And now for something somewhat different. After I posted my article on “Does the Universe Need God?“, there were a few responses at the Intelligent Design blog Uncommon Descent, including a list of questions by Vincent Torley. Vincent then went the extra mile by inviting me to write a guest post for UD. Not my usual stomping grounds, but I ultimately agreed, precisely for that reason.
Here’s the post, which I’m cross-posting below. This might be controversial, as a lot of people on my side of things will say that there’s little point in engaging with people on the other side. And admittedly, this is a subject where feelings can be pretty entrenched. But you never know — not everyone has their mind made up on every issue, and it’s good to try to explain yourself to unsympathetic audiences on occasion. That’s all I tried to do here — to explain how I think about these things, not necessarily to pick a fight or even persuade any skeptics. I tried pretty hard to be as clear and unpretentious as I can be. (Success is for you to decide.) In a world of shouting and diatribe, I remain optimistic that real communication can occasionally occur! We’ll see how it goes.
I wanted to thank Vincent Torley and Denyse O’Leary for the opportunity to write a guest blog post, and apologize for how long it’s taken me to do so. I’ve written an article for the forthcoming Blackwell Companion to Science and Christianity, entitled Does the Universe Need God?, in which I argued that the answer is “no.” Vincent posed a list of questions in response. After thinking about it, I decided that my answers would be more clear if I simply wrote a coherent argument, rather than addressing the questions individually.
My goal is to try to explain my own thinking to an audience that is not predisposed to agree. We can roughly break people up into two groups: naturalists such as myself, who think that the best explanation we have for the universe involves physical quantities obeying laws of Nature and nothing else; and those who believe that a better explanation can be found by invoking a powerful being/designer/creator/God. (For the sake of simplicity I’m going to use “God” to refer to this notion, but feel free to substitute the more accurate description of your choice.) Obviously there are many nuances that are being passed over by this simple distinction, but hopefully it will suffice for this moment.
The dispute between these two camps isn’t one where people often change their minds at the drop of an argument. Minds do change, in either direction — but typically after extended periods of reflection, not suddenly in response to a single killer blog post. So persuasion is not my goal here; only explanation. I’ve succeeded if an open-minded person who disagrees with me reads the post and still disagrees, but at least understands why I hold my positions. (After giving an earlier talk, one of the theologians in the audience told me that I had persuaded him — not that God didn’t exist, but that the argument from design wasn’t the way to get to Him. That sort of real-time response is more than one can generally hope for.)
What I want to do is to elaborate on some crucial aspects of how science is done that bear directly on the issues raised by my article and some of the responses to it that I’ve seen. In particular, I want to talk about simplicity, laws, openness, explanation, and clarity. This isn’t supposed to be a comprehensive treatise on the philosophy of science, nor is it especially rigorous, or anything really new — just some thoughts on issues relevant to this conversation.
I will be taking one thing for granted: that what we’re interested in doing here is science. There are many kinds of consideration that may lead people to theism or atheism that have nothing whatsoever to do with science; likewise, one may believe that there are ways of understanding the natural world that go beyond the methods of science. I have nothing to say about that right now; that’s a higher-level discussion. I’m just going to presume that we all agree that we’re trying to be the best scientists we can possibly be, and ask what that means.
With all that throat-clearing out of the way, here’s what I have to say about these five issues.
Fabio Gironi recently interviewed me at length for an issue of Speculations, a “Journal of Speculative Realism.” The subject was science and philosophy, which I’ve been known to opine about at some length. But here we’re talking great length indeed. The interview isn’t available separately, but you can download the pdf of the whole issue here (or buy it as a bound copy). My bit starts on page 313. (The rest of the issue is also worth checking out.)
I’m a big believer that academic disciplines should engage in messy interactions, not keep demurely separate from each other. But it’s a tricky business. Just because I’m (purportedly) an expert in one thing doesn’t make me an expert in everything else; on the other hand, it is possible that one area has something to offer another one. So I am in favor of dabbling, but with humility. It’s good for people to have thoughts and opinions about issues outside their immediate expertise, and to offer them in good faith, but it’s bad if they become convinced that experts in other areas are all idiots. So when you find yourself disagreeing with the consensus of expertise in some well-established field, it might very well be because of your superior insight and training, or maybe you’re just missing something. Hopefully in an exchange like this I have something to offer without making too many blunders that would make real experts cringe.
