Bill's science

Updated league tables for maths grants

2011-11-05T10:28:00.001-07:00

New updated tables for maths EPSRC grants for UK maths departments.

On the TV about Turing

2009-08-28T05:05:00.000-07:00

Very short interview about on BBC NW news Alan Turing at the Museum of Science and Industry, next to The Baby.

Where was Alan Turing's office at Manchester?

2009-08-28T01:23:00.000-07:00

So sitting here in the Alan Turing Building I was wondering where the great man used to sit and think. The Mathematics Department was housed in the attic of the John Owens Building until about 1952 when the department moved to the Williamson Building. I went to the university archive but all we could find was his personnel record (a single index card) and an entry in the 1953-54 University Calendar. It is not clear where the Computing Machine Laboratory would have been when it started in 1948. My suspicion is that at least at first he was in that attic. The reverse of the card has his home address and a newspaper obituary.

The address in Hale is new to me, but I think the one in Wilmslow has a blue plaque.

EIT and Electric Fish Bill on the TV News

2009-08-22T05:06:00.001-07:00

Here is a clip of me on BBC NW Tonight the interview was by Stuart Flinders.

The fish are Black Ghost Knife Fish and we bought them from Oasis Aquarium in Manchester
Why is the idea behind the moment tensors? These were described by Habib Ammari at the EIT meeting and in his book. My hypothesis is that the fish can detect the difference between the moment tensors of the objects.
Details on the science behind the electric fish can be found in Mark Nelson's talk the week before in Manchester. The sldes and a video stream of the talk are on line.
I am not actually "doing experiments" I leave that to the experts. The fish are in the School of Maths for observation and to stimulate discussion.
Why am I using a Game Boy Advance? It has a plug in module to convert it to a Digital Sampling Oscilloscope and Spectrum Analyser
With the live Fish Cam (user fish password fish) you can see the School of Maths Aquarium yourself. It depends on the light how well you can see, and the knife fish don't like the lights so it is often off.

Salients and reverse salients

2009-08-04T05:47:00.000-07:00

Which maths department are better than the average of that university and which are worse?

And what are the advantages/disadvantages of each?

I posted a chart to stimulate discussion.

Comparing Maths Departments 2009

2009-07-30T08:08:00.000-07:00

I finally got around to uploading an updated web page Comparing Maths Departments in the UK. It now has a great big table that can be sorted by clicking on any column heading (thanks to Steven Liem in EPS Faculty IS support).

Bristol on many measures of research output seems to have joined the COWI club, there are some discussion of big departments doing generally better in the RAE, and yet some departments "punching above their weight".

Elelctric fish, intensive care and geophysics

2009-06-13T01:46:00.000-07:00

What do these have in common? Weakly electric fish see in dark or murky water using electrosensing. Geophysicists use electric and electromagnetic fields to probe the earth and in intensive care medicine electrical impedance measurements being are used to monitor the lungs of patient who are on ventilator machines.

The mathematics of Inverse Problems is what brings these things together and at a meeting at the University of Manchester 15-19 June 2009 mathematicians, physicians, geophysicists and biologists studying weakly electric fish come together. Hopefully sharing information between these communities will lead to breakthroughs in all of these fields.

On Thursday the 18th June 12-1pm (BST) a lecture by Prof Mark Nelson "Electrosensory data acquisition and signal processing strategies in electric fish" will be video-streamed for all to see.

As the fish are the real experts the School of Mathematics has temporarily set up its own aquarium of weakly electric fish. Details here (we also have a live "fish cam"). For news stories on our electric fish follow that link too.

Wolfram Alpha

2009-05-20T01:04:00.000-07:00

I tried Wolfram alpha for the first time today. I was pleased that it handled some mathematical queries without any special syntax. I asked Fourier transform of absolute value. It worked by I just tried it again and it timed out. Typing names of various chemicals was informative. Other information it gives was found to be inaccurate. For example it thinks The University of Manchester was founded in 1851. Take your pick from 1824 or 2004, but 1851 is just wrong. Source information is given, but it does not reference each fact separately so one cannot tell where they gone wrong. It seems they have used sources uncritcally without checking, or perhaps used out of date information (for example 1851 is probably listed as the founding date of the old Victoria University of Manchester, pre 2004). There is a feedback form but no reaction yet.

