What is an elementary particle?

Democritus famously proposed that all matter consists of microscopic particles, called 'atoms', which are not themselves composed of other particles. By historical accident, it is the chemical elements which are referred to as atoms, despite the fact that they are composed of smaller particles. Nevertheless, it is currently believed that there are particles which are not composed of other particles, and these entities, which include electrons, photons and quarks, are dubbed 'elementary particles'. The Democritean vision of elementary particles as miniature snooker balls, however, has been somewhat vitiated by quantum theory, and it is not merely the classical notion of a particle as a localisable entity which has been undermined, but the mereological notion that a composite system has a unique decomposition into elementary entities.

According to modern theoretical physics, the fundamental types of things which exist are quantum fields, and particles are merely excited states of the underlying quantum field. Given that these modes of excitation satisfy the principles of quantum theory, they are often dubbed 'excitation quanta'. Even when there are no particles present, the quantum field is simply in its lowest-energy state, and this non-zero energy of the so-called 'vacuum state' duly has a detectable effect.

Because particles are excitation quanta of an underlying field, their identity conditions are more akin to those of waves or vibrations in a continuous medium than miniature snooker balls. For example, if one begins with a number of separate travelling waves on the surface of a body of water, and they merge together to form a standing wave, then the individual identities of the original constituent waves would be lost. This has some similarity with quantum phenomena: For example, there are conditions under which one can say that there is an N-particle state of a quantum field, but in which it appears to be impossible to individuate N distinguishable particles; there are states of a quantum field in which there are simply an indefinite number of particles present; and given a quantum field state in which no particles are present in one reference frame, this is the same state for which there will be many particles present in an accelerated reference frame.

The analogy with vibrations or oscillations in a continuous medium also leads to a better understanding of what an elementary particle might be. On a classical level, Fourier analysis treats each wave as an element in a vector space. By selecting a basis for a vector space, one can decompose any element as a linear combination of basis vectors; select a different basis, and one can decompose the same element as a different linear combination. In Fourier analysis, plane waves are selected as the preferential basis vectors, and in a sense, these are the elementary waves. As Roberto Torretti points out, telecommunication companies use Fourier analysis to "literally superpose the electromagnetic renderings of many simultaneous long-distance messages in a single wave train that is echoed by satellite and then automatically analyzed at the destination exchange into its several components, each one of which is transmitted over a separate private telephone line...the signal could also be split into other, meaningless components if the analysis were not guided by human interests and aims." (The Philosophy of Physics, p393).

This clearly undermines the Democritean mereological concept of elementarity, in which a composite entity has a unique decomposition into a set of indivisible entities.

It is also well-known amongst physicists that the classical description of the oscillations in a continuous medium can be quantized. When the vibrations in a crystalline solid are so quantized, one obtains elementary modes of excitation called 'phonons'. (These are also considered to be the elementary modes of the sound waves in a solid). Similarly, when the oscillations of the electrons in a plasma are subjected to a quantum description, the elementary modes of excitation are called 'plasmons'. In this context, elementarity seems to correspond to nothing more than the choice of a particularly convenient decomposition of oscillatory behaviour.

Richard Feynman once described the function of high-energy particle colliders as akin to smashing watches together, and then looking at the gears, cogs and springs which fly out, in order to better understand how the watches are put together. Given the considerations above, a better analogy might be to imagine high-energy incoming waves, which collide and merge, and then split apart into different, smaller, outgoing waves. Certainly, when elementary particles and anti-particles collide, and transform into different types of outgoing particles, the use of an analogy which employs composite systems, such as watches, breaks down somewhat.

So these are the mereological questions which beset elementary particles, but even if we successfully elucidate the quantum concepts of parts and wholes, we are still left with the question, 'What is an elementary particle?'. Attempts to answer this question have employed the notions of intrinsic properties and extrinsic properties.

An intrinsic property of an object can be defined to be a property which the object possesses independently of its relationships to other objects. In contrast, an extrinsic property can be defined to be a property which an object possesses depending upon its relationships with other objects. Thus, one might deem that a particle's mass and charge are intrinsic properties, whilst its velocity is an extrinsic property, depending as it does upon the reference frame chosen.

