function should satisfy non-negativity, symmetry, and identity of indiscernibles. But is there any reason it should satisfy the triangle inequality?

It’s useful here to unpack what exactly the triangle inequality says. Stated formally, given any three points a, b and c in a metric space with metric d, it says that . One notable thing about this is that it puts constraints on the distance between any two points (a and c), constraints that depend on the distances between those two points and an arbitrary third point. In a sense, the distance between two points is not completely independent of those points’ distances from other points. (I’m tempted to use the term ‘extrinsic’ here, but it’s a troublesome enough term in philosophy that I think I should avoid it. I mean roughly what Philip Bricker means when he uses it in a similar context, though.)

The triangle inequality is thought to apply in physical space because of our implicit path-based notions of distance. That is, a general definition of distance that can apply to both Euclidean and non-Euclidean spaces is that of the infinum of the lengths of all possible curves that go from one point to another. This definition is clearly dependent on points other than the two the distance relation applies to: if I want to find the distance between a and c, I have to consider the lengths of all the possible curves that have them as endpoints, and these are going to depend on what other points besides a and c exist in the space I’m considering.

The result of this path-based notion of distance is that if points a and b are quite close to one another and points b and c are also quite close to one another, then points a and c can’t be that far apart — because we have at the very least a possible short path from a to c: that which goes from a to b, then from b to c.

Thus, when we consider whether the triangle inequality applies to distances between Lewisian possible worlds, we should ask ourselves the following:

1. Must it be true that if World 1 is close to World 2, and World 2 to World 3, that World 1 must also be fairly close to World 3?
2. Do we expect the distances between two worlds to be constrained by the existence of other worlds? That is, does the distance between World 1 and World 2 depend partly on the distances between World 1 and other possible worlds, and World 2 and other possible worlds?

If it’s bizarre that I’m even considering distance functions that don’t obey the triangle inequality, consider that it is well known in psychology that perceived similarity between certain types of stimuli do not. In these cases, violations of the triangle inequality tend to occur when the dimensions on which the stimuli differ are what Tversky and Gati (in the linked paper) call ’separable’. Intuitively, separability is the weakness of the dependence between changes in a stimulus’ value in one dimension and changes in its value in other dimensions. The less dependent they are, the more separable the nature of the stimuli, and the greater the violation of the triangle inequality. (That’s my quick and dirty explanation of the Tversky/Gati paper, but I recommend reading the whole thing — it’s fascinating.) For possible worlds, among the dimensions we would want to consider are spatiotemporal similarity and violation of laws of nature (these have been listed by Lewis as contributing to the distance function). Now, it’s clear that the two are not independent, but the question is whether they are dependent enough such that possible worlds are separable in Tversky and Gati’s sense.

Running

From the end of Thomas Bernhard’s Woodcutters:

I should have stayed in London at all costs, I told myself, and I kept on running in the direction of the Inner City, without knowing why, and I told myself that London had always brought me happiness and Vienna unhappiness, and I went on running, running, running, as though now, in the eighties, I was once more running away from the fifties, running into the eighties, the dangerous, benighted, mindless eighties, and again it struck me that instead of going to this tasteless artistic dinner I ought to have read my Gogol or my Pascal or my Montaigne, and as I ran it seemed to me that I was running away from the Auersberger nightmare, and with ever greater energy I ran away from the Auersberger nightmare and toward the Inner City, and as I ran I reflected that the city through which I was running, dreadful though I had always felt it to be and still felt it to be, was still the best city there was, that Vienna, which I found detestable and had always found detestable, was suddenly once again the best city in the world, my own city, my beloved Vienna, and that these people, whom I had always hated and still hated and would go on hating, were still the best people in the world: I hated them, yet found it somehow touching — I cursed these people, yet could not help loving them — I hated Vienna yet could not help loving it.

Diversity in experimental particle physics

Slobodan Perovic just gave a talk on a project he’s working on: the reason behind the alleged crisis in fundamental physics. His general strategy is to compare the situation in particle physics with that of quantum mechanics in its early stages, and draw lessons from that. One of the problems he diagnoses in experimental particle physics, which he claims did not exist for quantum mechanics, is a lack of diversity in experimental apparatus. The idea is that using less diverse experimental apparatus decreases the chances of new discoveries, as it drastically narrows the space of possible discoveries. A more diverse array of apparatus would be able to cover more of the search space.

