Erdős-Bacon

This interview with Stephen Strogatz reminded me that I am frequently (well, maybe it happened once) asked what my Erdős-Bacon number is. The Erdős number, of course, is the number of degrees of separation between you and famous mathematician Paul Erdős, as judged by collaborations on research papers. Erdős has an Erdős number of zero; all of his collaborators (and there were many) have Erdős numbers of 1; their collaborators have Erdős numbers of 2, and so on. Bacon numbers work similarly, except that you’re looking at degrees of separation between you and Kevin Bacon, using appearances in movies or TV instead of papers.

Since you’re dying to know: my Erdős-Bacon number is six (at least using the relaxed standards typical in this game, according to which TV documentaries and appearances as “self” are counted). My Erdős number is four: I collaborated with Jim Bryan, who collaborated with Jason Fulman, who collaborated with Persi Diaconis, who collaborated with Paul Erdős. My Bacon number is two: I appeared in a NOVA special narrated by Jay Sanders, who appeared in Starting Over with Kevin Bacon. By the tricky mathematical operation known as “addition,” we end up with six.

That’s pretty typical for people who have finite EB numbers at all. Not as good as Strogatz himself, who has an EB number of four. And while I am tied with Stephen Hawking, I haven’t (as far as I know) appeared on any musical recordings, so I don’t have a finite Erdős-Bacon-Sabbath number. Always something left to shoot for.

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National Science Foundation Cancels Call for New Political Science Grant Proposals

Wow. This had been in the pipeline for a while, but I never got around to blogging about it. (First they came for…)

A couple of weeks before the deadline for new grant proposals in political science were due, the NSF has canceled the program, at least for this grant cycle. No explicit reason was given, but everyone knows why it happened. Back in March, Congress passed the Coburn Amendment to the Continuing Appropriations Act of 2013, which limits political science funding to research that “promotes national security or the economic interests of the United States.” That’s almost impossible standard to demonstrate, of course, so the NSF just canceled all of the funding, rather than invite endless Congressional hearings about this or that grant proposal. Annual NSF expenditures on political science amount to about $10 million, which is nothing on the scale of government budgets but an awful lot to the actual researchers.

(I don’t want to be needlessly partisan by suggesting that all Republicans in Congress are either dangerous demagogues or complete chowderheads. But Tom Coburn, R-OK, is a shining example of both.)

This is a disaster, and bodes very ill for the future. I certainly wouldn’t want to defend my own research as promoting national security or the US economy. Because, frankly, it doesn’t. Even Coburn isn’t going after physics (yet), but it’s not an unrealistic dystopian scenario to imagine that a criterion like that could be applied across the board to all federal support for science. Conservatives are already up in arms about biologists studying duck penises. (It’s pretty clear that someone working for the GOP has a Google alert that searches for the word “penis.”)

Meanwhile, the Cato Institute, a libertarian think tank, has just come out arguing against all public funding for science, full stop. I’m sure the free market will happily step in there and help us out with particle physics and cosmology.

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Bloggy Tweaks

I took a few minutes to update some stuff on the blog. As always, what is intended as an improvement might end up making things worse, so feel free to chime in. In no particular order:

  • The death of Google Reader reminded me that not everyone uses RSS feeds. So I’ve added a couple of features that make it easy for people to know when a new post is up (since that’s not every day). On the right you’ll notice that you can subscribe to posts via email, which seems to work pretty well. There’s also a new Twitter feed for the blog that will notify you of new posts. This is separate from my own Twitter account, which often links to new blog posts but not always.
  • You used to be able to edit comments, but that featured died when it started to think that everyone was a spammer. I’ve replaced it with a new editing plugin. Let me know if it works. Update: nope. See below.
  • More experimentally, I’ve installed a comment rating system, so you can up- or down-vote comments. Not sure if this is a good idea or not, and I worry that it adds clutter to the comment threads. So this one is definitely in a probationary period, feel free to chime in.

