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Sentimental Education

Posted in Education, The Universe and Stuff with tags education, Lecturing, Particle Physics, Physics on March 10, 2011 by telescoper

We’ve now reached the half-way point of the Spring Semester, which means that my teaching load has just doubled; I do the “Particle” bit of a third-year module on “Nuclear and Particle Physics”, which means I have 11 lectures from now until the end of the Semester to tell the students everything I know about particle physics. More than enough time.

Anyway, the first lecture today, as it was last year, was all about Natural Units. I always find it fun doing this, partly because the students stare at me as if I’ve taken leave of my senses. Come to think of it, they do that anyway.

The other night I was having a drink with some colleagues after work. Various topics came up, but we spent a bit of time talking about teaching. It appears that I’m in a small minority of my physics colleagues in that I actually like teaching. In fact, the older I’ve got the more I enjoy it. There’s always a limit, of course, and I wouldn’t like to do so much teaching that I couldn’t do other things, especially research, but I wouldn’t like to be in a job that didn’t involve teaching at all. I think most of my colleagues would jump at the chance to abandon teaching altogether. I can’t understand that attitude, mainly because I find it so rewarding myself, but I’m in a minority of one about so many things nowadays that I’ve ceased worrying about it.

I do sometimes wonder why I find teaching so rewarding. Perhaps it’s because I’m already middle-aged and don’t have any kids of my own. Teaching at least gives me a chance to play some sort of a role in someone else’s development as a person. I can’t guarantee that it’s necessarily a positive role, but there you are. Another thing is that sometimes when I travel about at conferences and whatnot I get to meet people I taught years ago. It means a lot when they say they remember the lectures, especially if they’ve now embarked on scientific careers of their own.

One of the problems of the government’s push for greater concentration of research funds and the simultaneous slashing of teaching budgets is that the quality of University teaching is bound to suffer. If research funding is allocated only to self-styled research “superstars” then Universities will obviously spare them from other duties. Teaching loads for ordinary foot soldiers will increase, with obvious consequences in decreasing enthusiasm among lecturing staff.

It’s already the case that teaching is grossly undervalued, and it’s probably worse in physics departments than anywhere else because, without research funding, most would simply go bust. Teaching funding is nowhere near sufficient to cover the real cost of a physics degree and in any case we can’t deliver advanced physics training without access to the research labs.

On top of this there’s the way teaching is entirely disregarded in promotion cases. On paper, promotion to Professor requires demonstrated commitment to teaching. In reality, all that committees care about is how much research income the candidate brings in. Excellence in teaching counts very little, if anything at all, in the assessment of a promotion case. I think this situation must change, especially with tuition fees set to rise to unprecedented levels, but all the forces currently at play are acting in precisely the wrong direction.

If we concentrate physics research funding any further then we’ll have a small number of rich institutions stuffed full of research professors whom the undergraduates never see. The less successful academics in these departments will be put on teaching-only contracts, not because they like teaching but because their alternative is Her Majesty’s Dole. Meanwhile, less favoured research labs – i.e. those who don’t get lucky in the REF – won’t be able to sustain world-class research or teaching activities and will be forced to shut up shop. Further research concentration is bad news all round for the higher education system.

But I digress.

One of the other things we talked about in the pub was the National Lottery. As regular readers of this blog might know, I put the princely sum of £1 on the lottery every Saturday. Some think this is strange, but I see it partly as one of those little rituals we all invent for ourselves and partly as a small price to pay for a little frisson of excitement when the numbers are drawn.

But I do sometimes wonder what on Earth I would do if I won a multi-million pound jackpot prize. Would I quit my job? Would I quit teaching? Actually, I’m not sure I would do either of those. If I could ditch the admin stuff, I would of course do so. I don’t have a car and have no interest in getting one, especially a fancy one. I don’t need a bigger house, or a yacht. In fact, frankly, there’s nothing that I would really want to buy that I couldn’t buy already. It’s not that I have a huge salary, just that I’m not exactly very materialistic.

So even if I were rich I’d probably carry on doing pretty much what I do now. And that thought brings home just how lucky we are, those of us working in academia. For all the frustrations, the fact remains that we are fortunate to be getting paid for things that we enjoy doing.

Or am I just a sentimental old fool?