Now, I have serious doubts about whether there is any lack of progress in experimental particle physics to be explained, but even supposing there is, I’m rather skeptical that a lack of diversity in the apparatus is responsible for it. To the extent that there is a lack of methodological diversity in experimental particle physics, I do not think it is due to uniformity in apparatus.

A preliminary consideration supporting that last statement is the following. We can agree that condensed matter physics is in an extremely healthy state, and has been for the last 50 years. But I’m not sure that they have any more diversity in their experimental apparatus than particle physicists do. It is more common in condensed matter physics to order entire machines from a vendor, whereas particle physicists tend to have to build their own machines. And there just aren’t that many different vendors offering STEMs or whatever.

I think that the following factors do much more to reduce methodological diversity in experimental particle physics:

1. Recycling of personnel across different labs. With the Tevatron winding down, physicists who used to work there will go (or have gone) to either Wall Street or the LHC. This leads to a certain homogenizing of methods even across different experiments. This happens to a much smaller extent in condensed matter physics, since budding researchers are expected to start their own lab rather than join another established collaboration.
2. Institutional factors like the Particle Data Group’s publications. Their Review of Particle Physics is often referred to as the ‘Bible’ by particle physicists. Every particle physicist has a copy on his/her bookshelf. The Review lays out, among other things, data analysis methods that are ’standard’ for the field. To my knowledge, there is no such equivalent publication in condensed matter.
3. Compared to condensed matter labs, the institutional setup for particle physics collaborations is less amenable to the introduction of new methods. Publications under the collaboration’s authorship have to be approved not just by one’s immediate supervisor, but by a hierarchy of scientists within the collaboration, before they are given the collaboration’s collective blessing and allowed to be made public. Now, if one wants to publish something about a new general strategy for statistical analysis, something not specific to the particular setup of one’s experiment, independent publication would probably be OK. So the barriers don’t exist for some kinds of methodological innovation. But if one wants to use a new method that is specific to the conditions of one’s experiment, that, I think, will have to go through the administrative hierarchy for approval. In condensed matter, there are fewer layers of approval to go through.

Detexify

A symbol recognition program allowing one to look up the syntax for LaTeX symbols by drawing them. After some experimentation I’ve concluded that it doesn’t work all that well yet (or perhaps I draw really badly). But it has some sort of machine learning algorithm built in so that users can teach the program which is the ‘right’ symbol for their drawing. A great idea — I always hated poring through those symbol tables.

TTYtter

After I started using Tweetie as my Twitter client on my Macbook, I began hankering for a Twitter client for my desktop at work that could thread conversations like Tweetie did (together with other more common functionalities like tracking hashtags, direct messaging, search, retweeting, URL shortening, and many others). But most of the feature-rich Twitter clients that are compatible with Linux seemed to be based on Adobe AIR, which is quite a chore to install on 64-bit Linux. After some painstaking reading through feature lists, I found TTYtter, which runs from the command line and had all the features I wanted. Lightweight with simple commands without (unlike other command line scripts like BLT) sacrificing functionality.

Explanation and Statistical Mechanics

Found a draft paper/chapter/talk of David Albert’s somewhere on the internet, titled Physics and Chance (PDF). The main purpose of the paper is to argue that the probability distribution that “we have from Boltzmann and Gibbs, or something like it,” is true. And he wants to argue that it is true and not just a useful instrument for the purpose of predicting the values of particular parameters.

Albert uses David Lewis’ account of laws of nature to argue for the truth of the probability distribution. The Lewisian view is that the laws of nature are those true statements about the world that have the best combination of simplicity and informativeness. Albert argues that not only does Boltzmannian statistical mechanics satisfy this requirement, but also that the laws of the special sciences are not laws of nature. He thinks the only laws of nature are the fundamental laws of physics that give us the microdynamics of systems, plus Boltzmannian statistical mechanics, plus the Past Hypothesis. (I will lump Boltzmannian and Gibbsian statistical mechanics together for now, as Albert does.)

