To nobody’s surprise, universities are increasingly putting some effort into putting high-quality course lectures on the Web. (Where this ultimately will lead isn’t completely clear.) We’ve already mentioned Leonard Susskind’s lectures on GR at Stanford. Now from Harvard, we have a course on Justice by Michael Sandel. (Via Julian Sanchez.) They really went all-out on the production values, teaming with the local public TV station WGBH; this looks a lot better than what you would get from someone in the middle of the room with a hand-held camera.

The lectures were held in Harvard’s Sanders Theater, which is quite a beautiful space. You get something of an idea what it’s like to be a Harvard undergrad; there are a lot of students in the class. Most professors don’t wear suits and ties, however.

Back for the third and final day of the Philosophy and Cosmology conference in honor of George Ellis’s birthday. I’ll have great memories of my time in Oxford, almost all of which was spent inside this lecture hall. See previous reports of Day One, Day Two.

It’s become clear along the way that I am not as accurate when I’m trying to represent philosophers as opposed to physicists; the vocabularies and concerns are just slightly different and less familiar to me. So take things with an appropriate grain of salt.

Tuesday morning: The Case for Multiverses

9:00: Bernard Carr, one of the original champions of the anthropic principle, has been instructed to talk on “How we know multiverses exist.” Not necessarily the title he would have chosen. Of course we don’t observe a multiverse directly; but we might observe it indirectly, or infer it theoretically. We should be careful to define “multiverse,” not to mention “exist.”

There certainly has been a change, even just since 2001, in the attitude of the community toward the multiverse. Quotes Frank Wilczek, who tells a parable about how multiverse advocates have gone from voices in the wilderness to prophets. That doesn’t mean the idea is right, of course.

Carr is less interested in insisting that the multiverse does exist, and more interested in defending the proposition that it might exist, and that taking it seriously is perfectly respectable science. Remember history: August Comte in 1859 scoffed at the idea we would ever know what stars were made of. Observational breakthroughs can be hard to predict. Rutherford: “Don’t let me hear anyone use the word `Universe’ in my department!” Cosmology wasn’t respectable. For what it’s worth, the idea that what we currently see is the whole universe has repeatedly been wrong.

So how do we know a multiverse exists? Maybe we could hop in a wormhole or something, but let’s not be so optimistic. There are reasons to think that multiverses exist: for example, if we find ourselves near some anthropic cutoff for certain parameters. More interesting, there could be semi-direct observational evidence — bubble collisions, or perhaps giant voids. Discovering extra dimensions would be good evidence for the theories on which the multiverse is often based.

The only direct observations that currently exists that might bear directly on multiverses is the prediction of giant voids and dark flows by Laura Mersini-Houghton and collaborators.

Carr believes that the indirect evidence from finely-tuned coupling constants is actually stronger. Existence of planets requires a very specific relationship between strength of gravity and electromagnetism, which happens to exist in the real world. There is a similar gravity/weak tuning needed to make supernovae and heavy elements. Admittedly, many physicists dislike the multiverse and find it just as unpalatable as God. But ultimately, multiverse ideas will become normal science by linking up with observations; we just don’t know how long it will take.

9:45: George Ellis follows Carr’s talk with what we’ve been waiting for a while — a strong skeptical take on the multiverse idea.

There are lots of types of multiverses: many-worlds, separated by space or time, or completely disjoint. Anthropic arguments are what make the idea go. The project is to make the apparently improbable become probable.

The very nature of the scientific enterprise is at stake: multiverse proponents are proposing that we weaken the idea of scientific proof. Science is about two things: testability and explanatory power. Is it worth giving up the former to achieve the latter?

The abstract notion of a multiverse doesn’t get you anything; you need a specific model, with a distribution of probabilities. (Does Harry Potter exist somewhere in your multiverse?) But if there is some process that generates universes, how do you test that process? Domains beyond our particle horizon are unobservable. How far should we expect to be able to extrapolate? Into a region which, in principle, we will never be able to observe.

In the good old days we accepted the Cosmological Principle, and assumed things continued uniformly forever beyond our observable horizon. Completely untestable, of course. If all the steps in the extrapolation are perfectly tenable, extrapolations are fine — but that’s not the case here. In particular, the physics of eternal inflation (gravity plus quantum field theory, Coleman-de Luccia tunneling) has never been tested. It’s unknown physics used to infer an unobservable realm. Inflation itself is not yet a well-defined theory, and not all versions of inflation are eternal. We haven’t even found a scalar field!

