After a very busy working weekend I have neither the time nor the energy for a proper blog post, do here’s something I found on my phone. I can’t remember where it came from, but it’s a model of the late Sir Patrick Moore made entirely from vegetables. Now that’s something you don’t see every day..Follow @telescoper
A few months have passed since I last won a dictionary as a prize in the Independent Crossword competition. That’s nothing remarkable in itself, but since my average rate of dictionary accumulation has been about one a month over the last few years, it seems a bit of a lull. Have I forgotten how to do crosswords and keep sending in wrong solutions? Is the Royal Mail intercepting my post? Has the number of correct entries per week suddenly increased, reducing my odds of winning? Have the competition organizers turned against me?
In fact, statistically speaking, there’s nothing significant in this gap. Even if my grids are all correct, the number of correct grids has remained constant, and the winner is pulled at random from those submitted (i.e. in such a way that all correct entries are equally likely to be drawn) , then a relatively long unsuccessful period such as I am experiencing at the moment is not at all improbable. The point is that such runs are far more likely in a truly random process than most people imagine, as indeed are runs of successes. Chance coincidences happen more often than you think.
I try this out in lectures sometimes, by asking a member of the audience to generate a random sequence of noughts and ones in their head. It seems people are very conscious that the number of ones should be roughly equal to the number of noughts that they impose that as they go along. Almost universally, the supposedly random sequences people produce only have very short runs of 1s or 0s because, say, a run like ‘00000’ just seems too unlikely. Well, it is unlikely, but that doesn’t mean it won’t happen. In a truly random binary sequence like this (i.e. one in which 1 and 0 both have a probability of 0.5 and each selection is independent of the others), coincidental runs of consecutive 0s and 1s happen with surprising frequency. Try it yourself, with a coin.
Coincidentally, the subject of randomness was suggested to me independently yesterday by an anonymous email correspondent by the name of John Peacock as I have blogged about it before; one particular post on this topic is actually one of this blog’s most popular articles). What triggered this was a piece about music players such as Spotify (whatever that is) which have a “random play” feature. Apparently people don’t accept that it is “really random” because of the number of times the same track comes up. To deal with this “problem”, experts are working at algorithms that don’t actually play things randomly but in such a way that accords with what people think randomness means.
I think this fiddling is a very bad idea. People understand probability so poorly anyway that attempting to redefine the word’s meaning is just going to add confusion. You wouldn’t accept a casino that used loaded dice, so why allow cheating in another context? Far better for all concerned for the general public to understand what randomness is and, perhaps more importantly, what it looks like.
I have to confess that I don’t really like the word “randomness”, but I haven’t got time right now for a rant about it. There are, however, useful mathematical definitions of randomness and it is also (sometimes) useful to make mathematical models that display random behaviour in a well-defined sense, especially in situations where one has to take into account the effects of noise.
I thought it would be fun to illustrate one such model. In a point process, the random element is a “dot” that occurs at some location in time or space. Such processes can be defined in one or more dimensions and relate to a wide range of situations: arrivals of buses at a bus stop, photons in a detector, darts on a dartboard, and so on.
The statistical description of clustered point patterns is a fascinating subject, because it makes contact with the way in which our eyes and brain perceive pattern. I’ve spent a large part of my research career trying to figure out efficient ways of quantifying pattern in an objective way and I can tell you it’s not easy, especially when the data are prone to systematic errors and glitches. I can only touch on the subject here, but to see what I am talking about look at the two patterns below:
You will have to take my word for it that one of these is a realization of a two-dimensional Poisson point process and the other contains correlations between the points. One therefore has a real pattern to it, and one is a realization of a completely unstructured random process.
I show this example in popular talks and get the audience to vote on which one is the random one. In fact, I did this just a few weeks ago during a lecture in our module Quarks to Cosmos, which attempts to explain scientific concepts to non-science students. As usual when I do this, I found that the vast majority thought that the top one is random and the bottom one is the one with structure to it. It is not hard to see why. The top pattern is very smooth (what one would naively expect for a constant probability of finding a point at any position in the two-dimensional space) , whereas the bottom one seems to offer a profusion of linear, filamentary features and densely concentrated clusters.
In fact, it’s the bottom picture that was generated by a Poisson process using a Monte Carlo random number generator. All the structure that is visually apparent in the second example is imposed by our own sensory apparatus, which has evolved to be so good at discerning patterns that it finds them when they’re not even there!
