Mathematics is vital!

October 13, 2010

[This is a painful post to write and probably to read, I attempt to soften the blow by including some geometric construction projects I have been working on!]

I write this as a UK mathematician recently moved to the US. A move decided upon before the election, let alone any mention of the deep cuts that the wonderful Science is Vital campaign is fighting. The brain drain for mathematics has been underway for a while. I was following the jobs listing in the UK closely for a couple of years and saw only a handful of permanent jobs.

 


Compound of five cubes made from laser cut and tabbed paper. No glue.

 

I am a firm believer in mathematics and mathematical thought. I believe that the ideas of mathematics are amongst the greatest cultural treasures and greatest achievements of mankind. On the other hand I believe that true mathematical thought is central to having a well-informed, engaged and active population. To me, therefore, the case for mathematics is clear both from an elitist and a populist stand point.

 

Students stand next to the Hexayurt they built, a project they initiated for the Mathematical Thought course I am currently teaching. The hexayurt is a simple structure that takes geometry into disaster relief housing.

 

Yet for a long time I felt that only the elitist case was being made, with some additions from utility in science. I have heard many people say the only answer from their teachers when asked “Why do we have to study mathematics?” was “You need to pass GCSE to get a job”. I wrote those feelings off, I could find many counter-examples and perhaps I was being over-critical. Unfortunately my denial could only go so far. I have already mentioned Science is Vital. Before that the same accusations could have been levelled at scientists. Yet when really pushed scientists from the great and the good through to the lowly lab workers rallied. 36,000 signed the petition, thousands marched wearing lab coats. If the cuts come no one can say that scientists went down gently.

What about mathematicians? We are smaller and quieter, have a harder time getting press coverage. Maybe an equivalent event would not have worked just for mathematics. Perhaps it is understandable that no protest had emerged from within mathematics as the first problems came. So what happened after the banner was raised by the scientists? Surely the pent up frustration led to overwhelming support?

Nope

The three big organisations of mathematics in the uk, the London Mathematical Society, Institute for Mathematics and its Applications and the Royal Statistical Society do not mention the cuts on their home pages, let alone Science is Vital. None is listed in Science is Vital’s long list of supporting organisations.

Marcus du Sautoy, a mathematician, currently Professor for Public Understanding of Science is not listed as a signatory, and does not seem to have said anything public

[Edit 14/10/10: Many apologies to Marcus, he did sign (though should be listed)  has written about the cuts making the case for mathematics in the New Statesman, and has given talks in Oxford and elsewhere. This is a great relief!]

similarly David Spiegelhalter, Ian Stewart, and Tim Gowers

[EDIT 14/10/10 corrections welcome, I am searching as I can online but that is not a perfect system]

all mathematicians with a public reputation and some access to the media all seem silent. It is very unfair to name names, I do so here as these are my heroes, people who do great things for mathematics and its popular perception. The fact that even they did not join the campaign reveals to me the depth of the issue.

In fact in following this event and even searching for mathematicians getting active the thing I could find was Michael Atiyah who was listed as first author on a letter calling on the government to cut military R&D rather than basic science.

EDIT [14/10/10]: Chris Budd also took part in a great debate in the Economist about the essential role of mathematics in innovation.

 

Four parallel sets of lines make up an octagonal weave, closely related to the Ammann-Beenker tiling.

 

Perhaps less notable mathematicians were more busy, signing and joining the protest, I would love to hear from those who did. For all other mathematicians I want to conclude by screaming:

Wake up, fight for your subject!

No longer accept the bad reputation our beloved subject has, change it!

Say how esoteric abstract nonsense has changed the world!

Say how mathematical thinking can help live a fulfilled, productive life!

Make the case!

If not you, who?

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Posted by gelada

Would an Alternative Vote make a difference?

May 10, 2010

[Update 10/5/10:

For a far less back of the envelope calculation, based on a poll including second intention rather than guesswork, you can look at this study from the Electoral Reform Society. They give a prediction of 281 Conservatives, 262 Labour and 79 Lib Dems. This, however only takes into account second choice. Making some assumptions for third choice makes things significantly more favourable to the Lib Dems, mainly at the expense of Labour.

