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I’m giving a talk here in Paris tomorrow on the question of how to interpret the cosmological redshift.  The talk is based on the paper David Hogg and I wrote last year.  I said a bit about the argument of the paper in a previous post.  I’ll quickly recap the big idea, but then I want to comment on some followups to our paper: a blog post by Sean Carroll (from way back when we first posted our paper) and a recent paper by MichaÅ‚ Chodorowski.

First the background.  The most important fact in cosmology is that the light from distant galaxies is redshifted.  This fact is the observational basis for the idea of the expanding Universe.  Most of the time, when you see a redshift, it’s a Doppler shift — that is, it’s caused by the fact that the observed object is moving away from you.  In the cosmological context, though, people often say that the observed redshift has a different explanation: they say that the galaxies aren’t “really” moving, but rather that space itself is expanding, which causes the light to be stretched out in wavelength.  Hogg and I argue for the rehabilitation of the idea that the galaxies are moving and the observed redshift can be regarded as a Doppler shift.

The main thing to realize about all this is that we’re talking purely about a question of interpretation: everybody (at least, everybody sane)  agrees on the physics — the argument is only about what words to wrap around the physics.    Sean Carroll expressed this well in his blog post:

 These are not arguments about the theory €” everyone agrees on what GR predicts for observables in cosmology. These are only arguments about an analogy, i.e. the translation into English words.

…

The point is, arguments about analogies (and, by extension, the proper words in which to translate some well-accepted scientific phenomenon) are not "right" or "wrong." The analogies are simply "useful" or "useless," "helpful" or "misleading." And which of these categories they fall into may depend on the context.

This is 100% right.  We argue in our paper that the expanding-space picture in cosmology (particularly the metaphor of a stretching rubber sheet or balloon)  is misleading, in that it leads people to some incorrect intuitions about the nature of space, and we try to suggest different a way of looking at things.  But our way has its flaws too: all of these verbal descriptions are at best incomplete at capturing the whole picture.  We try to argue forcefully in favor of our way of looking at things, but the truth is that I’d be happies if people are exposed to several different ways, not just ours.

Here’s something else Sean says:

On the other hand, there is another pernicious mistake that people tend to make: the tendency, quite understandable in Newtonian mechanics, to talk about the relative speed between two far-away objects. Subtracting vectors at distinct points, if you like. In general relativity, you just can't do that. And realizing that you just can't do that helps avoid confusions along the lines of "Don't sufficiently distant galaxies travel faster than light?" And reifying a distinction between the Doppler shift and the cosmological redshift is a good first step toward appreciating that you can't compare the velocities of two objects that are far away from each other.

The beginning of this is exactly right: A central idea of general relativity is that you can’t compare vectors at distant points, which means that there’s no well-defined way to talk about the velocity of A relative to B, when A and B are far apart.   But I think he goes completely off the rails in the last sentence.

Sean seems to think that the expanding-rubber-sheet metaphor helps to convey the idea that you can’t talk about velocities of distant objects, but I think it does precisely the opposite.  The rubber-sheet picture virtually demands that you think of things that are just sitting still on the rubber sheet as being “really” at rest.  In its most extreme form (found in a lot of textbooks and pop-science books), the rubber-sheet metaphor says that distant galaxies are not moving with respect to us — that is, not that their velocities with respect to us are undefined, but that they’re zero!

In effect, the rubber sheet acts in people’s minds like a sort of aether, i.e., a preferred frame to use in defining all motions.  This is precisely the opposite of how you want to understand space in relativity.

Anyway, that post of Sean’s is ancient history (more than a year old).  Here’s something much more recent: the paper by Chodorowski called “The kinematic component of the cosmological redshift.” Chodorowski adopts a similar philosophy to us in some ways: he, like us, observes that if you want to talk about the velocity of a distant galaxy, you need to adopt a prescription for “carrying” its velocity vector over to us.  But while we argue that the most natural prescription is to carry the vector along the light path, he says that it’s more natural to carry the vector from one location to the other at a fixed moment in time.  Figure 1 of his paper illustrates this:

I tend to disagree with his assessment of which path is more natural.  The reason is that the comparison we want to make is between the galaxy’s velocity at the time of emission and our velocity now.  That is, the two vectors we want to compare live at the lower right and upper left of his diagram. If you follow Chodorowski’s path from right to left across the bottom, you then have to make a right turn and head up the t axis.  (He also considers the alternative where you go straight up first and then across.)  My preferred path is along the solid curve in the figure.

But the truth is that these “naturalness” questions are always matters of taste.  Chodorowski’s point of view is a very reasonable and sensible one, and this is a very nice paper.