Albert first makes a case for the necessity of statistical mechanics when we want to predict which macrostates follow from which macrostates. This makes a prima facie case for statistical mechanics being an informative addition to the fundamental microdynamical laws. But this sort of informativeness, one based on macrostates, and specifically on macrostates that are amenable to human observation (we don’t know yet that stat mech would work for other types of macrostates, if they exist), seems thoroughly instrumental. (Perhaps informativeness itself is an inherently instrumental property — I’ll leave that as an open question.) So, if this type of informativeness, informativeness about macrostates, is the main support for statistical mechanics being part of the laws of nature, it’s not clear how Albert establishes the truth rather than the instrumental value of statistical mechanics.

My objection aside, Albert anticipates that objections to his view will arise from those who see laws in the special sciences as being explanatory independent of the laws of physics. He examines Philip Kitcher’s argument that Arbuthnot’s regularity, which was a constant preponderance of births of males over females in London, is explained not by microphysical principles but by R. A. Fisher’s argument from parental expenditure. Kitcher writes that the microphysical account “would not show that Arbuthnot’s regularity was anything more than a gigantic coincidence”. Albert pounces on the word “coincidence” and says that that’s where statistical mechanics has to come in. He says that it is only by reference to the statistical mechanical probability distribution that Kitcher’s talk of “coincidence” makes any sense.

On its face, this claim is utterly batty. After all, Arbuthnot did not consult the SM probability distribution before regarding it as a coincidence. He thought it was a coincidence from the point of view of a model that assumed sex determination worked like a “two-sided die”. Whether he was justified in using that model is beside the point. What’s important is that Arbuthnot, and the myriad other researchers in the special sciences who tried to explain away regularities, did not determine the coincidental character of those regularities by doing statistical mechanical calculations.

Albert admits this. He admits that we don’t explicitly consult statistical mechanics to decide if certain large-scale regularities we observe are coincidental. His only reply is that our lack of consultation isn’t any evidence against the existence of the SM probability distribution. Fine. But surely the burden of proof is on Albert here, to show how the distribution is relevant to the special sciences when the special sciences evidently carry on working, with reasonable success, without (usually) referring to statistical mechanics.

To be fair, Albert does have some sort of positive account of how it may be that the SM probability distribution grounds our identification of coincidences in the special sciences. He claims that if he were right that the laws of nature are just the microphysical laws and statistical mechanics, then some foggy, unconscious acquaintance with that probability distribution would have been hard-wired into organisms by natural selection.

This is highly implausible to me. Natural selection favours (among other things) characteristics instrumental to the survival of the organism. And as far as day-to-day survival is concerned, it seems far more useful, and far easier from a neural architecture point of view, to hard-wire the regularities of the special sciences directly into the brain, instead of hard-wiring some vague acquaintance with SM and expecting the brain to propagate those probabilities all the way up to make predictions about complex systems. It is also probably easier to simply hard-wire an ability to learn large-scale regularities.

In any case, the more problematic issue is that Albert’s attempt at a positive argument for the relevance of SM probabilities to special science explanations is made by asking us to assume first that he is right about the completeness of microphysics + stat mech. But that’s exactly what people like Kitcher are questioning when they bring up the independence of the laws of the special sciences.

The folk reductionism gets worse. Albert argues that his proposed package of the complete laws of nature explains macroscale happenings like the descent of man and Arbuthnot’s regularity, because if you started with his pet Past Hypothesis, with the uniform probability distribution over the microstates compatible with that, and propagated the probabilities forward in time according to classical statistical mechanics, you’d find that the descent of man and Arbuthnot’s regularity come out as highly probable events:

it is precisely because the account of the descent of man by random mutation and natural selection involves vastly fewer and more minor and less improbable such coincidences than any of the imaginable others that it strikes us as the best and most plausible explanation of that descent we have.

(I’ve left out Albert’s trademark emphases to avoid annoying readers.)

There are similar claims like this throughout the paper. At other points he claims that statistical mechanics also explains why large objects in our world do not spontaneously disintegrate into statuettes of the British royal family, because if we take the Past Hypothesis plus initial uniform probability distribution blah blah, we will find that the probability of large objects disintegrating thus is very low.

My problem with those claims is that there is no evidence whatsoever that if you indeed take the Past Hypothesis, put a uniform probability distribution on the initial states of the universe compatible with that, and evolve that thing forward in time, you’d really find that the descent of man, the longevity of macroscopic objects, etc. come out as highly probable events. Albert is asking us to accept these claims on faith, since we can’t make any serious attempt at those calculations. But if one is sceptical about the truth of traditional statistical mechanics in the first place, then one is hardly going to accept on faith the claim that it will indeed give the probabilities Albert wants for those macroscopic events.

