Archive for December, 2008

Who put the Bang in Big Bang?

Posted in The Universe and Stuff with tags , , , , , on December 29, 2008 by telescoper

Back from the frozen North, having had a very nice time over Christmas, I thought it was time to reactivate my blog and to redress the rather shameful lack of science on what is supposed to be a science blog. Rather than writing a brand new post, though, I’m going to cheat like a TV Chef by sticking up something that I did earlier. I’ve  had the following piece floating around on my laptop for a while so I thought I’d rehash it and post it on here. It is based on an article that was published in a heavily revised and shortened form in New Scientist in 2007, where it attracted some splenetic responses despite there not being anything particular controversial in it! It’s not particularly topical, but there you go. The television is full of repeats these days too.

Around twenty-five years ago a young physicist came up with what seemed at first to be an absurd idea: that, for a brief moment in the very distant past, just after the Big Bang, something weird happened to gravity that made it push rather than pull.  During this time the Universe went through an ultra-short episode of ultra-fast expansion. The physicist in question, Alan Guth, couldn’t prove that this “inflation” had happened nor could he suggest a compelling physical reason why it should, but the idea seemed nevertheless to solve several major problems in cosmology.

Twenty five years later on, Guth is a professor at MIT and inflation is now well established as an essential component of the standard model of cosmology. But should it be? After all, we still don’t know what caused it and there is little direct evidence that it actually took place. Data from probes of the cosmic microwave background seem to be consistent with the idea that inflation happened, but how confident can we be that it is really a part of the Universe’s history?

According to the Big Bang theory, the Universe was born in a dense fireball which has been expanding and cooling for about 14 billion years. The basic elements of this theory have been in place for over eighty years, but it is only in the last decade or so that a detailed model has been constructed which fits most of the available observations with reasonable precision. The problem is that the Big Bang model is seriously incomplete. The fact that we do not understand the nature of the dark matter and dark energy that appears to fill the Universe is a serious shortcoming. Even worse, we have no way at all of describing the very beginning of the Universe, which appears in the equations used by cosmologists as a “singularity”- a point of infinite density that defies any sensible theoretical calculation. We have no way to define a priori the initial conditions that determine the subsequent evolution of the Big Bang, so we have to try to infer from observations, rather than deduce by theory, the parameters that govern it.

The establishment of the new standard model (known in the trade as the “concordance” cosmology) is now allowing astrophysicists to turn back the clock in order to understand the very early stages of the Universe’s history and hopefully to understand the answer to the ultimate question of what happened at the Big Bang itself and thus answer the question “How did the Universe Begin?”

Paradoxically, it is observations on the largest scales accessible to technology that provide the best clues about the earliest stages of cosmic evolution. In effect, the Universe acts like a microscope: primordial structures smaller than atoms are blown up to astronomical scales by the expansion of the Universe. This also allows particle physicists to use cosmological observations to probe structures too small to be resolved in laboratory experiments.

Our ability to reconstruct the history of our Universe, or at least to attempt this feat, depends on the fact that light travels with a finite speed. The further away we see a light source, the further back in time its light was emitted. We can now observe light from stars in distant galaxies emitted when the Universe was less than one-sixth of its current size. In fact we can see even further back than this using microwave radiation rather than optical light. Our Universe is bathed in a faint glow of microwaves produced when it was about one-thousandth of its current size and had a temperature of thousands of degrees, rather than the chilly three degrees above absolute zero that characterizes the present-day Universe. The existence of this cosmic background radiation is one of the key pieces of evidence in favour of the Big Bang model; it was first detected in 1964 by Arno Penzias and Robert Wilson who subsequently won the Nobel Prize for their discovery.

The process by which the standard cosmological model was assembled has been a gradual one, but it culminated with recent results from the Wilkinson Microwave Anisotropy Probe (WMAP). For several years this satellite has been mapping the properties of the cosmic microwave background and how it varies across the sky. Small variations in the temperature of the sky result from sound waves excited in the hot plasma of the primordial fireball. These have characteristic properties that allow us to probe the early Universe in much the same way that solar astronomers use observations of the surface of the Sun to understand its inner structure,  a technique known as helioseismology. The detection of the primaeval sound waves is one of the triumphs of modern cosmology, not least because their amplitude tells us precisely how loud the Big Bang really was.

The pattern of fluctuations in the cosmic radiation also allows us to probe one of the exciting predictions of Einstein’s general theory of relativity: that space should be curved by the presence of matter or energy. Measurements from WMAP reveal that our Universe is very special: it has very little curvature, and so has a very finely balanced energy budget: the positive energy of the expansion almost exactly cancels the negative energy relating of gravitational attraction. The Universe is (very nearly) flat.

The observed geometry of the Universe provides a strong piece of evidence that there is an mysterious and overwhelming preponderance of dark stuff in our Universe. We can’t see this dark matter and dark energy directly, but we know it must be there because we know the overall budget is balanced. If only economics were as simple as physics.