Here’s a sample of the interview.
SC: I would be extremely suspicious of any attempts to judge that the world must ‘necessarily’ be some way rather than any other. I can imagine different worlds—or at least I think I can—so I don’t believe that this is the only possible world. That would also go for any particular feature of the laws this world follows, including their stability. Maybe the laws are constant through time, maybe they are not. (Maybe time is a fundamental concept, maybe it isn’t). We don’t yet know, but it seems clear to me that these are empirical questions, not a priori ones. Because we want to understand the world in terms that are as simple as possible, the idea that the underlying laws are stable is an obvious first guess, but one that must then be tested against the data. Said in a slightly different language: any metaphysical considerations concerning what qualities the world should properly have can be taken seriously and incorporated into Bayesian priors for evaluating theories, but ultimately those theories are judged against experiment. We should listen to the world, not decide ahead of time what it must be.
David Hume, famous scolder of those who would derive “ought” from “is,” was born 300 years ago today. In point of fact Hume, while not enjoying the name recognition of Plato/Aristotle/Descartes/Kant, is certainly in the running for greatest philosopher of all time. He was a careful thinker, resistant to dogmatic answers, and a relatively sprightly writer as philosophers go. An empiricist who was as persuasive about the temptations of radical epistemological skepticism as anyone, but was still able to resist them. His tercentenary is well worth celebrating.
Dan Sperber, via Henry Farrell, suggests that we celebrate by posting quotes from Hume. When I first encountered him as a college freshman, it was in the context of a theology course where we were reading Dialogues Concerning Natural Religion. I was intrigued when our professor pointed out a passage that seemed to prefigure Darwin’s theory of natural selection, which wasn’t going to appear until 82 years later. My dog-eared copy seems to have gone missing, but I found the quote at The Rough Guide to Evolution.
“And this very consideration too, continued PHILO, which we have stumbled on in the course of the argument, suggests a new hypothesis of cosmogony, that is not absolutely absurd and improbable. Is there a system, an order, an economy of things, by which matter can preserve that perpetual agitation which seems essential to it, and yet maintain a constancy in the forms which it produces? There certainly is such an economy; for this is actually the case with the present world. The continual motion of matter, therefore, in less than infinite transpositions, must produce this economy or order; and by its very nature, that order, when once established, supports itself, for many ages, if not to eternity.
But wherever matter is so poised, arranged, and adjusted, as to continue in perpetual motion, and yet preserve a constancy in the forms, its situation must, of necessity, have all the same appearance of art and contrivance which we observe at present. All the parts of each form must have a relation to each other, and to the whole; and the whole itself must have a relation to the other parts of the universe; to the element in which the form subsists; to the materials with which it repairs its waste and decay; and to every other form which is hostile or friendly. A defect in any of these particulars destroys the form; and the matter of which it is composed is again set loose, and is thrown into irregular motions and fermentations, till it unite itself to some other regular form.”
To me now, it looks like something of a cross between Darwin — successful forms persevering among the chaos — and the Lucretius/Boltzmann scenario of the universe coming into existence through the random motion of atoms. (What makes Lucretius and Hume brilliant thinkers but Boltzmann and Darwin influential scientists is that the latter grappled closely with data, not just with ideas.)
The common thread among all these thinkers: trying to explain the origins of order in the absence of teleology. The fact that we can do that successfully in biology, and are hot on the trail in cosmology, is a milestone achievement in the history of human thought.
Richard Carrier (author of Sense and Goodness Without God) has a longish blog post up about moral ontology, well worth reading if you’re into that sort of thing. (Via Russell Blackford.) Carrier is a secular materialist, but a moral realist: he thinks there are such things as “moral facts” that are “true independent of your opinion or culture.”
Carrier goes to great lengths to explain that these moral facts are not simply “out there” in the same sense that the laws of physics arguably are, but rather that they express relationships between the desires of particular humans and external reality. (The useful analogy is: “bears are scary” is a true fact if you are talking about you or me, but not if you are talking about Superman.)
I don’t buy it. Not to be tiresome, but I have to keep insisting that you can’t squeeze blood from a turnip. You can’t use logic to derive moral commandments solely from facts about the world, even if those facts include human desires. Of course, you can derive moral commandments if you sneak in some moral premise; all I’m trying to say here is that we should be upfront about what those moral premises are, and not try to hide them underneath a pile of unobjectionable-sounding statements.
