Teaching mistakes

The academic year has begun, and I’m teaching our second-year Quantum Mechanics course again. I was pretty happy with last year’s version, and the students didn’t completely disagree.

This year, there have been a few changes to the structure of the course — although not as much to the content as I might have liked (“if it ain’t broke, don’t fix it”, although I’d still love to use more of the elegant Dirac notation and perhaps discuss quantum information a bit more). We’ve moved some of the material to the first year, so the students should already come into the course with at least some exposure to the famous Schrödinger Equation which describes the evolution of the quantum wave function. But of course all lecturers treat this material slightly differently, so I’ve tried to revisit some of that material in my own language, although perhaps a bit too quickly.

Perhaps more importantly, we’ve also changed the tutorial system. We used to attempt an imperfect rendition of the Oxbridge small-group tutorial system, but we’ve moved to something with larger groups and (we hope) a more consistent presentation of the material. We’re only on the second term with this new system, so the jury is still out, both in terms of the students’ reactions, and our own. Perhaps surprisingly, they do like the fact that there is more assessed (i.e., explicitly graded, counting towards the final mark in the course) material — coming from the US system, I would like to see yet more of this, while those brought up on the UK system prefer the final exam to carry most (ideally all!) the weight.

So far I’ve given three lectures, including a last-minute swap yesterday. The first lecture — mostly content-free — went pretty well, but I’m not too happy with my performance on the last two: I’ve made a mistake in each of the last two lectures. I’ve heard people say that the students don’t mind a few (corrected) mistakes; it humanises the teachers. But I suspect that the students would, on the whole, prefer less-human, more perfect, lecturing…

Yesterday, we were talking about a particle trapped in a finite potential well — that is, a particle confined to be in a box, but (because of the weirdness of quantum mechanics) with some probability of being found outside. That probability depends upon the energy of the particle, and because of the details of the way I defined that energy (starting at a negative number, instead of the more natural value of zero), I got confused about the signs of some of the quantities I was dealing with. I explained the concepts (I think) completely correctly, but with mistakes in the math behind them, the students (and me) got confused about the details. But many, many thanks to the students who kept pressing me on the issue and helped us puzzle out the problems.

Today’s mistake was less conceptual, but no less annoying — I wrote (and said) “cotangent” when I meant “tangent” (and vice versa). In my notes, this was all completely correct, but when you’re standing up in front of 200 or so students, sometimes you miss the detail on the page in front of you. Again, this was in some sense just a mathematical detail, but (as we always stress) without the right math, you can’t really understand the concepts. So, thanks to the students who saw that I was making a mistake, and my apologies to the whole class.

Songs about f*&%ing

First, my apologies that I couldn’t resist the almost not-safe-for-work title, especially to those expecting posts about astrophysics and cosmology rather than a reference to a 1987 record by Big Black (which it’s worth pointing out can be found in its entirety on YouTube). But this is not a post about Big Black.

Rather, it’s a brief reminiscence of another album with a similar subject matter and a very different style, Liz Phair’s Exile in Guyville, which I was shocked to discover is about to have its 20th anniversary, also commemorated with an article and interview in the Chicago Tribune.

I lived in Chicago in the early 90s when Exile In Guyville was released, although I don’t think I heard it until I left town and moved to Toronto a few months later. But she was already a presence on the scene when Chicago was taking its place in the world of post-Nirvana indie-rock (led by the Smashing Pumpkins, along with Urge Overkill, who never quite capitalised on the marquee placement of their “Girl, You’ll Be A Woman Soon” cover on the Pulp Fiction soundtrack, and my favourite, Eleventh Dream Day). It was a record full of great songs about fucking and love and being a lonely twenty-something hipster in a big city, and was a sort of homage to the Rolling Stones’ own Exile on Main Street, all of which was enough to make rock critics (and wannabes like me) wet their pants — although by now I’m sure the Stones reference is irrelevant to record’s brilliance. “Guyville” was code (surfacing first in an Urge Overkill song) for the Wicker Park neighbourhood which was the center of the Chicago rock scene, and home to my second-favourite Chicago bar, the still-going-strong Rainbo Club (alas, my favourite, Ciral’s House of Tiki, closed in 2000).

And the title of this post also covers The Book of Mormon, which I went to see in London’s West End last week, the filthy and wonderful musical comedy from the creators of South Park. Despite songs about sex with amphibians (and worse), a character named “General Butt Fucking Naked” (sort of named after a real Liberian warlord), and being self-consciously suffused with coarse stereotyping of Africans and the eponymous Mormons, manages to be old-fashioned, warm-hearted and strangely, uncynically, affirming of the ability of individuals to actually make a difference in each other’s lives.