I also tried a fish Gnathonemus petersii. It got the common name wrong "Peter's elephantnose fish" instead of the correct "Peters' elephantnose fish". A look at the Latin name reveals that it is clearly named after Peters. A common mistake on the internet, but a glance at Wikipedia would have sorted them out!

So overall I am sure I will use it and it will develop. But without properly verifiable references it is less trustworthy than a well referenced Wikipedia article.

Ironic "construction manager of the year" award.

2008-12-22T02:57:00.000-08:00

I love the Alan Turing Building, home of the School of Mathematics at Manchester. It is designed to maximize chance encounter and people therefore run in to each other and stand around talking about mathematics. Just as it was intended.

But like many construction project in the UK it is let down by lack of attention to detail. My PhD students have been in a room that is for most of the time too cold as cooled air is blown in. Rather ironically negating the value of the solar panels on the roof. Other rooms suffer from basic errors of control theory in their heading and ventilation.

Only now, a year and a half after we moved in, is sound insulation to be installed in the walls. Turns out they forgot to put it in at the time!

Just minor niggles you might say in an otherwise great building. However I read that Tony Grindrod has been nominated for Construction Manager of the Year for his work on the Alan Turing Building. So the state of the construction industry in the UK must be really bad. Just imagine the problems of the projects managed by less celebrated construction managers!

"The Baby" at MOSI

2008-07-09T02:48:00.000-07:00

As part of Making Maths at Manchester we visited the Museum of Science and Industry to see the replica of "The Baby" or Manchester Small Scale Experimental Machine. The first computer to store its program in electronic memory.

We had an entertaining talk by volunteers who had worked with Tom Kilburn on the recreation of his machine, using the same racks from phone exchanges but replacing many of the valves and switches. They commented that the front panel switches, on which the program can be input, were from the radio selector of a Spitfire, so if anyone had a spitfire with a broken switch they were out of luck as all the remaining spares had been bought for this project.

Sir Bobby Charlton and land mines

2008-06-17T03:38:00.001-07:00

A group of us at the University of Manchester and Lancaster University were approached by Sir Bobby Charlton to see if we can come up with a faster way to clear anti-personnel mines. We went to a demonstration of what an explosive charge similar to that in a typical mine could do. The toe was blown off the wellington boot and went 20 or 30 m in the air.

The video is from Telegraph TV

This was covered in the Telegraph newspaper Saturday 28th June 2008, in the sports section, and there is an online version of the article

Bad science: Cubic litres!

2008-02-02T04:43:00.000-08:00

I enjoy Ben Goldacre's Bad Science column in Saturday's Guardian. Today's included this

I know I'm wrong to care. On the BBC news site "crews were hopeful the 20m cubic litres of water could be held back and not breach the dam wall". And that'll be a struggle, since "cubic litres" are a nine-dimensional measuring system, so the hyperdimensional water could breach the dam in almost any one of the five other dimensions you haven't noticed yet.

I just love the idea of the water by-passing the dam in the extra dimensions. I have always felt that really a universe with only three spacial dimensions was just right. From "Flat Land" [W] we know how noisy it would be in one dimension (sound intensity does not decay with distance), and in two dimensions we could not tie our shoe laces, and a body could have only one oriface to the gut serving both purposes. An in four dimensions shoe laces would also be a problem as any curve embedded in four dimensions is unknotted. In a strange way the higher dimensional spaces are pretty boring places. All the lovely regular polytopes in three and four dimensions. Then from dimension five all the way out to Hilbert space there are just the three. Well there is a more interesting story for exotic differentiable structures on n-spheres but I am not sure what influence that would have on the life of nine-dimensional beings.

It reminds me of a story told by Sir Christopher Zeeman

At 2am on the Sunday morning I was sitting on the lavatory contemplating my theorem, when suddenly it hit me that I use the same proof to unknot n-dimensional spheres in (n + 3)-dimensions, for all n. Once I had seen that, I was able to reduce the original proof in 5-dimensions down to ten lines, which I published as a one-page paper in the Bulletin of the AMS.