]

The latest piece in the politics game is voting reform. Both the Conservatives and Liberal Democrats are actually quite keen on this, as the present system gives some level of support to Labour. Each party is, of course, wants to get a system that they get the most benefit from. A lot of different arguments are therefore brought out to try to make what is often a partisan case appear neutral. A favorite is the mathematics of Arrow’s theorem, that with certain reasonable assumptions the perfect voting system cannot exist.

Of course the lack of a perfect system does not mean that different options are not better or worse. Tim Gowers has given a mathematicians thoughts on how the current system is unfair. In a similar vein the Fabian society pointed out a couple of years ago that “‘first past the post’ now fails in its own terms” in an uncannily accurate piece of future gazing. The trouble is working out what effects the different systems will have. First past the post is not too hard, we have the result of the last election, and the effects of boundary changes are not hard to work out. This, of course, makes it popular to adapt as the powerful can control the result, the classic, often quoted  example of this are the Texas voting districts.

The result for proportional representation is easy to calculate, however it is also susceptible to control as votes are often cast for a party rather than an individual. In its purest form it would also break the link to constituencies that many hold dear.There are ways to adapt this, including larger constituencies (put forward but the SDP-Liberal alliance in the 1980′s) and the Icelandic system where votes literally wander round the Island until they find a candidate.

The third system, in the UK is single transferable vote, or alternative vote. This was proposed by the Jenkins report, commissioned at the start of Blair’s years , but never put to a referendum. How would this effect the parties? It is more complicated, but we do have some data (the last election) that can be combined with guesses as to how people might give their voting priority.

To begin, look at each seat and see how many candidates could win (assuming that the votes transferred in the right way):

There are 218 seats where the winning candidate achieved more than 50% of the vote. For these seats the complications of voting systems and Arrow’s theorem can be put aside. A further 284 seats have two possible candidates and 120 three. It is not surprising that the number then quickly drops off, but one seat Torfaen in Wales has 8 candidates who could make it (of course several of them would need to be very lucky with how the votes came together!). Another two seats Islwyn, also in Wales and Barnsley East have a total of 7 possible candidates.

There are therefore a majority of seats that might be affected by the alternative vote system.How will these change? Making some guesses I put together a simple model here. This sees quite a lot of change, with 71 seats changing hands and a further 12 impossible to even guess at. Out of this, drum roll please, comes a prediction:

The model has python code, so you can play with the guess work if you like. The take home message, though is that the closer positions of Labour and the Liberal Democrats hurt the Conservatives, mainly to Labour’s advantage. The Liberal Democrats see an increased share of the seats, but do not come close to their proportional position.

Of course this speculation misses one key fact. People do not vote exactly the way they want, they vote to try to effect things in the direction they want as much as possible. If you change the system therefore, the voting behaviour will change as well.

As I dived into the detail of the election stats I was struck by the sheer number of independent and small party candidates. Many of these were able to obtain several thousand votes. With the constant rhetoric we face about not wasting votes this is a stunning achievement. Even if these people are not going to make the impact to get into parliament they are there agitating and doing. There are people out there willing to make a stand, and other willing to listen. They give me hope whatever happens in Westminster.

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Posted by gelada

Laptops are not the problem…

November 10, 2009

I am going to disagree with Doron Zeilberger. Which is not something I often do. His latest piece describes the Shocking state of contemporary “Mathematics”. Its not the subject of the post (summed up in the title) that I am going to disagree with though. To my mind he nails it. Its a small detail. Yet something I think is important.

For those of you who do not know Zeilberger is one of the strongest proponents of the use of computers to do mathematics (which I wrote about here). So ironically I am going to complain about his use of computers.

The outline of his message is that mathematics has become divided into small specialities:

topological algebraic Lie theorists, algebraic analytic number theorists, pseudo-spectral graph theorists

and this problem is made worse by the fact that even general talks have no more than a few minutes of general history and motivation before leaping into the details that only a fellow expert on the analytic and algebraic topology of local Euclidian metrization of infinitely differentiable Riemannian manifolds could understand.

