I recently received an anonymous tipoff (from Haley Gomez) drawing attention to the remarkable similarity in visual appearance between esteemed Plumian Professor of Astronomy and Experimental Philosophy at the University of Cambridge Rob Kennicutt and the Muppet Show’s resident comedian Fozzie Bear. I hear they sound similar too! I wonder if by any chance they might be related?
Fozzie Bear
Today’s the day. My annual Staff Appraisal with the Big Boss. I’ve filled in the forms and am ready to go. I expect it will go pretty much like this, except without the beards.
Another busy day – mainly filled with form-filling but also including a tutorial and a meeting of our cosmology discussion group – and tonight, for the second week running, I’m off to a lecture at Cardiff Scientific Society. This time it’s by our own Haley Gomez entitled Smoking Supernovae. And here am I trying to give up!
Anyway, I’m going to do what I usually do when I haven’t got time for a proper post and that is put up a bit of poetry. Appropriate for the time of year, in hopeful anticipation of the forthcoming spring, I offer you this (from a poem entitled In February written by Alice Meynell).
Rich meanings of the prophet-Spring adorn,
Unseen, this colourless sky of folded showers,
And folded winds; no blossom in the bowers;
A poet’s face asleep in this grey morn.
Now in the midst of the old world forlorn
A mystic child is set in these still hours.
I keep this time, even before the flowers,
Sacred to all the young and the unborn
As a cosmologist, I am often asked why it is that people talk about the cosmological constant as if it were some sort of vacuum energy or “dark energy“. I was explaining it again to a student today so I thought I’d jot something down here so I can use it for future reference. In a nutshell, it goes like this. The original form of Einstein’s equations for general relativity can be written
The precise meaning of the terms on the left hand side doesn’t really matter, but basically they describe the curvature of space-time and are derived from the Ricci tensor 
In standard cosmology we usually assume that we can describe the matter-energy content of the Universe as a uniform perfect fluid, for which the energy-momentum tensor takes the simple form
in which 
Einstein famously modified (or perhaps generalised) the original equations by adding a cosmological constant term 
Doing this essentially modifies the description of gravity, or appears to do so because it happens to be written on the left hand side of the equation. In fact one could equally well move the term involving 
The new energy-momentum tensor needed to make this work is of the form
where
So the cosmological constant now looks like you didn’t modify gravity at all, but created an additional contribution to the pressure and density of the original fluid. In fact, considering the correction terms on their own it is clear that the cosmological constant acts exactly like an additional perfect fluid contribution with 
This is just one simple example wherein a modification of the gravitational part of the theory can be made to look like the appearance of a peculiar form of matter. More complicated versions of this idea – most of them entirely speculative – abound in theoretical cosmology. That’s just what cosmologists are like.
Over the last few decades cosmology has suffered an invasion by been stimulated and enriched by particle physicists who would like to understand how such a mysterious form of energy might arise in their theories. That at least partly explains why, in one sense at least, modern cosmologists prefer to dress to the right.
Incidentally, another interesting point is why people say such a fluid describes a cosmological “vacuum” energy. In the cosmological setting, i.e. assuming the fluid is distributed in a homogeneous and isotropic fashion then the energy density of the expanding Universe varies with (cosmological proper) time according to
so for our strange fluid, the second term in brackets vanishes and we have 
I hope this clarifies the situation.
Recently a wooden fence appeared around the Council Nursery in Bute Park, clearly erected to hide what’s going on inside from prying eyes. Walking into work the other day I noticed that one of the gates was open so I went and had a look. I was shocked by the scale of the building work I saw inside. Foundations are being laid for an enormous new building, mysteriously entitled the Nursery Education and Training Centre.
