Science is a process of exploration – of continually challenging our assumptions and seeing how well they stand up to scrutiny.

So a blog and a discussion are something we should certainly include on the site. And we're starting today! We're going to look for key areas of science where fresh thinking is particularly needed.

We've got full-scale discussion facilities through a link with the new European science teaching web portal STELLA. The Stella portal's been set up to enable ideas in science education to be shared, and it includes a discussion forum section. Through this you can give your views on the topics we open up here – or start up some new ones of your own.

We've started off with two issues. One is the question of fashion in science. The big breakthroughs are often unexpected – so how do we find the unfashionable places to look?

And we also ask: with astronomy and space of such interest to young people, can the school curriculum be developed to build around them in a bigger way? 

Let us know what you think – tell Stella!

Fashion Followers or Fashion Leaders?

by Howie Firth - 12:15 on 17 February 2009

'It has always been true, and it is true now more than ever, that the path of wisdom for a young scientist of mediocre talent is to follow the prevailing fashion.'

That was one of the finest scientists that the UK has produced in the past century, Freeman Dyson. His work covers a number of key areas of physics, including quantum field theory, solid state physics, and nuclear engineering.

He said that in 1981,  in a paper that's included in his book From Eros to Gaia.

'Any young scientist who is exceptionally gifted or exceptionally lucky is concerned first of all with finding and keeping a job,' said Dyson back in 1981. 'To find and keep a job, you have to do competent work in an area of science that the mandarins who control the job market find interesting. The scientific problems that the mandarins find interesting are, almost by definition, the fashionable problems. Nowadays the award of jobs is usually controlled not by a single mandarin but by a committee of mandarins. A committee is even less likely than an individual to break loose from the fashionable trends of the day. It is no wonder that young scientists who care for their own survival tend to keep close to the beaten paths. The leading institutions of higher learning offer security and advancement to those who skillfully follow the fashion, and only a slim chance to those who do not.'

But says Dyson, there are fields which are more unfashionable than others – and among them his own field of mathematical physics. This is the field which supplies language and ideas to the more practical areas of physics – and its rhythms can run at a very different speed to those of scientific fashion.

He gives the example of the Norwegian mathematician Sophus Lie. In the 1870s and 1880s he constructed, almost single-handedly, the mathematical theory of continuous groups.

A group is a set of operations which is closed, in that whatever combination of them you carry out, you always stay within the set. For instance, the army combination of Left Turn, Right Turn, About Turn and Stand Still form a group of rotations. If we extend them to inclue the full spectrum of possible turns by any amount of degrees, however large or however small, we get to a continuous group.

It took nearly a hundred years before it was realised that Lie's theory is the key to huge areas of modern physics, from quantum theory and relativity to crystallography and solid state physics. The language of Lie groups is the most natural and elegant one for so many of these fundamental fields.

A second example taken by Dyson is the work of Hermann Grassmann who as a high-school teacher introduced in 1844 the ideas of a vector, a vector space and an anti-commuting algebra – again absolutely key ideas for modern physics. He remained a teacher through his life – 'ignored by the academic mandarins of his time,' notes Dyson. Indeed he started a second career as a student and translator of Sanskrit. And the mathematics that he developed was for the following centruy to build on.

So where should a young physicist look today if she wants to be unfashionable? Look, says Dyson, at those areas of mathematics that are beautiful but which don't seem to fit in coherently to the rest of the field.

'Unfashionable mathematics is mainly concerned with things of accidental beauty, special functions, particular number fields, exceptional algebras, sporadic finite groups. It is among these unorganised and undisciplined parts of mathematics that I would advise you to look for the next revolution in physics.'

So he continues, there are finite groups such as the one nicknamed the 'Monster'. There are unusual polyhedra. There are the zeroes of the Riemann zeta function. There are the incompleteness theorems of Kurt Godel. All these are fascinating and beautiful, and so far don't seem to quite fit into any overall structure. So look among such areas, says Dyson.

'At any particular moment in the history of science, the most important and fruitful ideas are often lying dormant merely because they are unfashionable. Especially in mathematical physics, there is commonly a lag of fifty or a hundred years between the conception of a new idea and its emergence into the mainstream of scientific thought.

'Organisations which only support research where there is no risk and no chance of mistakes will in the end only support mediocrity. If we proceed with good sense and courage to support unfashionable people doing things that orthodox opinion considers irrelevant or crazy, there is a good chance that we shall rescue for science an occasional Sophus Lie or Hermann Grassmann, people whose ideas will still be famous long after our contemporary fashionable excitements are forgotten.'

So Dyson raises some big questions, that go to the very heart of science.

Are we indeed focusing so exclusively on the fashionable areas of research that are missing those which are unfashionable?

Is this why we are still unable to bring together the two great pillars of modern physics, relativity and quantum theory, into a single coherent theory?

If this is indeed the case, what do we do about it?

And in the light of Dyson's pointers, are there any other areas of unfashionable science which we could highlight for the really keen researcher – and the eventual benefit of us all?

We'd like to get your comments on this and other blogs that we post up. Thanks to Stella we can now host a full-scale discussion on this and other topics. Click here to join in.

If instead of joining the full discussion, you'd prefer to leave a comment with us, then the form below is available and we can post it up for you on the forum.

STELLA is the European science teaching portal, with which we now have a link. So join the discussion – tell Stella!

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