Do we have any of that six-dimensional spherical pasta for lunch? Funny how it never seems to get knotted? Oh and pour me a cubic litre of hyper-beer.

Advice on choosing an undergraduate maths course in the UK

2008-01-20T07:48:00.000-08:00

I am often asked for advice on choosing a place to study maths for a first degree in the United Kingdom. I summarised my thoughts in
this essay. Actually my page on league tables of U.K. maths departments stemmed from this, in answer to pondering questions including "Which are the largest UK maths departments?", and if there is any objectiveevidence to support the widely held opinion that COWI (Cambridge-Oxford-Warwick and Imperial... but not necessarily in that order) are the top four UK mathematics departments.

Any comments on the essay -- please post on this blog.

League table madness

2008-01-14T07:06:00.000-08:00

I posted Some comparative figures and league tables of UK mathematics departments. I wrote the bash scripts to pull out the data on EPSRC grants etc while watching TV over Christmas. Please feel free to post comments here.

Highlights of 2007

2007-12-21T07:19:00.000-08:00

Journalist Chloe Stothard asked for my five most memorable things this year, a story that ran in the Times Higer Education Supliment, as
So what were the high notes of 2007?(free subscription required). Mine (with links) were

We moved, with the rest of the School of Mathematics, to our new purpose-designed Alan Turing Building and now the school is finally all under one (solar power-generating) roof after the merger between the Victoria University of Manchester and UMIST.

We were part of an event with 120 sixth-form students from all over the country solving mathematical problems for two days - "Making Maths at Manchester".

I attended a meeting in Graz in Austria on electrical impedance tomography, a subject I have worked on since 1985. It had seemed like a very difficult (and hence interesting to a mathematician) technique without an important medical application. But lung and intensive care specialists have now found it is just the tool they need to monitor lung function in real time. (see programme sessions: EIT applications 1, special session 3, EIT clinical applications 2)

All my family enjoyed scuba diving together in Cyprus in summer, and it was wonderful to watch the confidence and curiosity of my children Katie and Sam underwater.

I met Sir Bobby Charlton, who came to the university to talk about technology for land-mine clearance. He made a touching appeal from the heart that something better should be done to help, having witnessed young lads who had lost limbs to anti-personnel mines when they were playing football in Cambodia. It was really inspiring to meet someone making such good use of his celebrity status.

General ignorance of negative numbers.

2007-11-09T12:33:00.000-08:00

It is often said that the UK National Lottery (run by Camelot) is a "tax on ignorance". As much as any gambling game with a negative expected gain, theargument is it preys on the triumph of optimism over the laws of probability. This story takes another turn as the Camelot brought out as seasonal scratch card in which to win one had to reveal a number lower than a given number. With a winter seasonal slant the numbers were temperatures in Celsius and negative.

According the the ManchesterEvening News

Tina Farrell, from Levenshulme [a suburb of Manchester], called Camelot after failing to win with several cards.

The 23-year-old, who said she had left school without a maths GCSE,
said: "On one of my cards it said I had to find temperatures lower than
-8. The numbers I uncovered were -6 and -7 so I thought I had won, and
so did the woman in the shop. But when she scanned the card the machine
said I hadn't.

"I phoned Camelot and they fobbed me off with
some story that -6 is higher - not lower - than -8 but I'm not having
it.

I found that rather sad. I suppose it shows the disparity in the standards of education in our city that people can leave school without being able to order negative numbers, and at the same time we are getting more and mathematically stronger applicants for our maths degree courses at the University of Manchester.

It also makes me glad that the
city is not still being threatened with a super
casino, to further part the mathematically challenged from
their money.

Wildfires set the air alight (maths on YouTube)

2007-08-04T07:01:00.000-07:00

My colleage John Dold's work on bush fires appeared in New Scientist. It explains why firefighters thought they saw the "air catching fire". There is a video with a commentary by John on YouTube (and linked on this New Scientist Blog) which includes work on the influence of the slope of the ground on the spreading of the fire. Before I had only seen frivolity on YouTube (cat herding being my favorite) so it is nice to see it used to spread the word about some really interesting and useful applied mathematics.

Since writing that I looked for maths on YouTune and came across Timothy Gowers lecture The Importance of Mathematics, which I recommend.