There’s a helpful sign on the fence to explain what’s going on:
You probably can’t read the text but, amongst other things, it states that a new wall will be built “along the line of the existing conifer hedge, which will be felled by the Council’s arborists in advance of the construction” (my emphasis). Nasty pesky hedges. Nearly as bad as trees. Get in the way of our nice new brick wall. Get rid of them. Still, at least the brick wall might hide some of the horrors lurking inside…
It will allow people an insight into the council’s impressive horticultural operation which supplies the city with its colourful displays of flowers and shrubs. For example, there will be a special area for teaching demonstrations by horticultural staff and large windows situated at the back of the centre will allow people to look out over the working part of the nursery.
The facility will also boast excellent learning assets including a classroom and an IT and archive room which will house a variety of resources on park heritage, natural history and environmental themes.
The centre will be available for hire by community and corporate groups and additional facilities will include a catering kiosk and public toilets.
Excellent. People can go inside and see what plants and trees look like on the internet, rather than actually having to walk around in the outside in the fresh air and see the real thing. Mind you, before long so much of Bute Park will have been covered in tarmac that’s the only way people will be able to see foliage of any sort.
I’ve nothing against the idea of encouraging more people into the Park, but not by ploughing it up and building things in it! Do people really want to go into Bute Park to look at greenhouses rather than simply enjoy its serene natural beauty out in the open?
Even more disturbingly, take a look at the artist’s impression to the right of the map. It shows a path wide enough to be considered a road. There are even pedestrians on it. They’re taking a bit of a risk, as the Council clearly intends this to be used by motor vehicles driving into and out of the Nursery. All the speed limit signs in the park have been removed to allow the new influx of road vehicles to drive around at high speed, so this new path will no doubt be just as dangerous as the rest of the park has become.
But wait a minute. Look where the path goes. It doesn’t stop at the planned new entrance to the Nursery. It carries on towards the River Taff, which is just a few yards away. I wonder why?
Let’s take a look across the River from the Nursery gate:
That’s one of the stands of the SWALEC Stadium (the cricket ground) to the right, and part of the Wales Institute of Sport to the left. In between these two is a road which runs from Sophia Gardens towards the River Taff where it comes to a dead end exactly opposite the new Nursery Road.
Let’s have a sweepstake on when the Council starts building its new bridge…
There’s a Council byelection in my ward next month. There’s only one party standing to have stated its opposition to the rapacious exploitation of this beautiful park, and that’s the Green Party. They’ve got my vote.
Just a quick post to pass on the news that the Higher Education Funding Council for England (HEFCE) has announced the list of panel members for the forthcoming Research Excellence Framework (REF), a massive exercise in bean counting which will drag on until 2014.
Much as I enjoy ploughing through HEFCE’s fascinating documents, in this case I went straight to the Physics (& Astronomy) sub-panel, which is:
All estimable folk and a good selection of different expertise. There’s also a good geographical spread with members from the English regions, Scotland, Northern Ireland, and of course Wales. Oh, wait a minute. Not Wales. Apparently Wales doesn’t merit any representation on the Physics REF panel. Nor did it last time. Why am I thinking to myself “here we go again”?
To be perfectly honest, I don’t really understand why Welsh universities are being forced to take part in the REF anyway. Or those from Scotland and Northern Ireland for that matter. The REF is driven by an English agenda which is certainly at variance with Welsh priorities. Whereas in England, HEFCE is allocating funding using a formula involving an exceedingly steep weighting towards “internationally leading” research, here in Wales the equivalent body HEFCW is resisting the urge to concentrate research cash so heavily according to such a doubtful measure of research quality.
And don’t get me started on the so-called “impact” measures. All I can say about them is that Kafka would have been proud.
The Welsh Assembly Government has recently taken steps to protect Welsh students against the effects of Higher Education cuts imposed by Westminster. However, there will be substantial cuts in resource to Welsh universities in order to pay for this. At the same time as making “efficiency savings”, as is appropriate for the age of austerity, we’re also being forced to participate in a monstrously wasteful bureaucratic exercise of little relevance to the needs or aspirations of Welsh universities.
I think there’s a strong case for HEFCW to show a bit of real independence and withdraw from the REF altogether.
