The Academy: Axiom 1

September 3, 2011

The rule

This post is not trying to do anything clever. It is making a statement that seems self-evident:

There are three ways to gain understanding of the world:

  • Personal experience
  • Systems of rules
  • Stories

All are equally important, and each has its strengths and weaknesses.

The important point is not the content of the statement but the stating of it. This is not just something that feels correct (to me) but something that feels fundamental. This mirrors one of the quests of mathematics to find the simplest statements on which to build the whole subject. I have my suspicions that the same thing would not work completely here, though writing the “Elements of the Academy” with this as one of the axioms might make a curious exercise!

This axiom maps onto the world of academia. The Sciences are primarily concerned with the use of rules to understand the world; the Arts centred on the creation of objects that attempt to transfer personal experience; and the Humanities write, dissect and try to understand the stories of the world.

All three areas, of course, do and should take advantage of the strengths of the other two methods as well as their primary concern.

The story

As a mathematician I obviously come from the grand tradition of finding rules to understand the world. For much of human history this was known to be rather limited in its scope. It was applicable to commerce, certainly; but also to questions of measurement, and to the study of the stars and music. Then, with the acceptance of arguments based on infinitesimals and the genius of Newton and Liebniz, the models of calculus opened up a vast array of phenomena to understanding through rules. It was so successful that many started to believe that it would eventually explain everything.

I do not believe this to be the case. Chaos theory shows that even perfect models can be severely limited by small, unavoidable, measurement errors. The work of Gödel and Turing shows that even in the purely theoretical world, there are unanswerable questions. Some even believe that as fundamental a system as arithmetic might contain contradictions. Before we even get to these hard limits we must deal with the soft limits imposed by the great ideas that we have yet to have.

Unfortunately, or fortunately depending on situation and personal preference,  the world offers many questions that we cannot answer with a systematic, rules based approach. Questions we cannot ignore. I wanted to define for myself the other options, and place them in some imagined framework.

The personal experience

I don’t believe I have said much here. It is, as I stated, self-evident. I also think it is important. It has been useful and practical to me. So, if you have managed to read this far, I thank you, but ask one further thing. Think about it yourself and see if it is a useful for you too.

Acknowledgements

This post grew out of a string of tweets, out of which grew very valuable discussion with  Colin Wright (@ColinTheMathmo) and Daniel Colquitt (@danielcolquitt), on twitter and elsewhere.

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Posted by gelada

Imagine you will talk to monkeys…

January 13, 2011

We have all sat in lectures, looking around to wonder if anyone is still able to follow. In writing a talk it is often hard to judge the right standard, and in general we make the lecture harder than it should be. Perhaps the answer is simple, imagine you are writing for a less knowledgable audience. So here is a handy guide, simply work out what level you are speaking for and go down a couple of levels. Alternatively if you loose track in a talk, try to work out just how many levels up the speaker has drifted!

  • Talk to author of “The Book“
  • Talk to self
  • Talk to co-author
  • Talk to specialists
  • Talk to colleagues
  • Talk to mathematics students
  • Talk to general audience
  • Talk to Secondary/High school children
  • Talk to Primary/Grade school children/Elderly Colleagues
  • Talk to Monkeys
  • Talk to Furniture

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Posted by gelada

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

My dream Royal Institution

April 16, 2010

I grew up with the Christmas lectures. They were as much part of christmas as the Turkey. The Royal Insititution was a place of magic. Yet, the swanky Mayfair location completely passed me by. Davy was a man who had made a lamp. Faraday had something to do with electricity. I had not heard of Bragg or Porter. The magic came instead from one man: Bill Coates1:

A figure in the shadows of the lectures, but always there if you knew where to look. The man responsible for scientific demonstrations beyond anything else in the world at that time (to my knowledge). The RI was a place of magic and it was clear that this came  from Coates’ almost mythical prep room.

When I got to visit and work in the prep room last year2 therefore, it was a dream come true. Yet a dream tinged with sadness. This was a space neglected by the redevelopment, still brilliantly staffed but with out of date facilities. In fact, worse than neglect, the facilities had been cut, the workshops in the basement taken away by the refurbishment.

The current debate3, like the priorities of the leadership in the redevelopment, does not seem to capture what made the RI great and unique. The prestige of the building has been pushed with the development of a fancy restaurant. The prestige of cutting edge science has been pushed with a new nano-technology group. The building of magical machines to demonstrate science has been left behind. The building is prestigious, but it is in Mayfair where there is no shortage of prestigious locations; many more prestigious and more experienced at hosting events. The science of the RI is great, its place in history is secure, yet today many places do cutting edge research; many far better funded. What about science communication and science machines? They certainly live as deep in the Institution’s bones. Faraday’s popular lectures, especially his Chemical History of the Candle, put the place on the map at the time, more even than his work on electricity. Twenty five years ago I would argue the RI was ahead of everyone else in the world. That is no longer the case. There has been recent great development in science communication, others have caught up with the RI. As an example the Centre for Life in Newcastle has a wonderful line in informative, exciting science and shows with meat that rival Faraday’s candle. It is however a far less crowded field, something the country desperately needs and the RI is well within the leading group.

The standard rebuttal to all arguments about the RI (for the last decade, maybe longer) is that you are trying to recapture the glory of the past, not moving towards the future. Perhaps you could say this here. Bill Coates was a completely unique individual and not someone who can ever be replaced. No one will be able to create traffic jams for a science event today like Faraday did. This is true, but I also think these are ideas which are only just getting started. Today there are worlds available that simply would not have been possible before, even to a genius like Coates. We have laser-cutters, 5-axis routers, even 3d printing. The ability to transform ideas into objects has increased beyond recognition, moving from a highly skilled job to a semi-skilled one, even a mathematician can do it. It is not even that expensive. The MIT FabLab project gets you a good set up of machines for just $50,000 (~£32,500). Even better the designs can be released for others to make. Many schools have these machines, or at least access to them, and there has been a recent explosion of Maker Faires, hackerspaces and FabLabs where people come together with the desire to build stuff.

Let me sum up with my personal dream, vision, reinvention for the RI. That is what everyone says the RI needs after all. A scientific fab lab. A space with open access to all UK scientists kitted out with a workshop and computer manufacturing machines. Anyone with vague ideas for sciencey things to build can come along and get support from the scientifically knowledgeable and technically skilled staff (that the RI already has). After all the standard PhD does not have a lot of practical training in manufacturing. This would be combined with the other expertise the staff of the RI have in abundance: science communication, the christmas lectures, shows, masterclasses. An RI like this would be a place of magic for me once more, even to my more cynical adult mind. Perhaps I am not the only one.

Footnotes

1 BACK TO POST
In 1986 Coates retired, but the magic continued in the hands of Bryson Gore and others.

2 BACK TO POST
I was making material for How do shapes fill space? my exhibit at the 2009 Royal Society Summer exhibition. The RI was one of the partners and provided workshop space.

3 BACK TO POST
The problems started with the weak financial situation revealed (but not completely caused) by the credit crunch. This has been combined with the fight between the council and Susan Greenfield the director they made redundant. She has not gone quietly, and is now suing for unfair dismissal. In addition her supporters organised a Special General Meeting to try to remove the council but failed. This has of course led to open season on visions and reinventions for the RI, that I am leaping on board. You can find a lot more with a Google or Google News search. This story will probably run for a while!

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Posted by gelada

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