The top process is also generated by a Monte Carlo technique, but the algorithm is more complicated. In this case the presence of a point at some location suppresses the probability of having other points in the vicinity. Each event has a zone of avoidance around it; the points are therefore anticorrelated. The result of this is that the pattern is much smoother than a truly random process should be. In fact, this simulation has nothing to do with galaxy clustering really. The algorithm used to generate it was meant to mimic the behaviour of glow-worms which tend to eat each other if they get too close. That’s why they spread themselves out in space more uniformly than in the “really” random pattern.
I assume that Spotify’s non-random play algorithm will have the effect of producing a one-dimensional version of the top pattern, i.e. one with far too few coincidences to be genuinely random.
Incidentally, I got both pictures from Stephen Jay Gould’s collection of essays Bully for Brontosaurus and used them, with appropriate credit and copyright permission, in my own book From Cosmos to Chaos.
The tendency to find things that are not there is quite well known to astronomers. The constellations which we all recognize so easily are not physical associations of stars, but are just chance alignments on the sky of things at vastly different distances in space. That is not to say that they are random, but the pattern they form is not caused by direct correlations between the stars. Galaxies form real three-dimensional physical associations through their direct gravitational effect on one another.
People are actually pretty hopeless at understanding what “really” random processes look like, probably because the word random is used so often in very imprecise ways and they don’t know what it means in a specific context like this. The point about random processes, even simpler ones like repeated tossing of a coin, is that coincidences happen much more frequently than one might suppose.
I suppose there is an evolutionary reason why our brains like to impose order on things in a general way. More specifically scientists often use perceived patterns in order to construct hypotheses. However these hypotheses must be tested objectively and often the initial impressions turn out to be figments of the imagination, like the canals on Mars.
Perhaps I should complain to WordPress about the widget that links pages to a “random blog post”. I’m sure it’s not really random….Follow @telescoper
I came across a blog post this morning entitled Does Science Produce Too Many PhDs? I think the answer is an obvious “yes” but I’ll use the question as an excuse to rehash an argument I have presented before, which is that most analyses of the problems facing yearly career researchers in science are looking at the issue from the wrong end. I think the crisis is essentially caused by the overproduction of PhDs in this field. To understand the magnitude of the problem, consider the following.
Assume that the number of permanent academic positions in a given field (e.g. astronomy) remains constant over time. If that is the case, each retirement (or other form of departure) from a permanent position will be replaced by one, presumably junior, scientist.
This means that over an academic career, on average, each academic will produce just one PhD who will get a permanent job in academia. This of course doesn’t count students coming in from abroad, or those getting faculty positions abroad, but in the case of the UK these are probably relatively small corrections.
Under the present supply of PhD studentships an academic can expect to get a PhD student at least once every three years or so. At a minimum, therefore, over a 30 year career one can expect to have ten PhD students. A great many supervisors have more PhD students than this, but this just makes the odds worse. The expectation is that only one of these will get a permanent job in the UK. The others (nine out of ten, according to my conservative estimate) above must either leave the field or the country to find permanent employment.
The arithmetic of this situation is a simple fact of life, but I’m not sure how many prospective PhD students are aware of it. There is still a reasonable chance of getting a first postdoctoral position, but thereafter the odds are stacked against them.
The upshot of this is we have a field of understandably disgruntled young people with PhDs but no realistic prospect of ever earning a settled living working in the field they have prepared for. This problem has worsened considerably in recent years as the number of postdoctoral positions has almost halved since 2006. New PhDs have to battle it out with existing postdoctoral researchers for the meagre supply of suitable jobs. It’s a terrible situation.
Now the powers that be – in this case the Science and Technology Facilities Council – have consistently argued that the excess PhDs go out into the wider world and contribute to the economy with the skills they have learned. That may be true in a few cases. However, my argument is that the PhD is not the right way to do this because it is ridiculously inefficient.
What we should have is a system wherein we produce more and better trained Masters level students and fewer PhDs. This is the system that exists throughout most of Europe, in fact, and the UK is actually committed to adopt it through the Bologna process. Not that this commitment seems to mean anything, as precisely nothing has been done to harmonize UK higher education with the 3+2+3 Bachelors+Masters+Doctorate system Bologna advocates.
The training provided in a proper two-year Masters programme will improve the skills pool for the world outside academia, and also better prepare the minority of students who go on to take a PhD. The quality of the PhD will also improve, as only the very best and most highly motivated researchers will take that path. This used to be what happened, of course, but I don’t think it is any longer the case.
