Andrew Jaffe: Leaves on the Line

Many plays about science suffer from trying to do too much, telling a story while teaching science, but Nick Payne’s two-hander “Constellations”, now on at the Royal Court Theatre in London, has science and a scientist at its center, adding to the drama, not distracting us with jargon or science fictional twists.

“Constellations” is the story of Roland and Marianne, a beekeeper and a cosmologist. Without giving away too many spoilers, I’ll say that the play tells us the story of their relationship, as it might play out in the myriad possible universes of the multiverse, each one subtly different from the rest (while of course there would be vastly many more that are not subtly, but radically, different — but a play about empty, boring Universes would be less compelling). In one, Marianne tells Roland “I sit in front of the computer all day and analyse data from the Cosmic Microwave Background” which readers will know is pretty much exactly what I do. In others, she is still an astrophysicist, sometimes more theoretical, sometimes more observational (or she is the same, just choosing to highlight different parts of her work to impress Roland or drive him away). Sometimes we see their relationship end, sometimes continue, sometimes restart, as the play pushes forward in time and between the universes. And we return, repeatedly, to one particular version of their story, towards a climax in the future of one or more of the Universes, which puts the comedy of many of the situations into tragic relief.

Playwright Nick Payne needs one of his characters to be a scientist, able to describe the underlying ideas, but manages to avoid too much heavy-handed exposition, limiting the explicit discussion of cosmology to flirty conversations early on in their relationship (I don’t know about my peers, but I find cosmology very good for flirting, at least with the right people). Sally Hawkins’ Marianne and Rafe Spall’s Roland are improbably attractive but manage to get across at least some of the neediness and nerdiness of someone burrowed so deeply into both the technical problems and the broad themes of something like cosmology or beekeeping, making us care about them and their fate (or fates?).

Thanks to my Sussex University colleagues Andrew Liddle and Kathy Romer, who both acted as consultants for the play, for inviting me along to see this excellent production.

Continuing my recent, seemingly interminable, series of too-technical posts on probability theory… To understand this one you’ll need to remember Bayes’ Theorem, and the resulting need for a Bayesian statistician to come up with an appropriate prior distribution to describe her state of knowledge in the absence of the experimental data she is considering, updated to the posterior distribution after considering that data. I should perhaps follow the guide of blogging-hero Paul Krugman and explicitly label posts like this as “wonkish”.

(If instead you’d prefer something a little more tutorial, I can recommend the excellent recent post from my colleague Ted Bunn, discussing hypothesis testing, stopping rules, and cheating at coin flips.)

Deborah Mayo has begun her own series of posts discussing some of the articles in a recent special volume of the excellently-named journal, “Rationality, Markets and Morals” on the topic Statistical Science and Philosophy of Science.

She has started with a discussion Stephen Senn’s “You May Believe You are a Bayesian But You Are Probably Wrong”: she excerpts the article here and then gives her own deconstruction in the sequel.

Senn’s article begins with a survey of the different philosophical schools of statistics: not just frequentist versus Bayesian (for which he also uses the somewhat old-fashioned names of “direct” versus “inverse” probability), but also how the practitioners choose to apply the probabilities that they calculate: either directly in terms of inferences about the world versus using those probabilities to make decisions in order to give a further meaning to the probability.

Having cleaved the statistical world in four, Senn makes a clever rhetorical move. In a wonderfully multilevelled backhanded compliment, he writes

If any one of the four systems had a claim to our attention then I find de Finetti’s subjective Bayes theory extremely beautiful and seductive (even though I must confess to also having some perhaps irrational dislike of it). The only problem with it is that it seems impossible to apply.

He discusses why it is essentially impossible to perform completely coherent ground-up analyses within the Bayesian formalism:

This difficulty is usually described as being the difficulty of assigning subjective probabilities but, in fact, it is not just difficult because it is subjective: it is difficult because it is very hard to be sufficiently imaginative and because life is short.

And, later on:

The … test is that whereas the arrival of new data will, of course, require you to update your prior distribution to being a posterior distribution, no conceivable possible constellation of results can cause you to wish to change your prior distribution. If it does, you had the wrong prior distribution and this prior distribution would therefore have been wrong even for cases that did not leave you wishing to change it. This means, for example, that model checking is not allowed.

I think that these criticisms mis-state the practice of Bayesian statistics, at least by the scientists I know (mostly cosmologists and astronomers). We do not treat statistics as a grand system of inference (or decision) starting from single, primitive state of knowledge which we use to reason all the way through to new theoretical paradigms. The caricature of Bayesianism starts with a wide open space of possible theories, and we add data, narrowing our beliefs to accord with our data, using the resulting posterior as the prior for the next set of data to come across our desk.