Anyway, I feel a poll coming on…

17 Comments »

A First Problem in Astrophysics

Posted in Education, The Universe and Stuff with tags astronomy, iron, iron sun hypothesis, Physics, Sun on February 25, 2011 by telescoper

When I first arrived at Cambridge University (nearly 30 years ago) to begin my course in Natural Sciences, eventually leading to a specialism in Physics, one of the books we were all asked to buy was the Cavendish Problems in Physics. One of the first problems I had to solve for tutorial work was from that collection, and I have been setting it (in a slightly amended form) for my own students ever since I started lecturing. I thought I’d put it up here because I think there might be a few budding theoretical astrophysicists who’ll find it interesting and because it provides a simple refutation of a crazy theory that has been doing the rounds on Twitter all morning.

I like this problem because it involves a little bit of lateral thinking, because not all the information given seems immediately relevant to the question being asked, but you can get a long way by just writing down the pieces of information given and thinking about how you might use simple physical ideas to connect them to the answer.

If you haven’t seen this problem before, why not have a go?

Using only the information given in this Question, estimate the ratio of the mean densities of the Earth and Sun:

i) the angular diameter of the Sun as seen from Earth is half a degree

ii) the length of 1° of latitude on the Earth’s surface is 100km

iii) the length of a year is 3×10⁷ seconds

iv) the acceleration due to gravity at the Earth’s surface is 10 m s^-2.

HINT: You do not need to look up anything else, not even G!

The answer you should get is that the mean density of the Earth is something like 3.5 times that of the Sun, although the information given in the question isn’t all that accurate.

In fact the mean density of the Earth is about 5500 kg per cubic metre, and that of the Sun is about 1400 kg per cubic metre; the average density of the Sun is just 40% higher than water, which is perhaps surprising to the uninitiated….

The density of solid iron on the other hand is about 7900 kg per cubic metre, and even higher than that if it is compressed…

UPDATE: I’ve added my Solution.

12 Comments »

Bayes’ Razor

Posted in Bad Statistics, The Universe and Stuff with tags Bayes Factor, Bayesian Model Selection, Bayesian probability, Cosmology, Evidence, Ockham's Razor, Physics, Science, Theory of Everything, William of Ockham on February 19, 2011 by telescoper

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 $p$ , but we fear it may not fit the data. We therefore add a couple more parameters, say $q$ and $r$ . These might be the coefficients of a polynomial fit, for example: the first model might be straight line (with fixed intercept), the second a cubic. We don’t know the appropriate numerical values for the parameters at the outset, so we must infer them by comparison with the available data.

Quantities such as $p$ , $q$ and $r$ are usually called “floating” parameters; there are as many as a dozen of these in the standard Big Bang model, for example.

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 $M$ which has a set of $N$ floating parameters represented as a vector $\underline\lambda = (\lambda_1,\ldots \lambda_N)=\lambda_i$ ; in a sense each choice of parameters represents a different model or, more precisely, a member of the family of models labelled $M$ .

Now assume we have some data $D$ and can consequently form a likelihood function $P(D|\underline{\lambda},M)$ . In Bayesian reasoning we have to assign a prior probability $P(\underline{\lambda}|M)$ to the parameters of the model which, if we’re being honest, we should do in advance of making any measurements!

The interesting thing to look at now is not the best-fitting choice of model parameters $\underline{\lambda}$ but the extent to which the data support the model in general. This is encoded in a sort of average of likelihood over the prior probability space:

$P(D|M) = \int P(D|\underline{\lambda},M) P(\underline{\lambda}|M) d^{N}\underline{\lambda}.$

This is just the normalizing constant $K$ usually found in statements of Bayes’ theorem which, in this context, takes the form

$P(\underline{\lambda}|DM) = K^{-1}P(\underline{\lambda}|M)P(D|\underline{\lambda},M).$

In statistical mechanics things like $K$ are usually called partition functions, but in this setting $K$ is called the evidence, and it is used to form the so-called Bayes Factor, used in a technique known as Bayesian model selection of which more anon….

The usefulness of the Bayesian evidence emerges when we ask the question whether our $N$ parameters are sufficient to get a reasonable fit to the data. Should we add another one to improve things a bit further? And why not another one after that? When should we stop?

