Unfinished work

Today our drawing class visited the Russell Cotes museum, perched on Eastcliff, Bournemouth. The museum is furnished with many fine exhibits, and is endowed with a beautiful garden, looking out over the cliff-top towards the sea. As Terry Pratchett once said, it's amazing how precisely the sky fits the sea at the horizon. The picture here is drawn with an ink-pen, and is, sadly, unfinished.

Million-dollar treasure hunt!

With the publication of my book imminent, I can now reveal for the first time, exclusively to readers of McCabism, that the book contains the clues to buried treasure, estimated by De Beers at a million dollars. If the reader numbers all the words in the book, and then takes the first letter of the prime-numbered words, the resulting string of letters can be transformed by a single mathematical operation into the instructions for finding the buried treasure. The rest I leave up to you. May the best man, or woman, win!

Nicolas Cage

What is it with Nicolas Cage at the moment? It only seems like a few weeks ago that he was compulsively bursting into flames, and whizzing about on his moped in 'Ghost Rider', and now he appears in 'Next' as a man with the ability to see two minutes into the future! It sounds like the premise of an M. Night Shyamalan movie, but in fact it's yet another film based on a story by Philip K.Dick.

Imagine if there were a whole set of people who could see 2 minutes into the future. They could get together, and form a chain, enabling them to see hours and days into the future. In such a scenario, the individual at the base of the chain sees one of his comparably-afflicted friends, 2 minutes into the future, telling him what HE can see 2 minutes into his future, and he, in turn, sees a third individual telling him what HE can see 2 minutes into his future, and so on.
Or perhaps this would work with just two such afflicted individuals. Individual A sees 2 minutes into his future where individual B is telling him what he can see 2 minutes into his future, but individual B sees individual A telling him what he can see 2 further minutes into the future, and so on.

In fact, what if the single Nicolas Cage character just spent all his time writing down what he sees two minutes into the future? Right now, he would see what he's writing down 2 minutes into the future, which would describe what happens 4 minutes into the future, which, in turn, is a description of what happens 6 minutes into the future, and so on.

Iain Nicolson and the Dark Side of the Universe

I'm currently reading 'Dark Side of the Universe', by the Scottish astronomy writer Iain Nicolson. This is a fabulous, fabulous book. It's a brilliantly written introduction to, and exposition of all the issues surrounding dark matter and dark energy in cosmology. There are many popular books on this subject, but none have the authority and clarity of Nicolson's. It's accessible to non-specialists and non-scientists, but still manages to be completely accurate and reliable. Nicolson reasons clearly about his subject, and impartially weighs the competing evidence supporting different theories. It's also beautifully illustrated.

Michael Schumacher and irony

Michael Schumacher was in London this morning to promote a road safety campaign. Two things concern me here: (1) The scarf. It was indeed slightly cooler today, but I still didn't feel the need to wear a scarf. And certainly not one looking like that. (2) Michael Schumacher promoting road safety? This would be the same Michael Schumacher who, on two separate occasions, deliberately rammed opponents as he tried to win the world championship; the same Michael Schumacher who would veer diagonally across the track to prevent other drivers from passing; the same Michael Schumacher who would give his opponents brake-tests behind the safety-car before a re-start; the same Michael Schumacher who deliberately parked his car across the track in qualifying at Monaco last year in an attempt to stop other drivers beating his time; the same Michael Schumacher who, after being involved in a major first-lap shunt would deliberately drag a damaged car back onto the track, leave it in gear, and then alight from it in an attempt to get the race stopped; the same Michael Schumacher who drove a car in 1994 which was equipped with concealed, and illegal, traction control and launch control software?

It certainly appears to be the same man.

The Aharonov-Bohm effect

One of the most frequently discussed topics in the philosophy of physics is the Aharonov-Bohm effect. I have therefore to admit, shamefully, that this is a topic to which I have never really paid much attention. The basic idea involves electrons passing through a double-slit in a barrier, and forming an interference pattern upon a screen. When a solenoid is placed between the barrier and the screen, the interference pattern changes, undergoing a phase-shift. There seems to be widespread disagreement about what the effect really demonstrates. It is often claimed, for example, that it demonstrates the existence of a non-local interaction between the electromagnetic field and the electrons. The electromagnetic field remains undetectable in the region of space outside the solenoid, the region of space traversed by the classical electron paths. Hence it is sometimes claimed that this demonstrates a non-local interaction between the electromagnetic field and the electrons.