Rather, most of us take a vaguely Jaynesian view, after the cranky Edwin Jaynes, as espoused in his forty years of papers and his polemical book Probability Theory: The Logic of Science — all probabilities are conditional upon information (although he would likely have been much more hard-core). Contra Senn’s suggestions, the individual doesn’t need to continually adjust her subjective probabilities until she achieves an overall coherence in her views. She just needs to present (or summarise in a talk or paper) a coherent set of probabilities based on given background information (perhaps even more than one set). As long as she carefully states the background information (and the resulting prior), the posterior is a completely coherent inference from it.

In this view, probability doesn’t tell us how to do science, just analyse data in the presence of known hypotheses. We are under no obligation to pursue a grand plan, listing all possible hypotheses from the outset. Indeed we are free to do ‘exploratory data analysis’ using (even) not-at-all-Bayesian techniques to help suggest new hypotheses. This is a point of view espoused most forcefully by Andrew Gelman (author of another paper in the special volume of RMM).

Of course this does not solve all formal or philosophical problems with the Bayesian paradigm. In particular, as I’ve discussed a few times recently, it doesn’t solve what seems to me the most knotty problem of hypothesis testing in the presence of what one would like to be ‘wide open’ prior information.

Nearly two-and-a-half years after its launch, the end of ESA’s Planck mission has begun. (In fact, the BBC scooped the rest of the Planck collaboration itself with a story last week; you can read the UK take at the excellent Cardiff-led public Planck site.)

Planck’s High-Frequency Instrument (HFI) instrument must be cooled to 0.1 degrees above absolute zero, maintained at this temperature by a series of refrigerators — which had been making Planck the coldest known object in space, colder than the 2.7 degrees to which the cosmic microwave background itself warms even the most regions of intergalactic space. The final cooler in the chain relies on a tank of the Helium-3 isotope, which has finally run out, within days of its predicted lifetime — and giving Planck more than twice as much time observing the Universe as its nominal 14-month mission.

The Low-Frequency Instrument (LFI) doesn’t require such cold temperatures, although in fact they do use one of the earlier stages in the chain, the UK-built 4-degree cooler, as a reference against which it compares its measurements. LFI will, therefore, continue its measurements for the next half-year or so.

But our work, of course, goes on: we will continue to process and analyse Planck’s data, refining our maps of the sky, and get down to the real work of extracting a full sky’s worth of astrophysics and cosmology from our data. The first, preliminary, release of Planck data happened just one year ago, and yet more new Planck science will be presented at a conference in Bologna in a few months. The most exciting and important work will be getting cosmology from Planck data, which we expect to first present in early 2013, and likely in further iterations beyond that.

The astronomy community in the UK and beyond suffered a terrible blow last week with the passing of Steve Rawlings, Professor of Astrophysics at Oxford. I spent quite a lot of time in Oxford a few years ago, and was lucky to get to know Steve a bit. He had spent the last several years working on the Square Kilometre Array, the massive next-generation radio telescope being developed in the UK and internationally.

The detailed circumstances of his death aren’t yet known, and I hope that they remain irrelevant except for their tragic untimeliness. Much more important is that we remember his contributions and his friendship. My condolences to his wife, his family and his friends in Oxford and throughout the world.

I made it back onto the BBC today, this time to discuss Stephen Hawking on his 70th birthday (most of the people more qualified than me are actually at a meeting in his honour in Cambridge). (Actually, my very first appearance on the BBC, which generated one of my very first blog posts, was to talk about Hawking’s bet with Preskill and Thorne about the fate of information supposedly lost into a black hole — Hawking had originally claimed that a black hole destroys any information that fell into it, which would be a violation of the tenets of quantum mechanics, but has since, somewhat controversially, conceded.)

I have been lucky enough to meet Stephen, and was even invited to a dinner party at his house, where I got to see him posing with his Presidential Medal of Freedom, awarded by Barack Obama in 2009. So I was especially disappointed to subsequently hear that he was too ill to actually attend his conference in Cambridge. I wish him a very Happy Birthday and a speedy recovery.

It’s not hard to talk about Hawking: he’s been involved with some truly exciting breakthroughs in theoretical physics over the last few decades, perhaps most importantly for teasing out the relationship between the properties of black holes and the laws of thermodynamics. This seemingly formal analogy was realized to be much more than that with Hawking’s discovery that black holes are not, in fact, “black” — rather, they glow at a temperature inversely proportional to the mass of the black hole, emitting what has come to be called Hawking Radiation.