Now, in terms of these concepts, classical physics offers a nice clear definition of an elementary particle: it is a system which has a unique intrinsic state. Souriau and Cushman-de Vries define an elementary system to be one in which the restricted Poincare group acts transitively upon its 'space of motions', (Structure of Dynamical Systems: A Symplectic View of Physics‎, p173). The space of motions here is the set of all possible histories of a system. Within special relativity, the Poincare group provides the group of all possible transformations between those reference frames which are unaccelerated, and therefore free from the influence of forces. (One also says that the Poincare group is the space-time symmetry group of special relativity). Those properties which change under the action of the Poincare group, must be extrinsic properties, and histories which are related by a Poincare transformation are the same intrinsic history. Now, if the (restricted) Poincare group acts 'transitively' upon the space of histories of a system, it entails that any two histories, v and w, are related by a Poincare transformation g, v=gw, and therefore there is only one intrinsic history. In classical physics, an elementary particle has a unique intrinsic state, and a unique intrinsic history.

However, the situation changes in a subtle fashion in quantum theory. Here, Wigner established that each type of elementary particle corresponds to an irreducible Hilbert space representation of the restricted Poincare group. (An irreducible representation is one in which there are no subspaces invariant under the group action, apart from the null vector and the entire Hilbert space). However, the irreducibility of a group representation does not entail the transitivity of the group action, and neglect of this fact has a tendency to lead some authors astray.

For example, the mathematician J.M.G. Fell adopted Wigner's notion that the irreducibility of a representation is the defining characteristic of an elementary particle representation, and argued that the ensuing group action is "essentially" transitive upon the state space of such a representation. He argued from this that an elementary particle has only one intrinsic state:

"It can never undergo any intrinsic change. Any change which it appears to undergo (change in position, velocity, etc.) can be 'cancelled out' by an appropriate change in the frame of reference of the observer. Such a material system is called an elementary system or an elementary particle. The word 'elementary' reflects our preconception that, if a physical system undergoes an intrinsic change, it must be that the system is 'composite', and that the change consists in some rearrangement of the 'elementary parts'," (Fell, J.M.G., and Doran, R.S. (1988). Representations of *-Algebras, Locally Compact Groups, and Banach *-Algebraic Bundles, p31).

Unfortunately, Wigner's irreducible representations are representations upon infinite-dimensional Hilbert spaces, whilst the Poincare group has only 10 dimensions. A group can only act transitively upon a space with the same dimension as the group itself, hence in quantum theory, the restricted Poincare group has many different 'orbits' upon the state spaces of elementary particles. Each orbit corresponds to a different intrinsic state of the elementary particle. Essentially, this is because a particle is represented in quantum theory by a wave-function, a field-like object, and the multitude of possible, locally-varying, intrinsic changes in such an object cannot be cancelled out by the rigid transformations of the Poincare group.

One needs to carefully distinguish the false notion that the space-time symmetry group acts transitively upon the quantum state space of an elementary system, from the correct notion that any vector in such a state space is 'cyclic' with respect to the action of the space-time symmetry group. If one takes the orbit of the action of the space-time symmetry group upon an arbitrary vector, and if one then takes the set of all superpositions of the elements in that orbit (technically, if one takes the topological closure of the complex linear span of all the elements in the orbit), then one obtains the entire state space. The vector chosen is said to be a cyclic vector, and the representation is said to be cyclic. In the case of an irreducible representation of the space-time symmetry group, the orbit of a single state takes one through a sufficient number of orthogonal states to span the entire infinite-dimensional state space. However, this doesn't entail that there is only one intrinsic state! The mathematical operation of taking a linear combination of a set of states does not correspond to a change of physical reference frame.

In the Stanford Encyclopedia of Philosophy, Meinard Kuhlmann asserts that:

The physical justification for linking up irreducible representations with elementary systems is the requirement that “there must be no relativistically invariant distinction between the various states of the system” (Newton & Wigner 1949). In other words the state space of an elementary system shall have no internal structure with respect to relativistic transformations. Put more technically, the state space of an elementary system must not contain any relativistically invariant subspaces, i.e., it must be the state space of an irreducible representation of the relevant invariance group. If the state space of an elementary system had relativistically invariant subspaces then it would be appropriate to associate these subspaces with elementary systems. The requirement that a state space has to be relativistically invariant means that starting from any of its states it must be possible to get to all the other states by superposition of those states which result from relativistic transformations of the state one started with. (2006, Section 5.1.1).

It is indeed true, by definition, that under an irreducible representation of the space-time symmetry group, there can be no non-trivial subspace which is invariant under the action of the symmetry group. However, for the reasons explained above, this does not entail that there can be no "relativistically invariant distinction between the various states of the system". There can indeed be such a distinction, defined by the different orbits of the symmetry group. Note also that Kuhlmann conflates an irreducible group representation with a cyclic representation; irreducibility is not the same thing as cyclicity.

In modern physics, then, elementarity is far from elementary.