Some new tweaks behind the scenes, but hopefully those won’t affect the user experience.

Update: So the comment editor didn’t play well with the like buttons (annoying but forgivable) and inserted slashes after every apostrophe (unforgivable). I’ve deactivated it. Still can’t figure out why the previous comment editor (“Ajax Edit Comments”) thinks everything is spam.

Further update: Now I’ve installed yet another comment editor. We’ll see how it works.

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Philosophy, Physics, and How It All Fits Together

Richard Marshall at 3AM magazine has been doing a series of interviews with all kinds of thinkers, especially philosophers; some recent examples include Dan Dennett, Tim Maudlin, Rebecca Kukla, Alex Rosenberg, and Craig Callender. And I’m the latest subject. Given the venue, we talk as much (or more) about philosophy than about physics, and a lot about how they fit together.

3am

Spoiler alert: I think it’s possible to have productive grown-up interactions between philosophy and science. I guess I’m just a radical bomb-thrower at heart.

Click through if this kind of thing floats your boat:

I think emergence is absolutely central to how naturalists should think about the world, and how we should find room for higher-level concepts from tables to free will in a way compatible with the scientific image. But “weak” emergence, not strong emergence. That is simply the idea that there are multiple theories/languages/vocabularies/ontologies that we can use to usefully describe the world, each appropriate at different levels of coarse-graining and precision. I always return to the example of thermodynamics (fluids, energy, pressure, entropy) and kinetic theory (collections of atoms and molecules with individual positions and momenta). Here we have two ways of talking, each perfectly valid within a domain of applicability, but with the domain of one theory (thermodynamics) living strictly inside the domain of the other (kinetic theory). Crucially, the “emergent” higher-level theory can exhibit features that you might naively think are ruled out by the lower-level rules; in particular, thermodynamics famously has an arrow of time defined by the Second Law (entropy increases in isolated systems), whereas the microscopic rules of the lower-level theory are completely time-symmetric and arrowless.

I think this example serves as a paradigm for how we can connect the manifest image to the scientific image. Sure, there’s nothing like “free will” anywhere to be found in the ultimate laws of physics. But that’s not the only question to ask; at the higher-level description, we should ask whether our best emergent theory of human beings includes the idea that they are (in the right circumstances) rational decision-making agents with freedom of action. Until we come up with a better description of human beings, I’m perfectly happy to say that free will is “real.” It’s not to be found in the most fundamental ontology, but it’s not incompatible with it either; it’s simply a crucial part of our best higher-level vocabulary.

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Vi Hart on Twelve-Tone Music

Chances are good that you’ve already seen, or at least seen a link to, Vi Hart’s astonishing video about twelve-tone music. It has almost a million views, which represents a pretty tiny fraction of the total number of people on Earth, but I suspect the correlation with readers of this blog is high.

But I’m posting it anyway, because there might still be some readers who haven’t watched it yet, and that would be a shame. It’s that good. Now, it is a #longwatch, as they say in Twitter-land — half an hour long! Let’s just say it’s more rewarding than catching the latest episode of Two Broke Girls.

Crazy shapes.

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Talking Back to Your Elders

When I was young and as yet unformed as a theoretical physicist, cosmology was in a transitional period. We had certainly moved beyond the relatively barren landscape of the 60’s and 70’s, when pretty much the only things one had to hang one’s hat on were very basic features like expansion, rough homogeneity, and the (existence of) the cosmic microwave background. By the late 80’s we were beginning to see the first surveys of large-scale structure, there was good evidence for dark matter, and the inflationary paradigm was somewhat developed. In the 90’s things changed quite rapidly, unbelievably so in retrospect. We detected primordial anisotropies in the CMB and began to study them in detail, large-scale-structure surveys really took off, we discovered the acceleration of the universe, and techniques like gravitational lensing matured into usefulness.

My students and postdocs will readily testify that I am fond of complaining how much harder it is to come up with interesting new ideas that aren’t already ruled out by the data.

