## From Real Time to Imaginary Time

Posted in Brighton, Education, The Universe and Stuff with tags , , , , , , , , , , , on February 24, 2014 by telescoper

Yesterday, after yet another Sunday afternoon in my office on the University of Sussex campus, I once again encountered the baffling nature of the “real time boards” at the bus-stop at Falmer Station (just over the road from the University). These boards are meant to show the expected arrival times of buses; an example can be seen on the left of the picture below, taken at Churchill Square (in the City Centre).

The real-time board system works pretty well in central Brighton, but it’s a very different story at Falmer, especially for the Number 23 which is my preferred bus home. Yesterday provided a typical illustration of the problem: the time of the first bus on the list, a No. 23, was shown as “1 min” when I arrived at the stop. It then quickly moved to “due” (a word which I’ll comment about later). It then moved back to “2 mins” for about 5 minutes and then back to “due” again. It stayed like that for over 10 minutes at which point the bus that was second on the list (a No. 28 from Lewes) appeared. Rather than risk waiting any longer for the 23 I got on the 28 and had a slightly longer walk home from the stop at the other end. Just as well I did because the 23 vanished entirely from the screen as soon as I boarded the other bus. This apparent time-travel isn’t unusual at Falmer, although I’ve never really understood why.

By sheer coincidence when I got to the bus stop to catch a bus to campus this morning there was a chap from Brighton and Hove buses there. He was explaining what sometimes goes wrong with the real time boards to a lady, so I joined in the conversation and asked him if he knew why Falmer is so unreliable. He was happy to oblige. It turns out that the way the real-time boards work depends on each bus having a GPS system that communicates to a central computer via a radio link. If the radio link drops out for some reason – as it apparently does quite often up at Falmer (mobile phone connectivity is poor here also) – the system looks up the expected time of the bus after the one that it has lost contact with. Thus it is that a bus can apparently be “due” and then apparently go back in time. Also, if a bus has to divert from the route programmed into the GPS tracker then it is also removed from the real-time boards.

However, there is another system in operation alongside the GPS tracker. When a bus actually stops at a stop and opens its doors the onboard computer communicates this to the central system at the same time as the location signs inside the bus are updated. At this point the real-time boards are reset.

The unreliability I’ve observed at Falmer is in fact caused by two problems: (i) the patchy radio coverage as the bus wanders around the hilly environs of Falmer campus; and (ii) the No. 23 is on a new route around the back of campus which means that it vanishes from the system entirely when it wanders off the old route, as would happen if the bus were to break down.

Mystery solved then, in a sense, but it means there’s a systematic problem that isn’t going to be fixed in the short-term. Would it be better to switch off the boards than have them show inaccurate information? Perhaps, but only if it were always wrong. In fact the boards seem to work OK for the more frequent bus, the No. 25. My strategy is therefore never to rely on the information provided concerning the No. 23 and just get the first bus that comes. It’s not a problem anyway during the week because there’s a bus every few minutes, but on a Sunday evening it is quite irksome to see apparently random times on the screens.

All this talk about real-time boards reminds me of a question I was asked in a lecture last week. I was starting a new section of my Theoretical Physics module for 2nd Year students on Complex Analysis: the Cauchy-Riemann equations, Conformal Transformations, Contour Integrals and all that Jazz. To start the section I went on a bit of a ramble about the ubiquity of complex numbers in physics and whether this means that imaginary numbers are, in some sense, real. You can find an enjoyable polemic on this subject, given the answer “no” to the question here.

Anyway, I got the class to suggest examples of the use of complex numbers in physics. The things you’d expect came up such as circuit theory, wave propagation etc. Then somebody mentioned that somewhere they had heard of imaginary time. The context had probably been provided Stephen Hawking who mentioned this in his book A Brief History of Time. In fact the trick of introducing imaginary time is called a Wick Rotation and the basic idea is simple. In special relativity we deal with four-dimensional space-time intervals of the form

$ds^2 = -c^2dt^2 + dx^2 + dy^2 +dz^2$,

i.e. the metric describing Minkowski space. The minus sign in front of the time bit is essential to the causal structure of space-time but it causes quite a few mathematical difficulties. However if we make the substitution

$\tau \rightarrow i c t$

then the metric becomes

$ds^2 = d\tau^2 + dx^2 + dy^2 +dz^2$,

which corresponds to a four-dimensional Euclidean space which is in many situations much easier to handle mathematically.