Before going to bed I couldn’t resist a late night post of this wonderful version of a Rodgers & Hart ballad called It Never Entered My Mind recorded by Miles Davis for the Blue Note label in the early 50s. Listening to the later Miles Davis playing a standard tune such as this is a bit like trying to recognise an old friend from a photograph of his skeleton, but here he sticks quite closely to the original composition. With that hauntingly melancholic tone, however, it is pure Miles Davis all the way through.
The composition is a standard AABA form, but with interesting harmonic movements: the A sections (which aren’t identical) consist of repeated notes followed by descending scales whereas the B section – the middle eight – starts with a drop of a minor sixth followed by an ascending scale. It’s a simple device but wonderfully effective, especially in the hands of a genius. I think this track is an absolute gem.
The other musicians featured are Horace Silver (piano), Percy Heath (bass) and Art Blakey (drums). Bonus marks to those who can put names to the other jazz legends shown in the photographs, but don’t let the task of identifying them distract you from the beautiful music…
Yesterday’s post about Bayesian statistics has generated over a thousand hits in just a day – highly unusual for a Saturday posting at In the Dark. I guess that proves that there’s a lot of interest out there in such matters, so I’ll return to the theme as soon as I have both the time and the energy, which might take a while because those are conjugate variables!
After yesterday’s exertions I felt like relaxing this morning, and I did so by transferring some of my old vinyl (and even shellac!) records into digital format using a USB turntable. I’m a bit frustrated by the fact that some of my favourite classic old jazz records aren’t available on Youtube and am thinking of correcting that at some point myself, despite my latent technophobia.
However, in the course of rooting about in my record collection I found a vinyl single of this record by Sting, the Ben Liebrand remix to be precise. It is, of course, a homage to the late Quentin Crisp whose book The Naked Civil Servant I read after seeing the wonderful film starring John Hurt, which was broadcast on the BBC in 1975, when I was 12. I found inspiration in both, for reasons I probably don’t need to spell out. Crisp emigrated to the United States in 1981 and lived the last years of his life in a dingy one-room apartment in New York City.
There’s another quasi-biographical connection with this record. When I was a little kid living in Benwell, my Dad used to play the drums with local jazz bands. At the time Sting (or plain Gordon Sumner as he was then known) was working as a supply teacher in the area and he played the double-bass with local groups too, including the Phoenix Jazz Band and the River City Jazz Band; the latter was certainly a band my father played with from time to time. My Dad once told me that he had played with Sting on a number of occasions, and he’d even practised in our garage, but I’m not sure how much of that is actually true.
Incidentally, in case you didn’t know, Sting got his nickname playing with jazz bands in the North-East. He always refused to wear the band uniforms but instead tended to turn up for gigs wearing a black and yellow hooped jumper which made him look a bit like a bee, hence the name.
This isn’t a jazz record, of course, but it does feature Branford Marsalis (brother of the trumpeter Wynton Marsalis) on soprano saxophone. I bought a soprano saxophone some time ago and tried to play along with the track just now – the chords aren’t very complicated so it shouldn’t have been too difficult even for an incompetent like me. However, I’m finding the soprano sax quite a recalcitrant beast which is very difficult to play in tune. I’m not sure why. I manage all right with its bigger brother the tenor sax. Perhaps it’s my embouchure? Or, as jazz musicians say, I haven’t got the chops?
I’ll just quote one particularly telling verse from the lyrics:
Takes more than combat gear to make a man
Takes more than a license for a gun
Confront your enemies, avoid them when you can
A gentleman will walk but never run
It’s been quite while since I posted a little piece about Bayesian probability. That one and the others that followed it (here and here) proved to be surprisingly popular so I’ve been planning to add a few more posts whenever I could find the time. Today I find myself in the office after spending the morning helping out with a very busy UCAS visit day, and it’s raining, so I thought I’d take the opportunity to write something before going home. I think I’ll do a short introduction to a topic I want to do a more technical treatment of in due course.