As a warm-up, here is an example of logic in action:
The first two statements are the premises, the last one is the conclusion. (Obviously there are logical forms other than syllogisms, but this is a good paradigmatic example.) Notice the crucial feature: all of the important terms in the conclusion (“Socrates,” “mortal”) actually appeared somewhere in the premises. That’s why you can’t derive “ought” from “is” — you can’t reach a conclusion containing the word “ought” if that word (or something equivalent) doesn’t appear in your premises.
This doesn’t stop people from trying. Carrier uses the following example (slightly, but not unfairly, paraphrased):
At the level of everyday practical reasoning, there’s nothing wrong with this. But if we’re trying to set up a careful foundation for moral philosophy, we should be honest and admit that the logic here is obviously incomplete. There is a missing premise, which should be spelled out explicitly:
Crucially, this is a different kind of premise than the other three in this argument; they are facts about the world that could in principle be tested experimentally, while this new one is not.
Someone might suggest that this is isn’t a premise at all, it’s simply the definition of “ought.” The problem there is that it isn’t true. You can’t claim that Wilt Chamberlain was the greatest basketball player of all time, and then defend your claim by defining “greatest basketball player of all time” to be Wilt Chamberlain. When it comes to changing your oil, you might get away with defining “ought” in this way, but when it comes to more contentious issues of moral obligation, you’re going to have to do better.
Alternatively, you’re free to say that this premise is just so obviously true that no reasonable person could possibly disagree. Perhaps so, and that’s an argument we could have. But it’s still a premise. And again, when we get to issues more contentious than keeping your engine going, it will be necessary to make those premises explicit if we want to have a productive conversation. Once our premises start distinguishing between the well-being of individuals and the well-being of groups, you will inevitably find that they begin to seem a bit less self-evident.
Observe the world all you like; you won’t get morality off the ground until you settle on some independent moral assumptions. (And don’t tell me that “science makes assumptions, too” — that’s obviously correct, but the point here is that morality requires assumptions in addition to the assumptions we need to get science off the ground.) We can have a productive conversation about what those assumptions should be once we all admit that they exist.
The ontological proof for the existence of God (really “proofs” or perhaps “arguments,” as there are various versions) has popped up in the blogs a few times recently: e.g. Ophelia Benson, Josh Rosenau, Jerry Coyne. You’ve probably heard this one; it was most famously formulated by Saint Anselm, and most famously trashed by Immanuel “Existence is not a predicate” Kant. A cartoon version of it would be something like
Now, this is a really cartoonish version of the argument — it’s not meant to be taken seriously. This kind of ontological proof is a favorite whipping-argument for atheists, just because it seems so prima facie silly. Just ask Jesus and Mo.
This kind of mockery is a little unfair (although only a little). What’s important to realize is that the ontological proof is perfectly logical — that is, the conclusions follow inevitably from the premises. It’s the premises that are a bit loopy.
It’s instructive and fun to see this in terms of formal logic, especially because the proof requires modal logic — an extension of standard logic that classifies propositions not only as “true” or “false,” but also as “necessarily true/false” and “possibly true/false.” That is, it’s a logic of hypotheticals.
So here is one formalization of the ontological argument, taken from a very nice exposition by Peter Suber. First we have to define some notation to deal with our modalities. We denote possibility and necessity via:
Just given these simple ideas, a few axioms, and a fondness for pushing around abstract symbols, we’re ready to go. Remember that “~” means “not,” a “v” means “or,” and the sideways U means “implies.” Take “p” to be the proposition “something perfect exists,” and we’re off: Read More
In our last discussion of morality and science, an interesting argument was raised in the comments (by rbd and then in more detail by Ben Finney), concerning an analogy between morality and health. Sam Harris has also brought it up. It’s worth responding to because it (1) sounds convincing at first glance, and (2) has exactly the same flaw that the morality-as-science argument has. That’s what a good analogy should do!
If I can paraphrase, the argument is something like this: “You say that morality isn’t part of science because you don’t know what a `unit of well-being’ is — it’s not something that could in principle be measured by doing an experiment. But one could just as easily say that you don’t know what a `unit of health’ is, and therefore medicine isn’t part of science. The lack of some simple measurable quantity is a simplistic attack against a sophisticated problem.”
This gets right to the point. Because, in fact, I don’t know what a “unit of health” is, which is why medicine is not — solely — part of science.