How to spot a concealed religious agenda

Amanda Gefter composes a perceptive checklist of disingenuous techniques used by religious authors writing about science:

Red flag number one: the term "scientific materialism". "Materialism" is most often used in contrast to something else - something non-material, or supernatural. Proponents of ID frequently lament the scientific claim that humans are the product of purely material forces. At the same time, they never define how non-material forces might work. I have yet to find a definition that characterises non-materialism by what it is, rather than by what it is not.

The invocation of Cartesian dualism - where the brain and mind are viewed as two distinct entities, one material and the other immaterial - is also a red flag. And if an author describes the mind, or any biological system for that matter, as "irreducibly complex", let the alarm bells ring.

Misguided interpretations of quantum physics are a classic hallmark of pseudoscience, usually of the New Age variety, but some religious groups are now appealing to aspects of quantum weirdness to account for free will. Beware: this is nonsense.

When you come across the terms "Darwinism" or "Darwinists", take heed. True scientists rarely use these terms, and instead opt for "evolution" and "biologists", respectively.

Far be it from me, of course, to suggest any recent articles in The Sunday Times to which this checklist may be applied...

Branson and Ecclestone

Curious one this.

Late last week, it appeared that Sir Richard Branson's Virgin Group were on the verge of buying the Honda Formula 1 team. Bernie Ecclestone, in particular, seemed to be very keen on the idea:

"I've spoken to Richard's people about it. He would love to do it.

"I'd like it very much. It would be super. We're working to try to make it happen."

Ecclestone even added some glowing personal praise of Branson:

"He’s exactly the type of person we would want in the sport...Sir Richard Branson is a wonderful guy. I met him at Monza last year and we got on very well."

By Saturday morning, however, Branson was giving interviews to the BBC, criticising the financial structure and environmental credentials of Formula 1:

"If Bernie Ecclestone can make it more cost-effective for the likes of the Virgin brand to come into the sport, and if he can champion clean motor-car racing - which is possible to do by making sure all the cars run on clean fuels - then at some stage we might be interested in getting involved...I think there are faults that would need to be rectified before we could go into F1."

By Monday morning, Honda announced that they have been unable to find a 'serious' potential buyer of the F1 team.

If we take this Honda statement at face value, and assume that it is not merely some complex negotiating ploy, and that the Virgin Group were indeed never seriously interested in purchasing the Honda F1 team, then one might be tempted to think that Branson has taken Bernie for a ride. The public perception will be that Branson took a look at Formula 1, found that it was too costly and insufficiently eco-friendly, and turned his nose up at the opportunity. On the plus side for Branson, he gets free publicity for the Virgin Group, and in particular, for their plans to fly 747s powered by biofuels. On the negative side, Branson potentially enrages a powerful fellow billionaire.

This incident, of course, takes place in the midst of continuing negotiations between the Formula One Teams Association (FOTA) and Bernie Ecclestone, to increase the proportion of Formula 1's commercial revenue which goes to the teams, rather than the private equity company, CVC, which owns Formula 1. Moreover, Max Mosley has made it his post-scandal purpose in life to make Formula 1 both cheaper and greener. In any future negotiations with Bernie, both FOTA and Max Mosley will be able to deploy the following rhetorical lever: 'Look what happened when Richard Branson tried to get involved in F1. He wanted to participate, but found the sport too costly and insufficiently green. We need to change.'

It'll be interesting to see what Bernie's got to say about Branson now...

Far Foreign Land

European Cup Final, Brussels, May 1985

Walking down a narrow street, I saw a crew of scallies laughing almost hysterically. Seeing my quizzical look, they pointed at a shop. It was a jeweller with no protective metal grating over the window...There was a supermarket by the bourse and, at the entrance, there stood a Liverpool fan. 'You're scouse?' he said. There was no need for an answer and he knew what I was there for. 'It's free to us today,' he said, handing me a tray of beer...On the way back to the square, the group of Liverpool fans by the jeweller had been replaced by riot police. Glass was scattered all over the street, studded with empty display trays. There was hysteria - and pride - in my laughter. This was turning into an excellent day.

We set off for the ground and there seemed to be more and more small confrontations...We boarded a tram to head north to the ground, slurring and swearing and exuding threatening, drunken boorishness. At our stop, we stood up to get off and Robert collapsed...We hauled him from the middle of the road towards the stadium, two of us with his arms over our shoulder while his feet dragged behind. He appeared unconscious. Then, on the approaches to the ground, a group of young men up ahead snatched the takings from a smallholder and ran away with his strongbox. The man went in pursuit, leaving the stall unattended. Without seeming to open his eyes, Robert deftly unhooked his arm from around my shoulder and pocketed a Juventus scarf...