On the design of Buildings in which to do Mathematics

2007-07-29T10:16:00.002-07:00

As the School of Mathematics at Manchester moves in to our new purpose designed Alan Turing Building, I am moved to reflect on the requirements of a building in which to do mathematics.

I am reminded of a letter written by Charles Dodgson (a.k.a. Lewis Carroll), his tongue firmly in his cheek, enumerating the requirements for buildings for the school of mathematics. Dodgson starts with a basic observation

it has occurred to me to suggest for your consideration how desirable roofed buildings are for
carrying on mathematical calculations: in fact, the variable character of the weather in Oxford renders it highly inexpedient to attempt much occupation, of a sedentary nature, in the open air.

how much more true this seems in Manchester (well that opinion might be revised given the recent floods in Oxford). He also anticipates the modern trend towards open-plan offices

it is often impossible for students to carry on accurate mathematical calculations in close contiguity to one another, owing to their mutual conversation; consequently these processes require different rooms in which irrepressible conversationalists, who are found to occur in every branch of Society, might be carefully and permanently fixed.

While this is true to some extent about calculations, our own experience is that mathematics is often a social activity performed in groups of two or three around a blackboard, or in, its absence, the back of an envelope or even a table napkin or beer mat.

He continues with many more comical suggestions. My favourites are A piece of open ground for keeping Roots and practising their extraction: it would be advisable to keep Square Roots by themselves, as their corners are apt to damage others. and A narrow strip of ground, railed off and carefully levelled, for investigating the properties of Asymptotes, and testing practically whether Parallel Lines meet or not: for this purpose it should reach, to use the expressive language of Euclid, "ever so far".

When we were asked about three years ago to express our own ideas about the design of a new building for the School of Mathematics, formed recently by the merger of the Mathematics Departments at UMIST and the (Victoria) University of Manchester, we were considerably less flippant. We had clear ideas about what worked and what did not. During the 60s and seventies many universities build high rise buildings to save on the costs of land. Experimental sciences were often not accommodated in high rise buildings due to practical considerations. For example heavy machinery or protection from vibration. Mathematics departments had no such reason and were often put in to the high rise buildings. There is anecdotal evidence that to some extent we, as a community colluded with this. High rise buildings were very fashionable and the promise of a new building is very tempting and perhaps its failings hard to anticipate. I wonder if to some extent we act like parent: in a determination not to repeat theworst aspects of the way we were parented we create a different set of problems ourselves.

So what is wrong with high-rise buildings as places in which to do mathematics? Well it is not the height per-se. One has to understand to some degree the social nature of mathematical collaboration. Of course Dodgson is right that there is a necessity for quiet solitude. Mathematical work is often characterised by long periods of intense concentration during which interuptions are unwelcome. However often progress is made by a chance encounter with a colleague who gives one a lead from the benefit of their own expertise. Of course it is often the case in the 21st century that what we are working on is so specialised that the only conceivable collaborators are on the other side of the planet, and progress is made by emails and scribbled notes faxed to each other. But there is something about a chance encounter in the corridor that allows one to ask an expert a stupid question. Even if you have been worrying about it for months, not knowing quite how to put the question, one can at least pretend the question has just occurred to you. Some how committing a statement of your ignorance to paper or email is braver: physical evidence that you did not understand something perhaps you should have. So it seems to me, and to many of my colleagues that an important aspect of the design of buildings in which to do mathematics is that the public spaces, corridors, stair ways and halls, are pleasant enough places to linger a while and have a discussion. Preferably with black boards close at hand (the topic of mathematicians and their blackboards discussed in Sasha Borovik's blog, although mainly in the context of teaching. I am able to disclose that Sasha has a white board in his new office!). Those of us who had the privilege to work or study at the old Mathematics Institute at Warwick, will understand exactly what I mean. The Isaac Newton Instute and the wider cluster of buildings constituting the Centre for Mathematical Sciences at Cambridge is a great example of building with these principles in mind. Jonathan Glancey's article in the Guardian explains.

So our own building new building, the Alan Turing Building, takes account of some at least of these design criteria. Only three floors are devoted to mathematics, and the lower of these has a large public area in an atrium and teaching rooms not all exclusively for mathematics.