Computer Simulation of the Cosmic Web

The concordance cosmology has been constructed not only from observations of the cosmic microwave background, but also using hints supplied by observations of distant supernovae and by the so-called “cosmic web” – the pattern seen in the large-scale distribution of galaxies which appears to match the properties calculated from computer simulations like the one shown above, courtesy of Volker Springel. The picture that has emerged to account for these disparate clues is consistent with the idea that the Universe is dominated by a blend of dark energy and dark matter, and in which the early stages of cosmic evolution involved an episode of accelerated expansion called inflation.

A quarter of a century ago, our understanding of the state of the Universe was much less precise than today’s concordance cosmology. In those days it was a domain in which theoretical speculation dominated over measurement and observation. Available technology simply wasn’t up to the task of performing large-scale galaxy surveys or detecting slight ripples in the cosmic microwave background. The lack of stringent experimental constraints made cosmology a theorists’ paradise in which many imaginative and esoteric ideas blossomed. Not all of these survived to be included in the concordance model, but inflation proved to be one of the hardiest (and indeed most beautiful) flowers in the cosmological garden.

Although some of the concepts involved had been formulated in the 1970s by Alexei Starobinsky, it was Alan Guth who in 1981 produced the paper in which the inflationary Universe picture first crystallized. At this time cosmologists didn’t know that the Universe was as flat as we now think it to be, but it was still a puzzle to understand why it was even anywhere near flat. There was no particular reason why the Universe should not be extremely curved. After all, the great theoretical breakthrough of Einstein’s general theory of relativity was the realization that space could be curved. Wasn’t it a bit strange that after all the effort needed to establish the connection between energy and curvature, our Universe decided to be flat? Of all the possible initial conditions for the Universe, isn’t this very improbable? As well as being nearly flat, our Universe is also astonishingly smooth. Although it contains galaxies that cluster into immense chains over a hundred million light years long, on scales of billions of light years it is almost featureless. This also seems surprising. Why is the celestial tablecloth so immaculately ironed?

Guth grappled with these questions and realized that they could be resolved rather elegantly if only the force of gravity could be persuaded to change its sign for a very short time just after the Big Bang. If gravity could push rather than pull, then the expansion of the Universe could speed up rather than slow down. Then the Universe could inflate by an enormous factor (1060 or more) in next to no time and, even if it were initially curved and wrinkled, all memory of this messy starting configuration would be lost. Our present-day Universe would be very flat and very smooth no matter how it had started out.

But how could this bizarre period of anti-gravity be realized? Guth hit upon a simple physical mechanism by which inflation might just work in practice. It relied on the fact that in the extreme conditions pertaining just after the Big Bang, matter does not behave according to the classical laws describing gases and liquids but instead must be described by quantum field theory. The simplest type of quantum field is called a scalar field; such objects are associated with particles that have no spin. Modern particle theory involves many scalar fields which are not observed in low-energy interactions, but which may well dominate affairs at the extreme energies of the primordial fireball.

Classical fluids can undergo what is called a phase transition if they are heated or cooled. Water for example, exists in the form of steam at high temperature but it condenses into a liquid as it cools. A similar thing happens with scalar fields: their configuration is expected to change as the Universe expands and cools. Phase transitions do not happen instantaneously, however, and sometimes the substance involved gets trapped in an uncomfortable state in between where it was and where it wants to be. Guth realized that if a scalar field got stuck in such a “false” state, energy – in a form known as vacuum energy – could become available to drive the Universe into accelerated expansion.We don’t know which scalar field of the many that may exist theoretically is responsible for generating inflation, but whatever it is, it is now dubbed the inflaton.

This mechanism is an echo of a much earlier idea introduced to the world of cosmology by Albert Einstein in 1916. He didn’t use the term vacuum energy; he called it a cosmological constant. He also didn’t imagine that it arose from quantum fields but considered it to be a modification of the law of gravity. Nevertheless, Einstein’s cosmological constant idea was incorporated by Willem de Sitter into a theoretical model of an accelerating Universe. This is essentially the same mathematics that is used in modern inflationary cosmology.  The connection between scalar fields and the cosmological constant may also eventually explain why our Universe seems to be accelerating now, but that would require a scalar field with a much lower effective energy scale than that required to drive inflation. Perhaps dark energy is some kind of shadow of the inflaton

Guth wasn’t the sole creator of inflation. Andy Albrecht and Paul Steinhardt, Andrei Linde, Alexei Starobinsky, and many others, produced different and, in some cases, more compelling variations on the basic theme. It was almost as if it was an idea whose time had come. Suddenly inflation was an indispensable part of cosmological theory. Literally hundreds of versions of it appeared in the leading scientific journals: old inflation, new inflation, chaotic inflation, extended inflation, and so on. Out of this activity came the realization that a phase transition as such wasn’t really necessary, all that mattered was that the field should find itself in a configuration where the vacuum energy dominated. It was also realized that other theories not involving scalar fields could behave as if they did. Modified gravity theories or theories with extra space-time dimensions provide ways of mimicking scalar fields with rather different physics. And if inflation could work with one scalar field, why not have inflation with two or more? The only problem was that there wasn’t a shred of evidence that inflation had actually happened.