A particularly important feature of Bayesian reasoning is that it gives precise motivation to things that we are generally taught as rules of thumb. The most important of these is Ockham’s Razor. This famous principle of intellectual economy is variously presented in Latin as Pluralites non est ponenda sine necessitate or Entia non sunt multiplicanda praetor necessitatem. Either way, it means basically the same thing: the simplest theory which fits the data should be preferred.
William of Ockham, to whom this dictum is attributed, was an English Scholastic philosopher (probably) born at Ockham in Surrey in 1280. He joined the Franciscan order around 1300 and ended up studying theology in Oxford. He seems to have been an outspoken character, and was in fact summoned to Avignon in 1323 to account for his alleged heresies in front of the Pope, and was subsequently confined to a monastery from 1324 to 1328. He died in 1349.
In the framework of Bayesian inductive inference, it is possible to give precise reasons for adopting Ockham’s razor. To take a simple example, suppose we want to fit a curve to some data. In the presence of noise (or experimental error) which is inevitable, there is bound to be some sort of trade-off between goodness-of-fit and simplicity. If there is a lot of noise then a simple model is better: there is no point in trying to reproduce every bump and wiggle in the data with a new parameter or physical law because such features are likely to be features of the noise rather than the signal. On the other hand if there is very little noise, every feature in the data is real and your theory fails if it can’t explain it.
To go a bit further it is helpful to consider what happens when we generalize one theory by adding to it some extra parameters. Suppose we begin with a very simple theory, just involving one parameter 
Quantities such as
Obviously, having three degrees of freedom with which to describe the data should enable one to get a closer fit than is possible with just one. The greater flexibility within the general theory can be exploited to match the measurements more closely than the original. In other words, such a model can improve the likelihood, i.e. the probability of the obtained data arising (given the noise statistics – presumed known) if the signal is described by whatever model we have in mind.
But Bayes’ theorem tells us that there is a price to be paid for this flexibility, in that each new parameter has to have a prior probability assigned to it. This probability will generally be smeared out over a range of values where the experimental results (contained in the likelihood) subsequently show that the parameters don’t lie. Even if the extra parameters allow a better fit to the data, this dilution of the prior probability may result in the posterior probability being lower for the generalized theory than the simple one. The more parameters are involved, the bigger the space of prior possibilities for their values, and the harder it is for the improved likelihood to win out. Arbitrarily complicated theories are simply improbable. The best theory is the most probable one, i.e. the one for which the product of likelihood and prior is largest.
To give a more quantitative illustration of this consider a given model 
Now assume we have some data 
The interesting thing to look at now is not the best-fitting choice of model parameters 
This is just the normalizing constant 
In statistical mechanics things like
The usefulness of the Bayesian evidence emerges when we ask the question whether our
The answer is that although adding an extra degree of freedom can increase the first term in the integral defining 
This is a satisfying result that is in nice accord with common sense. But I think it goes much further than that. Many modern-day physicists are obsessed with the idea of a “Theory of Everything” (or TOE). Such a theory would entail the unification of all physical theories – all laws of Nature, if you like – into a single principle. An equally accurate description would then be available, in a single formula, of phenomena that are currently described by distinct theories with separate sets of parameters. Instead of textbooks on mechanics, quantum theory, gravity, electromagnetism, and so on, physics students would need just one book.
The physicist Stephen Hawking has described the quest for a TOE as like trying to read the Mind of God. I think that is silly. If a TOE is every constructed it will be the most economical available description of the Universe. Not the Mind of God. Just the best way we have of saving paper.
Now here’s a short video called a (presented by the legendary Harriet Parfitt) explaining the joys of studying in the School of Physics & Astronomy at Cardiff University. It’s somewhat spoiled by the appearance of yours truly (filmed during a recent first-year Astrophysical Concepts lecture) but apart from that it’s really rather good!
In the Dark 