People were staggering, collapsing, throwing up...We met a group of mates who had come by coach. A fellow passenger we all knew had leapt off as soon as they arrived and attacked two people, one an Italian, with an iron bar. That we'd long believed him to be psychotic did not lessen the shock.

This is Tony Evans's memoir of life as a Liverpool-supporting scouse 'scally'. It's a gripping insight into what, for many modern Liverpool fans, especially those from the South, will be a totally alien culture.

Evans is now Football Editor at The Times, where he recently produced a personal list of the 50 Greatest Liverpool players. It'll evoke numerous cherished memories amongst Liverpool fans, but my favourite is the following devastating line:

And, while we're on the subject of leaving people out, if you're looking for McManaman, he's on Setanta.

And it was all yellow

With immense sadness, I noticed that Coldplay received not a single award at the Brits this week, despite being nominated in four categories. Surely, even in these financially straitened times, there is a place in our hearts for mind-rottingly bland music?

Gullibility

Psychologist Stephen Greenspan recently published a book entitled Annals of Gullibility: Why We Get Duped and How to Avoid it. In the week of its publication, Greenspan learnt that he had lost more than half his retirement investment portfolio to a certain B. Madoff Esq.

Both The Times and Scientific American, refer to Greenspan's experience as 'ironic'.

Ironic? I'll say.

The branch tapping at the windowpane

David Z.Albert is never less than interesting. He first came to my attention with a provocative paper, which suggested that the global state of the universe might be the vacuum of quantum field theory. His 1992 book, Quantum Mechanics and Experience, is something of a unique work, successfully expounding a many-worlds interpretation of quantum theory without the use of difficult mathematics, and extending the notions of quantum superposition and branching worlds to include subjective experience.

Albert, however, was hookwinked by the makers of the disreputable 2004 film, What the Bleep Do We Know!?:

He spent four hours patiently explaining to the filmmakers why quantum mechanics has nothing to do with consciousness or spirituality, only to see his statements edited and cut to the point where it appears as though he and the spirit warrior are speaking with one voice. "I was taken," Albert admits. "I was really gullible, but I learned my lesson." Yet the real shame with this film is that it plays on people’s fascination with science while distorting and misrepresenting that science.

Albert has now co-written an excellent article in Scientific American on quantum nonlocality, (the branch tapping at the windowpane of modern physics). In this phenomenon, two particles can be prepared into a so-called 'entangled' state, a superposition of correlated states. In such a state, a particular property of both particles is indefinite, but it is guaranteed that when a measurement of that property is performed on one of the particles, the state of the entire system will collapse into one of the correlated states in the superposition, and the value of that property will become definite for both particles. Although the preparation of the entangled state requires the particles to be in close proximity to each other, they can then be separated to a great distance without breaking the entangled state. A measurement can be performed upon one of the particles, instantaneously selecting one of the correlated states in the superposition, thereby instantaneously selecting a definite value for the relevant property on both the measured system and the remote system. This appears at first sight to be 'spooky' action-at-a-distance, which violates the notion of locality associated with relativity.

Abner Shimony, however, proposes an interesting resolution to the apparent discrepancy between quantum theory and relativity. Shimony proposes that the quantum state describes the evolution of objective potentialities, as well as objective actualities, and suggests that while actualities satisfy relativistic locality, potentialities need not:

Relativistic locality is the domain of actuality, while potentialities have careers in space-time (if that word is appropriate) which modify and even violate the restrictions that space-time structure imposes upon actual events. The peculiar kind of causality exhibited when measurements at stations with space-like separation are correlated is a symptom of the slipperiness of the space-time behavior of potentialities.

Whilst one actuality cannot instantaneously cause another spatially distant actuality, the transformation of potentiality to actuality (otherwise known as the 'collapse of the wave-function'), is instantaneous. In the case of a spatially separated entangled system, the transformation of potentiality to actuality in one place causes the instantaneous transformation of potentiality to actuality in a spatially distant place.

Note, however, that unless some notion of absolute simultaneity can be re-injected into modern physics, the instantaneous transformation of potentiality to actuality in two spatially distant places, will presumably only be simultaneous in the reference frame of the system performing the measurement on one of the particles.

Shimony's proposal also requires a significant extension of our physical ontology to embrace the existence of objective potentialities, a notion which would require significant fleshing out...

Conservatism

At the weekend I read Anthony Quinton's superb analysis of conservatism in the Blackwell Companion to Contemporary Political Philosophy. It's an article of mild vintage now (dating from 1995), but, quite apart from the main body of argument, contains at least one vital and pertinent admonition, which messrs Blair and Bush would have been wise to heed:

Democracy...is...not seen [by conservatism] as a good in itself. But representative parliamentary institutions, continuously developed in parallel with the political maturity of the population, is, in advanced Western societies, an historically established mode of proceeding and, therefore, worthy of preservation. That does not make it a universal political panacea.