This episode provides a fascinating glimpse into the historical and sociological development of cosmology in the eighties and nineties. Inflation is undoubtedly a beautiful idea. But the problems it solves were theoretical problems, not observational ones. For example, the apparent fine-tuning of the flatness of the Universe can be traced back to the absence of a theory of initial conditions for the Universe. Inflation turns an initially curved universe into a flat one, but the fact that the Universe appears to be flat doesn’t prove that inflation happened. There are initial conditions that lead to present-day flatness even without the intervention of an inflationary epoch. One might argue that these are special and therefore “improbable”, and consequently that it is more probable that inflation happened than that it didn’t. But on the other hand, without a proper theory of the initial conditions, how can we say which are more probable? Based on this kind of argument alone, we would probably never really know whether we live in an inflationary Universe or not.

But there is another thread in the story of inflation that makes it much more compelling as a scientific theory because it makes direct contact with observations. Although it was not the original motivation for the idea, Guth and others realized very early on that if a scalar field were responsible for inflation then it should be governed by the usual rules governing quantum fields. One of the things that quantum physics tells us is that nothing evolves entirely smoothly. Heisenberg’s famous Uncertainty Principle imposes a degree of unpredictability of the behaviour of the inflaton. The most important ramification of this is that although inflation smooths away any primordial wrinkles in the fabric of space-time, in the process it lays down others of its own. The inflationary wrinkles are really ripples, and are caused by wave-like fluctuations in the density of matter travelling through the Universe like sound waves travelling through air. Without these fluctuations the cosmos would be smooth and featureless, containing no variations in density or pressure and therefore no sound waves. Even if it began in a fireball, such a Universe would be silent. Inflation puts the Bang in Big Bang.

The acoustic oscillations generated by inflation have a broad spectrum (they comprise oscillations with a wide range of wavelengths), they are of small amplitude (about one hundred thousandth of the background); they are spatially random and have Gaussian statistics (like waves on the surface of the sea; this is the most disordered state); they are adiabatic (matter and radiation fluctuate together) and they are formed coherently.  This last point is perhaps the most important. Because inflation happens so rapidly all of the acoustic “modes” are excited at the same time. Hitting a metal pipe with a hammer generates a wide range of sound frequencies, but all the different modes of the start their oscillations at the same time. The result is not just random noise but something moderately tuneful. The Big Bang wasn’t exactly melodic, but there is a discernible relic of the coherent nature of the sound waves in the pattern of cosmic microwave temperature fluctuations seen by WMAP. The acoustic peaks seen in the WMAP angular spectrum  provide compelling evidence that whatever generated the pattern did so coherently.

There are very few alternative theories on the table that are capable of reproducing the WMAP results. Some interesting possibilities have emerged recently from string theory. Since this theory requires more space-time dimensions than the four we are used to, something has to be done with the extra ones we don’t observe. They could be wrapped up so small we can’t perceive them. Or, as is assumed in braneworld cosmologies our four-dimensional universe exists as a subspace (called a “brane”) embedded within a larger dimensional space; we don’t see the extra dimensions because we are confined on the subspace. These ideas may one day lead to a viable alternative to inflationary orthodoxy. But it is early days and not all the calculations needed to establish this theory have yet been done. In any case, not every cosmologist feels the urge to make cosmology consistent with string theory, which has even less evidence in favour of it than inflation. Some of the wilder outpourings of string-inspired cosmology seem to me to be the physics equivalent of nausea-induced vomiting.

So did inflation really happen? Does WMAP prove it? Will we ever know?

It is difficult to talk sensibly about scientific proof of phenomena that are so far removed from everyday experience. At what level can we prove anything in astronomy, even on the relatively small scale of the Solar System? We all accept that the Earth goes around the Sun, but do we really even know for sure that the Universe is expanding? I would say that the latter hypothesis has survived so many tests and is consistent with so many other aspects of cosmology that it has become, for pragmatic reasons, an indispensable part our world view. I would hesitate, though, to say that it was proven beyond all reasonable doubt. The same goes for inflation. It is a beautiful idea that fits snugly within the standard cosmological and binds many parts of it together. But that doesn’t necessarily make it true. Many theories are beautiful, but that is not sufficient to prove them right. When generating theoretical ideas scientists should be fearlessly radical, but when it comes to interpreting evidence we should all be unflinchingly conservative. WMAP has also provided a tantalizing glimpse into the future of cosmology, and yet more stringent tests of the standard framework that currently underpins it. Primordial fluctuations produce not only a pattern of temperature variations over the sky, but also a corresponding pattern of polarization. This is fiendishly difficult to measure, partly because it is such a weak signal (only a few percent of the temperature signal) and partly because the primordial microwaves are heavily polluted by polarized radiation from our own Galaxy. Although WMAP achieved the detection of this polarization, the published map is heavily corrupted by foregrounds.

