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?

4 Comments | General, Mathematics | Tagged: , , , , , , , , , , , , | Permalink
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!

2 Comments | General, Main Article | Tagged: , , , , , , , | Permalink
Posted by gelada

The Laws of Gelada (How to be a grad student)

March 3, 2010

Irving Herman‘s Laws for graduates can make good little scientists. How can we make misbehaved big scientists?1 The original Herman rules have Hx numbers my versions are down under Gx.

H1. Your vacation begins after you defend your thesis.

G1. (Force yourself if necessary) to take some time off.2

H2. In research, what matters is what is right, and not who is right.

G2. In research, what matters is good and useful answers, and not who gives them.3

H3. In research and other matters, your adviser is always right, most of the time.

H4. Act as if your adviser is always right, almost all the time.

H5. If you think you are right and you are able to convince your adviser, your adviser will be very happy.

G3. In research, your adviser is probably right more often than you.

G4. Assume your adviser is wrong if you do not agree with him.

G5. If you are right and are able to convince your adviser, everyone gains. 4

H6. Your productivity varies as (effective productive time spentper day)1,000.

H7. Your productivity also varies as 1/(your delay in analysing acquired data)1,000.

G6. Your productivity varies and is not necessarily tied to effort.

G7. Keep on top of routine tasks, but do not be ruled by them.5

GH8. Take data today as if you know that your equipment will break tomorrow.

GH9. If you would be unhappy to lose your data, make a permanent back-up copy of them within five minutes of acquiring them.6

H10. Your adviser expects your productivity to be low initially and then to be above threshold after a year or so.

G10. Realise your productivity will not be high initially. Aim to be more productive, but always allow for variation.7

H11. You must become a bigger expert in your thesis area than your adviser.

G11. You must be more passionate about your thesis area than your adviser.8

H12. When you cooperate, your adviser’s blood pressure will go down a bit.

H13. When you don’t cooperate, your adviser’s blood pressure either goes up a bit or it goes down to zero.

G12. Do not care about your advisors blood pressure.

G13. Cooperate with your advisor. You will get more out of them. They should know a lot that you care about. Thats why you picked them isn’t it?9

H14. Usually, only when you can publish your results are they good enough to be part of your thesis.

H15. The higher the quality, first, and quantity, second, of your publishable work, the better your thesis.

G14. Ideas are only good enough for your thesis when you are proud of them, you can do things with them and you can communicate them to others.

G15. The more interesting you find your results the better your thesis.10

H16. Remember, it’s your thesis. You (!) need to do it.

G16. Remember, it’s your thesis, your research.11

H17. Your adviser wants you to become famous, so that he/she can finally become famous.

G17. Care about your work and find it important. Do not chase fame.

H18. Your adviser wants to write the best letter of recommendation for you that is possible.

G18. Be aware of politics, sell what you do well.12

H19. Whatever is best for you is best for your adviser.

H20. Whatever is best for your adviser is best for you.

G19. Think hard and decide what is best for you.

G20. Listen to authorities (like your advisor), but do not be ruled by them.13

Footnotes

1 BACK TO POST
A few years ago Irving Herman, a physicist at Columbia published a set of laws for graduate students in Nature. To be fair he does say that some of his comments are slightly exaggerated and should not be taken completely seriously. However he also claims these as laws. Which is a very strong rhetoric. On my side my laws can also be slightly exaggerated and are usually highly idealistic, but if you are not idealistic about science you are probably better in a different career anyway.

I came across these recently in Eric Weinstein’s twitter and his comments were the spark and much of the inspiration for this post. I have included his comments on specific laws below. Here is his overall opinion:

New Topic: Thoughts on Prof. Irving Herman’s “20 Laws All Grad Students Should Follow” or “On Being Science ‘Help’ ” as published in Nature. Tweet

I am delighted that colleagues in academe are starting to write down the ‘meta-rules’ of new science that select against strong scientists. Tweet

My goal as taxpayer & scientist is to get you, the young scientist, out of Irving Herman’s dystopia before he can help you become ‘better’. Tweet

and he concludes:

Yet being a scientist isn’t about any of this idiocy. This is about survival in universities & why basic research must reform or leave them. Tweet

2 BACK TO POST
A PhD is hard work, but…Practically taking time off can renew focus, give perspective and thus generate more ideas. More importantly, you are not a robot or slave. Take time off to remember why you are doing this crazy thing.

Herman’s Law 1:”Your vacation begins after you defend your thesis.”
Weinstein’s Excercise:Translate into German without use of a dictionary.

Eric Weinstein Tweet

3 BACK TO POST
It is often better to be productively wrong than unproductively right. Liebnitz/Newton’s Calculus was wrong (and many, most noticably Berkerley spotted this) but those who ignored or were ignorant of this did better maths for 100 years.

4 BACK TO POST
Of course you should treat your advisor with respect, especially for the work that he or she has done. They do have more experience and know more, so they are probably right. However they are also better at arguing than you. Give your intuitions confidence and be persuaded out of them by reasoning not authority.

(“in other matters” your advisor is just another human being, saying that they are mostly right there is crazy!)

3. In research and other matters, your adviser is always right, most of the time.
Just who is this guy? Nature? Physics? Columbia? Anyone?

Eric Weinstein Tweet

Herman’s Law #4. “Act as if your adviser is always right, almost all the time.”
That would be ‘Science … with Benefits’…wouldn’t it?

Eric Weinstein Tweet

5 BACK TO POST
Productive time is essential, but what is it? It is certainly more than time spent in the lab/office. Learn what helps make you productive. Maybe a weekend of surfing leads regularly to great results on a Monday. Routine tasks do need to be done. Keep on top of them so you can relax and think, do not hope you can get PhD students on day to do them, or become a lab assistant for your supervisor!