These are very significant discoveries, teaching us something crucial about the connections between the three great theories of physics, quantum mechanics, gravity and thermodynamics. But it’s safe to say that no one yet fully understands exactly what those relationships are.

And of course Hawking’s nonscientific accomplishments are well-known and justly valorised. He has lived with — triumphed over — ALS for far longer than any of his doctors had predicted. He has written one of the best-selling popular science books of all time, A Brief History of Time. And, needless to say, he’s done some amazing scientific work, just some of which I’ve mentioned above.

There have been very many very brilliant physicists through the centuries. So it would certainly be premature, if not churlish, to take the long view and ask where Hawking would sit in the pantheon of physicists from Archimedes through Newton, Einstein and beyond. Indeed, as my friend and colleague Peter Coles has just written, Hawking’s peers have so far decided that the time is not yet ripe to elevate him to the top of the table. (Peter has also written a short book on the subject, picking apart some of the interactions between scientists, the media and the wider public.)

I spent a quick couple of days last week at the The Controversy about Hypothesis Testing meeting in Madrid.

The topic of the meeting was indeed the question of “hypothesis testing”, which I addressed in a post a few months ago: how do you choose between conflicting interpretations of data? The canonical version of this question was the test of Einstein’s theory of relativity in the early 20th Century — did the observations of the advance of the perihelion of Mercury (and eventually of the gravitational lensing of starlight by the sun) match the predictions of Einstein’s theory better than Newton’s? And of course there are cases in which even more than a scientific theory is riding on the outcome: is a given treatment effective? I won’t rehash here my opinions on the subject, except to say that I think there really is a controversy: the purported Bayesian solution runs into problems in realistic cases of hypotheses about which we would like to claim some sort of “ignorance” (always a dangerous word in Bayesian circles), while the orthodox frequentist way of looking at the problem is certainly ad hoc and possibly incoherent, but nonetheless seems to work in many cases.

Sometimes, the technical worries don’t apply, and the Bayesian formalism provides the ideal solution. For example, my colleague Daniel Mortlock has applied the model-comparison formalism to deciding whether objects in his UKIDSS survey data are more likely to be distant quasars or nearby and less interesting objects. (He discussed his method here a few months ago.)

In between thoughts about hypothesis testing, I experienced the cultural differences between the statistics community and us astrophysicists and cosmologists, of which I was the only example at the meeting: a typical statistics talk just presents pages of text and equations with the occasional poorly-labeled graph thrown in. My talks tend to be a bit heavier on the presentation aspects, perhaps inevitably so given the sometimes beautiful pictures that package our data.

On the other hand, it was clear that the statisticians take their Q&A sessions very seriously, prodded in this case by the word “controversy” in the conference’s title. In his opening keynote, Jose Bernardo up from Valencia for the meeting discussed his work as a so-called “Objective Bayesian”, prompting a question from the mathematically-oriented philosopher Deborah Mayo. Mayo is an arch-frequentist (and blogger) who prefers to describe her particular version as “Error Statistics”, concerned (if I understand correctly after our wine-fuelled discussion at the conference dinner) with the use of probability and statistics to criticise the errors we make in our methods, in contrast with the Bayesian view of probability as a description of our possible knowledge of the world. These two points of view are sufficiently far apart that Bernardo countered one of the questions with the almost-rude but definitely entertaining riposte “You are bloody inconsistent — you are not mathematicians.” That was probably the most explicit almost-personal attack of the meeting, but there were similar exchanges. Not mine, though: my talk was a little more didactic than most, as I knew that I had to justify the science as well as the statistics that lurks behind any analysis of data.

So I spent much of my talk discussing the basics of modern cosmology, and applying my preferred Bayesian techniques in at least one big-picture case where the method works: choosing amongst the simple set of models that seem to describe the Universe, at least from those that obey General Relativity and the Cosmological Principle, in which we do not occupy a privileged position and which, given our observations, are therefore homogeneous and isotropic on the largest scales. Given those constraints, all we need to specify (or measure) are the amounts of the various constituents in the universe: the total amount of matter and of dark energy. The sum of these, in turn, determines the overall geometry of the universe. In the appropriate units, if the total is one, the universe is flat; if it’s larger, the universe is closed, shaped like a three-dimensional sphere; if smaller, it’s a three-dimensional hyperboloid or saddle. What we find when we make the measurement is that the amount of matter is about 0.282±0.02, and of dark energy about 0.723±0.02. Of course, these add up to just greater than one; model-selection (or hypothesis testing in other forms) allows us to say that the data nonetheless give us reason to prefer the flat Universe despite the small discrepancy.

