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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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

The strange quest: Mathematics as Concrete Art

October 10, 2009

I have to confess that this post has not been an easy one to write. I wanted to express some ideas that are difficult to put into words. The central, rather playful, thesis is that pure mathematics itself is a branch of concrete art.

Let me begin with some easy facts. This month, I have had the great fortune to be able to take part in a studio exhibition with a group of constructive/concrete artists, including members of the systems group from the 1960’s.  The exhibition was curated by Trevor Clarke in Peter Lowe’s studio.  As a result I have had a chance to have some fascinating conversations with several artists, including Peter Lowe, Trevor Clarke and Jeffrey Steele.

IMG_0131

Spirograph by Richard Grimes

One goal of the exhibition is to start dialogues between artists and technicians, in the spirit of the studio exhibitions that started the systems group in the 1950’s around Adrian Heath and Kenneth and Mary Martin.  With that in mind I would like to give some of the ideas that emerged for me from the conversations.

Constructive and Concrete art arose from a natural conclusion of the process of abstraction. In the case of concrete art this is explicit and stated in Van Doesberg’s “Manifesto of Concrete Art”. Abstraction began by cutting away the figurative and symbolic content of artworks. As this program progresses more and more is cut away until, in a natural conclusion, one is left with nothing. Nothing is a fascinating concept. It is certainly not a trivial one, as we see with relatively late arrival of zero as a number. It does not, however, give a large space in which ideas can work. An empty canvas is an empty canvas and one ends up unable to tell the profound from the lazy. Concrete art emerges from this vacuum as the attempt to produce artworks that are not empty but have no figurative or symbolic meaning. It seems that this goal can be achieved in two distinct ways. One can either take the subconscious or irrational approach that leads to mysticism or the hyper-rational approach to create small works with their own logic.  For obvious reasons I want to consider the second here.

This would seem to argue for a very subjective art, as we must not only consider different personal opinions about a piece, but the individual world that each piece inhabits. Constructivism is more ambitious than this. The idea of removing figure and symbol is not nihilism, but a desire to address raw or objective beauty. It is of course fully accepted that no such beauty exists. This leads to a strange quest, where the goal is known to be unobtainable.

Being interviewed by Peter Lowe about hyperbolic geometry.

Being interviewed by Peter Lowe about hyperbolic geometry.

I come into this from a different point of view. My art does not contain mathematics in order to have no content, but to communicate mathematics. The mathematics is precisely the symbolic meaning. Yet what is mathematics? My personal definition is that mathematics is any concept that can be considered without reference to the real world. I know that this is an intellectual land grab, but I favour overlapping disciplines anyway. Putting this definition together with the constructivist quest for beauty led to some interesting similarities. Let us consider a parallel history of the two topics.

In the late nineteenth century, while painting was starting the move to abstraction with the work of impressionists and others, mathematics was starting a re-examination of its axiomatic roots. Just as art became more abstract the concepts and fields of mathematics were being cut back to rest on top of the set theory of Cantor and Dedekind.  By the 1930’s the impossibilities inherent in both quests were becoming apparent. A year after Van Doesberg published the “Manifesto of Concrete Art”, Göodel published “On formally undecidable propositions of Principia Mathematica and related systems”.  This work showed that whatever axioms one considered (that allow arithmetic) there would always be holes, statements that the axioms did not say were true or false, and one could never be sure that there was not a contradiction a statement both true and false. This was the end of the dream of a perfect mathematical machine. Pure mathematics thus joined in the strange quest, seeking patterns and structure without the possibility of obtaining a final goal.

Work by Gary Woodley

Work by Gary Woodley

In fact by the 1940’s the two subjects were recognising their similarities. Hardy published “A mathematician’s Apology” in 1940 that claimed that mathematics was an art form. With the humility that only a Cambridge academic can feel for his own place in the world he declared:

“A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.”

The quest of a mathematician, to Hardy, was to find beauty and truth, yet without defining exactly what he meant by either. This bears a striking similarity to the vision of constructivism that I described above.  It is no surprise therefore that, perhaps unaware that mathematics had been declared an art, in 1949 Max Bill considered “The Mathematical Approach in Contemporary Art”.

I want to reverse Bill and consider that perhaps the mathematical structure itself, from guage theory to groups, from motives to matrices from the games of Conway to the technical depth of Grothendieck, stopping on the way to take in the Hopf fibration and bifurcation, the Penrose tiling, and the 57-cell, is simply one giant work of concrete art put together by a cast of thousands.  An edifice built with some logical consistency on the Zermelo-Frankael axioms and the fudge factor axiom of choice.

So here’s to everyone pursuing the strange quest in the belief that the universe has an inexhaustible supply of secrets, and there will always be new beauty to be found even in some of its simplest corners.

Works by Trevor Clarke and John Bremner

Works by Trevor Clarke and John Bremner

The show

A studio presentation linking a selection of historical and contemporary autonomous works with a focus on modular investigations including:

Alexander Rodchenko*
Anthony Hill
Dirk Verhaegen
Edmund Harriss
Freddy Van Parys
Gary Woodley
Getulio Alviani
Jean Spencer
John Bremner
Kenneth Martin
Mary Martin
Peter Lowe
Richard Grimes
Trevor Clarke

Curated by Trevor Clarke in response to an invitation from Peter Lowe to stage a studio exhibition.

By appointment only during October (Contact me by email)

*reconstructions

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Posted by gelada

Surfaces in 3 and 4 dimensions

August 18, 2009

I hope the title is not too confusing, given my previous posts on surfaces. The title of this post is also the title of a work of mine that I have mentioned here a couple of times before. It has just gone up in the common room of the Maths Department of Imperial College. If you are a London mathematician take a look and let me know what you think!

Here is the work in place. The order was chosen by Anne Rowlands and Andy Pope. I love seeing how they chose to interpret my work!

Picture 173

Picture 174

2 Comments | Art | Tagged: , , , , , , , , , | Permalink
Posted by gelada

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