Future generations of experiments, such as the Planck Surveyor (due for launch in 2009), will have to grapple with the thorny issue of foreground subtraction if substantial progress is to be made. But there is a crucial target that justifies these endeavours. Inflation does not just produce acoustic waves, it also generates different modes of fluctuation, called gravitational waves, that involve twisting deformations of space-time. Inflationary models connect the properties of acoustic and gravitational fluctuations so if the latter can be detected the implications for the theory are profound. Gravitational waves produce very particular form of polarization pattern (called the B-mode) which can’t be generated by acoustic waves so this seems a promising way to test inflation. Unfortunately the B-mode signal is very weak and the experience of WMAP suggests it might be swamped by foregrounds. But it is definitely worth a go, because it would add considerably to the evidence in favour of inflation as an element of physical reality

Besides providing strong evidence for the concordance cosmology, the WMAP satellite has also furnished some tantalizing evidence that there may be something missing. Not all the properties of the microwave sky seem consistent with the model. For example, the temperature pattern should be structureless, mirroring the random Gaussian fluctuations of the primordial density perturbations. In reality the data contains tentative evidence of strange alignments, such as the so-called “Axis of Evil” discovered by Kate Land and Joao Magueijo. These anomalies could be systematic errors in the data, or perhaps residual problems with the foreground that have to be subtracted, but they could also indicate the presence of things that can’t be described within the standard model. Cosmology is now a mature and (perhaps) respectable science: the coming together of theory and observation in the standard concordance model is a great advance in our understanding of the Universe and how it works. But it should be remembered that there are still many gaps in our knowledge. We don’t know the form of the dark matter. We don’t have any real understanding of dark energy.  We don’t know for sure if inflation happened and we are certainly a long way from being able to identify the inflaton. In a way we are as confused as we ever were about how the Universe began. But now, perhaps, we are confused on a higher level and for better reasons…

Christmas Closure

Posted in Uncategorized with tags , , on December 23, 2008 by telescoper

Dear Readers (and Associate Professors),

I’m shortly going to be climbing aboard the Deadwood Stage (with some other faggots) in order to spend Christmas with my friends in the  North.

That means that I’ll be offline for a few days but as soon as I’ve sobered up I’ll be back with more of the random drivel that this blog is famous for.

In the meantime, I’d just like you wish anyone who reads this a very Merry Christmas and a Happy New Year or, failing that, a felicitous non-denominational yuletide.

Set ’em up, Joe!


Silver Linings

Posted in Science Politics, The Universe and Stuff with tags on December 19, 2008 by telescoper

They say that bad news sells newspapers, so I shouldn’t be surprised with the large number of hits my previous post and the one before that about the Research Assessment Exercise has generated.

However, I heard some news today which has at least provided a bit of a silver lining and put me in a better mood for the Christmas break. My recent application for a grant to the Science and Technology Facilities Council to fund research over the next three years into departures from the concordance cosmological model has actually been selected.

Owing to a budgetary crisis, STFC grants rounds have been very competitive in recent years so I’m quite relieved to have been successful in the present dire financial context. Obviously, somebody out there seems to like what I do. Being a theorist I’m also quite cheap, which probably helped. Or maybe it was just an administrative error…

Anyway, thanks to this grant I will be able to employ a postdoctoral research assistant and spend a bit more of my time on research. It also helps fund a bit of infrastructure within the department. Overall it amounts to about £350K which sounds a lot, but is actually quite small by the standards of particle physics and astronomy grants. STFC isn’t actually Tesco but every little helps.

All I have to do now is convince a potential postdoc to come and work with me in the 35th 22nd best Physics department in the country. What could be simpler?

The Authorized Version

Posted in Science Politics with tags , on December 18, 2008 by telescoper

Following on from my previous post about the 2008 Research Assessment Exercise, I’ve been told that Cardiff University’s preferred measure of research activity is not the simple grade point average that I computed there, but an index of research power which is the average multiplied by the number of staff submitted.

Partly out of interest and partly so as not to incur the wrath of the University Thought Police I recalculated the list sorted by the official measure. So here is the authorized version, as sanctioned by the powers that be:

1. University of Cambridge 402.6
2. University of Oxford 371.3
3. Imperial College London 348.7
4. University College London 277.8
5. University of Manchester 215.3
6. University of Durham 191.1
7. University of Edinburgh 169.4
8. University of Warwick 132.6
9. University of Nottingham 126.7
10. University of Glasgow 125.8
11. Queen’s University Belfast 125.0
12. University of Bristol 121.9
13. University of Southampton 120.0
14. University of Birmingham 117.7
15. University of Leicester 114.8
16. University of St Andrews 91.8
17. University of Liverpool 91.7
18. University of Leeds 90.5
19. Queen Mary, University of London 87.5
20. University of Sheffield 86.6
21. Lancaster University 76.6
22. Cardiff University 75.9
23. University of Exeter 75.6
24. University of Strathclyde 74.4
25. University of Hertfordshire 72.8
26. Royal Holloway, University of London 71.3
27. University of Surrey 69.4
28. University of York 67.6
29. University of Bath 57.6
30. University of Sussex 54.0
31. Swansea University 52.9
32. Heriot-Watt University 51.7
33. University of Central Lancashire 51.1
34. Loughborough University 41.9
35. King’s College London 41.8
36. Liverpool John Moores University 39.6
37. Aberystwyth University 35.7
38. Keele University 22.5
39. Armagh Observatory 16.9
40. University of the West of Scotland 6.7
41. University of Kent 6.6
42. University of Brighton 2.3