There is a claim that a multiverse is implied by the fine-tuning of the universe to allow life. At best a weak consistency test. Can never actually do statistical tests on the purported ensemble. Another claim is that the local universe, if it’s inside a bubble, should have a slight negative curvature — but that’s easily avoided by super-Hubble perturbations, so it’s not a strong prediction. We could, however, falsify eternal inflation by observing that we live in a “small” (topologically compact) universe. But if we don’t, it certainly doesn’t prove that eternal inflation is right. Finally, it’s true that we might someday see signatures of bubble collisions in the microwave background. But if we don’t, then what? Again, not a firm prediction.

Ultimately: explanation and testability are both important, but one shouldn’t overwhelm the other. “The multiverse theory can’t make any prediction because it can explain anything at all.” Beware! If we redefine science to accommodate the multiverse, all sorts of pseudo-science might sneak inside the tent.

There are also political/sociological issues. Orthodoxy is based on the beliefs held by elites. Consider the story of Peter Coles, who tried to claim back in the 1990′s that the matter density was only 30% of the critical density. He was threatened by a cosmological bigwig, who told him he’d be regarded as a crank if he kept it up. On a related note, we have to admit that even scientists base beliefs on philosophical agendas and rationalize after the fact. That’s often what’s going on when scientists invoke “beauty” as a criterion.

Multiverse theories invoke “a profligate excess of existential multiplicity” in order to explain a small number of features of the universe we actually see. It’s a possible explanation of fine tuning, but is not uniquely defined, is not scientifically testable, and in the end “simply postpones the ultimate metaphysical question.” Nevertheless — if we accumulated enough consistency tests, he’d be happy to eventually become convinced.

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The previous post on the Philosophy and Cosmology conference in Oxford was growing to unseemly length, so I’ll give each of the three days its separate post.

Monday morning: The Case for Multiverses

9:00: We start today as we ended yesterday: with a talk by Martin Rees, who has done quite a bit to popularize the idea of a multiverse. He wants to argue that thinking about the multiverse doesn’t represent any sort of departure from the usual way we do science.

The Big Bang model, from 1 second to today, is as uncontroversial as anything a geologist does. Easily falsifiable, but it passes all tests. How far does the domain of physical cosmology extend? We only see the universe out to the microwave background, but nothing happens out there — it seems pretty uniform, suggesting that conditions inside extend pretty far outside. Could be very far, but hard to say for sure.

Some people want to talk only about the observable universe. Those folks need aversion therapy. After all, whether a particular distant galaxy eventually becomes observable depends on details of cosmic history. There’s no sharp epistemological distinction between the observable and unobservable parts of the universe. We need to ask whether quantities characterizing our observable part of the universe are truly universal, or merely local.

So: what values of these parameters are consistent with some kind of complexity? (No need to explicitly invoke the “A-word.”) Need gravity, and the weaker the better. Need at least one very large number; in our universe it’s the ratio of gravity to electromagnetic forces between elementary particles. Also need departure from thermodynamic equilibrium. Also: matter/antimatter symmetry, and some kind of non-trivial chemistry. (Tuning between electromagnetic and nuclear forces?) At least one star, arguably a second-generation star so that we have heavy elements. We also need a tuned cosmic expansion rate, to let the universe last long enough without being completely emptied out, and some non-zero fluctuations in density from place to place.

If the amplitude of density perturbations were much smaller, the universe would be anemic: you would have fewer first-generation stars, and perhaps no second-generation stars. If the amplitude were much larger, we would form huge black holes very early, and again we might not get stars. But ten times the observed amplitude would actually be kind of interesting. Given an amplitude of density perturbations, there’s an upper limit on the cosmological constant, so that structure can form. Again, larger perturbations would allow for a significantly larger cosmological constant — why don’t we live in such a universe? Similar arguments can be made about the ratio of dark matter to ordinary matter.

Having said all that, we need a fundamental theory to get anywhere. It should either determine all constants of nature uniquely, in which case anthropic reasoning has no role, or it allows ranges of parameters within the physical universe, in which case anthropics are unavoidable.

10:00: Next up, Philip Candelas to talk about probabilities in the landscape. The title he actually puts on the screen is: “Calabi-Yau Manifolds with Small Hodge Numbers, or A Des Res in the Landscape.”