6 BACK TO POST
Agreement for both of these, it is good to put a little time into insurance against disasters.

7 BACK TO POST
Coming back to the “productivity is complicated” idea. Sometimes you have to get lost, following blind alleys for weeks or months to chase up the great result. It is easy to be productive by finding more routine tasks to do, is that your ambition?

8 BACK TO POST
If you are passionate about your area you will of course think about it and study it more. You should be doing all this for passion and not because your supervisor says that it is interesting.

9 BACK TO POST
Cooperation is a good thing. We do need to work together, to help find the right or useful ideas and communicate them. It is useful to achieve other goals however, not as a goal in its own right.

10 BACK TO POST
Find out what is important to you, what you feel are the big questions. Chase them. Take into account the opinions of others (such as journals) but remember they can be wrong.

11 BACK TO POST
You are paying for this and working very hard on it. Take pride in it, make it your own and do the best job you can. For yourself not your supervisor.

12 BACK TO POST
It is good to show your work achievements and ideas in the best light. Do not however do something for no other reason than it looks good.

13 BACK TO POST
The summary of this post. To be a good scientist is to respect authority while questioning it.

19. Whatever is best for you is best for your adviser.
20. Whatever is best for your adviser is best for you.
So,we may catch Pyonyang yet?

Eric Weinstein Tweet

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Posted by gelada

Use of Mathematics and Hyperscopes

July 27, 2009

The new “Use of Mathematics” A-level has been hotly debated recently. I would like to start by saying that I agree that things need to be done on this topic. There are some deep issues in the Mathematical culture in Britain and this A-level is aimed at addressing them. A good account of this is given in the open letter sent by ACME to various political figures.

Although changes need to be made, however, we need to be careful about nature of this change.  The proposal at the moment is too much about fitting numbers into equations.  (See Tim Gowers’ analysis). One way to think about the new A-level is that it could play a role similar to “Classical Civilization” when compared to Latin and Greek. This is already slightly troubling as the perception could easily be that this is a light-weight maths.  However there is a good argument for Classical Civilization as interesting history of Ancient Greece and Rome, that informs so much of our culture is made accessible without the language barrier.  Is the same true of mathematics, are there useful mathematical tools that are hidden behind a complex language?  I do not think so, and I will illustrate that with an example. But first some pretty pictures!

Images from a Hyperscope

IMG_0869IMG_0873IMG_0872IMG_0867

A hyperscope is a hyperbolic kaleidascope. It has five mirrors arranged in a pentagon. However the mirrors are not flat. Each is bent so that they meet at 90 degrees. Forming this shape:

Right angled pentagon

Right angled pentagon

As the mirrors meet at 90 degrees there are precisely four chambers round each corner, but as they are bent each chamber is a slightly different shape to the last. The result is a glimpse into the negatively curved world of the Hyperbolic plane.

Using one red mirror shows how the extra hyperbolic space is folded away to fit in Euclidean space.

Using one red mirror shows how the extra hyperbolic space is folded away to fit in Euclidean space.

In order to make this I wanted to use standard A4 acrylic mirrors, so I did not need to do any cutting. Each mirror is placed into a groove cut into a piece of MDF, and the mirrors have to fit tightly at the corners. I was therefore faced with a problem. I knew the width of my mirrors but they would be bent, so I needed to make this the distance round a circular arc.  Now let us assume I have successfully completed “Use of Maths” A-level and I recognise this as a mathematical problem. I go onto the world’s best source of equations (wikipedia) to see if I can find anything. In real life I did exactly that, as I am lazy and wanted the answer quick. Unfortunately the ratio between the length of a cord (a line between two points on a circle) and an arc (the curve between two points) is not given.  A couple of google searches later and I gave up.

I gave up as I had a better option. I could just work it out myself. It is not hard, just involving a little trigonometry.  I illustrate with an image. The arc is labelled A, the radius r and the cord C, the angle is \theta. An additional line splits C in two and gives two right angled triangles. Which should hint to the answer.

Arc-cord-ratio

This example is to me “Use of mathematics”. I had a practical problem and wanted to solve it. There was a little trick to realising the tools I needed to solve it, but after that the mathematics was basic. In fact I was lucky enough to have learned all the mathematics I needed here by the time I was 13.  As someone who is perhaps more thoughtful than pratical I have to confess that my perfect calculations failed on “Use of the real world” and the mirrors had 1mm too little space. Luckily such things can be bodged.

If we are going to invest the money in developing a new A-level, therefore, let us play on those practical connections that mathematics has and get people involved in them. Some people, like I did, become engaged in the logic and clarity of maths itself. However for most it is only when they find out how it can solve a problem for them that it becomes interesting. So lets get people building mathematical toys to illustrate trigonomety and geometry. Designing fabric patterns to show symmetry. Working with the basics of google’s pagerank algorithm to show the power of linear algebra. Encoding and decoding messages to learn about factoring prime numbers.  With a little imagination we should be able to cover the whole syllabus.

There is even a model for what we might want to achieve. The Salter’s A-level in Chemistry is a full Chemistry A-level. It is not “Use of Chemistry” as it covers the full criteria (subjects the A-level must cover). However the teaching starts with the applications and moves back to the theory. The theory is therefore seen in a wider context from the start.  Why are we being less ambitious for maths? Is the subject really only accessible to some people? Can’t we find the ways to motivate children to put in the hard work required to gain useful and beautiful insights? We need the changes in the maths syllabus to make a real difference and not just make things look good so the numbers show the problem is getting better.

2 Comments | Art, Main Article, Mathematics | Tagged: , , , , , , , , , , | Permalink
Posted by gelada

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