Well, it’s actually quite surprising how much things change. I don’t think it means very much, but 22nd certainly sounds much better than 35th.

But, being a Newcastle United supporter, I’ve never been a great fan of league tables.

Res Judicata

Posted in Science Politics with tags , , , , on December 18, 2008 by telescoper

Today is the day people working in British Universities have waited for in a mixture of hope and apprehension for several years. The results of the 2008 Research Assessment Exercise (RAE) were published at 0.01am GMT today (18th December).

I had a look just after midnight and the webserver crashed, but only for a few minutes and I soon got back in and found the bad news. The relevant one for me as an astrophysicist is the table for Unit of Assessment 19 which is Physics & Astronomy. Results are given as a list of numbers, consisting of the number of staff entered (not necessarily an integer, for accounting reasons) followed by the percentage of work judged by the panel to be in each of four categories explained in the following excerpt from the RAE website

The quality profiles displayed on this website are the results of the 2008 Research Assessment Exercise (RAE2008), the sixth assessment in this current format of the quality of research conducted in UK Higher Education Institutions (HEIs). The UK funding bodies for England, Northern Ireland, Scotland and Wales will use the RAE2008 results to distribute funding for research from 2009-10.

The results follow an expert review process conducted by assessment panels throughout 2008. Research in all subjects was assessed against agreed quality standards within a common framework that recognised appropriate variations between subjects in terms of both the research submitted and the assessment criteria.

Submissions were made in a standard form that included both quantitative and descriptive elements. Full details of the contents of, and arrangements for making, submissions were published in ‘Guidance on submissions‘ (RAE 03/2005).

The RAE quality profiles present in blocks of 5% the proportion of each submission judged by the panels to have met each of the quality levels defined below. Work that fell below national quality or was not recognised as research was unclassified.

4* Quality that is world-leading in terms of originality, significance and rigour.
3* Quality that is internationally excellent in terms of originality, significance and rigour but which nonetheless falls short of the highest standards of excellence.
2* Quality that is recognised internationally in terms of originality, significance and rigour.
1* Quality that is recognised nationally in terms of originality, significance and rigour.
Unclassified Quality that falls below the standard of nationally recognised work. Or work which does not meet the published definition of research for the purposes of this assessment.

The ‘international’ criterion equates to a level of excellence that it was reasonable to expect for the UOA, even though there may be no current examples of such a level in the UK or elsewhere. It should be noted that ‘national’ and ‘international’ refer to standards, not to the nature or geographical scope of particular subjects.

For my own department, the School of Physics & Astronomy, at Cardiff University, I found the following

Cardiff University (32.30) 5 45 30 20

which means that we entered 32.30 people, but only 5% of the work was judged to be at the top level (4*), 45% at 3*, 30% at 2* and 20% at 1*. On their own these figures don’t mean very much but one can do a quick comparison with the rest of the table to see that for us this is an enormous disappointment. We have a much lower fraction of 4* than the majority of departments, and also a significantly higher fraction of 1*. These findings are very worrying.

If I were working an English University with these results I would be very concerned about their financial implications, but it’s a bit more complicated with us being here in Wales. The numbers given in the table are translated into money by the funding councils and Wales has its own one of these (HEFCW, different from the English HEFCE). There are many fewer physics departments in Wales and we’re not competing with the bigger English ones for funding. We don’t yet know how much our research funds will be cut. It might not be as bad as if we were in England, but it’s clearly not good. We won’t know how much dosh will be involved until March 2009. t’s not just a matter of funding, it’s also the national and international perception of the department in the physics community.

I can see there will be a post mortem to find out what went wrong, as most of us were confident of a much better outcome. Perhaps the format of the RAE (focussing on research papers as the measure of output) is not favourable to a department with so many instrument builders in it?

But with the economy in deep recession making further cuts in research funding likely in the future, and our major external funder (STFC) already struggling to make ends meet, this poor showing in the RAE this has cast a gloomy shadow over Christmas.

Of course many places did much better, including my old department at Nottingham which has

University of Nottingham (44.45) 25 40 30 5

which can be interestingly compared with Cambridge, who have

University of Cambridge (141.25) 25 40 30 5

You can see that apart from the different numbers of staff the profile is exactly the same. I’m sure their publicity machine will pick up on this so I won’t be the last to mention it! Well done, Nottingham!