Chodorowski’s two options correspond in effect to figuring out (a) the relative velocity of the galaxy and us back then (at the time of emission), and (b) the relative velocity of the galaxy and us now.  Hogg and I calculate something that can best be described as (c) the velocity of the galaxy then relative to us now.   In my dream world, people who want to understand the nature of the redshift would examine what happens when you do all three possibilities, and why they’re different.

One more thing on this whole business of the “trick” perpetrated in a graph in a climate-change paper.  Nate Silver says this:

Actually, what you have is a scientist, Dr. Jones, talking candidly about sexing up a graph to make his conclusions more persuasive. This is not a good thing thing to do — I’d go so far as to call it unethical — and Jones deserves some of the loss of face that he will suffer. Unfortunately, this is the sort of thing that happens all the time in both academia and the private sector — have you ever looked at the graphs in the annual report of a company which had a bad year? And it seems to happen all too often on both sides of the global warming debate (I’d include some of the graphics from An Inconvenient Truth in this category, FWIW.)

But let’s be clear: Jones is talking to his colleagues about making a prettier picture out of his data, and not about manipulating the data itself. Again, I’m not trying to excuse what he did — we make a lot of charts here and 538 and make every effort to ensure that they fairly and accurately reflect the underlying data (in addition to being aesthetically appealing.) I wish everybody would abide by that standard.

Silver’s clearly a really smart guy and knows a lot about how to handle data, but boy is this wrong. A graph in a scientific paper, or for that matter a blog post, is a part of an overall argument and is designed to convey certain information and not other information.  The person who makes such a graph has to make choices about what to include and what not to include, and those choices necessarily involve consideration of how the graph fits into the larger argument.

Silver seems to imagine that a graph is an objective representation of The Way Things Are, but it just isn’t.  I’m not saying merely that this notion of objectivity is an ideal that can never be fully achieved: I don’t even think it’s meaningful as an ideal to strive for.  Any graph you make will be selective.  Deal with it.

Of course, I’m not saying that anything goes: you can’t fake your data, and you can’t be deliberately deceptive.  But as far as I can tell, there’s precisely no evidence that Jones did anything like that.  In his use of words like “sexing up” and “unethical,” Silver is making a serious accusation without supplying evidence.  He should know better.

I know it’s just about Thanksgiving, but check out the runner-up in Wired’s contest for best Halloween costume:

She’s the cosmic microwave background radiation! Her name is Jessica Kirpatrick, and she’s a graduate student at U.C. Berkeley, working with my old friend and former housemate David Schlegel.

One or two Halloweens from now, this costume will be out of date: there should be a much better CMB map.

Thanks to Ken Ganga for passing this along.

Apparently that’s what some people are calling the revelations found in a bunch of emails by climate scientists that were hacked into and made public by climate change deniers.  Stephen “Freakonomics” Dubner gets the vapors, talking about how this exposes the “very ugly side” of climate science.  For a less heated discussion, check out Andrew Revkin’s summary of the controversy, and for the mainstream climate science point of view, go to RealClimate.

I know nothing at all about climate science (although I share 1/2 of my genes with someone who does), so I won’t say anything about the scientific merits of the issues.  But I have been a scientist for quite a while, so naturally I’ve spent a lot of time talking to and emailing other scientists.  As far as I can tell, what’s in this trove of emails is exactly what you’d expect to find if you listened in on the private conversations of a bunch of scientists discussing any remotely controversial subject.  Personally, I rarely call people who disagree with me “idiots,” for instance, but I’ve certainly heard that, and a lot worse, from colleagues.  If this is as “ugly” as it gets, things are just fine.

One supposed smoking gun in the emails is the scientist Phil Jones’s statement  that he used a “trick” in a graph to “hide the decline” in temperature in a time series.  From Revkin’s article,

Dr. Mann, a professor at Pennsylvania State University, confirmed in an interview that the e-mail message was real. He said the choice of words by his colleague was poor but noted that scientists often used the word "trick" to refer to a good way to solve a problem, "and not something secret."

That’s exactly true. In my experience,  scientists use “trick” very often to mean simply “good idea,” not anything underhanded. If you’re going to worry about anything in that quote, it should be the bit about “hiding”:  science isn’t supposed to be about hiding things, right?  So let’s look at that.  Here’s the full quote from the email (via RealClimate):

 I've just completed Mike's Nature trick of adding in the real temps to each series for the last 20 years (ie from 1981 onwards) and from 1961 for Keith's to hide the decline.