The second and third floors contain offices for academic staff, post docs, visitors and postgraduate students, as well as research seminar rooms and a large common room spanning a bridge across the atrium. The corridors are glass walled walkways facing the atrium. Hopefully one can not only encounter colleagues by chance (and the layout is designed to increase the chance) but one can also spot a colleague on another level on the other side of the building. While there are lifts most of the time it will be quicker to take the stairs. Interestingly the fourth floor, accommodating the Astronomy and Astrophysics group which is part of a different School, is designed quite differently. Their corridors are between offices and do not have a view over the atrium.

There were of course many things that were frustrating for the academics who had to deal with the Estates Department and architects (Sheppard and Robson). Misunderstandings and going back on what had been agreed. I think in time it would be really helpful if those involved wrote a helpful guide to other academics involved in the planning of a new building. However to a large extent the mathematicians moving in to the new building are optimistic, and only time will tell if we have swapped one set of problems from the high rise phase of architectural error to new ones in the age of the steel frame and atrium.

Collingwood, Stuart Dodgson, 1870-1937, The Life and Letters of Lewis Carroll (Rev. C. L. Dodgson), Project Gutenberg (specific section on-line)
Glancey, Jonathan, "form + function = faculty squared", The Guardian, Monday July 14, 2003 Guardian Unlimited.
Picadilly Partnership, Description of main features of architecture and design including energy conservation measures. Accessed July 2007
School of Mathematics web site

Helix or Spiral?

2007-01-02T04:30:00.000-08:00

I had the great privilage to visit Willi Kalender at the Institute for Medical Physics, University of Erlangen-Nürnberg. He welcomed me and invited me to hang my coat on a rather nice helix mounted on the wall with coat hangers on it. "By the way" he said "that is a SPIRAL coat hanger".

Prof Kalender is the father of a method of three dimensional computerized tomography he calls Multi-Slice Spiral CT, which greatly improved medical X-ray tomography. Relative to the patient the x-ray source describes a helical trajectory around the patient. Actually the source goes around in a circle relative to the hospital, and the patient moves through the machine in a direction normal to the plane of the circle. So why did he call it "Spiral"? I must add that Willi speaks excellent English, and checked his dictionary carefully. There are at least two instances in which "spiral" is used as a synonym for "helix". A "spiral stair case" and a "spiral bound" book. So he went for the more informal sounding word.

The Oxford Dictionary of English (revised edition).( Ed. Catherine Soanes and Angus Stevenson. Oxford University Press, 2005. Oxford Reference Online. Oxford University Press. Manchester University. 2 January 2007 t140.e74434)

spiral

adjective
winding in a continuous and gradually widening (or tightening) curve, either around a central point on a flat plane or about an axis so as to form a cone: a spiral pattern.

• winding in a continuous curve of constant diameter about a central axis, as though along a cylinder; helical. • (of a stairway) constantly turning in one direction as it rises, around a solid or open centre. • (Medicine) (of a fracture) curving round a long bone lengthwise. • short for spiral-bound: a spiral notebook.

Indeed the etymology stems from the Latin Spira meaning coil. However in modern mathematical English it is clear that a spiral is a plane curve and a helix a curve on a cylinder. Of course I am a mathematician, and also something of a pedant. So would avoid calling a mathematical curve by the wrong name, just as I would be careful not to say ball when I mean sphere, or linear when I mean affine, so I am likely to talk and write about CT with a helical source trajectory. However on the way back I mused that in mathematics it is usual for a great mathematician to invent something and call it something mundane while everyone else calls it after them. For example when Smale is talking about Morse-Smale dynamical systems he calles them "Simple" (with characteristic modesty). So I was thinking that we should talk of "Kalender Tomography", thus crediting the man who fathered the technique while remaining true to the mathematical terminology.