It will be interesting to see what the newspapers make of the new RAE results. They are significantly more complicated than previous versions which just gave a single number. The scope for flexibility in generating league tables is clearly greatly enhanced by this complexity so we can bet the hacks will have a field day. I thought I’d get a headstart by doing a straightforward ranking using a simple weighted average using 4=4*, 3=3*, etc and then sorting them by the average thus obtained:

1. Lancaster University 2.9
2. University of Bath 2.85
3. University of Cambridge 2.85
4. University of Nottingham 2.85
5. University of St Andrews 2.85
6. University of Edinburgh 2.8
7. University of Durham 2.75
8. Imperial College London 2.75
9. University of Sheffield 2.75
10. University College London 2.75
11. University of Glasgow 2.75
12. University of Birmingham 2.7
13. University of Exeter 2.7
14. University of Sussex 2.7
15. University of Bristol 2.65
16. University of Liverpool 2.65
17. University of Oxford 2.65
18. University of Southampton 2.65
19. Heriot-Watt University 2.65
20. University of Hertfordshire 2.6
21. University of Manchester 2.6
22. University of Warwick 2.6
23. University of York 2.6
24. King’s College London 2.55
25. University of Leeds 2.55
26. University of Leicester 2.55
27. Royal Holloway, University of London 2.55
28. University of Surrey 2.55
29. Swansea University 2.55
30. Queen Mary, University of London 2.5
31. Queen’s University Belfast 2.5
32. Loughborough University 2.45
33. Liverpool John Moores University 2.4
34. University of Strathclyde 2.35
35. Cardiff University 2.35
36. University of Brighton 2.3
37. University of Central Lancashire 2.3
38. Keele University 2.25
39. Armagh Observatory 2.25
40. University of Kent 2.2
41. Aberystwyth University 1.95
42. University of the West of Scotland 1.8

So you can see we are languishing at 35th place out of 42.

This is supposed to be the last RAE and we don’t know what is going to replace it. I don’t at all object to the principle that research funding should be peer-assessed but this particular exercise was enormously expensive in the effort spent at Universities preparing for it, not to mention the ridiculous burden placed on the panel of having to read all those papers.

Crucial Verbalism

Posted in Crosswords, Literature with tags , , , , , on December 13, 2008 by telescoper

It’s a cold and rainy day and I’m lacking the inspiration to do anything energetic before making dinner, so I thought I’d pick something to blog about. Looking back over the past three months or so, I realise I’ve at least mentioned most things that I’m interested in, at least those that I’m willing to write about on here. But there is one other thing I haven’t covered yet and which I spend a lot of my spare time doing (especially during seminars) and that is solving cryptic crossword puzzles. In fact I simply can’t put a crossword down until I’ve solved all the clues, behaviour which I admit is bordering on the pathological. Still, I think of it as a kind of mental jogging, forcing your brain to work in unaccustomed ways is probably good for its fitness for other more useful things.

I can’t remember when I first started doing these, or even how I learned to do them. But then people can learn languages simply by picking them up as they go along so that’s probably how I learned to do crosswords.

If you’ve never done one of these puzzles before, you probably won’t understand the clues at all even if you know the answer and I can’t possibly explain them in a single post. In a nutshell, however, they involve clues that usually give two routes to the word to be entered in the crossword grid. One is a definition of the solution word and the other is a subsidiary cryptic allusion to it. Usually the main problem to be solved involves the identification of the primary definition and secondary cryptic part, which are usually heavily disguised.

The secondary clue can be of many different types. The most straightforward just exploits multiple meanings. For example, take

Fleeces, things often ordered by men of rank [6]

The answer to this is RIFLES which is defined by “fleeces” in one sense, but “men of rank” (soldiers) also order their arms hence giving a different meaning. Other types include puns, riddles, anagrams, hidden words, and so on. Many of these involve an operative word or phrase instructing the solver to do something with the letters in the clue, e.g.

Port’s apt to make you steer it erratically [7]

has the solution TRIESTE, which is an anagram of STEER+IT, port being the definition.

Most compilers agree however that the very best type of clue is of the style known as “&lit” (short for “and literally what it says”). Such clues are very difficult to construct and really beautiful when they work because both the definition and cryptic parts comprise the same words read in different ways. Here’s a simple example

The ultimate of turpitide in Lent [5]

which is FEAST. Here we have “e” as the last letter of turpitude in “fast” (lent) giving “feast” but a feast is exactly what the clue says too. Nice.

Some clues involve more than one element of this type and some defy further explanation altogether, but I hope this at least gives you a clue as to what is involved.

Cryptic crosswords like the ones you find in British newspapers were definitely invented in the United Kingdom, although the crossword itself was probably born in the USA. The first great compiler of the cryptic type used the pseudonym Torquemada in the Observer. During the 1930s such puzzles became increasingly popular with many newspapers, including famously The Times, developing their own distinctive style. People tend to assume that The Times crossword is the most difficult, but I’m not sure. I don’t actually buy that paper but whenever I’ve found one lying around I’ve never found the crossword particularly hard or, more importantly, particularly interesting.