In other words, the “trick” in question consisted of plotting the supposedly problematic data in plain sight, while comparing it with another data set.  No actual hiding was done — in fact, apparently the paper explicitly displays the supposedly “hidden”material. I don’t know which of his own papers Jones is referring to, but the original source of the “trick” is Figure 5b in this Nature paper, in which the supposedly “hidden” data are right there in view.

So here’s what Jones is guilty of: behaving in a completely scientifically appropriate manner, and then describing that he did somewhat inaccurately in a private email exchange later.

Let me repeat that I’m not qualified to make judgments on the science: this just isn’t my field.  But here’s what I can say.  Some climate change deniers claim essentially that the mainstream community is engaged in a massive conspiracy to suppress the truth.  If they were right, this trove of hacked emails would prove it.  But from everything I’ve seen, what’s contained in them is pretty much exactly what you’d expect under the opposite hypothesis — that the climate science community is behaving like a normal, healthy scientific community.  Rather than bolstering the conspiracy theorists’ claims, the new data provides strong evidence falsifying them.

Here’s the opening of an article in the New York Times:

In 2002 Responsible Travel became one of the first travel companies to offer customers the option of buying so-called carbon offsets to counter the planet-warming emissions generated by their airline flights.

But last month Responsible Travel canceled the program, saying that while it might help travelers feel virtuous, it was not helping to reduce global emissions. In fact, company officials said, it might even encourage some people to travel or consume more.

A bit later, we find

For Mr. Francis of Responsible Travel, the final straw came when he noticed that carbon offsets were being offered by private jet companies and helicopter tour operators, which generate very high emissions per passenger. "The message was, €˜Don't worry, you can offset the emissions,' " he said. "But you don't really need to see Sydney from the air, do you? And you can travel in a commercial airliner."

Skepticism about carbon offsets is certainly warranted, mostly because it’s hard to verify whether the emission reduction being paid for is actually occurring.  But that’s not the objection being raised here: what the above seems to be saying is that regardless of whether the offsets work, they’re bad if they don’t cause people to fly less.  That’s nonsense.  If buying the offsets really does offset the carbon emission of flying, then it’s OK (from a carbon emission point of view) to buy the offsets and fly. In fact, not flying would then be no more “virtuous” than flying.

Let me be 100% clear about one thing: the “If” in that last paragraph is a big “If.”  It’s quite possible that offsets don’t work, in which case people shouldn’t use them.   In fact, that possibility seems quite likely to me.

What I’m objecting to (again) is the very common notion that even if things like offsets do work there’s something morally unsavory about them.  In fact, people quite often make the comparison with virtue and sin explicit, derisively referring to things like carbon offsets as “buying indulgences.”  Personally, I think that this attitude is unhelpful. When it comes to figuring out what to do about carbon emissions and climate change, all that matters is what works; there is no separate notion of “virtue” to be considered.

To be fair, the rest of the article does raise the real issues, suggesting doubt that the offsets currently on offer really do sufficiently reduce carbon emissions by the claimed amount, and claiming that ones that did do so would be priced much higher than those on offer.  I just wish we could have this discussion without mixing it all up with ill-considered moralizing.  For one thing, figuring out what works is a hard enough problem without that distraction.  For another thing, you may have noticed that people really don’t like being lectured to about their morals.  Casting the debate in simplistic moralizing terms is not likely to be politically effective, it seems to me.

My brother Andy pointed me to this climate science blog.  I don’t know much about climate science, but I do know about probability and data modeling, and I like the way this guy writes about them.  For instance, he has a really nice piece illustrating how you can model the climate at a variety of levels of complexity from very simple up to  massively complex simulations.  The point of this post is to debunk the notion, which seems to be widespread, that the only reason scientists believe in climate change is because of complicated black-box simulation codes.  He illustrates how  you can see the big picture very easily from much simpler models.

His most recent post is about his born-again Bayesianism.   It’s generally very sensible and worth reading, although I want to point out one important distinction that I think he blurs a bit.  The word Bayesian can describe two different (but overlapping) kinds of people:it can refer to

1. People who use a specific set of statistical techniques, or
2. People who have a certain philosophical stance about the meaning of probability.

Personally, I think that you absolutely have to be a Bayesian in the second sense of the term: the frequentist notion of probability strikes me as utterly incoherent.  But I think you should be completely agnostic as far as the first point is concerned.  Bayesian and frequentist statistical techniques are just tools.  They’re both perfectly sensible, and you should use whichever tool is more convenient for the problem you’re trying to solve at the moment.

I think that some people think that being a Bayesian in sense 2 means that you have to be a strict Bayesian in sense 1 — that is, that you can never calculate a confidence interval again.  Fortunately, it just isn’t so. For instance, I cowrote a paper quite a while ago in which we analyzed the same data set from both Bayesian and frequentist points of view to illustrate the relation between the two.