Today was the deadline for submitting so-called “White Papers” proposing the next generation of the European Space Agency satellite missions. Because of the long lead times for these sorts of complicated technical achievements, this call is for launches in the faraway years of 2028 or 2034. (These dates would be harder to wrap my head around if I weren’t writing this on the same weekend that I’m attending the 25th reunion of my university graduation, an event about which it’s difficult to avoid the clichéd thought that May, 1988 feels like the day before yesterday.)

At least two of the ideas are particularly close to my scientific heart.

The Polarized Radiation Imaging and Spectroscopy Mission (PRISM) is a cosmic microwave background (CMB) telescope, following on from Planck and the current generation of sub-orbital telescopes like EBEX and PolarBear: whereas Planck has 72 detectors observing the sky over nine frequencies on the sky, PRISM would have more than 7000 detectors working in a similar way to Planck over 32 frequencies, along with another set observing 300 narrow frequency bands, and another instrument dedicated to measuring the spectrum of the CMB in even more detail. Combined, these instruments allow a wide variety of cosmological and astrophysical goals, concentrating on more direct observations of early Universe physics than possible with current instruments, in particular the possible background of gravitational waves from inflation, and the small correlations induced by the physics of inflation and other physical processes in the history of the Universe.

The eLISA mission is the latest attempt to build a gravitational radiation observatory in space, observing astrophysical sources rather than the primordial background affecting the CMB, using giant lasers to measure the distance between three separate free-floating satellites a million kilometres apart from one another. As a gravitational wave passes through the triangle, it bends space and effectively changes the distance between them. The trio would thereby be sensitive to the gravitational waves produced by small, dense objects orbiting one another, objects like white dwarfs, neutron stars and, most excitingly, black holes. This would give us a probe of physics in locations we can’t see with ordinary light, and in regimes that we can’t reproduce on earth or anywhere nearby.

In the selection process, ESA is supposed to take into account the interests of the community. Hence both of these missions are soliciting support, of active and interested scientists and also the more general public: check out the sites for PRISM and eLISA. It’s a tough call. Both cases would be more convincing with a detection of gravitational radiation in their respective regimes, but the process requires putting down a marker early on. In the long term, a CMB mission like PRISM seems inevitable — there are unlikely to be any technical showstoppers — it’s just a big telescope in a slightly unusual range of frequencies. eLISA is more technically challenging: the LISA Pathfinder effort has shown just how hard it is to keep and monitor a free-floating mass in space, and the lack of a detection so far from the ground-based LIGO observatory, although completely consistent with expectations, has kept the community’s enthusiasm lower. (This will likely change with Advanced LIGO, expected to see many hundreds of sources as soon as it comes online in 2015 or thereabouts.)

Full disclosure: although I’ve signed up to support both, I’m directly involved in the PRISM white paper.


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Another technical note: I’ve just reformatted the whole blog. Let me know if there are any problems (or if you just think it’s ugly).

Infrastructure problems

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Just a quick note that the blog has been having some issues with its infrastructure: pointers to individual entries seem to be broken.

I’m on the case — apologies if you can’t get to anything you’re looking for.

Update: fixed, I think. Let me know if there are any further problems. (The blog should be a bit faster, too, as I’ve moved over to statically publishing all the pages. Don’t worry if you don’t know what that means.)

About a year ago, I wrote about TimeWave a festival of art, science and technology coming this May to London, with tendrils snaking out to New York and LA.

As part of the festival, we’re organising Quest for the Grail: An International Adventure Game, later this month: from noon to 5pm in London and right afterwards, noon to 5pm in Manhattan, New York.

The London teams will “hunt for objects in Clerkenwell hotspots…from the Order of St. John to Blackfriars Bridge to the International Magic Shop. You may be looking for a charm against the Plague, a tombstone or a silver goblet. Your team may be asked to invent something - the holiest of drinks.” The game continues with New York teams searching in “Manhattan hotspots…from Clinton Castle to the tombstones of Trinity Church to the Grand Lodge of the Masons. You may be looking for a marker of a headless ghost who haunts Wall Street, a symbol of George Washington or a troll in the East Village”, aided by London players and puppetmasters overseeing the games.

Unfortunately, I’m in sunny California recovering from my winter (and many years) of Planck work, but if you’re in either city and would like to play, you can join as an individual, a half-team of five, or a full team of ten players. There’s more information on the site, or you can contact the organisers directly at grail@timewavefestival.com.

Planck 2013: the PR

Yesterday’s release of the Planck papers and data wasn’t just aimed at the scientific community, of course. We wanted to let the rest of the world know about our results. The main press conference was at ESA HQ in Paris, and there was a smaller event here in London run by the UKSA, which I participated in as part of a panel of eight Planck scientists.