As a Guardian reader, I have to say I enjoy their crosswords best, primarily because each day brings a different setter each of which has a different style to the others. Unlike some other newspapers they are not anonymous, but identified by a weird and wonderful collection of pseudonyms (Janus, Rufus, Shed, Logodaedalus, Gordius, Chifonie, Paul, Quantum, Brummie, etc). The best of them is the great Araucaria (whose name comes from the Monkey-Puzzle tree) and who is revered by crossword fans the length and breadth of the country for the brilliance of his clues. Araucaria is such a witty compiler that his clues often have you laughing out loud when you see how they fall into place. He is, in fact, a retired clergyman called John Graham who has been setting clues for the Guardian and other newspapers and magazines for over forty years. In fact, the Financial Times has a compiler called Cinephile who is the same person. (CINEPHILE is an an anagram of CHILE PINE, which is another word for the Monkey-Puzzle tree).

As it happens, today’s Guardian prize crossword was by Araucaria and, as usual, it was fun although it wasn’t as difficult as many of his. He followed a common tactic of connecting several clues together but as soon as you realise that

Writers’ relation to 10, maybe [6]

is BRONTE (note the position of the apostrophe indicating several writers with the same name, cryptic part is “bro” for relation and an anagram of “ten”) then the various references to the Brontes were straightforward. The only really difficult other clue is

Picture rhyme for MC in MND [10]

the answer to which is ILLUSTRATE (MND is Midsummer Night’s Dream, which explains the rhyme reference to PHILOSTRATE, a character in that play).

I also like to do the bi-weekly crossword set by Cyclops in Private Eye which has clues which are not only clever but also laced with a liberal helping of lavatorial humour and topical commentary which is right up my street. Many of the answers (“lights” in crossword parlance) are quite rude, such as

Local energy source of stress for Bush [5]

which is PUBES (“pub” from “local”+ E for energy +S for “source of stress”; Bush is the definition).

On Saturdays the Guardian crossword involves a prize so I religiously send my completed grid in the post. There are many hundreds of correct entries per week so it’s quite unlikely to win – the winner is drawn “at random” from all the correct entries. I’ve won the prize nine times over the years, an average of once every two years or so, with the result that I now have more dictionaries than I know what to do with. I don’t actually think a dictionary is a very good prize for a crossword puzzle, as surely every solver has one already! A few years ago The Guardian used to offer fancy fountain pens and watches, which are more like it. I also won a digital radio from the Financial Times puzzle, but I’ve got out of the habit of doing that one nowadays. The same is true for Salamanca in the New Statesman, which I won a couple of times years ago but have stopped doing since I lost interest in the rest of the magazine. I send off the answers to the Eye crossword every time but have never won it yet. That one has a cash prize of £100.

Anyway, Torquemada, who I mentioned above, was eventually followed as the Observer’s crossword compiler by the great Ximenes (real name D.S. Macnutt) who wrote a brilliant book called the Art of the Crossword which I heartily recommend if you want to learn more about the subject.

One of the nice stories in his book concerns the fact that crossword puzzles of the cryptic type were actually used to select recruits for British Intelligence during the Second World War, but this had a flip side. In late May 1944 the chief crossword setter for the Daily Telegraph was paid a visit by some heavies from MI5. It turned out that in a recent puzzle he had used (quite innocently and by sheer coincidence) the words MULBERRY, PLUTO, NEPTUNE and OVERLORD all of which were highly confidential code words to be used for the forthcoming D-Day invasion…

The current Observer crossword setter is the estimable Azed (real name Jonathan Crowther) who follows in the footsteps of his predecessor Ximenes. On balance I think this is consistently the best crossword I have ever done, although it is often a source of total frustration because it is quite convoluted and idiosyncratic. It is a bit different from other puzzles because it doesn’t involve any black squares like you would find in the standard `Everyman’ type of grid. This makes a very dense and intricate task for the solver, but does have the advantage that clues intersect more frequently than in the usual type. The problem with solving Azed is usually getting started as the clues are quite difficult and the words often very obscure. The one concession is that all answers are usually in the Chambers dictionary, and if they aren’t the compiler gives another hint. I’ve been tackling Azed for so long now that the Chambers has become in my mind a much more definitive dictionary than the OED. I also have several copies at home in different rooms, and one in my office at work.

Solving the Azed puzzle is hard enough, but for the special competition puzzles every four weeks one also has to supply a clue of one’s own. The winners of this competition are selected by Azed himself and there is an archive on the web of successful clues. As well as the winner of each competition, there is an annual prizewinner who produces the most good clues over the set of 13 competitions each year, and a roll of honour of all contributed clues that are deemed worthy. I’ve gradually clawed my way up this league table from 118th in 2006-7 to 46th in 2007-8 and, after four of the thirteen rounds this year, I’m currently in 28th place. I have to admit though that I am envious of the talents of many of the other competitors who routinely produce brilliant clues that even my best ones can’t compete with. For the same reasons that I don’t really enjoy setting examination questions, I don’t really like writing clues as much as solving them. My position in the roll of honour belies the fact that I’ve never produced a single clue that has won any of the individual competitions. I’m always the bridesmaid. You can find some of my more successful clues on the archive here.