A Calabi-Yau is the kind of manifold you need in string theory to compactly ten dimensions down to four, picked out among all possible manifolds by the requirement that we preserve supersymmetry. There are many examples, and you can characterize them by topological invariants as well as by continuous parameters. But there is a special corner in the space of Calabi-Yau’s where certain topological invariants (Hodge numbers) are relatively small; these seem like promising places to think about phenomenology — e.g. there are three generations of elementary particles.

Different embeddings lead to different gauge groups in four dimensions: E₆, SO(10), or SU(5). Various models with three generations can be found. Putting flux on the Calabi-Yau can break the gauge group down to the Standard Model, sometimes with additional U(1)’s.

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Greetings from Oxford, a charming little town across the Atlantic with its very own university. It’s in the United Kingdom, a small island nation recognized for its steak and kidney pie and other contributions to world cuisine. What you may not know is that the UK has also produced quite a few influential philosophers and cosmologists, making it an ideal venue for a small conference that aims to bring these two groups together.

The proximate reason for this particular conference is George Ellis’s 70th birthday party. Ellis is of course a well-known general relativist, cosmologist, and author. Although the idea of a birthday conference for respected scientists is quite an established one, Ellis had the idea of a focused and interdisciplinary meeting that might actually be useful, rather than just bringing together all of his friends and collaborators for a big party. It’s to his credit that they invited as many multiverse-boosters as multiverse-skeptics. (I would go for the party, myself.)

George is currently very interested and concerned by the popularity of the multiverse idea in modern cosmology. He’s worried, as many others are (not me, especially), that the idea of a multiverse is intrinsically untestable, and represents a break with the standard idea of what constitutes “science.” So he and the organizing committee have asked a collection of scientists and philosophers with very different perspectives on the idea to come together and hash things out.

It appears as if there is working wireless here in the conference room, so I’ll make some attempt to blog very briefly about what the different speakers are saying. If all goes well, I’ll be updating this post over the next three days. I won’t always agree with everyone, of course, but I’ll try to fairly represent what they are saying.

Saturday night:

Like any good British undertaking, we begin in the pub. I introduce some of the philosophers to Andrei Linde, who entertains us by giving an argument for solipsism based on the Wheeler-deWitt equation. The man can command a room, that’s all I’m saying.

(If you must know the argument: the ordinary Schrodinger equation tells us that the rate of change of the wave function is given by the energy. But for a closed universe in general relativity, the energy is exactly zero — so there is no time evolution, nothing happens. But you can divide the universe into “you” and “the rest.” Your own energy is not zero, so the energy of the rest of the universe is not zero, and therefore it obeys the standard Schrodinger equation with ordinary time evolution. So the only way to make the universe real is to consider yourself separate from it.)

Sunday morning: Cosmology

9:00: Ellis gives the opening remarks. Cosmology is in a fantastic data-rich era, but it is also coming up against the limits of measurement. In the quest for ever deeper explanation, increasingly speculative proposals are being made, which are sometimes untestable even in principle. The multiverse is the most obvious example.

Question: are these proposals science? Or do they attempt to change the definition of what “science” is? Does the search for explanatory power trump testability?

The questions aren’t only relevant to the multiverse. We need to understand the dividing line between science and non-science to properly classify standard cosmology, inflation, natural selection, Intelligent Design, astrology, parapsychology. Which are science?

9:30: Joe Silk gives an introduction to the state of cosmology today. Just to remind us of where we really are, he concentrates on the data-driven parts of the field: dark matter, primordial nucleosynthesis, background radiation, large-scale structure, dark energy, etc.

Silk’s expertise is in galaxy formation, so he naturally spends a good amount of time on that. Theory and numerical simulations are gradually making progress on this tough problem. One outstanding puzzle: why are spiral galaxies so thin? Probably improved simulations will crack this before too long.

10:30: Andrei Linde talks about inflation and the multiverse. The story is laden with irony: inflation was invented to help explain why the universe looks uniform, but taking it seriously leads you to eternal inflation, in which space on extremely large (unobservable) scales is highly non-uniform — the multiverse. The mechanism underlying eternal inflation is just the same quantum fluctuations that give rise to the density fluctuations observed in large-scale structure and the microwave background. The fluctuations we see are small, but at earlier times (and therefore on larger scales) they could easily have been very large — large enough to give rise to different “pocket universes” with different local laws of physics.