In an interesting and provocative post, Peter Coles bemoans a generational shift among cosmologists: “When I was a lad the students and postdocs were a lot more vocal at meetings than they are now.” In particular, Peter is worried that people in the field (young and old) are “willing to believe too much,” and correspondingly unwilling to propose dramatic new ideas that might run counter to received opinion. Or even, presumably, just to express doubt that received opinion is on the right track. After all, even with all we’ve learned, there’s certainly much we don’t yet know.

I’m not sure whether there really has been a shift or not; there’s a big observational bias from the fact that I used to be one of those young folks, and now I am a wise old head. (Old, anyway.) But it’s completely plausible. Is it a bad thing?

There’s an argument to be made that widespread agreement with a basic paradigm is actually a good thing. People agree on what the important questions are and how to go about answering them. Ideas are held to a higher standard. Furthermore, it would be very hard to blame a young scientist who wanted to play by the rules rather than rocking the boat. It’s easy to say “challenge conventional wisdom!”, but the thing about conventional wisdom in a mature field is that it’s usually right. The exceptions are important and memorable (remember when everyone thought the cosmological constant was zero?), but most controversial new ideas are just wrong. Being wrong is an important part of the progress of science, but it’s hard to tell other people that they should be wrong more often.

At the end of the day, though, I agree with the spirit of Peter’s lament. I do think that the discourse within cosmology has become tamer and less willing to try out new ideas. Dark matter is well-established empirically, but we certainly don’t know that it’s WIMPs (or even axions). Inflation has had some successes, but we are very far indeed from knowing that it happened (and the problems with eternal inflation and predictability are extremely real). I have my own prejudices about what’s settled and what are interesting open questions, but the field would be healthier if youngsters would challenge people like me and make up their own minds.

Then again, you gotta eat. People need jobs and all that. I can’t possibly blame anyone who loves science and chooses to research ideas that are established and have a high probability of yielding productive results. The real responsibility shouldn’t be on young people to be bomb-throwers; it should be on the older generation, who need to be willing to occasionally take a bomb to the face, and even thank the bomb-thrower for making the effort. Who knows when an explosion might unearth some unexpected treasure?

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Are Dark Matter Particles Lighter Than We Thought?

The 2010’s is known among the cognoscenti as the Dark Matter Decade. At least among those cognoscenti who are optimists by nature. After years of effort, experimentalists have improved the reach of their detectors to the point where we might be close to directly detecting dark matter (DM) particles — at least if the DM falls into the Weakly Interacting Massive Particle paradigm, or comes close to it for some reason. (Not every dark matter model does; axions are the obvious counterexample.) Jennifer summarizes the current situation in the latest issue of Quanta; some previous updates are from Matt Strassler and Résonaances.

There are two things going on. One is that the experiments, which look for energy being deposited by a (rare but predictable) interaction between dark matter particles and atomic nuclei, are now cutting into large regions of the predicted parameter space for weakly-interacting dark matter. So if the DM is WIMP-like, we have a great chance of seeing it before the decade is out.

The other is that there are already some hints that we have seen something. But those hints are confusing. It’s unclear whether they amount to the first tentative glimpses of most of the matter in the universe, or just statistical fluctuations in the detectors.

Here’s a figure summarizing the situation, adapted from a paper earlier this year from the CDMS experiment.

Dark Matter limits

The horizontal axis is the mass of the DM particle in GeV (where a proton is about 1 GeV). The vertical axis is the strength with which the DM interacts with a proton or neutron. Lines are limits; anything above the line is supposedly ruled out. Colored regions are possible signals, if we optimistically interpret some of the data. The various limits come from CDMS’s Silicon detectors, CDMS’s Germanium detectors, a CDMS low-threshold analysis, EDELWEISS, XENON10, and XENON100. The possible signals come from CDMS’s Silicon detectors, DAMA, CoGeNT, and CRESST.