Among those who have done exceedingly well in this competition over the years are the novelist Colin Dexter (in the form of N.C. Dexter) and a chap called C.J. Morse who is in fact the man that provided the name Dexter used for the crossword-loving chief Inspector in his famous detective novels. In turns out that C.J. Morse recently had his eightieth birthday and, as a special present, last Sunday’s Azed puzzle included some of his competition clues, which are real crackers. I won’t repeat them here though as you can find them all on the archive. However, solvers were invited to submit a clue to the word MORSE for the purposes of the competition, so at least I can tell you what my attempt was. Here we go:

His signal art no astronomer can comprehend [5]

By way of explanation, anagram of “astronomer” can give “morse” plus “art no”; comprehend is used in the slightly unusual sense of “comprise”; signal in the sense of “remarkable” plus reference to Morse system of signals. In the context of this puzzle, to celebrate the skills of Mr Morse, I also think this overall qualifies as an “&lit”.

I doubt if it competes with the best of the entries but I’m still quite proud of it.

Misplaced Confidence

Posted in Bad Statistics, The Universe and Stuff with tags , , , on December 10, 2008 by telescoper

From time to time I’ve been posting items about the improper use of statistics. My colleague Ant Whitworth just showed me an astronomical example drawn from his own field of star formation and found in a recent paper by Matthew Bate from the University of Exeter.

The paper is a lengthy and complicated one involving the use of extensive numerical calculations to figure out the effect of radiative feedback on the process of star formation. The theoretical side of this subject is fiendishly difficult, to the extent that it is difficult to make any progress with pencil-and-paper techinques, and Matthew is one of the leading experts in the use of computational methods to tackle problems in this area.

One of the main issues Matthew was investigating was whether radiative feedback had any effect on the initial mass function of the stars in his calculations. The key results are shown in the picture below (Figure 8 from the paper) in terms of cumulative distributions of the star masses in various different situations.


The question that arises from such data is whether these empirical distributions differ significantly from each other or whether they are consistent with the variations that would naturally arise in different samples drawn from the same distribution. The most interesting ones are the two distributions to the right of the plot that appear to lie almost on top of each other.

Because the samples are very small (only 13 and 15 objects respectively) one can’t reasonably test for goodness-of-fit using the standard chi-squared test because of discreteness effects and because not much is known about the error distribution. To do the statistics, therefore, Matthew uses a popular non-parametric method called the Kolmogorov-Smirnov test which uses the maximum deviation D between the two distributions as a figure of merit to decide whether they match. If D is very large then it is not probable that it can have arisen from the same distribution. If it is smaller then it might have. As for what happens if it is very small then you’ll have to wait a bit.

This is an example of a standard (frequentist) hypothesis test in which the null hypothesis is that the empirical distributions are calculated from independent samples drawn from the same underlying form. The probability of a value of D arising as large as the measured one can be calculated assuming the null is true and is then the significance level of the test. If there’s only a 1% chance of it being as large as the measured value then the significance level is 1%.

So far, so good.

But then, in describing the results of the K-S test the paper states

A Kolmogorov-Smirnov (K-S) test on the …. distributions gives a 99.97% probability that the two IMFs were drawn from the same underlying distribution (i.e. they are statistically indistinguishable).

Agh! No it doesn’t! What it gives is a probability of 99.97% that the chance deviation between the two distributions is expected to be larger than that actually measured. In other words, the two distributions are surprisingly close to each other. But the significance level merely specifies the probability that you would reject the null-hypothesis if it were correct. It says nothing at all about the probability that the null hypothesis is correct. To make that sort of statement you would need to specify an alternative distribution, calculate the distribution of D based on it, and hence determine the statistical power of the test. Without specifying an alternative hypothesis all you can say is that you have failed to reject the null hypothesis.

Or better still, if you have an alternative hypothesis you can forget about power and significance and instead work out the relative probability of the two hypotheses using a proper Bayesian approach.

You might also reasonably ask why might D be so very small? If you find an improbably low value of chi-squared then it usually means either that somebody has cheated or that the data are not independent (which is assumed for the basis of the test). Qualitatively the same thing happens with a KS test.

In fact these two distributions can’t be thought of as independent samples anyway as they are computed from the same initial conditions but with various knobs turned on or off to include different physics. They are not “samples” drawn from the same population but slightly different versions of the same sample. The probability emerging from the KS machinery is therefore meaningless anyway in this context.

So a correct statement of the result would be that the deviation between the two computed distributions is much smaller than one would expect to arise from two independent samples of the same size drawn from the same population.

That’s a much less dramatic statement than is contained in the paper, but has the advantage of not being bollocks.