At face value, this might seem wrong. Quantum mechanically, it is the wave-function of each electron which propagates through space, and one might think that includes the space occupied by the solenoid. One might think that there is a local interaction between the electron wave-function and the electromagnetic field in this region, which changes the interference pattern on the screen. What the Aharonov-Bohm effect demonstrates is that a naive realist intepretation of quantum theory, which ascribes a definite trajectory through space to each electron, must accept a non-local interaction between the electromagnetic field and each electron.

Antigone Nounou writes "One might object that the wavefunction of a quantum particle, such as the electron, is extended over the entire space between the slits and the screen, but the truth is that the energies involved are so small that the electron cannot penetrate the solenoid, whether this is switched on or not," (p190, A Fourth Way to the Aharonov-Bohm Effect). "What is really important for the effect to happen is not just the material presence of the solenoid in the setup, for one then might claim that even when the solenoid is switched off the region inside it is still inaccessible to the electron and yet there is no A-B effect. What is crucial for the effect to happen is that the flux of the electromagnetic field inside modifies the space-time around it," (ibid. p192).

The electromagnetic field is idealised to be zero on the boundary of the solenoid, hence even if the electron wave-function interacts locally with the boundary of the solenoid, this local interaction cannot be responsible for changing the interference pattern.

Project Zeus

Mark gets his team "sweating facts and shitting stats" as they work to merge marketing with sales.

Drawing

I've always wanted to be able to draw properly, so I've enrolled on a drawing course at the arts institute, Bournemouth, and today was the first day. This was a massive amount of fun! In the morning, we drew various still-life objects with pencil and soft-graphite, and then in the afternoon we drew a live model with charcoal. This was really hard work, over two hours, about ten of us, each standing with a large sheet of paper on an easil, drawing, shading, and smudging, in a semi-circle around Ellie, the model. You can see the result here.

Mr Beardy

Mr Beardy lives next door. I don't know whether Mr Beardy is sad or happy, but I reckon Mr Beardy has got things just right.

Mr Beardy is a doctor, who lives in a medium-size Victorian house, within walking distance of the town centre. The Jurassic coast is 15 minutes away in one direction, and Hardy's Dorset lies in t'other. His children have now left for university. Mr Beardy owns a convertible, and, if the weather is nice, he peels down the roof, and drives away with his beard shooting the breeze. He also owns an old motorbike, which he occasionally teases into working order, popping and banging like a bag of old nails. Best of all, though, is Mr Beardy's garden. There is no hint of order or symmetry to Mr Beardy's garden: it's boisterous and ramshackle and wonderful. There are flower beds and garden benches here, a mazy path there, blossoming fruit trees and a small pond to the right, elms and birches and washing lines in the foreground, vegetable patches and a greenhouse in the background, and splitting the garden in twain is a row of bushes shouldering a wooden arch, engirdled with creeping plants and vines.

This is the type of garden I grew up in. Life as a child is an adventure in this type of garden. Too many children today grow up with ordered back-gardens the size of postage-stamps. These children also appear to grow up with no desire greater than to tick the check-boxes for: (i) career, (ii) family, (iii) mortgage, (iv) pension.

An old dog with sad, lonely eyes, who never barks, plays and sleeps and gazes into the house from Mr Beardy's garden. Perhaps his former play-mates have grown-up and forgotten him now they've gone to university. I think Mr Beardy, or his solemn grey-haired wife, should play with him more. Apart from that, however, I think Mr Beardy has got it just right. So here's a toast to Mr Beardy, and all his fellow Beardies, who make the world a more interesting place to live in!

Mind, brain, and space

The philosopher, Colin McGinn has listed five characteristics of mental states, which purportedly prevent them from being identified with brain states. Mental states are, he claims:

1. Unobservable — in the sense that they are not perceptible by means of the senses.

2. Asymmetrically accessible — in the sense that the owner of a mental state has a kind of immediate access to it that other people do not.