You can see why the purported hints are confusing. For one thing, they don’t really agree with each other (although they’re not too far apart). More importantly, the possible signals are apparently ruled out by some of the limits! XENON, in particular, seems incompatible even with CoGeNT and CDMS, while practically everything is incompatible with DAMA and CRESST. And no, you’re not reading the labels wrong; the recent CDMS results from their Silicon detectors are quoted both as a limit and as a signal. They see three events, where they would expect to see less than one. So the limits are what we can infer if those events are just a fluke, while the blue region is the best fit if they are actually dark matter.

Even though the various possible detections don’t completely agree with each other, they do share an intriguing property: they are pointing roughly to DM masses in the 5-15 GeV range. That is not where most people would have expected to find the dark matter. The mass isn’t precisely predicted, but typical WIMP models have masses in the 100-500 GeV range. So if this is indeed the dark matter, it’s noticeably lighter than people would have guessed. On the other hand, and in part because it’s not what was expected, it’s also a region of parameter space where the experiments are just a bit less reliable. It’s not too hard to imagine that there are backgrounds we haven’t completely taken into account, which would give the same kind of events that you might attribute to light dark matter. Rest assured that the experimenters are all over this issue.

Finally, there’s something potentially very intriguing about light dark matter. Remember that there’s about five or six times as much dark matter (by mass density) than ordinary matter in the universe. And almost all the mass of ordinary matter is in the form of nucleons (protons and neutrons). So if the dark matter particle is actually five or six GeV, it’s conceivable that there is precisely one dark matter particle per ordinary particle in the universe. And if that’s true, it’s irresistible to imagine that the origin of dark matter is somehow tied to the origin of ordinary matter — more particularly, to the asymmetry of matter and antimatter. If you could cook up a theory (and people have certainly been trying) where the dark particles carried anti-baryon number, the world would be a very interesting place. (Not that it’s not interesting already, but we would have an extra glimpse into just how interesting it is.)

dmmotivator_01

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Ze Is Zir Own Person

With the increasing acceptance of gay marriage, there’s a temptation to think that we as a society have basically done away with all relevant forms of discrimination. “Hey, we abolished slavery, gave women the vote, and let gay people get married! Perfect equality has finally been achieved.”

Then you read something depressing like this opinion piece in The American Conservative, and are jolted back to reality. It spins off an NPR piece on, naturally, those crazy college youths and their mixed-up ideas. Margot Adler reported on the trend among students to identify themselves not only by their name, but also by what pronouns they like to be called by.

Depending on what street corners you hang out on, you might not be aware that pronouns are an issue. Guys are he/him, and gals are she/her, right?

Of course that only makes sense if you buy into the idea that there are guys, and there are gals, and that’s just about all there is. But the reality is much more richly complex — and that’s a reality to which our society has not yet caught up.

My lovely wife Jennifer has a new book coming out next year — Me, Myself, and Why: Searching for the Science of Self. One of her chapters is on gender and sexuality — what it is, how it comes about, and how it gets expressed. Once you actually look at the science behind it all, rather than assuming that the categories bequeathed to you as a child represent universal truths, you quickly realize that this stuff is as complicated as all get-out. (That’s how the youths these days talk, right?)

tesseract Talking with Jennifer as she wrote her chapter (which, as usual for her, involved reading a pile of technical papers as well as interviewing many experts) led me to propose the Gender Tesseract. (I’m hoping this becomes a symbol of inclusiveness and understanding, and we sell bushels of T-shirts and bumper stickers.) A tesseract, as readers well know, is the four-dimensional equivalent of a cube. And roughly — very roughly, because these ideas arise from the human desire to stick things into categorical boxes, not from any fixed nature of reality — there are four important dimensions of gender/sexuality to be considered:

  • Gender Identity: how you think of yourself.
  • Gender Expression: how you dress/act/present yourself to the world.
  • Sexual Orientation: to whom you are attracted.
  • Biological Sex: what body parts you have. (Forgot about that one, didn’t you?)