The primary onus on a writer seeking to provide an intellectual defence of political conservatism, is to provide a rational foundation which refutes the view that conservatism is simply a self-interested attempt to preserve the status quo, by those who happen to possess the power, wealth and status in society at a point in time. To this end, Quinton argues as follows:

[The] main tradition of conservative thought derives from three central doctrines...The first and most obvious of them is traditionalism, which supports continuity in politics, the maintenance of existing institutions and practices and is suspicious of change, particularly of large and sudden change, and above all of violent and systematic revolutionary change...

The chief intellectual, rather than emotional, support for traditionalism is a sceptical view about political knowledge. Political wisdom for the conservative is embodied, first of all in the inherited fabric of established laws and institutions. This is seen as the deposit of a great historical accumulation of small adjustments to the political order, made by experienced political practitioners, acting under the pressure of a clearly recognized need and in a cautious, prudent way...Even less welcome to conservatives than abstract principles, such as doctrines of universally applicable natural or human rights, are utopias, systematic proposals for comprehensive social transformation.

Political scepticism in its turn rests on the third central doctrine of conservatism, the conception of human beings and society as being organically or internally related. Individual human beings are not fully formed...independently of the social institutions and practices within which they grow up. There is, therefore, no universal human nature. People's needs and desires and expectations differ, from time to time and from place to place.

As Quinton conceives it, conservatism is not a substantive political ideology:

An ideology derives political prescriptions or principles, even sometimes utopias, from theories about human nature and society...conservatism does not depend upon a substantive theory about universal human nature, issuing in universal political principles, such as lists of the rights of man...The desirability of [particular institutions, such as a monarchy or an established church, is, for a conservative] relative to the circumstances of a particular time and place, one in which they are historically established...As an ideology conservatism is, then, procedural or methodological rather than substantive. It prescribes no principles or ideals or institutions universally and so falls outside the scope of its own rejection of abstract theory.

Curiously, then, Quinton's account of conservatism implies a type of moral and political relativism with respect to substantive questions. Moreover, Quinton's defence of traditionalism does, in fact, tacitly presuppose a substantive theory of human society, even though this tacit theory is used to derive methodological, rather than substantive, political prescriptions. Let us turn now to this tacitly supposed theory of society, given that it raises some interesting questions.

As we've seen, Quinton argues that the prevailing political state is "the deposit of a great historical accumulation of small adjustments to the political order, made by experienced political practitioners, acting under the pressure of a clearly recognized need and in a cautious, prudent way." He then argues that, whilst a society will inevitably change due to extra-political factors, change should be gradual; large and sudden change, he argues, leads to unintended and unpredicted consequences. If the prevailing political system is subjected to large or sudden change, then:

A host of stabilities which provide a background of regularity within which life can be rationally and prudently led are jeopardized...It is not only that large political changes have many unintended results that are unwelcome. They also frequently fail to achieve their intended results or achieve opposite ones...The formation and running of a state is more like walking a girder high above the ground or driving a car along a narrow, winding road...There are innumerable ways in which it is possible to go wrong, indeed disastrously wrong, but only a very tightly restricted number of ways in which you can go right...Change should be in response both to a change in extra-political circumstances...and to a widely-felt need arising from it, and it should be gradual so that unplanned detrimental side-effects be counteracted.

Pace Quinton, there are a number of tacit substantive assumptions here about the nature of human society. In fact, these assumptions can be cast into the language of physics:

(1) Politically organised human society can, at best, attain a metastable state, a state which is capable of being perturbed into chaos by large and sudden politically-induced changes.

(2) Extra-political factors provide a constant source of change in a politically organised human society, but if the political response to such changes is gradual, then the metastable state can be maintained. Such a process of gradual change could be thought of as akin to a quasistatic process, a thermodynamic process in which equilibrium is maintained by performing the process very slowly. (The analogy doesn't quite work, however, because human society more closely resembles what Prigogine termed a dissipative system, a type of system far from thermodynamic equilibrium due to the large flows of energy through the system).