After the meeting, I had a couple of hours free, so I went across Madrid to the Reina Sofia, to stand amongst the Picassos and Serras. And I was lucky enough to have my hotel room above a different museum:

Saturday afternoon I received a call from a news producer at the BBC — could I come talk about the Mars Science Laboratory, launched earlier that day?

This was a tough question, publicity-monger though I am: I don’t actually know anything about Mars. I suppose to people outside of the very broad field of “astronomy”, studying the planets in the solar system is not very different from studying the Cosmic Microwave Background. After all, in both cases we use telescopes and satellites. But actually, the study of planets is much closer to geology (and, with increasing interest in the possibilities of life on those planets, to biology) than astronomy per se.

Nonetheless, I did actually know a little about the Mars Science Laboratory and its Curiosity rover: when I was visiting the Jet Propulsion Laboratory earlier this year (to work on the CMB), our group took a quick field trip across the lab to the shop where the satellite was being assembled. Everything else I admit that I learned from wikipedia and NASA PR materials in the two hours before the interview.

One of the difficulties in getting to the surface of Mars arises from its tenuous atmosphere: parachutes aren’t a very efficient braking system. Instead, the igloo-shaped structure above and below is part of the “Sky Crane”, an amazing contraption that will hover and lower the rover gently down to the Martian surface. The Curiosity rover itself is possibly the most sophisticated robot we’ve ever put on another planet: about the size of a Mini, it will scoot around the neighbourhood of the landing site, performing experiments and sending the results back to the human race. My favourite instrument is the ChemCam, which will use “laser induced breakdown spectroscopy” to analyse rocks on the Martian surface. This is the very science-fictiony idea of shooting a high-energy laser beam at a rock, high enough to vaporise it, and then take a careful spectroscopic picture of that vapour, which scientists will decode and use to figure out the rock’s constituent elements. (Of course if there were any real Martians, they might not take kindly to our shooting laser beams at their rocks, in which case we may need to figure out a defense against the Illudium Q-36 Explosive Space Modulator.)

Martians are, of course, one of the most important parts of MSL’s mission and the broader international program of exploring Mars. NASA is very careful to point out, however, that the point of the current mission is not to find life per se, but to help determine Mars’ habitability: could Mars now support life, or could it have in the past? The actual hunt for life will have to wait for a future mission.

Urban Sputnik, our collaboration with Vanessa Harden and Dominic Southgate of Gammaroot Design is currently on display at Imperial College in the main entrance of the Norman Foster-designed business school, located on Exhibition Road in London, just up the street from the Science Museum, the V&A Museum and the Natural History Museum. I’ve discussed the pieces that will be on display before, and if you’re anywhere near South Kensington in London over the next few days, please come and see them.

If that piques your interest, you can hear more from us directly: on Tuesday evening, November 8, we’ll be hosting a short presentation — with drinks and snacks — talking about the creation of the pieces and the science behind them.

For the second time this decade, the Nobel Prize in Physics has been awarded for cosmology, to Saul Perlmutter, Adam Riess and Brian Schmidt. They are among the leaders of the teams that used the properties of supernovae — exploding stars — to measure the rate of expansion of the Universe over time. In so doing, they found that the expansion has been speeding up for the last few billion years. This is difficult to accommodate in a Universe with matter that experiences gravity in the attractive way to which we are accustomed; instead it seems to require that the Universe today be dominated by an exotic form of matter given the purposely uninformative name “Dark Energy”. This is exemplified by Cosmological Constant, a term Einstein originally included in his equation of General Relativity but abandoned when it did not fit the available data — Einstein’s motivation was not to have an accelerating Universe, but a static one, with the attraction exactly balanced by the acceleration. In the late 1990s, those two groups began to see evidence of acceleration on larger scales than Einstein envisaged, evidence that has only got better over time (especially, I should say, when combined with evidence from the Cosmic Microwave Background on the flat overall geometry of the Universe).

I was impressed to see the Guardian liveblogging the announcement of the Nobel Prize in Physics, something that usually happens for Apple product announcements and high-profile sporting events. In the blog, Martin Rees makes the excellent point that, like much physics nowadays, these discoveries were made by teams of people, with excellent leadership by the prizewinners, absolutely, but that there should be a mechanism to recognise the full scope of highly expert scientists involved. (Indeed, the Gruber Cosmology prize, which was awarded for the same research in 2007, officially recognises “Saul Perlmutter & the Supernova Cosmology Project” and “Brian Schmidt & the High-z Supernova Search Team”.)