Linde represents the strong pro-multiverse view: “An enormously large number of possible types of compactification which exist e.g. in the theory of superstrings should be considered a virtue.” He said that in 1986, and continues to believe it. String theorists were only forced to take all these compactifications seriously by the intervention of a surprising experimental result: the acceleration of the universe, which implied that there was no magic formula that set the vacuum energy exactly to zero. Combining the string theory landscape with eternal inflation gives life to the multiverse, which among other things offers an anthropic solution to the cosmological constant problem.

Still, there are issues, especially the measure problem: how do you compare different quantities when they’re all infinitely big? (E.g. number of different kinds of observers in the multiverse.) Linde doesn’t think any of the currently proposed measures are completely satisfactory, including the ones he’s invented. A big problem with Boltzmann brains.

Another problem is what we mean by “us,” when we’re trying to predict “what observers like us are likely to see.” Are we talking about carbon-based life, or information-processing computers? Help, philosophers!

Linde thinks that the multiverse shows tendencies, although not cut-or-dried predictions. It prefers a cosmological constant to quintessence, and increases the probability that axions rather than WIMPs are the dark matter. Findings to the contrary would be blows to the multiverse idea. Most strongly, without extreme fine-tuning, the multiverse would not be able to simultaneously explain large tensor modes in the CMB and low-energy supersymmetry.

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One frustrating aspect of our discussion about the compatibility of science and religion was the amount of effort expended arguing about definitions, rather than substance. When I use words like “God” or “religion,” I try to use them in senses that are consistent with how they have been understood (at least in the Western world) through history, by the large majority of contemporary believers, and according to definitions as you would encounter them in a dictionary. It seems clear to me that, by those standards, religious belief typically involves various claims about things that happen in the world — for example, the virgin birth or ultimate resurrection of Jesus. Those claims can be judged by science, and are found wanting.

Some people would prefer to define “religion” so that religious beliefs entail nothing whatsoever about what happens in the world. And that’s fine; definitions are not correct or incorrect, they are simply useful or useless, where usefulness is judged by the clarity of one’s attempts at communication. Personally, I think using “religion” in that way is not very clear. Most Christians would disagree with the claim that Jesus came about because Joseph and Mary had sex and his sperm fertilized her ovum and things proceeded conventionally from there, or that Jesus didn’t really rise from the dead, or that God did not create the universe. The Congregation for the Causes of Saints, whose job it is to judge whether a candidate for canonization has really performed the required number of miracles and so forth, would probably not agree that miracles don’t occur. Francis Collins, recently nominated to direct the NIH, argues that some sort of God hypothesis helps explain the values of the fundamental constants of nature, just like a good Grand Unified Theory would. These views are by no means outliers, even without delving into the more extreme varieties of Biblical literalism.

Furthermore, if a religious person really did believe that nothing ever happened in the world that couldn’t be perfectly well explained by ordinary non-religious means, I would think they would expend their argument-energy engaging with the many millions of people who believe that the virgin birth and the resurrection and the promise of an eternal afterlife and the efficacy of intercessory prayer are all actually literally true, rather than with a handful of atheist bloggers with whom they agree about everything that happens in the world. But it’s a free country, and people are welcome to define words as they like, and argue with whom they wish.

But there was also a more interesting and substantive issue lurking below the surface. I focused in that post on the meaning of “religion,” but did allude to the fact that defenders of Non-Overlapping Magisteria often misrepresent “science” as well. And this, I think, is not just a matter of definitions: we can more or less agree on what “science” means, and still disagree on what questions it has the power to answer. So that’s an issue worth examining more carefully: what does science actually have the power to do?

I can think of one popular but very bad strategy for answering this question: first, attempt to distill the essence of “science” down to some punchy motto, and then ask what questions fall under the purview of that motto. At various points throughout history, popular mottos of choice might have been “the Baconian scientific method” or “logical positivism” or “Popperian falsificationism” or “methodological naturalism.” But this tactic always leads to trouble. Science is a messy human endeavor, notoriously hard to boil down to cut-and-dried procedures. A much better strategy, I think, is to consider specific examples, figure out what kinds of questions science can reasonably address, and compare those to the questions in which we’re interested.

Here is my favorite example question. Alpha Centauri A is a G-type star a little over four light years away. Now pick some very particular moment one billion years ago, and zoom in to the precise center of the star. Protons and electrons are colliding with each other all the time. Consider the collision of two electrons nearest to that exact time and that precise point in space. Now let’s ask: was momentum conserved in that collision? Or, to make it slightly more empirical, was the magnitude of the total momentum after the collision within one percent of the magnitude of the total momentum before the collision?