Supplementing Quinton's justification of traditionalism with some concepts from physics, these are the substantive theoretical claims about the nature of human society which conservatism tacitly assumes. Can such claims be justified, however? Doing so appears to require the very degree of political knowledge which conservatism avowedly rejects. What is the empirical basis for such claims? Quinton correctly points to the chaos which typically follows revolutionary change, such as that associated with the French Revolution, and the revolutions in Russia and China. However, conservatism is not uniquely distinguished politically by its resistance to revolutionary or radical change. Most of those in the modern Western world who subscribe to progressive reform, do not advocate revolution, and do not harbour utopias; they seek merely to gradually improve human society, and often find that their attempts to do so are resisted by political conservatives.

I'm far from convinced, then, about conservatism's intellectual credentials once it strays from the safe territory of utopias and revolutionary change, but Quinton's article is an excellent read.

The new physiognomy

Last August I wrote about a study of ice hockey players, which revealed that the larger the width-to-height ratio of a player’s face, the greater the aggression of that individual. I referred to it then as 'the new phrenology', but as Roger Highfield correctly dubs it in this week's New Scientist, it is actually 'the new physiognomy', the inference of personality from facial characteristics.

The basic message remains as before: people with wide faces are 'bad uns'. In addition, however, you might also be able to infer trust-worthiness and dominance from facial characteristics, as the diagram here illustrates. (The diagram, however, appears to be a glabrous cross-section through the hairiness dimension; how does facial-hair affect our impressions of trust-worthiness and dominance? Was I right to like Mr Beardy?)

This type of study, of course, is the result of research by psychologists. All behaviour is explicable, post-hoc, by psychologists, and Roger Highfield's article contains an absolute classic of the genre. It is suggested that "our prejudices about faces turn into self-fulfilling prophecies...Our expectations can lead us to influence people to behave in ways that confirm those expectations: consistently treat someone as untrustworthy and they end up behaving that way." It is then suggested that the effect also works the other way round, that there is also a self-defeating prophecy effect, particularly for those who look cute, in which "a man with a baby face strives to confound expectations and ends up overcompensating."

As I understand it, if the behaviour of an individual or group of individuals is contrary to some effect postulated by a psychologist, the psychologist then explains that behaviour by inventing an inverse effect. It's a simple trick, but if you play it really well, you could ultimately end up reaching the zenith of your profession, analysing contestants on Big Brother.

The leadership of philosopher kings

Those who work in scientific or technological institutions may be interested in a short paper on leadership structures by Gregory Canavan. Canavan's basic point is that all the individuals in a scientific organisation should spend some of their time doing creative, rather than administrative work. If the people with experience spend all of their time doing administrative work, then their ability and knowledge is wasted. Moreover, argues Canavan, to be an effective leader it is necessary to be engaged in creative work, because leadership requires inspiration, guidance and insight:

Managing is a function that can be applied easily to any process: producing cars, IRS forms, sausages,etc. Science requires leadership more than management. Doing science, particularly applied science, requires insight and inspiration on which way to go, not just a daily reckoning of where you have been. Many organizations have quietly substituted management for leadership. The result is generally polarization, lack of commitment, inflexibility, the premature loss of scientific excellence, and fossilization, which are sufficiently familiar and uncomfortable to require no elaboration.

In specific terms, Canavan argues that

1) The greatest number of people an individual can effectively manage is 7. Individuals who manage 7 people have no time for creative work at all.

2) Apart from those people on the lowest level in a company, each individual should lead (at most) 3 people. This takes up 3/7 of an individual's time. Assuming that 1/7 is taken up responding to one's own leader, this leaves 3/7 of the time for creative work.

3) Whilst the rule of seven creates log₇ 6N layers in an organisation containing N employees, the rule of three creates log₃ 2N layers. In an organisation containing 7,500 employees, for example, the rule of three generates 9 layers rather than 6. To ensure everyone is working creatively, it is necessary to add extra layers to a leadership hierarchy.

The main problem with Canavan's idea is hidden in his assertion that "If [an employee] doesn't feel an urge to do [creative work], he is probably in the wrong organization." This is true, but all organisations do harbour people in the wrong jobs, or people who possess a negligible amount of creative ability. For these people, a management role which involves administrative drudgery is both a refuge, and a means for advancing one's career to a higher salary scale. Nevertheless, Canavan's idea has a bracingly radical feel to it. Bravo!

The greatest scientific book ever written

Andrew Jaffe writes in Physics World that "Nowadays, science (or at least physics) progresses not by sustained argument in books but by short snippets. Books serve to consolidate knowledge and present it to students or to the public."

This is sadly true, and indicative of the way in which science in particular, and academia in general, has been mechanised, and transformed from a compulsion into a career. The output of most scientific research consists, not of genuine discovery, but of modestly scoped, often irrelevant, and even straightforwardly incorrect papers published in narrowly specialised journals.