The big problem with Dark Energy isn’t the observations, however, but the underlying theory — there is no good particle physics model which allows a cosmological constant anything like we see today. The simplest ideas say that it is just zero, and the next simplest give something that is about 10 to the power 122 or so too large.

Luckily, cosmologists and astrophysicists have ideas to solidify the supernova results and hopefully get a handle on the underlying nature of whatever is causing the acceleration, by mapping the expansion of the Universe in space and time in even more detail. There are a plethora of ground-based telescopes making observations already, but the next step will be to go to space. And it turns out that there is another reason why this is a great day for scientists studying Dark Energy: we have just had word that ESA has decided that one of its next M-class (“M” for “medium”) will be Euclid, a satellite explicitly designed to measure the properties of the accelerating Universe.

It’s been a busy few weeks, and that seems like a good excuse for my lack of posts. Since coming back from Scotland, I’ve been to:

• Paris, for our bi-monthly Planck Core Team meetings, discussing of the state of the data from the satellite, and of our ongoing processing of it;

• Cambridge, for yet more Planck, this time to discuss the papers that we as collaboration will be writing over the next couple of years; and

• Varenna, on Lake Como in northern Italy, for the Passion for Light meeting, sponsored by SIF (the Italian Physical Society) and EPS (the European Physical Society). The meeting was at least in part to introduce the effort to sponsor an International Year of Light in 2015, supported by the UN and international scientific organizations. My remit was “Light from the Universe”, which I took as an excuse to talk about (yes), Planck and the Cosmic Microwave Background. That makes sense because of what is revealed in this plot, a version of which I showed:

This figure (made after an excellent one which will be in an upcoming paper by Dole and Bethermin) shows the intensity of the “background light” integrated over all sources in the Universe. The horizontal axis gives the frequency of electromagnetic radiation — from the radio at the far left, to the Cosmic Microwave Background (CMB), the Cosmic Infrared Background (CIB), optical light in the middle, and on to ultraviolet, x-ray and gamma-ray light. The height of each curve is proportional to the intensity of the background, the amount of energy falling on a square meter of area per second coming from a particular direction on the sky (for aficionados of the mathematical details, we actually plot the quantity νI_ν to take account of the logarithmic axis, so that the area under the curve gives a rough estimate of the total intensity) which is itself also proportional to the total energy density of that background, averaged over the whole Universe.

Here on earth, we are dominated by the sun (or, indoors, by artificial illumination), but a planet is a very unusual place: most of the Universe is empty space, not particularly near a star. What this plot shows is that most of the background — most of the light in the Universe — isn’t from stars or other astronomical objects at all. Rather, it’s the Cosmic Microwave Background, the CMB, light from the early Universe, generated before there were any distinct objects at all, visible today as a so-called black body with temperature 2.73 degrees Kelvin. It also shows us that there is roughly the same amount of energy in infrared light (the CIB) as in the optical. This light doesn’t come directly from stars, but is re-processed as visible starlight is absorbed by interstellar dust which heats up and in turn glows in the infrared. That is one of the reasons why Planck’s sister-satellite Herschel, an infrared observatory, is so important: it reveals the fate of roughly half of the starlight ever produced. So we see that outside of the optical and ultraviolet, stars do not dominate the light of the Universe. The x-ray background comes from both very hot gas, heated by falling into clusters of galaxies on large scales, or by supernovae within galaxies, along with the very energetic collisions between particles that happen in the environments around black holes as matter falls in. We believe that the gamma ray background also come from accretion onto supermassive black holes at the centres of galaxies. But my talk centred on the yellow swathe of the CMB, although the only Planck data released so far are the relatively small contaminants from other sources in the same range of frequencies.

Other speakers in Varenna discussed microscopy, precision clocks, particle physics, the wave-particle duality, and the generation of very high-energy particles of light in the laboratory. But my favourite was a talk by Alessandro Farini, a Florentine “psychophysicist” who studies our perception of art. He showed the detailed (and extremely unphysical) use of light in art by even such supposedly realistic painters as Caravaggio, as well as using a series of optical illusions to show how our perceptions, which we think of as a simple recording of our surroundings, involve a huge amount of processing and interpretation before we are consciously aware of it. (As an aside, I was amused to see his collection of photographs with CMB Nobel Laureate George Smoot.)

And having found myself on the shores of Lake Como I took advantage of my good fortune:

(Many more pictures here.)

OK, this post has gone on long enough. I’ll have to find another opportunity to discuss speedy neutrinos, crashing satellites (and my latest appearance on the BBC World News to talk about the latter), not to mention our weeklong workshop at Imperial discussing the technical topic of photometric redshifts, and the 13.1 miles I ran last weekend.