Let me explain what I mean. Obviously we use science all the time when it comes to medicine. Similarly, we should be very ready to use science when it comes to morality — it’s an indispensable part of the endeavor. But in both cases there is a crucial component that lies outside the realm of science.
Here’s how we do medicine, in a cartoonishly simplified version that is nevertheless good enough for our present purposes. First, we decide what we mean by “healthy.” Then, we use science to try to bring it about.
That first step is not science, no matter how much science might be involved in the definition. Various measurable quantities certainly belong to the realm of science — height, weight, pulse, blood pressure, lifespan, time in the 40-yard dash, etc. But what we decide to label “healthy” is irreducibly a human judgment, not an empirical measurable. Some people might think that extreme thinness is part of being healthy, while others might prefer a more robust physique. Some people might define health as the state that maximizes life expectancy, while others might put more emphasis on quality of life even at the expense of total years. It matters not a whit what people actually think, of course — even if everyone in the world agreed on what “healthy” meant, it would still be a judgment rather than an empirical measurement. If one contrarian person came up with a different definition, they wouldn’t be “right” or “wrong” in the conventional scientific sense. There is no experiment we could do to answer the question one way or another.
In the real world, we more or less agree on what constitutes health, so the non-empirical status of this choice isn’t treated as a crucially important philosophical problem. (At least, until you start reading the literature on disability studies, and you realize that what you thought was obvious maybe is not.) We agree on what health is, and we set out to achieve it, and that second part is very much science.
Morality is exactly the same way, although with somewhat less unanimity in the first step. We agree (or not) on what morality is, and once we do the process of achieving it is very much a scientific issue, in the broad-but-perfectly-valid definition of “science” as “an understanding of how the world works based on empirical data.” Once again, it doesn’t matter whether we agree or not, because that first step is a decision we human beings make, not something we measure out there in the world.
While both health and morality are human choices rather than empirically measurable quantities, they certainly aren’t random choices. Human beings aren’t blank slates; we have preferences. Most of us would prefer to live longer and be free of aches and pains; these preferences feed into how we choose to define “health.” Likewise for morality. But “we broadly agree on X” is not, and never will be, the same statement as “X is a scientific truth.” Understanding our preferences, turning vague impulses into precise statements, constructing logical frameworks based on them — that’s what the philosophy of medicine/morality is all about.
The case of morality is actually much more difficult than the case of health, because most interesting moral questions involve tradeoffs between the interests of different people, not only the state of one individual. So even if we could do experiments to establish a unique map between mental states and human well-being, we wouldn’t really be any closer to reducing morality to science. All very fun to think about, though.
Last year we talked a bit about Sam Harris’s attempts to ground morality on science:
See especially the third one there, where I try to be relatively careful about what I am saying. (Wouldn’t impress a philosopher by a long shot, but by scientist/blogger standards I was careful.) Upshot: concepts relevant to morality aren’t empirical ones, and can’t be tested by doing experiments. Morality depends on science (you can make moral mistakes if you don’t understand the real world), but it isn’t a subset of it. Science describes what happens, while morality passes judgments on what should and should not happen, which is simply different.
By now Harris’s book The Moral Landscape has appeared, so you can read for yourself his explanations in full. In a different world — one where I had access to a dozen or so clones of myself with fully updated mental states, willing to tackle all the projects my birth-body didn’t have time to fit in — I would read the book carefully and report back. This is not that world.
Happily, Russell Blackford has written a longish and very good review, in the Journal of Evolution and Technology. He also blogged about it, and Jerry Coyne blogged about Russell’s review. As far as I can tell, Russell and I basically agree on all the substantive points, and he’s more trained in philosophy than I am, so you’re actually doing a lot better than something one of my clones would have been able to provide. It’s an extremely generous review, always saying “I liked the book but…” where I would have said “Despite the flaws, there are some good aspects…” So you’ll find in the review plenty of lines like “Unfortunately, Harris sees it as necessary to defend a naïve metaethical position…”
Any lingering urge I may have had to jump into the debate again in a substantive way has been dissipated by Harris’s response to Blackford’s review, which appears in the form of a letter to Jerry Coyne reprinted on his blog. It seems that very little communication is taking place at this point. Coyne paraphrases Blackford as asking “How do we actually measure well being?; for that is what we must do to make moral judgments.” Seems reasonable enough to me, and echoes very closely my first point here. Harris’s response is:
This is simply not a problem for my thesis (recall my “answers in practice vs. answers in principle” argument). There is a difference between how we verify the truth of a proposition and what makes a proposition true. How many breaths did I take last Tuesday? I don’t know, and there is no way to find out. But there is a correct, numerical answer to this question (and you can bet the farm that it falls between 5 and 5 million).