Scientists should stop writing papers, and should avoid the desire for a career in a particular discipline. There should be no desire to maximise citations, or to gain tenure in a university department. If science is a calling rather than a career, then knowledge and understanding should itself be sufficient reward. A true scientist should aim to finish life in abject loneliness and poverty.

The end product to which a true scientist should be aiming is the greatest scientific book ever written. This book will be stylishly and succinctly written with clarity and precision; it will synthesise concepts from different subjects and simultaneously solve multiple problems in disparate disciplines; it will tell an engrossing story; it will paint vivid pictures; it will cast speculative asides and footnotes like confetti through the text; it will re-cast the familiar as the unusual; it will titillate the reader, and hold him in suspense; it will defy convention; it will be a seamless blend of the lyrical and the analytical; it will integrate natural language concepts and mathematical concepts, the observational and the theoretical; and it will be as broad as it is deep. I look forward to reading it.

The evolution of the eye

Sir David Attenborough explains the evolution of the eye, for the benefit of those who may be suffering from a touch of epistemological astigmatism.

Stupidist epistemology and philosophy of science

Stupidist epistemology and philosophy of science studies the ways in which intelligender does and ought to influence our conceptions of knowledge, the knowing subject, and practices of inquiry and justification. It identifies ways in which dominant conceptions and practices of knowledge attribution, acquisition, and justification systematically disadvantage stupid people and other subordinated groups, and strives to reform these conceptions and practices so that they serve the interests of these groups. Various practitioners of stupidist epistemology and philosophy of science argue that dominant knowledge practices disadvantage stupid people by (1) excluding them from inquiry, (2) denying them epistemic authority, (3) denigrating their 'stupidine' cognitive styles and modes of knowledge, (4) producing theories of stupid people that represent them as inferior, deviant, or significant only in the ways they serve the interests of intelligent people, (5) producing theories of social phenomena that render stupid people's activities and interests, or intelligendered power relations, invisible, and (6) producing knowledge (science and technology) that is not useful for people in subordinate positions, or that reinforces intelligender and other social hierarchies. Stupidist epistemologists trace these failures to flawed conceptions of knowledge, knowers, objectivity, and scientific methodology. They offer diverse accounts of how to overcome these failures. They also aim to (1) explain why the entry of stupid people and stupidist scholars into different academic disciplines, especially in biology and the social sciences, has generated new questions, theories, and methods, (2) show how intelligender has played a causal role in these transformations, and (3) defend these changes as cognitive, not just social, advances.

The central concept of stupidist epistemology is that of a situated knower, and hence of situated knowledge: knowledge that reflects the particular perspectives of the subject. Stupidist philosophers are interested in how intelligender situates knowing subjects. They have articulated three main approaches to this question: stupidist standpoint theory, stupidist postmodernism, and stupidist empiricism. Different conceptions of how intelligender situates knowers also inform stupidist approaches to the central problems of the field: grounding stupidist criticisms of science and stupidist science, defining the proper roles of social and political values in inquiry, evaluating ideals of objectivity and rationality, and reforming structures of epistemic authority.

The Arctic Grand Prix

"Hi Gord. Bernie here."

"Hi Bernie! How's tricks?"

"Not bad, not bad. Bit of a problem with the trouble and strife, but musn't grumble I suppose."

"Indeed."

"Anyway. About your idea for a Snow Grand Prix."

"Yes."

"I like it. I like it a lot. Cars with studded tyres, cars bouncing off snowbanks, head-up displays for the drivers, and the first ever global sporting event covered entirely in the infrared part of the spectrum. Nobody will be able to get to the track, but hey, plus ca change..."

"Indeed."

"Thing is, the only parts of the world which can afford to pay for the right to host a Grand Prix these days, tend to be in the Middle East and South-East Asia. The countries with territory in the Arctic circle tend to be a bit flaky with the old GDP, and no-one seems to own Antarctica yet. At the end of the day, Gordon, Formula 1 is owned by a private equity company which needs to recoup its investment in some way. So..."

"I understand Bernie. It was only an idea."

"Sure."

"How's Max?"

"Oh, same old, same old..."

A trip to the linguistic foundry

You know when you walk through deep, freshly-fallen snow? What's the onomatopoeic word for the sound your footsteps make in the snow? It's definitely not 'crunch'. If the snow has lain for two or three days, and gone through a couple of freeze-and-thaw cycles, then it will make a crunching sound, but that's because of the higher ice content. Freshly-fallen snow doesn't crunch, it's a more complex, staggered, semi-muffled, compaction sound. I reckon you can refer to a staggered crunch as a 'scrunch', but what's the term for a semi-muffled scrunch?