More links

Definition of spiral in Wiktionary. It agrees with me that spiral=helix is informal. No I didn't write it!
Wordinfo defines speira (Greek) spira (Latin) saying "The Greek speira refers to anything which is wound or wrapped around something" which sounds like it covers helices and spirals and "in the plural, speirai, it includes the twisted folds or coils of a serpent" which is even more general.
MathWorld helix, spiral.
PlanetMath circular helix, Arcimedean spiral

More on blackboards

2006-10-21T09:34:00.000-07:00

(This post was on Bill's stuff but I have moved it as being more related to science and education)

A conversation on the train today on the subject of black boards. My friend Curtis asked how the new Maths building was going and if we had our blackboards sorted out. As we have been having a lot of blackboard related discussion prompted by Sasha Borovik's blog "Psychophysiology of blackboards" it led me to think about similar cases where a high technology alternative is proposed to something very simple and effective, and while the high-tech solution has many supposed advantages it simply does not do the basic function as well as the original.

An interesting example is the case of "electronic books". The idea is to make a small portable device that can store images of (perhaps several) books electronically and display the pages on a liquid crystal display. Such things exist, and they have advantages including: not needing to cut down trees (one would have to do some careful accounting to see if there was a net environmental benefit), the possibility of taking lots of reading material while travelling without the weight, the possibility of rapid electronic distribution over the Internet. However several technological challenges mean that that they do not yet work as well as a paper book. A recent contender is the Sony Reader. The resolution of portable screens is no-where near that achieved in printed media. Interestingly I was involved in a research project with HP Labs Bristol on liquid crystal displays. One aim is to make a bistable liquid crystal display so that pixels can be turned black or white without the need for to be frequently refresed. There is a bit about the project here. For "electronic paper" this is essential to provide the required resolution, and the page only needs to be changed at the rate of turning a page so slow is ok. But it is not yet "in the shops". Also contrast is a problem. Most laptop computer displays require a back light, and cannot be read in strong sunlight and this too is a problem for electronic books.

While we might see these problems overcome in the near future it currently the high technology replacement simply does not provide the basic functionality required of a paper book. And so it is with the humble blackboard. There are some very interesting "smart boards" widely deployed in schools. This consists of a touch sensitive screen on which an image is projected. A computer stores the lines drawn on the screen with a special pen and projects them on the screen. They have the advantage that previous screen-fulls of writing and drawing can be replayed, very much like the traditional over-head projector scroll. As the image is stored electronically it can also be made available to the students. I have not seen these devices deployed on the scale needed for a 200 seat university lecture theatre in which the entire wall is covered by several moving boards. Although technically it is feasible. However as a basic medium for writing it still does not approach the functionality of a blackboard. For example to writer must be careful not to obscure the projection, otherwise she cannot see what she is writing. Also the lights must be dimmed (or sunlight blocked) for the screen to be easily seen. This makes it harder for the students to take notes and increases the tenancy for them to fall asleep.

I can see perhaps that in a few years with as substantial effort, it might be possible to make an electronic system that achieves the functionality of a blackboard (as well as also having some advantages). But the result would be likely to be quite costly, require more maintenance, and provide only a marginal advantage over the low technology approach.

As an afterthought I wondered about electronic pianos. Not such a clear case as for piano players, and listeners to pianos up to a certain level a modern electronic piano provides an acceptable alternative in terms of its basic functionality. And of course has some additional functionality such as staying in tune, recording keystrokes, playing an accompaniment , etc. Interestingly electronic pianos are cheaper the conventional pianos again making the comparison with blackboards and books not so relevant.

p.s. 10/10/2006 Sasha Borovik's blog on blackboards gets mentioned in The Guardian

How many "centres" are there of a triangle

2006-10-12T08:46:00.000-07:00

One of my students wrote the centre of a triangle is (r1 + r2 + r3)/3. Well that is one definition, the centroid or centre of mass if it is has uniform density.

I immediately thought also of the

Circumcentre, the centre of the circumscribing circle

Incenter, the centre of the inscribing circle

Centroid, where the lines joining the mid point of each side to the opposite vertex meet.

Then some googling found me Jim Loy's page listing a few others

Orthocenter where the three altitudes of a triangle meet.

Gergonne point where the lines connecting the tangent points of the incircle to the opposite vertices meet

Fermat point (also called the isogonic center or the Rorricelli point) which minimizes the sum of the distances from the three vertices.

and three more as well! Then I found an even better page Geometry step by step from the land of the Incas(!) Listing 16 different kinds of centres of a triangle (with pretty colour pictures).