3. Subjective — in the sense that the nature of a mental state is knowable only from a single 'point of view'.

4. Non-spatial — in the sense that mental states do not take up a well-defined region of space.

5. Subject-dependent — in the sense that mental states only exist for a subject of awareness.

Now, as I argued a few weeks ago, non-commutative geometry is the best candidate for a mathematical structure which provides a common generalisation of the structures employed in quantum theory and relativity. And the crucial thing to note about non-commutative geometry is that it provides an algebraic representation of space, rather than a manifold of spatial points. Relationships between points in a manifold, such as spatial extension, are rendered obsolescent, and replaced with purely algebraic relationships. Hence, non-commutative geometry has the potential to dissolve one of the apparent barriers to resolving the mind-brain issue. McGinn's fourth point, that mental states are not spatially extended, is only a problem if brain states are held to be the states of spatially extended systems. Non-commutative geometry suggests that the spatial extension of any physical system, including the brain, is an illusion.

What is a presheaf?

Last Thursday's New Scientist contained a splash about topos theory, so on Friday I decided it was time to try and understand what a topos is. This seemed to go quite well, and I went to sleep at a reasonable hour on Friday night. On Saturday morning, however, I woke extremely late, at 11:30, with no memory of having woken earlier. I felt dislocated for the remainder of the day, the Grand Prix qualifying, Grand National, FA Cup semi-final, Bear Grylls, Doctor Who, and Match of the Day all merging into a timeless unity. And every day since, I've carried a headache of varying severity. I feel like something has blown a hole in my mind. I say this merely as a warning, for I am now about to tell you what I learnt on Friday.

A topos is a type of category. Recall that a category is a collection of objects, such that any pair of objects has a collection of 'morphisms' between them. The morphisms satisfy a binary operation called composition, which means that you can tack one morphism onto the end of another to get a new morphism. For example, the category Set contains all sets as objects and the functions between sets as morphisms. In fact, the category of sets is itself a topos. There are, however, topoi whose objects are not sets. Topos theory is therefore a generalisation of the concept of a set, within category theory.

A popular example of a topos is a topos of presheaves. So what is a presheaf? Here we need a couple of extra concepts from category theory. Categories can be related to each other by maps called 'functors', which map the objects in one category to the objects in another, and which map the morphisms in one category to the morphisms in the other category, in a way which preserves the composition of morphisms. Furthermore, one can relate one functor to another by something called a 'natural transformation'. Suppose that A is an object in a category C, and suppose that X is a functor from C to another category D, and Y is a functor from C to another category E. X maps A to X(A), an object in category D, and Y maps A to Y(A), an object in category E. A natural transformation N from X to Y defines the image of X in Y. Hence, a natural transformation is defined by a family of maps, N_A: X(A) → Y(A), for all the objects A in the category C.

Now, a presheaf is a functor from an arbitrary category into the category of sets. The collection of presheaves on a category can itself be treated as a category. The morphisms between the presheaves in such a category are natural transformations between functors. And not only is the collection of presheaves on a category itself a category, but it is a topos.

The general definition of a topos, I leave to another day.

Spring is the new Summer

May is my favourite month of the year. The weather is usually warm, but not oppressively so, the air is fragrant, fruit trees are in blossom, and the foliage grows deep green against an aquamarine sky. It's also FA Cup final and Champions' League Final month, miraculous Stephen Gerrard goals forever lodged in the memory. And it's a poignant month: Ayrton Senna crashed to his death at Imola on 1st May 1994, on one of the most beautiful days I can remember, the warm Bolognan air rich with pollen and petals; and Gilles Villenueve, the greatest free spirit in modern Grand Prix racing, was flung to his death from his cartwheeling Ferrari at Zolder on 8th May 1982.

Already, however, in mid-April this year it feels like May. What's more, when I look at the Sun, or enjoy its warmth, it also feels like the herald of interminable heat; five months of pestilential heat to come. The Woodland Trust have suggested that Spring in the new Summer, and they May not be wrong.

How to get a job with the Bank of England

There are a couple of rules-of-thumb which must be learnt:

1. If inflation rises for several consecutive months, raise interest rates slightly. Wait a bit. If inflation is still rising, then raise interest rates again.