The reporters tried to keep us honest, asking us to keep simplifying our explanations so that they — and their readers — could understand them. We struggled with describing how our measurements of the typical size of spots in our map of the CMB eventually led us to a measurement of the age of the Universe (which I tried to do in my previous post). This was hard not only because the reasoning is subtle, but also because, frankly, it’s not something we care that much about: it’s a model-dependent parameter, something we don’t measure directly, and doesn’t have much of a cosmological consequence. (I ended up on the phone with the BBC’s Pallab Ghosh at about 8pm trying to work out whether the age has changed by 50 or 80 million years, a number that means more to him and his viewers than to me and my colleagues.)

There are pieces by the reporters who asked excellent questions at the press conference, at The Guardian, The Economist and The Financial Times, as well as one behind the (London) Times paywall by Hannah Devlin who was probably most rigorous in her requests for us to simplify our explanations. I’ll also point to NPR’s coverage, mostly since it is one of the few outlets to explicitly mention the topology of the Universe which was one of the areas of Planck science I worked on myself.

Aside from the press conference itself, the media were fairly clamouring for the chance to talk about Planck. Most of the major outlets in the UK and around Europe covered the Planck results. Even in the US, we made it onto the front page of the New York Times. Rather than summarise all of the results, I’ll just self-aggrandizingly point to the places where I appeared: a text-based preview from the BBC, and a short quote on video taken after the press conference, as well as one on ITV. I’m most proud of my appearance with Tom Clarke on Channel 4 News — we spent about an hour planning and discussing the results, edited down to a few minutes including my head floating in front of some green-screen astrophysics animations.

Now that the day is over, you can look at the results for yourself at the BBC’s nice interactive version, or at the lovely Planck Chromoscope created by Cardiff University’s Dr Chris North, who donated a huge amount of his time and effort to helping us make yesterday a success. I should also thank our funders over at the UK Space Agency, STFC and (indirectly) ESA — Planck is big science, and these sorts of results don’t come cheap. I hope you agree that they’ve been worth it.

Planck 2013: the science

If you’re the kind of person who reads this blog, then you won’t have missed yesterday’s announcement of the first Planck cosmology results.

The most important is our picture of the cosmic microwave background itself: Planck CMB node full image

But it takes a lot of work to go from the data coming off the Planck satellite to this picture. First, we have to make nine different maps, one at each of the frequencies in which Planck observes, from 30 GHz (with a wavelength of 1 cm) up to 850 GHz (0.350 mm) — note that the colour scales here are the same:


At low and high frequencies, these are dominated by the emission of our own galaxy, and there is at least some contamination over the whole range, so it takes hard work to separate the primordial CMB signal from the dirty (but interesting) astrophysics along the way. In fact, it’s sufficiently challenging that the team uses four different methods, each with different assumptions, to do so, and the results agree remarkably well.

In fact, we don’t use the above CMB image directly to do the main cosmological science. Instead, we build a Bayesian model of the data, combining our understanding of the foreground astrophysics and the cosmology, and marginalise over the astrophysical parameters in order to extract as much cosmological information as we can. (The formalism is described in the Planck likelihood paper, and the main results of the analysis are in the Planck cosmological parameters paper.)

The main tool for this is the power spectrum, a plot which shows us how the different hot and cold spots on our CMB map are distributed: PlanckCl In this plot, the left-hand side (low ℓ) corresponds to large angles on the sky and high ℓ to small angles. Planck’s results are remarkable for covering this whole range from ℓ=2 to ℓ=2500: the previous CMB satellite, WMAP, had a high-quality spectrum out to ℓ=750 or so; ground- and balloon-based experiments like SPT and ACT filled in some of the high-ℓ regime.

It’s worth marvelling at this for a moment, a triumph of modern cosmological theory and observation: our theoretical models fit our data from scales of 180° down to 0.1°, each of those bumps and wiggles a further sign of how well we understand the contents, history and evolution of the Universe. Our high-quality data has refined our knowledge of the cosmological parameters that describe the universe, decreasing the error bars by a factor of several on the six parameters that describe the simplest ΛCDM universe. Moreover, and maybe remarkably, the data don’t seem to require any additional parameters beyond those six: for example, despite previous evidence to the contrary, the Universe doesn’t need any additional neutrinos.