This isn’t supposed to be a trick question; I don’t have any special knowledge or theories about the interior of Alpha Centauri that you don’t have. The scientific answer to this question is: of course, the momentum was conserved. Conservation of momentum is a principle of science that has been tested to very high accuracy by all sorts of experiments, we have every reason to believe it held true in that particular collision, and absolutely no reason to doubt it; therefore, it’s perfectly reasonable to say that momentum was conserved.

A stickler might argue, well, you shouldn’t be so sure. You didn’t observe that particular event, after all, and more importantly there’s no conceivable way that you could collect data at the present time that would answer the question one way or the other. Science is an empirical endeavor, and should remain silent about things for which no empirical adjudication is possible.

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Steve Hsu pulls out a provocative quote from philosopher of science Paul Feyerabend:

The withdrawal of philosophy into a “professional” shell of its own has had disastrous consequences. The younger generation of physicists, the Feynmans, the Schwingers, etc., may be very bright; they may be more intelligent than their predecessors, than Bohr, Einstein, Schrodinger, Boltzmann, Mach and so on. But they are uncivilized savages, they lack in philosophical depth — and this is the fault of the very same idea of professionalism which you are now defending.

It’s probably true that the post-WWII generations of leading physicists were less broadly educated than their pre-war counterparts (although there are certainly counterexamples such as Murray Gell-Mann and Steven Weinberg). The simplest explanation for this phenomenon would be that the center of gravity of scientific research switched from Europe to America after the war, and the value of a broad-based education (and philosophy in particular) has always been less in America. Interestingly, Feyerabend seems to be blaming philosophers themselves — “the withdrawal of philosophy into a `professional’ shell” — rather than physicists or any wider geosocial trends.

But aside from whether modern physicists (and maybe scientists in other fields, I don’t know) pay less attention to philosophy these days, and aside from why that might be the case, there is still the question: does it matter? Would knowing more philosophy have made any of the post-WWII giants better physicists? There are certainly historical counterexamples one could conjure up: the acceptance of atomic theory in the German-speaking world in the late nineteenth century was held back considerably by Ernst Mach‘s philosophical arguments. On the other hand, Einstein and Bohr and their contemporaries did manage to do some revolutionary things; relativity and quantum mechanics were more earth-shattering than anything that has come since in physics.

The usual explanation is that the revolutionary breakthroughs simply haven’t been there to be made — that Feynman and Schwinger and friends missed the glory days when quantum mechanics was being invented, so it was left to them to move the existing paradigm forward, not to come up with something revolutionary and new. Maybe, had these folks been more conversant with their Hume and Kant and Wittgenstein, we would have quantum gravity figured out by now.

Probably not. Philosophical presuppositions certainly play an important role in how scientists work, and it’s possible that a slightly more sophisticated set of presuppositions could give the working physicist a helping hand here and there. But based on thinking about the actual history, I don’t see how such sophistication could really have moved things forward. (And please don’t say, “If only scientists were more philosophically sophisticated, they would see that my point of view has been right all along!”) I tend to think that knowing something about philosophy — or for that matter literature or music or history — will make someone a more interesting person, but not necessarily a better physicist.

This might not be right, though. Maybe, had they been more broad and less technical, some of the great physicists of the last few decades would have made dramatic breakthroughs in a field like quantum information or complexity theory, rather than pushing harder at the narrow concerns of particle physics or condensed matter. Easy to speculate, hard to provide much compelling evidence either way.

George Tiller, a doctor and abortion provider in Kansas, was shot and killed outside his church on Sunday. The large majority of people on either side of the abortion debate are understandably horrified by an event like this. But it sets up a rhetorical dilemma for anyone who takes seriously the claim that abortion is murder. If George Tiller really was a “baby killer” comparable to Hitler and Stalin, it’s difficult to express unmitigated sadness at his murder. So we get Randall Terry, founder of Operation Rescue, admitting regret — but only that Tiller was a mass murderer who “did not have time to properly prepare his soul to face God.”