So Albert’s attempt to subsume the special sciences to statistical mechanics is extremely weak. The implicit request for us to put our faith in SM is a more general problem that recurs throughout the paper. As mentioned earlier, Albert argues that we need stat mech to make the correct macroscopic predictions; to get correlations of the macroscopic properties of one event with those of a later event. In this way, stat mech is more informative than microdynamics alone, and thus should be considered a Lewisian law of nature. But part of his way of showing that we need stat mech to make the correct macroscopic predictions is to say that without stat mech, we would have no reason not to predict that any given stone won’t spontaneously distintegrate into statuettes of some royal family. Merely to get things right about the ordinary rigid objects of Newtonian physics, of the “projectiles and levers and pulleys and tops”, he says, we need SM, because otherwise how can we assume that these rigid objects can even remain intact while we apply Newtonian mechanics to them?

But the thing is, the medium-term integrity of pulleys and levers would hardly seem like something that has to be explained away except in the light of statistical mechanics. If someone hasn’t already accepted the whole spiel about how intact pulleys are “improbable” because the phase space of microstates of disintegrated pulleys is so much larger than that of non-disintegrated pulleys, why should he take the intactness of large-scale objects to be something that begs to be explained away? The explanatory need that SM is supposed to fulfill wouldn’t even exist unless you already accept [that version of] SM. Again, Albert doesn’t provide an argument that would engage someone who is skeptical of the predictive accuracy of a statistical mechanics that involves starting with the Past Hypothesis, putting a uniform over the microstates of the universe consistent with that, and so on.

Finally, I just don’t see how Fisher’s principle regarding sex ratios, and other principles of the special sciences, would not also qualify as laws of nature. Why would one regard the Past Hypothesis + microdynamics + statistical mechanics as more informative than microdynamics + principles of special sciences? Sure, there are many, many such principles, so one sacrifices simplicity, but one also gains a lot in informativeness. For there is no evidence whatsoever that Albert’s proposal for the laws of nature is more informative than the “dappled” proposal with its myriad special science “laws”. If anything, the latter has been shown to be informative, while we can never determine if the former is informative, due to computational difficulties freely admitted by Albert. And isn’t it also rather implausible that some probability distribution on the initial state of the universe in fact explains why, say, zebras have stripes?

Intrinsic duplicates and their conscious lives

This is a tangential thought from way back, that I’d been procrastinating on converting from scrawl to proper prose. (It’s still untidy, but I’ve figured that if I’m going to post it only when it’s been tidied, then it’ll never be posted.) It concerns an argument in Brian Weatherson’s ‘Are Humeans Out of Their Minds?‘. Weatherson is mainly responding to an argument by John Hawthorne about whether causation is extrinsic. My concern, though, is not with his main response, but with his argument against one of Hawthorne’s claims, a secondary issue in the paper.

Hawthorne’s claim is:

An intrinsic duplicate of any region wholly containing me will contain a being with my conscious life.

Seems plausible enough. But Weatherson argues that the following example of what he calls totality qualia undermines the intuitive case for Hawthorne’s claim:

Tweedledee is facing a perfectly symmetrical scene. His visual field is symmetric, with two gentle mountains rising to his left and his right and a symmetric plain in between them. All he can hear are two birds singing in perfect harmony, one behind his left ear and one behind his right ear. The smells of the field seem to envelope him rather than coming from any particular direction. There is a cool breeze blowing directly on his face. It’s a rather pleasant scene, and the overwhelming feeling is one of symmetry.

Tweedledum is very much like Tweedledee. Indeed, Tweedledum contains a duplicate of Tweedledee as a proper part. But Tweedledum also has some sensors in his skin, and brain cells in what corresponds to a suspiciously empty part of Tweedledee’s brain, that allow him to detect, and feel, where the magnetic fields are in the vicinity. And sadly, though Tweedledum is facing a duplicate of the scene facing Tweedledee, there is a major disturbance in the magnetic field just to Tweedledum’s left. This produces a jarring sensation in Tweedledum’s left side. As a consequence, Tweedledum does not share Tweedledee’s feeling of symmetry.