Eddie-Izzard-Dress-to-Kill-8x62 In principle, all of these can be completely different for an individual person. Comedian Eddie Izzard, although he tends to perform in “boy mode” these days, has frequently appeared in women’s clothing — his gender expression (at least as far as clothes were concerned) was female. But he isn’t gay; his sexual orientation is toward (biological/self-identified) women. There shouldn’t be any problem imagining a person (for example) who is biologically female and wears what we think of as women’s clothing, but who thinks of themselves as male and is attracted to women people who are biologically female. All the vertices of the tesseract are open for business.

And of course the reality is infinitely more complicated than that. There’s no reason to locate one’s self at a vertex of the tesseract, rather than somewhere in the interior; yes, Virginia, there are bisexuals. And indeed there are asexuals and pansexuals and countless other variations. Even before I open my T-shirt store, the Gender Tesseract is hopelessly out of date. (Perhaps we should think of functions defined on the tesseract, rather than simply points within it.) As a member of the most boring, socially normative category, I try to keep in mind that I’m not an expert on other people’s sexuality and identity, and listen to what they have to say rather than telling them how to behave.

Which is tricky, because society loves telling you how to behave. Sometimes explicitly, sometimes indirectly. The most powerful indirect tool society has is language.

The idea of a unique gender binary — men, women, no other categories — is built into English and many other languages. Women are “she,” men are “he,” and there aren’t any other possibilities. Perhaps you don’t know whether a person you are talking about is male or female, in which case society has a rule for you: assume they are male, and refer to them as “he.”

That last one is actually pretty easy to fix. For a long time now, many people have used “they” as a singular pronoun in cases where the person being referred to is of unknown gender. I started using it years ago, and it works fine. (Following in the footsteps here of Shakespeare and Jane Austen, so I’m not exactly a trailblazer.) But what about when you know exactly who you are talking about, and that person doesn’t want to accept a simplistic gender binary?

Thus the quest for gender-neutral pronouns. This is a very tricky subject, as language always is — especially for something so anarchic as English, where there isn’t any central governing body that lays down the law. In English, anyone is allowed to just make up words, so people certainly have. One choice that is popular in the transgender community is to substitute ze for he/she and zir (pronounced “zeer”) for him/his/her. These neologisms can seem strained at first use, but there’s a chance they will catch on and eventually seem perfectly natural. I was intrigued (and pleased) to learn that some college kids are pushing the idea forward. We’ll see how it goes.

Rod Dreher, author of the American Conservative piece, was less pleased. It is in the nature of conservatism to resist change, so that shouldn’t come as much of surprise. What’s depressing is the sheer lazy stupidity of the “critique.” Actually there’s not much critique at all — Dreher merely points at something he doesn’t understand, and kind of giggles uncomfortably. He labels the students “deeply confused people,” and the sum of his counterargument is one word: “Honestly?”

Yes, honestly. Language matters, and matching how we speak about people to how they think about themselves is an important part of human dignity. I don’t know what the best linguistic solution is for the knotty realities of human gender and sexuality, but I welcome the attempts to do better. Perfect equality has not yet been achieved, but I like to think we’re moving in a good direction.

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Origins of Biological Complexity

Carl Zimmer has a great article in Quanta about the origins of biological complexity. Quanta, in case you’re wondering, is the new name for the Simons Foundation’s online science magazine, which is certainly going to be a go-to resource for reliable science stories much of the media would consider to be too subtle or insufficiently newsworthy.

Defining “complexity” is a notoriously tricky business, although we tend to think we know it when we see it. The quest for the One True Definition is a red herring, as what’s interesting is to see what patterns and laws we can associate with different kinds of complexity. In the biological realm, it seems natural to give at least some credit for the development of complexity to the pressures of natural selection. Having more highly-developed sensory apparatus or higher intelligence naturally goes along with greater complexity (or so we tend to think), and there can be obvious evolutionary advantages to these traits.