Complex variables and complex functions provide the theoretical physicist with a host of extremely elegant techniques for solving tricky problems. But does that mean they are somehow “built in” to nature? I don’t think so. I don’t think the Brighton & Hove Bus company uses imaginary time on its display boards either, although it does sometimes seem that way.

POSTSCRIPT. I forgot to include my planned rant about the use of the word “due”. The boards displaying train times at railway stations usually give the destination and planned departure time of the train, e.g. “Brighton 11.15″. If things are running to schedule this information is supplemented by the phrase “On Time”. If not, which is sadly a more likely contingency in the UK, this changes to “due 11.37″ or some such. This really annoys me.: the train is due at 11.15. If it doesn’t come until after then, it’s overdue or, in other words, late.

Posted in Biographical, Brighton, Education with tags , , on February 22, 2014 by telescoper

Here’s a chance to relive (if you were there) or experience for the first time (if you weren’t)  the hilarity of my attempts to pronounce the names of all the graduands from the School of Mathematical and Physical Sciences at the Winter Graduation Ceremony for the University of Sussex at the Dome, in Brighton, last month.  I blogged about this here and there are also some pictures here. My stint commences at about 1:35:30 and finishes about 1:48:00 so there’s not too much of me to put up with, and if you get bored with my voice there’s always the irrepressible Chancellor, Sanjeev Baskar, to keep you entertained…

## The National Student Survey: Feedback and Response

Posted in Education with tags , , , on February 21, 2014 by telescoper

So the 2014 National Student Survey is under way. The NSS is much maligned, largely because it seems to be regarded by the powers that be solely for the purpose of constructing meaningless league tables. In reality I think the NSS survey is actually rather valuable because it allows us to gather systematic feedback on things that we do well and things we do not so well so we can look to improve our teaching for future generations of students. This isn’t just a PR exercise, at least not here in the School of Mathematical and Physical Sciences at the University of Sussex. We really do listen. Here are our responses to last year’s survey in the Department of Physics & Astronomy:

and for the Department of Mathematics:

I hope the fact that we have responded to the feedback we’ve got will encourage more students to participate in this year’s National Student Survey, regardless of what they have to say; that way we can try to improve still further.

## Coming out as a scientist

Posted in Education, LGBT, The Universe and Stuff with tags , on February 14, 2014 by telescoper

So here I am sitting in the library at Burlington House, the Royal Astronomical Society Council meeting I was attending having just finished slightly ahead of schedule.

I only have time for a brief post, so I’ll take the opportunity to direct your attention to an interesting piece in the Grauniad by Tom Welton. Tom is Professor of Sustainable Chemistry at Imperial College. He was also a contemporary of mine in old Sussex days. He was doing a PhD in Chemistry in MOLS while I was doing mine in Astrophysics in MAPS. Come to think of it we both did DPhils actually.

Anyway, Tom’s piece is related to something I blogged about a while ago (being a gay scientist) but he turns it the other way round and writes about how the difficulties of coming out as a scientist to your gay friends..

## More Cuts to University Funding

Posted in Education, Politics, Science Politics with tags , , , , , , on February 11, 2014 by telescoper

Grim news arrived yesterday with the announcement by the Department of Business, Innovation and Skills of further deep cuts in funding for Higher Education in England. This announcement has been delayed due to internal wrangling over the allocation of funds but in the end the grant letter to HEFCE makes little attempt to sugar the pill:

The settlement will mean reductions in HEFCE funding for higher education institutions in 2014-15 and again in 2015-16 beyond those accounted for by the switch to publicly funded tuition fees. The Government has asked HEFCE to deliver the reductions in ways which protect as far as possible high-cost subjects (including STEM), widening participation (which is funded via the HEFCE Student Opportunity allocation), and small and specialist institutions.

The science budget is, of course, “ring-fenced” which means that recurrent funding for that is maintained at £1,573 million, the same cash levels as 2013-14. This has, for example, translated into the expected flat cash settlement for the Science & Technology Facilities Council (STFC), although there has been some rejigging of the way this money is allocated within STFC, and an apparent increase in funds available for international subscriptions. At least this should unblock the numerous programmes in STFC and elsewhere in the Research Councils that have been on hold pending the final budget allocations.

That said, the overall picture looks very bleak for Higher Education. The really important figure for HEFCE is buried in Annex 2 of the latest grant letter, which reveals that, including the ring-fenced funds, HEFCE will have just £4,091 million to allocate in 2014/15. The corresponding figure for the current year, 2013/14, was £5,014 million. That’s a cut in cash terms of an eye-watering 18.4%.