Here’s some advice from a physicist who has spent years on the committee that makes up GRE questions.  It’s mostly very good, which is in no way related to the fact that it mostly coincides with advice I’ve tried to give students over the years.  He believes more than I do in the validity of the GRE as a test of something useful, but that’s OK.

HT (for this, and for lots of other things I link to): Sean Carroll.

One nice thing about academic life is that you get to go on sabbatical from time to time. The trick is to play your cards right and make sure you have collaborators in nice places when the time comes.  I managed to do this pretty well, which is why I’m spending almost three months in Paris.

Over the past couple of weeks, I’ve been getting around the city mostly by bike.  Paris has a clever bike-rental system called Vélib.  You pay a small fee (5 euros for a week or 30 euros for a year) that gives you access to the bikes in the system.  There are an incredibly large number pickup and dropoff sites: in most of the city, you’re never more than a couple of blocks from one. You can take out a bike from any of the sites and drop it off at any of the others.  If you have it out for less than half an hour (which gets you pretty far), there’s no additional charge beyond your subscription fee.

There are Vélib stations right outside my apartment and my office:

It’s a great idea.  I hope more cities adopt things like this.  It’s way more fun than getting around on the Metro (and I say this as someone who kind of likes riding on the Metro).

Americans I’ve told about this ask me whether I’m scared of biking in the Paris traffic.  The answer is a definite no.  I haven’t done much urban biking since the mid-90’s, but I used to do it a lot then, when I was a grad student in Berkeley.  I don’t find biking in Paris to be significantly more dangerous or stressful than biking in Berkeley was.  Sure, you’ve got to pay attention, but in a lot of ways it’s a very bike-friendly city:

1. There are lots of bike lanes.
2. At least for the routes I’ve been traveling, I can arrange things so that, most of the time, I’m not biking past parallel-parked cars.  That’s really important: I think that car doors opening suddenly in front of you has got to be the biggest hazard of urban biking.  Most of the bike accidents I knew of when I lived in Berkeley were in this category.
3. There are tons of other cyclists, which means that drivers are more aware of the existence of bikes than in US cities.  A colleague of mine says that this is largely due to the Vélib program: when it first started, drivers weren’t as used to bikers as they are now.

So if you’re spending time in Paris, don’t be scared — try it out!  (Litigiousness paranoia disclaimer: You ride at your own risk.  If you take my advice and get into an accident, it’s not my fault — don’t sue me!)

There are certainly a few problems with the Vélib system:

1. It’s actually not easy to do it as an American.  To subscribe to the system, you either have to have a French bank account or a European-style credit card with a chip in it.  Rumor has it that American Express cards work, but I can’t confirm this.  I eventually had to get a colleague who lives here to launder the transaction.
2. The pickup and dropoff spots are all automated, of course.  They have a fixed number of spots, and if one is full, you can’t drop off your bike there.  (And of course, if it’s empty, you can’t pick up a bike there.)  But the kiosk at the station will show you a map of nearby stations that do have space / bikes.  You usually don’t have to go far. And if you’re getting near the end of your half-hour, and you come to a station that’s full, it’ll give you free extra time to get to another station.
3. As you can imagine, maintenance of the bikes is tricky.  Sometimes, you’ll get one out that has a problem (you can see a clear example in the top picture above). Savvy riders check out the bikes before taking one out, but you can always miss something.  For instance, the one I took to work this morning won’t stay in third gear unless you hang onto the gearshift — I couldn’t have found that out before selecting it.  If there is a problem, you can just check it back in and get another.  One thing the system seems to be missing: as far as I can tell, there’s no way for the user to flag a bike as having some sort of maintenance problem.  I’d think they’d want to implement that.

John Tierney writes about Martin Gardner, the great mathematical-puzzle writer.  I went through a huge Martin Gardner phase in my misspent youth, as I suspect did many other scientists and mathematicians.

Gardner’s best known for his Mathematical Games column in Scientific American.  When he stopped writing it in the early 1980s, the slot was taken over by Douglas Hofstadter.  I loved Hofstadter’s Gödel, Escher, Bach (again, probably lots of scientists, especially those about my age, would say the same), but I don’t remember liking his column at all.

As long as I’m free-associating here, there’s one more author of puzzle books that I remember loving when I was a kid: Raymond Smullyan.  He’s an actual academic mathematician (unlike Gardner), but I know him only as the writer of logic puzzles.  See, for example, the Hardest Logic Puzzle Ever.  For those who went through a Smullyanesque logic puzzle phase and remember some of the tricks, this puzzle is hard but doable.  If you didn’t, then yes, it’s probably extremely hard.