On those rare occasions when they attempt to actually talk to each other, people on opposite sides of the abortion debate usually end up talking past each other. Supporters of abortion rights speak in the language of the autonomy of the mother, and her right to control her own body: “If you don’t like abortion, don’t have one.” Opponents of abortion speak in terms of the personhood of the fetus. (Yes, Dr. Seuss’s Horton Hears a Who! — “A person’s a person, no matter how small” — is used to teach this point to Catholic children, over Theodor Geisel’s objections.) Opposition to abortion rights can also be a manifestation of the desire to control women’s sexuality, but let’s concentrate on those whose opposition is grounded in a sincere moral belief that abortion is murder.

If someone believes that abortion really is murder, talk of the reproductive freedom of the mother isn’t going to carry much weight — nobody has the right to murder another person. Supporters of abortion rights don’t say “No, this is one case where murder is completely justified.” Rather, they say “No, the fetus is not a person, so abortion is not murder.” The crucial question (I know, this is not exactly an astonishing new insight) is whether a fetus is really a person.

I have nothing original to add to the debate over when “personhood” begins. But there is something to say about how we decide questions like that. And it takes us directly back to the previous discussion about marriage and fundamental physics. The upshot of which is: how you think about the universe, how you conceptualize the natural world around us, obviously is going to have an enormous impact on how you decide questions like “When does personhood begin?”

In a pre-scientific world, life was — quite understandably — thought of as something intrinsically different from non-life. This view could be taken to different extremes; Plato gave voice to one popular tradition, by claiming that the human soul was a distinct, incorporeal entity that actually occupied a human body. These days we know a lot more than they did back then. Science has taught us that living beings and non-living objects are the same kind of things, deep down; we’re all made of the same chemical elements, and all of our constituents obey the same laws of Nature. Life is complicated, and rich, and fascinating, and not very well understood — but it doesn’t obey separate rules apart from those of the non-living world. Living organisms are just very complicated chemical reactions, not vessels that rely on supernatural essences or mystical élan vital to keep them chugging along. Except “just” is a terribly misleading adverb in this context — living organisms are truly amazing very complicated chemical reactions. Knowing that we are made of the same stuff and obey the same rules as the rest of the universe doesn’t diminish the value or meaning of human life in any way.

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Barack Obama has nominated Sonia Sotomayor to fill David Souter’s seat on the Supreme Court. I don’t know much about her on the merits; I was idiosyncratically rooting for Kathleen Sullivan, who I had met while I was a grad student and impressed me as uncommonly brilliant. One thing that immediately strikes you about Sotomayor is her personal history — raised in housing projects in the Bronx by a single Mom, she fought her way up to graduate summa cum laude from Princeton, and then to law school at Yale where she edited the Law Review. Doesn’t mean she’ll be a great Justice, but it’s an impressive record.

The opposition research has been out for a while, of course, because that’s how politics works. One of the things brought up by Sotomayor’s critics is this clip, where she talks about the difference in emphasis between a district court and an appellate court. (Appellate courts need to look beyond the facts of the case to consider implications of setting precedent for future decisions.)

This clip drives people crazy, because she says that the courts of appeals are “where policy is made.” You’re not supposed to say that! (As Sotomayor immediately jokes.) The legislatures make the laws, and the courts are merely referees, interpreting the words of the statutes by lights of their objective and unchanging meanings.

In reality, of course, Sotomayor is simply telling the truth — a cardinal sin in law as well as politics. In law and politics, and for that matter theology, we are presented with a sacred text of one form or another. And we are supposed to pretend that the text has a One True Meaning — we may, of course, argue at great length about the proper procedure for divining what that meaning actually is, but admitting that the text is inherently ambiguous (or even contradictory) is not allowed. We need to act as if the authors of Leviticus and the Framers of the Constitution were trying to say something very clear about contemporary debates, if only we had the interpretational acumen to figure out what it was.

Which is why, as much as I enjoy the rest of the world of human endeavor, science will always be my true home. Our job is to interpret the natural world, which really is unambiguous and non-contradictory, if only we can make sense of its behavior. Other fields have a professional obligation to pretend that there are right and wrong answers, but we actually have them. Yet another way in which being a scientist is so much easier than other jobs.

As I reached the end of what would be called high school in the US, I was certain that I wanted more than anything to become a mathematician. Soon afterwards, as a beginning maths undergraduate at Cambridge, I had become even more committed to the subject, after having spent some time reading about the history of the subject, and becoming enthralled by the lives and contributions of some of the great mathematicians. Among these, I found myself personally drawn to Bertrand Russell, partly because I was more interested in philosophy then than I am these days, but mostly because of the sheer grandness of the vision embodied in the Principia Mathematica – the opus co-authored by Russell with Alfred North Whitehead – and it’s later challenge from Gödel.