The main problem with this suggestion is that it requires big changes to the way both research and teaching are funded. The research councils turned away from funding Masters training many years ago, so I doubt if they can be persuaded to to a U-turn now. Moreover, the Research Excellence Framework provides a strong incentive for departments to produce as many PhDs as they possibly can, as these are included in an algorithmic way as part of the score for “Research Environment”. The more PhDs a department produces, the higher it will climb in the league tables. One of my targets in my current position is to double the number of PhDs produced by my School over the period 2013-18. What happens to the people concerned seems not to be a matter worthy of consideration. They’re only “outputs”…Follow @telescoper
Interesting analysis of the 2014 REF results by my colleague Seb Oliver. Among other things, it shows that Physics was the subject in which “Impact had the greatest impact”..
Originally posted on Seb Boyd:
The Impact of Impact
I wrote the following article to explore how Impact in the Research Excellence Framework 2014 (REF2014) affected the average scores of departments (and hence rankings). This produced a “league table” of how strongly impact affected different subjects. Some of the information in this article was used in a THE article by Paul Jump due to come out 00:00 on 19th Feb 2015. I’ve now also produced ranking tables for each UoA using the standardised weighting I advocate below (see Standardised Rankings).
|UoA||Unit of Assessment||
Effective Weight of GPA
ranking in each sub-profile as %
|24||Anthropology and Development Studies||40.2||35.0||24.8|
|6||Agriculture, Veterinary and Food Science||42.0||33.0||25.0|
|16||Architecture, Built Environment and Planning||48.6||31.1||20.3|
View original 1,558 more words
A very busy day at work has just ended without time to do a blog post, so before I go home I’ll just do a quickie about the classic album A Love Supreme made by the John Coltrane quartet in late 1964 and released in February 1965. The 50th anniversary of the release of this record has been marked by an extremely interesting programme on BBC Radio 4, broadcast a few days ago but still available on the BBC iPlayer.
A Love Supreme is one of my favourite jazz albums, not only because it’s glorious music to listen to but also for its historical importance. Shortly after making this record Coltrane comprehensively changed his musical direction, abandoning many of the structures that underpinned his earlier work and adopting an approach heavily influenced by the free jazz of the likes of Ornette Coleman and, especially, Albert Ayler. Not everyone likes the music Coltrane made after he made that transition (in 1965) but having taken his earlier style to such a high peak as A Love Supreme he and the rest of the band no doubt felt they couldn’t go any further in that direction.
There are glimpses of the later freer approach in the third track, Pursuance, when the drum and saxophone interchanges between Elvin Jones and Coltrane threaten to break the regular tempo apart, and on this (the second) track Resolution, when McCoy Tyner abandons his usual single-note lines in favour of much more complex chordal improvisations. I think Coltrane’s solo on the last track, Psalm, is entirely improvised and , accompanied by Jones’ rising and falling drum rolls, it acquires a hauntingly solemn atmosphere which makes the hairs stand up on the back of my neck every time I hear it. What a fantastic drummer Elvin Jones was.
But I haven’t got time to analyse the whole album – another’s words are in any case no substitute for listening to this masterpiece yourself – so I’ll just mention that Resolution is based on an 8-bar theme that’s very reminiscent of the theme Africa featured on Africa/Brass made a couple of years earlier. To me it sounds like Coltrane is just itching to cut loose on this track. His saxophone tone has a harder edge than usual for that period, giving the piece an anguished, pleading feel. Elvin Jones is also magnificent, his polyrhythmic accents spurring Coltrane to a climactic solo.
The intensity of Resolution ignites an even more dramatic onslaught on the next track, Pursuance, basically a blues taken at a very fast tempo, before the mood changes completely for the final part, Psalm. And all this builds from the opening track, Acknowledgement, which closes with the whole group chanting the words A Love Supreme in unison to a simple four-note figure stated at the opening of the piece.
Four tracks amounting to just over 30 minutes of music, but a masterpiece by any standards. If you’re thinking of starting a jazz collection, put it straight on your list! You could also listen to the whole thing via YoutubeFollow @telescoper
I thought I’d take a few minutes to celebrate the fact that the first first-author paper by my PhD student here at the University of Sussex, Mateja Gosenca, has just hit the arXiv. The abstract reads:
We explore the dynamical behaviour of cosmological models involving a scalar field (with an exponential potential and a canonical kinetic term) and a matter fluid with spatial curvature included in the equations of motion. Using appropriately defined parameters to describe the evolution of the scalar field energy in this situation, we find that there are two extra fixed points that are not present in the case without curvature. We also analyse the evolution of the effective equation-of-state parameter for different initial values of the curvature.
There has been a lot of interest recently in treating cosmological models as dynamical systems, and the class of models we studied has been analysed before (see the references in the paper) but this paper addresses them in a different (and perhaps slightly more elegant) way and in the context of quintessence models for dark energy. It also contains some very pretty multi-dimensional phase portraits, like this:
Of course these figures are self-explanatory, so I’ll say no more about them…Follow @telescoper