The answer is that although adding an extra degree of freedom can increase the first term in the integral defining $K$ (the likelihood), it also imposes a penalty in the second factor, the prior, because the more parameters the more smeared out the prior probability must be. If the improvement in fit is marginal and/or the data are noisy, then the second factor wins and the evidence for a model with $N+1$ parameters lower than that for the $N$ -parameter version. Ockham’s razor has done its job.

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.

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Admissions

Posted in Education with tags admissions, Physics, UCAS on February 11, 2011 by telescoper

Busy day today, necessitating an early start and a packed morning followed by a trip to the Big Smoke later on.

I thought I’d use my daily post to try a little experiment.

Yesterday I mentioned that applications to do Physics courses in the School of Physics & Astronomy at Cardiff University had increased enormously since last year. That prompted a couple of people to contact me, via email and Twitter, to admit that the same thing is happening at their institutions. With UCAS reporting that applications nationwide are up by only about 4%, I’m a bit confused as to what is going on.

I don’t know how many of my (1000+) daily readers work in UK universities, let alone which ones or whether they’re in a position to know what undergraduate applications are doing, but I would be very interested to hear whether this pattern is being repeated and whether it’s just physics that’s booming.

So, in lieu of a proper blog post for today, let me invite you to take part in a straw poll through the comments box. Where are you? What’s your subject? Are your applications up?

Do tell.

31 Comments »

Bristol and Back

Posted in Biographical, The Universe and Stuff with tags Bristol University, Colloquium, Physics on January 17, 2011 by telescoper

I almost did the unthinkable today by not posting anything on my blog. It’s been such a busy day that I wasn’t able to post at lunchtime, chiefly because I didn’t have a lunch break. I don’t want to let the side down, so I decided to put something up, but the following “quick” post will have to do for today.

After an interminable meeting (zzzz...) of the Board of Studies this morning in the School of Physics & Astronomy at Cardiff, where I work, I had to rush back to the office, grab my things and dash off to the station to catch a train to the fine city of Bristol, where I was giving a colloquium in the School of Physics at the University of Bristol. I got there just in time for a quick slurp of tea before heading off to do my bit. I hope the talk was OK, but that’s not really for me to judge.

After the colloquium I got the chance to relax over a pint of beer, chat to staff and students and was then whisked off for a splendid curry. One of the folks that looked after me was Professor Mark Birkinshaw, who taught a course I took when I was an undergraduate at Cambridge; he seemed quite chuffed when I told him I still had the notes! And if Anton is reading this, he asked me to pass on his good wishes to you too! Thence it was back by train in the rain to Cardiff.

I think that’s all I have the energy to write. In fact, this is the first time ever I’ve used the “Quick Post” feature on WordPress, a streamlined interface limited to shorter items without graphics and other complicated extras which I don’t usually use because my typical posts don’t count as “quick” on account of the fact that I usually keep on writing long after I’ve made the points I was going to make and have run out of useful things to say, the excessive verbosity of the resulting articles giving me a bad name in the blogosphere, which, notwithstanding its more problematic aspects, does seem to me at least to have the virtue of encouraging a more concise form of communication than is to be found in other contexts while at the same time … [continued, page 94]

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Einstein and the Eclipse

Posted in Biographical, The Universe and Stuff with tags Channel 4, Eclipse, Eddington, Einstein, general relativity, Ken Campbell, Physics, Six Experiments that Changed the World on January 4, 2011 by telescoper

Following on from my previous post, I thought you might be interested in this. It’s the last programme in a series called Six Experiments that Changed the World which was presented by the late Ken Campbell. It was made for Channel 4 and first broadcast in 2000. It’s in two parts. If you watch the second one, you might see someone you recognize…

4 Comments »

Spare me the Passive Voice!

Posted in Education with tags education, grammar, passive voice, Physics, reports, Science on December 16, 2010 by telescoper

I’ve felt a mini-rant brewing for a few days now, as I’ve been reading through some of the interim reports my project students have written. I usually quite enjoy reading these, in fact. They’re not too long and I’m usually pretty impressed with how the students have set about the sometimes tricky things I’ve asked them to do. One pair, for example, is reanalysing the measurements made at the 1919 Eclipse expedition that I blogged about here, which is not only interesting from a historical point of view but which also poses an interesting challenge for budding data analysts.

So it’s not the fact that I have to read these things that annoys me, but the strange way students write them, i.e. almost entirely in the passive voice, e.g. “The experiment was calibrated using a phlogiston normalisation widget…”.