The scale of the cuts makes it even more likely that if they continue there will be very little money available for HEFCE to allocate as a result of the 2014 Research Excellence Framework, in which case the vast expenditure across the sector preparing for that exercise may will have been wasted too.

For the time being, however, it seems that research has been spared the axe. The bulk of the cuts will therefore fall on teaching grants. HEFCE has been instructed to try to protect STEM subjects as it cuts expenditure on teaching, but will it be able to? The extra funds that have previously supplemented tuition fees have been steadily whittled away anyway, so expensive subjects like Physics only get about £1000 per year more than Arts subjects. There is already a strong incentive in the current funding model for universities to expand cheap subjects. That pressure will only increase with this new settlement.

The last paragraph of the grant letter says:

We recognise that our universities are one of our most valuable national assets. Higher education transforms people’s lives through excellent teaching and transforms society through research and the application of knowledge. The Government’s reforms have laid the foundations for a more securely funded, stronger, more confident and more responsive higher education sector. We will continue to work with the Council and the sector to communicate the enduring value of higher education to potential students and the wider world.

I’m sure readers of this blog will forgive me if I suggest that these words are rendered meaningless by the scale of the cuts announced in the grant letter. If the government really regarded our universities as “valuable national assets” it would be increasing investment in them, not cutting it. What worries me most is that these cuts will never be reversed, whatever the complexion of the next government as there seems to be more enthusiasm across the political spectrum for continued cuts than for investment in the future education of our young people. I’m increasingly ashamed of the legacy being left by my own generation.

## Breakfast with BIMM and Cake with MPS

Posted in Biographical, Education, Music with tags , on January 31, 2014 by telescoper

Another very busy day means I’ve almost reached the end of a very busy week. I spent this morning in a meeting with colleagues from the University of Sussex and representatives of the Brighton Institute for Modern Music (also known as BIMM), which focusses on courses intended to prepare students to work in some aspect of the popular music industry, including performing and songwriting as well as, e.g., management.

It’s one of the odd things about being a Head of School that you get invited to do strange things every now and again and this was one such occasion. The University of Sussex validates degree programmes for a number of education institutions, BIMM being one of them and it was my job to Chair a session this morning (at a location in central Brighton) that formed part of the validation process. We had some nice pastries for breakfast too.

Regular readers of this blog (both of them) will know that I’m not really up to date on popular beat combos so I wasn’t picked for this task for any music expertise; the idea was rather that being a complete ignoramus I could be an impartial Chair…

It was great to talk to have the chance to talk to some of the current BIMM students as well as the staff and one of the things that struck me was that although I work in a very different discipline, many of the educational challenges faced by the School of Mathematical and Physical Sciences and BIMM are very similar. I can’t talk about the details we discussed, but it was a very friendly meeting and there was lots of constructive discussion.

That business concluded it was back up to Falmer for a quick lunch and a meeting about undergraduate admissions. And finally, because it’s the last Friday of the month it was time this afternoon for our monthly MPS cake event. This month’s cake had a vaguely mathematical theme and also raised the issue of the correct plural of the word conundrum:

I thought it was appropriate to invite the Head of the Department of Mathematics, Miro Chlebik, to solve this particular conundrum by cutting the cake:

The cake vanished pretty quickly thereafter.

## Methods of Images

Posted in Biographical, Cute Problems, Education with tags , , , , on January 29, 2014 by telescoper

I’ve had a very busy day today including giving a lecture on Electrostatics and the Method of Images and, in an unrelated lunch-hour activity, filing my tax return (and paying the requisite bill). The latter was the most emotionally draining.

With no time for a proper post, I thought I’d give some examples of the images produced by yesterday’s graduands, including some who used a particular approach called the Method of Selfies. Unfortunately some of these are spoiled by having a strange bearded person in the background.

But first you might like to try the following example using the actual Method of Images:

Given two parallel, grounded, infinite conducting planes a distance a apart, we place a charge +q between the plates, a distance x from one of them. What is the force on the charge?

This is, in fact, from Griffiths, David J. (2007) Introduction to Electrodynamics, 3rd Edition; Prentice Hall – Problem 3.35.

And now here are some of the official pictures from yesterday

## Rites of Passage

Posted in Brighton, Education with tags , , , on January 28, 2014 by telescoper

Just back home from the drinks reception that followed today’s Winter Graduation Ceremony at the University of Sussex at the Dome, in Brighton. And a very nice event it was too!