The quantity most well-measured by Planck is related to the typical size of spots in the CMB map; it’s about a degree, with an error of less than one part in 1,000. This quantity has changed a bit (by about the width of the error bar) since the previous WMAP results. This, in turn, causes us to revise our estimates of quantities like the expansion rate of the Universe (the Hubble constant), which has gone down, in fact by enough that it’s interestingly different from its best measurements using local (non-CMB) data, from more or less direct observations of galaxies moving away from us. Both methods have disadvantages: for the CMB, it’s a very indirect measurement, requiring imposing a model upon the directly measured spot size (known more technically as the “acoustic scale” since it comes from sound waves in the early Universe). For observations of local galaxies, it requires building up the famous cosmic distance ladder, calibrating our understanding of the distances to further and further objects, few of which we truly understand from first principles. So perhaps this discrepancy is due to messy and difficult astrophysics, or perhaps to interesting cosmological evolution.

This change in the expansion rate is also indirectly responsible for the results that have made the most headlines: it changes our best estimate of the age of the Universe (slower expansion means an older Universe) and of the relative amounts of its constituents (since the expansion rate is related to the geometry of the Universe, which, because of Einstein’s General Relativity, tells us the amount of matter).

But the cosmological parameters measured in this way are just Planck’s headlines: there is plenty more science. We’ve gone beyond the power spectrum above to put limits upon so-called non-Gaussianities which are signatures of the detailed way in which the seeds of large-scale structure in the Universe was initially laid down. We’ve observed clusters of galaxies which give us yet more insight into cosmology (and which seem to show an intriguing tension with some of the cosmological parameters). We’ve measured the deflection of light by gravitational lensing. And in work that I helped lead, we’ve used the CMB maps to put limits on some of the ways in which our simplest models of the Universe could be wrong, possibly having an interesting topology or rotation on the largest scales.

But because we’ve scrutinised our data so carefully, we have found some peculiarities which don’t quite fit the models. From the days of COBE and WMAP, there has been evidence that the largest angular scales in the map, a few degrees and larger, have some “anomalies” — some of the patterns show strange alignments, some show unexpected variation between two different hemispheres of the sky, and there are some areas of the sky that are larger and colder than is expected to occur in our theories. Individually, any of these might be a statistical fluke (and collectively they may still be) but perhaps they are giving us evidence of something exciting going on in the early Universe. Or perhaps, to use a bad analogy, the CMB map is like the Zapruder film: if you scrutinise anything carefully enough, you’ll find things that look a conspiracy, but turn out to have an innocent explanation.

I’ve mentioned eight different Planck papers so far, but in fact we’ve released 28 (and there will be a few more to come over the coming months, and many in the future). There’s an overall introduction to the Planck Mission, and papers on the data processing, observations of relatively nearby galaxies, and plenty more cosmology. The papers have been submitted to the journal A&A, they’re available on the ArXiV, and you can find a list of them at the ESA site.

Even more important for my cosmology colleagues, we’ve released the Planck data, as well, along with the necessary code and other information necessary to understand it: you can get it from the Planck Legacy Archive. I’m sure we’ve only just begun to get exciting and fun science out of the data from Planck. And this is only the beginning of Planck’s data: just the first 15 months of observations, and just the intensity of the CMB: in the coming years we’ll be analysing (and releasing) more than one more year of data, and starting to dig into Planck’s observations of the polarized sky.

Breaking the silence (updated)

My apologies for being far too busy to post. I’ll be much louder in couple of weeks once we release the Planck data — on March 21. Until then, I have to shut up and follow the Planck rules.

OK, back to editing. (I’ll try to update this post with any advance information as it becomes available.)

Update (on timing, not content): the main Planck press conference will be held on the morning of 21 March at 10am CET at ESA HQ in Paris. There will be a simultaneous UK event (9am GMT) held at the Royal Astronomical Society in London, where the Paris event will be streamed, followed by a local Q&A session. (There will also be a more technical afternoon session in Paris.)

Probably more important for my astrophysics colleagues: the Planck papers will be posted on the ESA website at noon on the 21st, after the press event, and will appear on the ArXiV the following day, 22 March. Be sure to set aside some time next weekend!

Not-quite hacked

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This week, the New York Times, The Wall Street Journal and Twitter, along with several other news organizations, have all announced that they were attacked by (most likely) Chinese hackers.

I am not quite happy to join their ranks: for the last few months, the traffic on this blog has been vastly dominated by attempts to get into the various back-end scripts that run this site, either by direct password hacks or just denial-of-service attacks. In fact, I only noticed it because the hackers exceeded my bandwidth allowance by a factor of a few (and costing me a few hundred bucks in over-usage charged by my host in the process, unfortunately).

I’ve since attempted to block the attacks by denying access to the IP addresses which have been the most active (mostly from domains that look like 163data.com.cn, for what it’s worth). So, my apologies if any of this results in any problems for anyone else trying to access the blog.