I accept that people disagree about whether the passive voice is good style or not. Some journals actively encourage the passive voice while others go the opposite way entirely . I’m not completely opposed to it, in fact, but I think it’s only useful either when the recipient of the action described in the sentence is more important than the agent, or when the agent is unknown or irrelevant. There’s nothing wrong with “My car has been stolen” (passive voice) since you would not be expected to know who stole it. On the other hand “My Hamster has been eaten by Freddy Starr” would not make a very good headline.

The point is that the construction of a statement in the passive voice in English is essentially periphrastic in that it almost inevitably involves some form of circumlocution – either using more words than necessary to express the meaning or being deliberately evasive by introducing ambiguity. Both of these failings should be avoided in scientific writing.

Apparently our laboratory instructors tell students to write their reports in the passive voice as a matter of course. I think this is just wrong. In a laboratory report the student should describe what he or she did. Saying what “was done” often leaves the statement open to the interpretation that somebody else did it. The whole point of a laboratory report is surely for the students to describe their own actions. “We calibrated the experiment..” is definitely to be preferred to the form I gave above.

Sometimes it is appropriate to use the passive voice because it is the correct grammatical construction in the circumstances. Sometimes also the text just seems to work better that way too. But having to read an entire document written in the passive voice drives me to distraction. It’s clumsy and dull.

In scientific papers, things are a little bit different but I still think using the active voice makes them easier to read and less likely to be ambiguous. In the introduction to a journal paper it’s quite acceptable to discuss the background to your work in the passive voice, e.g. “it is now generally accepted that…” but when describing what you and your co-authors have done it’s much better to use the active voice. “We observed ABC1234 using the Unfeasibly Large Telescope..” is, to my mind, much better than “Observations of ABC1234 were made using..”.

Reading back over this post I notice that I have jumped fairly freely between active and passive voice, thus demonstrating that I don’t have a dogmatic objection to its use. What I’m arguing is that it shouldn’t be the default, that’s all.

My guess is that a majority of experimental scientists won’t agree with this opinion, but a majority of astronomers and theoreticians will.

This guess will now be tested using a poll…

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Take a note from me…

Posted in Education with tags lecture notes, lectures, Physics, Science, teaching on December 14, 2010 by telescoper

Having just given a lecture on probability and statistics to our first-year postgraduate students I thought I’d indulge in a bit of reflective practice (as the jargon goes) and make a few quick comments on teaching to see if I can generate some reaction. Part of the reason for doing this is that while I was munching my coffee and drinking my toast this morning – I’m never very coordinated first thing – I noticed an interesting post by a student on a blog that somehow wound up referring some traffic to one of my old posts about lecture notes.

I won’t repeat the entire content of my earlier discussion, but one of the main points I made was about how inefficient many students are at taking notes during lectures, so much so that the effort of copying things onto paper must surely prevent them absorbing the intellectual content of the lecture.

I dealt with this problem when I was an undergraduate by learning to write very quickly without looking at the paper as I did so. That way I didn’t waste time moving my head to and fro between paper and screen or blackboard. Of course, the notes I produced using this method weren’t exactly aesthetically pleasing, but my handwriting is awful at the best of times so that didn’t make much difference to me. I always wrote my notes up more neatly after the lecture anyway. But the great advantage was that I could write down everything in real time without this interfering with my ability to listen to what the lecturer was saying.

An alternative to this approach is to learn shorthand, or invent your own form of abbreviated language. This approach is, however, unlikely to help you take down mathematical equations quickly…

My experience nowadays is that students aren’t used to taking notes like this, so they struggle to cope with the old-fashioned chalk-and-talk style of teaching that some lecturers still prefer. That’s probably because they get much less practice at school than my generation. Most of my school education was done via the blackboard..

Nowadays, most lecturers use more “modern” methods than this. Many lecture using powerpoint, and often they give copies of the slides to students. Others give out complete sets of printed notes before, during, or after lectures. That’s all very well, I think, but what are the students supposed to be doing during the lecture if you do that? Listen, of course, but if there is to be a long-term benefit they should take notes too.

Even if I hand out copies of slides or other notes, I always encourage my students to make their own independent set of notes, as complete as possible. I don’t mean copying down what they see on the screen and what they may have on paper already, but trying to write down what I say as I say it. I don’t think many take that advice, which means much of the spoken illustrations and explanations I give don’t find their way into any long term record of the lecture.