This is all true. We have all been to too many such talks. He then starts to give the solutions:

One culprit is the pernicious laptop, it should be outlawed! It encourages the speaker to pass the cognitive speed-limit by orders of magnitude. Sure enough, the best invited talk was Michael Kiessling’s talk that used the ancient technology of overhead projector, and it would have been even better if he only used the blackboard…

Can this be? Computers are not just the future of maths, but they are holding it back? Is the blackboard really better? It encourages the speaker to turn his back to the audience. It concentrates so much of the time on the creation of too short often illegible notes on the topic. It has many issues. In the hands of a good speaker a piece of chalk and a board however can illuminate and inspire. So too can the pernicious laptop. Yes it introduces different problems, but it also solves some. With any talk a good speaker uses the tools well, a bad one does not.  I suspect that Michael Kiessling’s talk was so good partly as he has taken the time to master the OHP, and thus uses it because of those skills. The laptop is the default today, so it is where the bad speakers end up.

To be fair the quote above does have one more line:

and it would have been better still if he didn’t use anything, just told us a story.

This is where all talks should begin. Once you have the story it can be useful in some cases to add material. It is then up to you to master the blackboard OHP or laptop to add to your story.

Why is this minor quible important? A central theme to his piece is the importance of communicating, putting ones (necessarily focused to some extent) research into the general setting and context. Just as computers are going to be key to actually doing mathematics, removing some of the tactical and technical hurdles (even Alain Connes agrees with this). Computers and the internet are not pernicious, they are giving new options for communication and intuition.  Blogs are a great example. Tim Gowers and Terry Tao are both giving precisely the strategic overview we need. Even the Opinions are really a blog (though they could do with an update, at least an RSS feed! I hear wordpress do some good software…)

So please Ekhad, talk to Doron. Tell him that you can do a lot more than mathematics!

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Posted by gelada

Communication at the LMS

October 30, 2009

This is a cross posting of an article I have just put up on the Future of the LMS blog. I am posting it here as well as I think that the issues raised are of braoder interest. Especially the first paragraphs on the power of the web for mathematics.  To put it in context I have previously written about the LMS’s future and the importance of commication to mathematics.

One of the recurring themes in comments on this blog is the importance of communication, normally in the context of communication between members and the executive. Developments in this area are an essential part of taking the society forward, however we should also be considering communication in a wider setting.

Firstly communication as a whole is a rapidly changing area. In particular the internet is opening up opportunities that simply could not have been dreamt about even a few years ago. When this is mentioned in LMS discussions it is normally with a voice of doom as one of the effects is a potential reduction in money from publishing. Mathematics, however has a lot to gain from embracing this and it would be exciting to see the LMS taking a leading role. There are (at least) three different ways that mathematics communication can benefit:

  1. Communication between mathematicians and how mathematics takes place. A great example of this is the polymath projects started by Tim Gowers. These aim (already with success) to actually solve mathematical problems through massive collaboration. Another example is the often brilliant expository writing on wikipedia. This leads me naturally to…
  2. Making mathematics accessible. This is not just writing up on wikipedia, but videos on YouTube, photos, fractal art, the list goes on. As a simple example this YouTube video on Mobius transforms has been viewed over 1,500,000 times. Even if a small number of those communicated some understanding that is a significant increase in the number of people who know what a Mobius transform is!
  3. Finally the internet allows mathematicians to engage with a wider audience. The classic example here is Terry Tao, on his way to becoming a public intellectual through his blog, What’s New. The readership is very large, but he certainly does not achieve this by dumbing down. Many of his blog posts are incredibly technical. He also deals with questions of maths communication.

Therefore, can the LMS go beyond simply improving its website to play a role in leading how mathematics adapts to use these exciting new technologies and opportunities. Yes I am afraid that it will involve money! Though perhaps by getting ahead of the game potential new sources of revenue might reveal themselves.