I guess this piece in the NY Times has been getting some attention lately.  It’s about a crazy theory by Nelson and Ninomiya (NN for short) in which the laws of physics don’t “want” the Higgs boson to be created.  According to this theory, states of the Universe in which lots of Higgses are created are automatically disfavored: if there are multiple different ways something can turn out, and one involves creating Higgses, then it’ll turn out some other way.  Since the Large Hadron Collider is going to attempt to find the Higgs, this theory predicts that things will happen to it so that it fails to do so.

Sean Carroll has a nice exegesis of this.  I urge you to go read it if you’re curious about this business.  There’s a bit in the middle that explains the theory in a bit more detail than you might like (unless of course you like that sort of thing).  If you find yourself getting bogged down when he talks about “imaginary action” and the like, just skip ahead a few paragraphs to about here:

So this model makes a strong prediction: we're not going to be producing any Higgs bosons. Not because the ordinary dynamical equations of physics prevent it (e.g., because the Higgs is just too massive), but because the specific trajectory on which the universe finds itself is one in which no Higgses are made.

That, of course, runs into the problem that we have every intention of making Higgs bosons, for example at the LHC. Aha, say NN, but notice that we haven't yet! The Superconducting Supercollider, which could have found the Higgs long ago, was canceled by Congress. And in their December 2007 paper €” before the LHC tried to turn on €” they very explicitly say that a "natural" accident will come along and break the LHC if we try to turn it on. Well, we know how that turned out.

I think Sean’s overall point of view is pretty much right:

At the end of the day: this theory is crazy. There's no real reason to believe in an imaginary component to the action with dramatic apparently-nonlocal effects, and even if there were, the specific choice of action contemplated by NN seems rather contrived. But I'm happy to argue that it's the good kind of crazy. The authors start with a speculative but well-defined idea, and carry it through to its logical conclusions. That's what scientists are supposed to do. I think that the Bayesian prior probability on their model being right is less than one in a million, so I'm not going to take its predictions very seriously. But the process by which they work those predictions out has been perfectly scientific.

Because I’m obsessed with Bayesian probabilities, I want to pick up a bit on that aspect of things.  NN propose an experiment to test their theory.  We take a million-card deck of cards, in which one says “Don’t turn on the LHC.”  We pick a card at random from the deck, and if we get that one card, we junk the LHC.  Otherwise, we go ahead and search for the Higgs as planned.  According to NN, if their theory is right, that card will come up because the Universe will want to “protect itself” from Higgses.

I don’t think I buy this, though.   I don’t think there’s any circumstance in which this proposed experiment will provide a good test of NN’s theory.  To see why, we have to dig into the probabilities a bit.

Suppose that the Bayesian prior probability of NN’s theory being true (that is, our estimate of the probability before doing any tests) is p(NN).  As Sean notes, p(NN) is a small number.  Also, let p(SE) be the probability that Something Else (a huge fire, an earthquake, whatever) destroys the LHC before it finds the Higgs.  Finally, let p(C) be the probability that we draw the bad card when we try the experiment.  We get to choose p(C), of course, simply by choosing the number of cards in the deck.  So how small should we make it?  There are two constraints:

1. We have to choose  p(C) to be larger than p(SE).  Otherwise, presumably, even if NN’s theory is true, the Universe is likely to save itself from the Higgs simply by causing the fire, so the card experiment is unlikely to tell us anything.
2. We have to choose p(C) to besmaller than p(NN).  The idea here is that if p(C) is too large, then our level of surprise when we pick that one card isn’t great enough to overcome our initial skepticism.  That is, we still wouldn’t believe NN’s theory even after picking the card.  Intuitively, I hope it makes sense that there must be such a constraint — if we did the experiment with 10 cards, it wouldn’t convince anyone!  The fact that the constraint is that p(C)<p(NN) comes from a little calculation using Bayes’s theorem.  Pester me if you want details.

In order for it to be possible to design an experiment that meets both of these constraints, we need p(SE)<p(NN).  That is, we need to believe, right now, that NN’s crazy theory is more likely than the union of all of the possible things that could go catastrophically wrong at the LHC. Personally, I think that’s extremely far from being the case,which means that NN’s proposed test of their theory is impossible even in principle.

(Constraint 1 already makes the experiment impossible in practice: it says that we have to take a risk with the LHC that is greater than all the other risks.  Good luck getting the hundreds of people whose careers are riding on the LHC to assume such a  risk.)