Whether a picture is symmetric is a property of its internal features, but it is also a feature that can be destroyed without changing the internal features by just adding more material to one side. It is a totality property of pictures, a property the picture has because it stops just where it does. Similarly, totality qualia are qualia that we have in part because we don’t have any more feelings than we actually do. Feelings of symmetry are totality qualia in this sense, as are many of the feelings of calm and peacefulness associated with Tweedledee’s state. It is not intuitive that totality qualia should be intrinsic to a region. Indeed, it seems intuitive that a duplicate of me that was extended to produce more sensory features would lack these feelings. Hence a duplicate of me would not share my conscious life in all respects, so Hawthorne’s [claim] is also false.

Note that that final sentence quoted contains an invalid inference. Hawthorne’s claim is that a region that is a duplicate of a region containing you would contain at least one being that has your conscious life. It’s quite possible that it also contains beings that do not share your conscious life. So the mere fact that a duplicate of you would not share your conscious life under some conditions does not undermine Hawthorne’s claim.

In other words, we shouldn’t be talking about the conscious lives of duplicates of you, specifically. We should be talking about duplicates of regions containing you, and the conscious lives that these duplicated regions contain. In the final paragraph quoted, Weatherson seems to be arguing against the claim that any duplicate of me will itself share my conscious life in all respects. But this is different from the claim that any duplicate of a region containing me will contain a being that shares my conscious life.

Once we see that Hawthorne’s claim deals with duplicating regions and not just the being itself, we can see that totality qualia don’t have the implications Weatherson thinks they do. Because if we are duplicating a region that contains the being minus the region containing the sensors that cause totality qualia, then the duplicate itself is also going to be a region containing the being but not the relevant sensors, and hence the being in that region would have the same totality qualia as its duplicate. If, on the other hand, we are duplicating a region that contains the being and the region containing the symmetry-upsetting sensors, then the duplicate will also contain the being and the sensors. Once again the conscious life of the being is duplicated.

Put another way, in order to check Hawthorne’s claim, it doesn’t do, as Weatherson does, to have one region containing the being but without the sensors, and then duplicate just the being-without-sensors, and put this duplicate into a region containing sensors. The larger region-with-sensors isn’t a duplicate of the first region, so it’s not relevant to Hawthorne’s claim. On the other hand, if we try to dodge this by taking the region to be duplicated to be just the being-without-sensors, then when we duplicate said region, all we’d get is a region containing a being-without-sensors. Which corroborates Hawthorne’s claim.

Suppose we take the latter course — our duplicated region is just the region that consists of the being-without-sensors, and nothing else (I think this is the duplication that Weatherson wants us to imagine, in his argument). Weatherson could then say that that region containing a being-without-sensors could be embedded in a world that has, in fact, sensors at the requisite locations. That world would then contain a being whose sensation of symmetry is upset.

That’s for the world in which the region-without-sensors is embedded. But for the purposes of evaluating Hawthorne’s claim, we want to know if the region-without-sensors contains a being with an upset sense of symmetry, since that’s the region being duplicated; not any larger region. If the region-without-sensors in this new world-with-sensors is indeed a duplicate of the original region-without-sensors, then it would seem that any effects on the being’s brain (and hence his conscious life — I’m assuming physicalism here, obviously) that are due to the sensors must be confined to regions in the world outside of the region-without-sensors. So while it would be accurate to say that that world contains a being with a sense of asymmetry, it’s not at all clear that we would say that the region-without-sensors contains a being with a sense of asymmetry. Does a region containing me, minus the region of space occupied by my left kidney, contain a person two kidneys, or a person with one kidney? If you pick the latter answer, then I don’t see why one should say that the region-without-sensors contains a being with an upset sense of symmetry. After all, all the “upset” is outside that region. And what if I ask if the region taken up by my right kidney contains a person with two kidneys? Does any region, even a point, that is a proper part of the region taken up by my entire body contain a person with two kidneys?

One might try to get around this by arguing that you can’t have two conscious beings in the same world such that one is a part of the other. Then you could say that there is only one conscious life that we can assign to any given region and its proper parts, and somehow argue towards discounting the conscious life that is unaffected by the sensors in favour of the conscious life that is affected by the sensors. However, even if we accept the principle of having only one conscious life assigned to a being and its proper parts, I see no reason to always decide in favour of the conscious life that incorporates “more sensors”.