Both the second and third points above are about public engagement with mathematics. There is excellent work taking place in mathematics public engagement. From school visits of students in the Undergraduate ambassador scheme to the Television programs of Marcus du Sautoy, to Science fairs like Bath Taps. The effort, however, is rather disparate. Consider, for example, large science festivals such as the Royal Society Summer exhibition. Last year there was no mathematics focussed exhibit. This year there was, but not through any planning, simply because I had an idea. I phoned several colleagues as was easily able to put together the team needed, including three other mathematicians (the exhibit “How do shapes fill space?” looked at topics in geometry and the theory of tilings). Similarly for next year’s Big Bang festival the LMS and IMA were contacted to arrange for a large mathematics stand but had to change plans after they were unable to fill it. The approach from the Big Bang shows the demand for mathematics at these events, and I can also say from the RSSE experience that the organisers were excited to be able to include mathematics. We therefore have the demand and the ability, all that is left is the organisation to provide the sparks.

I am not saying that the LMS is not already involved in engagement and education. There is excellent work being done. It is, however, rather limited. Let us compare briefly with the IoP. The IoP has a massive commitment to outreach, from school projects and teacher days, through grants for schools and outreach to innovative engagement activities like the recent “Lab in a Lorry” exhibits that travel round schools and events. In 2007 they provided 119 schools grants and a further 21 public engagment grants*. In contrast, last year the LMS gave out the tiny sum of £3,570 in education grants, with a further £1,000 by council for a discussion dinner**, out of a total grant spending of £234,000 ***. The IoP is obviously a far larger organisation than the LMS, however their annual spend on “Impact” which comprises education and public engagement is about £3,500,000 from an annual expenditure (not including publishing) of about £10,000,000 – £11,000,000. Even in terms of proportion, however, the entire LMS spending on education and engagement is small, about £125,000 of £750,000****. These are the numbers for promotion of mathematics, not just public engagement and so includes all money spent on interaction with government and research councils as well.

I have raised a variety of topic here without giving specific ideas about how they might be pursued. There are many things I would love to try, but mathematics needs more than that. We need to get a multiplicity of different voices. The difficult mathematics and technical detail of Terry Tao’s blog will reach a different audience to Marcus du Sautoy’s television programs, the blogs being set up by maths undergrads can reach different people still. There is no single path to public engagement, and so it needs to be opened as wide as possible. The best way to do this? Take something about the LMS that few would argue is not its greatest strength: the grants program, and add a significant amount for public engagement. Use the same philosophy as the main programs, plenty of small, easy to access grants aimed at filling the gaps in the standard funding sources. Open up grants to set off ambitious ideas that might fall flat, but could start working and then get big funding from EPSRC and elsewhere. Such a move into the work of public engagement would also show that the LMS is serious about this and enable it to take (with the IMA) a central role at the heart of UK outreach.

One final comment. This is not a zero sum game. Relatively small investments in these sorts of activities could help to pull other money into mathematics. Public engagement money is a natural example, but serious online projects could also attract funding from schemes like the EPSRC “Digital Britain” stream. (Claiming back some of the money lost from the Mathematics pool!). In the long term public engagement also helps to spread the message that mathematics is an essential part of a healthy society and economy. This public awareness is essential to obtain greater government funding for mathematics and even in the current climate defend the present funding. Unfortunately it is true that a small funding change from EPSRC makes far more difference than the entire LMS budget.

* (http://www.iop.org/aboutus/Annual_Review/file_30997.pdf P0 and P6)

** (http://www.lms.ac.uk/policy/annualreports/LMS_ARA_08.pdf P31-32)

*** (http://www.lms.ac.uk/policy/annualreports/LMS_ARA_08.pdf P21)

**** A note on the numbers, it is hard to get a close comparison as the accounting differs between the reports of the two organisations. The figures for the IoP were calculated by adding the three major expenditure streams (Opportunities, Members and Impact, P17). For the LMS the totals come from the total expenditure for Advancing Mathematics, Enabling research, Conference programmes and Promoting Mathematics, compared to the total spend on Promoting mathematics, P21.

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Posted by gelada

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