This misses the point, to say the least. The problem of measuring well-being is not simply one of practice, it’s very much one of principle. I know what a breath is; I don’t know what a “unit of well-being is.” The point of these critiques is that there is no such thing as a unit of well-being that we can look inside the brain and measure. I’m pretty sure that’s a problem of principle. Of course, Russell and Jerry and I (and David Hume, and a large number of professional moral philosophers) may be wrong about this. The way to provide a counter-argument would be to say “Here is a precise and unambiguous definition of how to measure well-being, at least in principle.” That doesn’t seem to be forthcoming.
Latter Harris says this:
The case I make in the book is that morality entirely depends on the existence of conscious minds; minds are natural phenomena; and, therefore, moral truths exist (and can be determined by science in principle, if not always in practice).
Taken at face value, this implies that truths about the best TV shows or most delicious flavors of ice cream also exist. My opinion that The Wire is the best TV show of all time is a natural phenomenon — it reflects the state of certain neurons in my brain. That doesn’t imply, in any meaningful sense, that the state of my brain provides evidence that The Wire “really is” the best TV show of all time. Nor, more programmatically and importantly, does it provide unambiguous guidance concerning which new programs should be green-lit by studio executives. The real problem — how do you balance the interests of different people against each other? — is completely ignored.
At heart I think the problem is that Sam and some other atheists are really concerned about the idea that, without objective moral truths based on science, the field of morality becomes either the exclusive domain of religion, or simply collapses into nihilism. Happily for reality, that’s an extremely false dichotomy. Morality isn’t out there to be measured like some empirical property of the physical world, but that doesn’t mean it’s impossible to be moral or to speak about morality in a rational, thoughtful way. Pretending that morality is a subset of science is, in its own way, just as much an example of wishful thinking as pretending that morality is handed down by God. We have to face up to that temptation and accept the world as it is.
As a special behind-the-scenes tidbit for loyal blog readers, I will reveal here that The Pointless Universe was actually my second entry in the Edge World Question Center. My first, making the same point but using different words, was entitled “Dysteleological Physicalism.” To me, that kind of title is totally box office, and I’m happy to take credit for coining the phrase. (Expect T-shirts and bumper stickers soon.) But apparently not everyone agrees, and it was gently suggested that I come up with something less forbidding. Here is my original version.
The world consists of things, which obey rules. A simple idea, but not an obvious one, and it carries profound consequences.
Physicalism holds that all that really exists are physical things. Our notion of what constitutes a “physical thing” can change as our understanding of physics improves; these days our best conception of what really exists is a set of interacting quantum fields described by a wave function. What doesn’t exist, in this doctrine, is anything strictly outside the physical realm — no spirits, deities, or souls independent of bodies. It is often convenient to describe the world in other than purely physical terms, but that is a matter of practical usefulness rather than fundamental necessity.
Most modern scientists and philosophers are physicalists, but the idea is far from obvious, and it is not as widely accepted in the larger community as it could be. When someone dies, it seems apparent that something is *gone* — a spirit or soul that previously animated the body. The idea that a person is a complex chemical reaction, and that their consciousness emerges directly from the chemical interplay of the atoms of which they are made, can be a difficult one to accept. But it is the inescapable conclusion from everything science has learned about the world.
If the world is made of things, why do they act the way they do? A plausible answer to this question, elaborated by Aristotle and part of many people’s intuitive picture of how things work, is that these things want to be a certain way. they have a goal, or at least a natural state of being. Water wants to run downhill; fire wants to rise to the sky. Humans exist to be rational, or caring, or to glorify God; marriages are meant to be between a man and a woman.
This teleological, goal-driven, view of the world is reasonable on its face, but unsupported by science. When Avicenna and Galileo and others suggested that motion does not require a continuous impulse — that objects left to themselves simply keep moving without any outside help — they began the arduous process of undermining the teleological worldview. At a basic level, all any object ever does is obey rules — the laws of physics. These rules take a definite form: given the state of the object and its environment now, we can predict its state in the future. (Quantum mechanics introduces a stochastic component to the prediction, but the underlying idea remains the same.) The “reason” something happens is because it was the inevitable outcome of the state of the universe at an earlier time.