2. If economic growth is falling and inflation is low, then lower interest rates.

You now know everything that a Bank of England economist knows.

Sets and Categories

There are basically two approaches to the foundation of mathematics: set theory and category theory. In his book, 'Infinity and the Mind', Rudy Rucker argues that "if reality is physics, if physics is mathematics, and if mathematics is set theory, then everything is a set." However, category theory is able to embrace objects which are not sets, hence mathematics cannot be identified with set theory, and it may be, therefore, that the physical universe is not a set, but an object in a category.

A category consists of a collection of objects such that any pair of objects has a collection of 'morphisms' between them. The morphisms satisfy a binary operation called composition, which means that you can tack one morphism onto the end of another. In addition, each object has a morphism onto itself called the identity morphism. For example, the category Set contains all sets as objects and the functions between sets as morphisms; the category of topological spaces contains all topological spaces as objects, and has continuous functions as morphisms; and the category of smooth manifolds contains all smooth manifolds as objects and has 'smooth' (infinitely-differentiable) maps as morphisms. However, the definition of a category does not require the morphisms to be special types of functions, and the objects need not be special types of set.

The notion of an object in a category is held by many to provide the best definition of a structure. The philosopher of mathematics, David Corfield argues that "category theory allows you to work on structures without the need first to pulverise them into set theoretic dust. To give an example from the field of architecture, when studying Notre Dame cathedral in Paris, you try to understand how the building relates to other cathedrals of the day, and then to earlier and later cathedrals, and other kinds of ecclesiastical building. What you don't do is begin by imagining it reduced to a pile of mineral fragments."

The crucial distinction between a set and a structure is as follows: two sets are the same if and only if they have the same elements. In contrast, two structures are the same if and only if they are isomorphic. Sets can be equipped with structures, but whilst two different sets can be equipped with isomorphic structures, they are, nevertheless, different sets. Different sets with the same structure are different instances of the same structure. The question, then, is this: is our physical universe a specific structured set, or is it a structural object in a category?

What is the coolest intro ever?

Duck suggests that Hawaii Five-0 may be the coolest TV intro ever. He might be right, but I've got a soft spot for Thunderbirds. And the intro to Grand Prix wasn't bad either...

How to resign

Patrick McGoohan demonstrates the correct technique for tending one's resignation.

How many times will your heart beat?

Each Thursday morning, between 3am and 4am UK time, Dr Karl answers any science questions whatsoever that Radio 5 listeners can throw at him. This week, he was joined by Dr Chris Smith. It's brilliant stuff. For example, you know the feeling that one nostril is partially blocked whilst the other is free? Well, apparently this is by design: larger molecules take longer to lock into the nerve cell receptors in the nose, and these require reduced airflow. Other smaller molecules lock into place quickly, and these can be smelt via the larger airflow in the other nostril. (If the BBC Radio Player doesn't work via this link, go to the Up all Night page, look for Thursday, and click on 'Listen' next to 'Dr Karl answers your science questions').

Deja vu

So, here we go again: Chelsea v Liverpool in the first leg, at Stamford Bridge, on 25th April, and then the return leg, at Anfield on 1st May. Tasty.

The managers are already warming up. Benitez pointed out that Mourinho "has good relationships with managers of teams he beats...He fights with the managers of the top sides," while Mourinho argued "It is a tie where we know we start from behind and why is simple: Liverpool play only in the Champions League and Chelsea plays in the Champions League, Premiership and FA Cup."

And for those worried about who we might face in the final, remember that Portsmouth beat Man U. 2-1, so Portsmouth would have beaten Roma 9-2...

Concorde and Bernoulli's principle

There were people in Reading who said they got used to the sight and sound of Concorde flying over at about 11:10am each day. These people are the living dead.

Concorde didn't just fly over each day; it ripped a deep sonic wound through the morning sky. It was a living, surging, accelerating phoenix, desperate to reach the greatest speed possible, impatient at being held below Mach 1 until it reached Oceanic airspace.