The Winter Graduation ceremony is primarily taken up with postgraduate degrees, and within School of Mathematical and Physical Sciences the largest proportion of those are in Mathematics, especially in the MSc courses in Financial Mathematics and Corporate and Financial Risk Management on which we have a large number of overseas students, e.g. From China. My first graduation ceremony as Head of School therefore presented me with some pronunciation challenges as I read out the names of the graduands. I was a bit nervous beforehand, not because I’m afraid of making a fool of myself but because these days everything is captured on video for posterity and I didn’t want to ruin anyone’s record of their Big Day. I practised quite a lot actually, and think it was OK.

I am always impressed at students who have the courage to travel halfway around the world to study in a foreign land. Graduation is a rite of passage for all students, but it must be of even greater significance for students from abroad.

I’ve attended graduation ceremonies at a number of other universities, and the big difference with Sussex is how much less formal it is. A great deal of credit for that must go to the Chancellor, the brilliantly funny and approachable Sanjeev Bhaskar, who ran the show in inimitable style. He also has a lovely head of hair.

Sanjeev always had a word with the graduands as they crossed the stage, often a hug, and very allowed them to take a selfie, once sitting in the Chancellor’s chair! I found it all very amusing, which helped me relax before my turn at the podium with the list of names. I’ve sat through a large number of dull and stuffy graduation ceremonies in my time, and much prefer the Sussex style!

Also graduating with top marks in our MSc in Cosmology was Mateja Gosenca, who is now my PhD student. Here we are at the drinks party after the graduation ceremony; Mateja is looking very happy holding her certificate as winner of the Sir William McCrea Prize for the best student on the MSc programme!

That one was taken with my Blackberry; here’s a much nicer version taken with a proper camera:

## How to Address Gender Inequality in Physics

Posted in Education, The Universe and Stuff with tags , , , , on January 26, 2014 by telescoper

Last night I was drinking a glass or several of wine while listening to the radio and thinking about a brainwave I’d had on Friday. Naturally I decided to wait until I reconsidered it in the cold light and sobriety of day before posting it, which I have now done, so here it is.

The idea that came to me simply joins two threads of discussion that have appeared on this blog before. The first is that, despite strenuous efforts by many parties, the fraction of female students taking A-level Physics has flat-lined at 20% for over a decade. This is the reason why the proportion of female physics students at university is the same, i.e. 20%. In short, the problem lies within our school system.

The second line of argument is that A-level Physics is not a useful preparation for a Physics degree because it does not develop the sort of problem-solving skills or the ability to express physical concepts in mathematical language on which university physics depends. Most physics admissions tutors that I know care much more about the performance of students at A-level Mathematics than Physics.

Hitherto, most of the effort that has been expended on the first problem has been directed at persuading more girls to do Physics A-level. Since all universities require a Physics A-level for entry into a degree programme, this makes sense but it has not been successful.

I now believe that the only practical way to improve the gender balance on university physics course is to drop the requirement that applicants have A-level Physics entirely and only insist on Mathematics (which has a much more even gender mix). I do not believe that this would require many changes to course content but I do believe it would circumvent the barriers that our current school system places in the way of aspiring female physicists.

Not all UK universities seem very interested in widening participation, but those that are should seriously consider this approach.

Posted in Education, The Universe and Stuff with tags , , , on January 24, 2014 by telescoper

An exciting new paper by a leading theoretical physicist prominent educationalist has just appeared on the arXiv. In it the author addresses the important question of whether information is destroyed in black holes students actually learn anything during lectures.

Until recently it was generally believed that any information falling into a black hole entering the mind of a student was lost forever even though black holes do evaporate students do take examinations after a finite time. This belief is motivated by the properties of Hawking radiation produced by black holes observations of examination scripts written by students, which some claim to be entirely random, i.e. devoid of any information content whatsoever.

This picture has however been challenged by a number of educationalists theorists with a variety of counter-arguments. For example, some have argued for a statistical interpretation in terms of the multiverse a very large class; although information may be destroyed in individual black holes students, in a infinite multiverse large enough class, there may be a finite number of examples in which some information is retained.

The latest article (referred to above) offers a different resolution of the Black Hole Information Student Education Paradox which rests on the idea that information radiated by black holes examination scripts written by students are not in fact entirely random, just produced so chaotically that, although information is present, for any practical purposes such information is so garbled that it is impossible to decipher.

This intriguing suggestion has led to a number of interesting, if somewhat speculative, extensions. Some have even argued that there may after all be some information present in the speeches of Education Minister Michael Gove, though this idea obviously remains highly controversial.

Stephen Hawking is 72.