And if the lecturer just reads out the printed notes, adding nothing by way of illustration or explanation, then the audience is bound to get bored very quickly.

My argument, then, is that regardless of what technology the lecturer uses, whether he/she gives out printed notes or not, then if the students can’t take notes accurately and efficiently then lecturing is a complete waste of time.

I like lecturing, because I like talking about physics and astronomy, but as I’ve got older I’ve become less convinced that lectures play a useful role in actually teaching anything. I think we should use lectures more sparingly, relying more on problem-based learning to instil proper understanding. When we do give lectures, they should focus much more on stimulating interest by being entertaining and thought-provoking. They should not be for the routine transmission of information, which is far too often the default.

Next year we’ll rolling out a new set of courses here in the School of Physics & Astronomy at Cardiff University. The express intent of this is to pare down the amount of material lectured to create more space for other types of activity, especially more exercise classes for problem-based learning. The only way to really learn physics is by doing it.

I’m not saying we should scrap lectures altogether. At the very least they have the advantage of giving the students a shared experience, which is good for networking and building a group identity. Some students probably get a lot out of lectures anyway, perhaps more than I did when I was their age. But different people benefit from different styles of teaching, so we need to move away from lecturing as the default option.

I don’t think I ever learned very much about physics from lectures, but I’m nevertheless glad I learned out how to take notes the way I did because I find it useful in all kinds of situations. Note-taking is a transferable skill, but it’s also a dying art.

13 Comments »

Ways of Thinking

Posted in Biographical, The Universe and Stuff with tags mathematics, Physics, Richard Feynman on November 25, 2010 by telescoper

I’m putting one more Richard Feynman clip up. This one struck me as particularly interesting, because it touches on a question I’ve often asked myself: what goes on in your head when do you mathematical calculations? I think I agree with Feynman’s suggestion that different people think in very different ways about the same kind of calculation or other activity.

There’s no doubt in my mind that I’ve become slower and slower at doing mathematics as I’ve got older, and probably less accurate too. I think that’s partly just age – and perhaps the cumulative effect of too much wine! – but it’s partly because I have so many other things to think about these days that it’s hard to spend long hours without interruption thinking about the same problem the way I could when I was a student or a postdoc.

In any case, although much of my research is mathematical, I’ve never really thought of myself as being in any sense a mathematical person. Many of my colleagues have much better technical skills in that regard than I’ve ever had. I was never particularly good at maths at school either. I was sufficiently competent at maths to do physics, of course, but I was much better at other things at that age. My best subject at O-level was Latin, for example, which possibly indicates that my brain prefers to work verbally (or perhaps symbolically) rather than, as no doubt many others’ do, geometrically or in some other abstract way.

Another strange thing is the role of vision in doing mathematics. I can’t do maths at all without writing things down on paper. I have to be able to see the equations to think about solving them. Amongst other things this makes it difficult when you’re working things out on a blackboard (or whiteboard); you have to write symbols so large that your field of view can’t take in a whole equation. I often have to step back up one of the aisles to get a good look at what I’m doing like that. Other physicists – notably Stephen Hawking – obviously manage without writing things down at all. I find it impossible to imagine having that ability.

But I endorse what Richard Feynman says at the beginning of the clip. It’s really all about being interested in the questions, which gives you the motivation to acquire the skills needed to find the answers. I think of it as being like music. If you’re drawn into the world of music, even if you’re talented you have to practice long for long hours before you can really play an instrument. Few can reach the level of Feynman (or a concert pianist) of course – I’m certainly not among either of those categories! – but I think physics is at least as much perspiration as inspiration.

In contrast to many of my colleagues I’m utterly hopeless at chess – and other games that require very sophisticated pattern-reading skills – but good at crosswords and word-puzzles. Maybe I’m in the wrong job?

3 Comments »

The Inconceivable Nature of Nature

Posted in The Universe and Stuff with tags eletromagnetic waves, Physics, Richard Feynman on November 19, 2010 by telescoper

I had a couple of requests to post yet another Feynman clip. This one – about electromagnetic waves and swimming pools – is one that I vividly remember watching on BBC when it was first broadcast donkeys’ years ago. I think it’s totally wonderful.

1 Comment »

In the Dark