And another thing: you know when you've taken a dump, and the main mass has been expelled, but there's a little straggler hanging on? You have to give it another squeeze, and maybe a wiggle, before the little fella plops into the bowl. What's the word for such a faecal straggler? If there isn't one already, how about calling it a brown loafer?

Dirac and Wittgenstein

Ludwig Wittgenstein famously insisted at the end of his Tractatus Logico-Philosophicus, "Whereof one cannot speak, thereof one must be silent."

Ironically, then, Graham Farmelo's recent biography of the British physicist Paul Dirac, reports that Dirac's verdict on his Cambridge contemporary was:

"Awful man. Never stopped talking."

Snow complaints

It's difficult to believe, I know, but some people are complaining. They're complaining, in fact, about the snow, about the fact that many children haven't gone to school for a couple of days, and about the fact that some adults didn't go to work on Monday.

The Federation of Small Businesses, (which also recently distinguished itself by complaining about the 'Take a Benylin day' advertising campaign), moaned that 20% of the workforce hadn't gone to work on Monday, and plucked a figure of £1.2bn as the cost to the economy. The System doesn't like it when people change their behaviour.

Those complaining about school closures, meanwhile, divide into two camps: those who complain about the loss to children's education; and those who complain that parents have to find alternative childcare arrangements at short-notice. Both complaints strike me as rather odd.

Firstly, the notion that our children receive an education at school is refuted on a daily basis by the ignorance, innumeracy and illiteracy of the majority of school-leavers. 10 years' worth of cumulative schooling appears to be insufficient to equip most children with the fundamentals, so a couple of days lost here and there hardly seem to be of any relevance.

Secondly, as I understand it, parents love their children, and earnestly seek to spend as much time with them as possible. Hence, what could be more fantastic for the modern parent, than a good excuse to take the day off work, and spend it playing in the snow with one's children?

Of course, if the real function of school is not to educate children, but to rid modern parents of their benighted offspring for a few hours, and to confine them to a localised region of space in which they cannot pose a nuisance to other members of the public, then the reason for the complaints becomes clear.

Overall, these snow complainers need to be reminded of the fact that their lifespan is finite, and as such, there will be a time in a few short years, when they're going to be dead. I hope the schools remain closed, and the economy loses even more money. Given human mortality, there is only one rational reaction to the current weather conditions:

It's snowed! Wheeeeeeeee!

The modern music scene

Back in fin de siecle Paris, UK Garage was the big new thing. As it evolved, the bass lines became more ruthless, and the rhythms more disjointed — especially in the 2-step style, with its characteristic absence of any tune whatsoever. Although garage was temporarily driven underground, young crews in East London resurrected it in the form of grime, a British version of hip-hop, whilst in Croydon a group of producers centred on the record shop Big Arse, stripped out the singing, ramped up the bass and created dubstep. Within a few years, dubstep conquered the world. This atmospheric style borrows from dub reggae its lack of imagination, and creates a striking sense of emptiness and predictability. Perhaps buoyed by dubstep’s success, garage producers set to work again, and produced a lighter style called funky house, or simply funky, which pretty much brings garage full circle.

The anti-thesis to House's thesis, was Techno. This came in two strains, Detroit techno and acid techno. Although the Detroit producers made free use of 'hydrofluoric acid', the metallic ping-pong tone wrested from the Rolf Harris Stylophone, they also often based tracks on funky basslines; acid techno, in contrast was predicated entirely on the Stylophone. Whilst there were offshoots such as Gabber, (a harder variant developed in Rotterdam, and played on the harpsichord at a manic tempo), everyone was happy with the formula. Until, that is, several lone producers independently thought something was getting lost in the maximal approach, and a minimal movement, centred on Berlin, took root in about 2003. The latest technology can create music with an appealing sense of nothingness, and is perhaps the most 'techno' techno yet.

Snowflake update

When most people in South-East England drew back their curtains this morning, the first question on their lips was probably: 'What are the temperature and humidity conditions for the different types of snowflake morphology?'

Fortunately, Kenneth Libbrecht of Caltech provides the answer:

Thin plates and stars grow around -2 C (28 F), while columns and slender needles appear near -5 C (23 F). Plates and stars again form near -15 C (5 F), and a combination of plates and columns are made around -30 C (-22 F)...snow crystals tend to form simpler shapes when the humidity (supersaturation) is low, while more complex shapes at higher humidities. The most extreme shapes -- long needles around -5C and large, thin plates around -15C -- form when the humidity is especially high.

Snowflakes

A winter couplet

Wheeeeeee! It's going to snow, it's going to snow!

But please, be careful, and don't crash your car into a hedgerow.