Nevertheless, as one gets older, reads more, and hopefully gains a more sophisticated knowledge of the subject, one’s tastes tend to change somewhat. In my case, a gradual shift in my interests from pure to applied mathematics, and finally to theoretical physics opened up an increasing range of giants to understand and respect. Somehow though, I have always retained a soft spot for Russell; perhaps because of his atheism, perhaps because of his breadth, but more so I think, because when I think of him I can quite viscerally recall the way reading about him made me feel about mathematics.

Because of this, while I have never become an avid reader of graphic novels, I’m hoping to get hold of a copy of Apostolos Doxiadis’ Logicomix, which I learned about via The Guardian, and which the web site describes as

Covering a span of sixty years, the graphic novel Logicomix was inspired by the epic story of the quest for the Foundations of Mathematics.

This was a heroic intellectual adventure most of whose protagonists paid the price of knowledge with extreme personal suffering and even insanity. The book tells its tale in an engaging way, at the same time complex and accessible. It grounds the philosophical struggles on the undercurrent of personal emotional turmoil, as well as the momentous historical events and ideological battles which gave rise to them.

The role of narrator is given to the most eloquent and spirited of the story’s protagonists, the great logician, philosopher and pacifist Bertrand Russell. It is through his eyes that the plights of such great thinkers as Frege, Hilbert, Poincaré, Wittgenstein and Gödel come to life, and through his own passionate involvement in the quest that the various narrative strands come together.

The web site contains a few samples of what to expect, plus a nice summary of the cast of characters. To a graphic novel newbie like myself, it isn’t obvious what to expect from a telling of this kind of sweeping academic story in such a format. But the team involved looks promising, and I’m sufficiently fascinated by the subject matter that I’m really looking forward to getting a look at Logicomix.

Henri Poincaré proved his “recurrence theorem” in 1890: in a mechanical system with bound orbits (particles can’t just run off to infinity), any state through which the system passes will be approached (to arbitrary accuracy) an infinite number of times in the future. That was eight years after Friedrich Nietzsche, in The Gay Science, asked us to imagine exactly such a scenario, in his notion of eternal return:

What if, some day or night, a demon were to steal after you in your loneliest loneliness and say to you: “This life as you now live it and have lived it, you will have to live once more and innumerable times more; and there will be nothing new in it, but every pain and every joy and every thought and sigh and everything unutterably small or great in your life will have to return to you, all in the same succession and sequence—even this spider and this moonlight between the trees, and even this moment and I myself. The eternal hourglass of existence is turned upside down again and again—and you with it, speck of dust!”

This is the kind of thing you come across when you’re writing a book about time. Nietzsche wanted to suggest that a well-lived life was one you wouldn’t mind knowing would recur throughout eternity, while the prospect would cause gnashing of teeth for most of us. Poincaré’s concerns were somewhat different.

While looking up this passage, I stumbled across one of my favorite Nietzsche quotes, just a few aphorisms prior:

Yes, my friends, regarding all the moral chatter of some about others it is time to feel nauseous! Sitting in moral judgment should offend our taste! Let us leave such chatter and such bad taste to those who have nothing else to do but drag the past a few steps further through time and who never live in the present,—which is to say the many, the great majority! We, however, want to become who we are,—the new, unique, incomparable ones, who give themselves their own laws, who create themselves! And to that end we must become the best learners and discoverers of everything that is lawful and necessary in the world: we must become physicists in order to be able to be creators in this sense,—while hitherto all valuations and ideals have been based on ignorance of physics or were constructed so as to contradict it. Therefore: long live physics! And even more so that which compels us to turn to physics,—our honesty!

A quote which engenders, as you might imagine, swift elaborations on the part of Nietzsche scholars that he certainly wasn’t talking about what we ordinarily mean by “physics.” But I’m not so sure. The substance of physics (experimental results, theoretical understandings) is of no help whatsoever in leading a moral life. But the method of physics — open-minded hypothesis testing and scrupulous honesty in confronting what Nature has to tell us — is a pretty good model for other aspects of our lives.

Not that physicists are, as a matter of empirical fact, any better at being good human beings on average than anyone else. Even we physicists could learn to be better physicists.