Ernst Haeckel coined the term “dysteleology” to describe the idea that the universe has no ultimate goal or purpose. His primary concern was with biological evolution, but the conception goes deeper. Google returns no hits for the phrase “dysteleological physicalism” (until now, I suppose). But it is arguably the most fundamental insight that science has given us about the ultimate nature of reality. The world consists of things, which obey rules. Everything else derives from that.
None of which is to say that life is devoid of purpose and meaning. Only that these are things we create, not things we discover out there in the fundamental architecture of the world. The world keeps happening, in accordance with its rules; it’s up to us to make sense of it.
Tim Maudlin is writing a two-volume introduction to the philosophy of physics, and I was fortunate enough to get a peek at a draft of Volume One, about space and time. There is one anecdote in there about Leibniz’s objections to Newtonian physics that is worth passing along. This came up in the course of the Leibniz-Clarke correspondence.
Leibniz was quite fond of proclaiming overarching a priori principles. Perhaps the most famous/infamous is the Principle of Sufficient Reason, which states that everything that happens does so for some good reason. But there was also the Principle of Identity of Indiscernibles, which states that if two things have all the same properties, they are really the same thing. Sounds reasonable enough (although one might worry what qualifies as a “property”), but it can get you in trouble if you take it too far.
Remember that Newton believed in absolute space — a rigid three-dimensional set of points that forms the arena in which physics takes place. Leibniz, on the other hand, claimed that space should be thought of purely in terms of relations between different points, without any metaphysical baggage of “absoluteness.” (From a modern perspective, Leibniz was closer to correct, given Galilean relativity; but once we allow for spacetime curvature in general relativity, the relational view becomes less useful.)
So far, so good. The weird part, to modern ears, comes in when we consider Newtonian cosmology. In order to explain matter in the universe, Newton departed from the strict consequences of his Laws of Motion. Instead, he imagined that empty space existed for an infinite period of time, before eventually God decided to create matter in it.
That’s the part Leibniz couldn’t go along with. He didn’t believe God would work that way, for reasons that amount to what we would now call the translational invariance of space. If God is going to create all this matter in empty space, Leibniz reasons, He has to put it somewhere. But where? Every point is equally good! Therefore there can’t be any “sufficient reason” to create it in one place rather than in some other place. Therefore there must be a deep metaphysical flaw at the heart of Newton’s theory. Interestingly, he didn’t go for “matter has been around forever,” but instead came down on the side of “there is no such thing as absolute space.”
Maybe he was worried about Boltzmann Brains?
The Philosophy of Science Association meeting in Montreal was great fun. For one thing it was in Montreal; for another I got to hang out with Doctor Free-Ride; and as a bonus there were some interesting and provocative talks about the nature of time. I chatted with Tim Maudlin, Huw Price, Craig Callender, Nick Huggett, Chris Wuttrich, David Wallace, John Norton, and other people I always learn from when I talk to. Philosophers always force you to think hard about things.
Here are the slides from my own talk, which was supposed to be about time but ended up being more about space. Not much in the way of original research, just some ruminations on what is and is not “fundamental” about spacetime (with the caveat that this might not be a sensible question to ask). I made two basic points, which happily blended into each other: first, that the distinction between “position” (space) and “momentum” is not a fundamental aspect of classical mechanics or quantum mechanics, but instead reflects the particular Hamiltonian of our world; and second that holography implies that space is emergent, but in a very subtle and non-local way. This latter point is one reason why many of us are skeptical of approaches like loop quantum gravity, causal set theory, or dynamical triangulations; these all start by assuming that there are independent degrees of freedom at each spacetime point, and quantum gravity doesn’t seem to work that way.
Sadly the slides aren’t likely to be very comprehensible. There’s a lot of math, and the equations don’t come out completely clearly — my first time using Slideshare, so perhaps they would look better if I uploaded a pdf file rather than PowerPoint. (Hint: the slides are much more clear if you click “Menu” at the bottom left, and switch to full-screen mode.) Also I didn’t make any attempt to have the slides stand by themselves without the accompanying words. But at least this will serve as documentation that I really did give a talk at the conference, no just hang out in restaurants in Montreal.