Carl looks at a new paper by Leonore Fleming and Daniel McShea that looks at the number of different part types, shapes, and colors in everyone’s favorite biological test subject, the Drosophila fruit fly. They argue that complexity increases even in the absence of any evolutionary pressure at all. That’s consistent with a proposal called the “Zero-Force Evolutionary Law,” which says that complexity and diversity simply tend to increase naturally, apart from any nudges evolution might provide. Fleming and McShea looked at the evolution of Drosophila raised in comfortable laboratory environments, where they were provided with unlimited food and perfectly livable conditions, and compared them to wild fruit flies. They conclude that, indeed, the absence of pressures led to increased measures of complexity in the population. Roughly speaking, there was less reason for crazy mutations to die off, so the genome could go galloping freely through the fitness landscape.

Other biologists are skeptical of this way of looking at things. I think the basic point is that it’s easy to see how diversity will increase in the absence of evolutionary pressures, but much harder to useful complexity (like eyes and brains) would develop. To which I imagine the appropriate response is “it depends on the conditions.” If we imagine that offspring survive and reproduce equally well no matter what kinds of mutations they undergo, and there are truly unlimited resources, then I would predict that some descendants would have just as many usefully complex outcomes as they would in the presence of selection pressures. But that’s only because there would be a ginormous number of descendants, and most of them would be utterly unviable in the real world. The fraction of descendants with useful complex features in the selection-free world would doubtless be much lower than in a world with natural selection.

Evolution is able to make some wonderful things, but it really is a blind watchmaker. Mutations and sexual shuffling of genes happen, and then natural selection culls away the less successful outcomes. It doesn’t actually accelerate the production of useful outcomes. So complexity happens naturally (at least, starting from simple states in open systems very far from equilibrium), but evolution brings it into focus.

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Cosmology and the Past Hypothesis

Greetings from sunny Santa Cruz, where we’re in week three of the Summer School on Philosophy of Cosmology. I gave two lectures yesterday afternoon, and in a technological miracle they’ve already appeared on YouTube. The audio and video aren’t perfect quality, but hopefully viewers can hear everything clearly.

These are closer to discussions than lectures, as I was intentionally pretty informal about the whole thing. Rather than trying to push any one specific model or idea, I gave an overview of what I take to be the relevant issues confronting someone who wants to build a cosmological model that naturally explains why the early universe had a low entropy. They are a little bit technical, as the intended audience is grad students in physics and philosophy who have already sat through two weeks of lecturing.

If there is one central idea, it’s the concept of a “cosmological realization measure” for statistical mechanics. Ordinarily, when we have some statistical system, we know some macroscopic facts about it but only have a probability distribution over the microscopic details. If our goal is to predict the future, it suffices to choose a distribution that is uniform in the Liouville measure given to us by classical mechanics (or its quantum analogue). If we want to reconstruct the past, in contrast, we need to conditionalize over trajectories that also started in a low-entropy past state — that the “Past Hypothesis” that is required to get stat mech off the ground in a world governed by time-symmetric fundamental laws.

The goal I am pursuing is to find cosmological scenarios in which the Past Hypothesis is predicted by the dynamics, not merely assumed. We imagine a “large universe,” one in which local macroscopic situations (like a box of gas or a lecture hall full of students) occur many times. Then we can define a measure over the microconditions corresponding to such situations by looking at the ways in which those situations actually appear in the cosmic history. The hope — still just a hope, really — is that familiar situations like observers or lecture halls or apple pies appear predominantly in the aftermath of low-entropy Big-Bang-like states. That would stand in marked contrast to the straightforward Boltzmannian expectation that any particular low-entropy state is both preceded by and followed by higher-entropy configurations. I don’t think any particular model completely succeeds in this ambition, but I’m optimistic that we can build theories of this type. We shall see.

Initial state/origin of the universe (Part 1) by Sean Carroll

Initial state/origin of the universe (Part 2) by Sean Carroll

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