There was also the evening flight to New York, where Concorde could take-off just after the Sun had set at Heathrow, and actually overtake the terminator on the Earth's surface, forcing the Sun to rise in the West, the passengers then alighting in daylight at JFK. On one of these evening flights, I was out in the garden when I saw Concorde go past at low speed and low altitude to the South, off its normal flightpath, and with its undercarriage still down. It disappeared from sight, but the sound continued to rumble away. Presently it appeared again, travelling in the opposite direction as it swept over the top of me. I later read that the undercarriage had failed to retract, and Concorde had been forced to return to Heathrow. A harbinger of more serious problems to come...

But did Concorde generate lift via Bernoulli's principle? Bernoulli's principle states that an increase in fluid velocity corresponds to a decrease in pressure, and a decrease in fluid velocity corresponds to an increase in pressure. Whilst Bernoulli's principle is often invoked to explain the phenomenon of aerodynamic lift generated by the air flow around an aircraft wing profile, there are alternative explanations which employ, in some combination: the 'Coanda effect', the notion of circulation, and Newton's third law. These alternative explanations are, at the very least, equally legitimate to the Bernoulli-principle explanation, and, amongst aerodynamicists, are considered to be superior to the Bernoulli-explanation. There is also a long-standing popular misconception associated with the Bernoulli-principle explanation, which has been widely disseminated, but which is completely false.

The Bernoulli-principle approach explains the lift generated by an aircraft wing as the consequence of lower pressure above the wing than below, resulting in a net upward force upon the wing. The lower pressure above the wing corresponds to faster air flow above the wing, in accordance with the Bernoulli principle. The Bernoulli principle itself merely states that lower pressure corresponds to faster airflow, and vice versa; it does not state that faster airflow causes lower pressure, any more than lower pressure causes faster airflow. Faster airflow does not have causal priority over lower pressure. However, at this point, the misconceived popular explanation implicitly assigns causal priority to faster airflow, explains the lower pressure as a consequence of the faster airflow, and explains the faster airflow above the wing as a consequence of the fact that wings have greater curvature above than below, and the air flowing over the top therefore follows a longer path than the air flowing below. Conjoined with this is a curious argument, which invokes the notion of a 'packet' of air, and claims that a packet of air which is divided at the leading edge of a wing must rejoin at the trailing edge, hence the air traversing the longer path over the top must travel faster to rejoin its counterpart at the trailing edge. This 'path-length' explanation of lift does not require the air at the trailing edge of the wing to be deflected downwards, despite the downdraught which can be experienced directly beneath a passing aircraft. If this explanation were true, and the cause of lift was merely the asymmetrical profiles of the upper and lower surfaces of a wing, then it would not be possible for an aeroplane to fly upside-down. In addition, experiment demonstrates that air passing over the upper surface of a wing travels at such speed that packets of air divided at the leading edge of the wing fail to rejoin at the trailing edge.

One alternative explanation argues that aircraft wings generate lift because they deflect air downwards, and, by Newton's third law, an action causes an equal and opposite reaction, hence the wing is forced upwards. According to this explanation, the trailing edge of a wing must point diagonally downwards to generate lift, and this is achieved either by tilting the wing downwards with respect to the flow of air, or by making the wing cambered, or both. Air is deflected downwards by both the lower and upper surfaces of the wing. The lower surface deflects air downwards in a straightforward fashion, given that the wing is either tilted with respect to the direction of airflow, or the lower surface is of a concave shape. However, the majority of the lift is generated by the downwards deflection of the air which flows above the wing. This explanation then depends upon the Coanda effect, the tendency of a stream of fluid to follow the contours of a convex surface rather than continue moving in a straight line. The flow over the surface of a wing is said to remain 'attached' to the wing surface. An aircraft wing is said to 'stall' when the boundary layer on the upper surface 'detaches' or 'separates', and is no longer guided downwards by the contours of the upper surface. In this circumstance, the lifting force generated by the upper surface of the wing suddenly becomes very small, and the lifting force that remains is generally insufficient to support the weight of the aircraft. To create lift at low speed, an aircraft must increase the angle of attack of the wing, and the upper surface is carefully contoured to prevent flow detachment under these conditions.

(See 'Explanation and discovery in aerodynamics' for further details)

Eternal sunshine of the spotless mind

I watched this film for the first time last night, and I have to say I was pretty disappointed. The basic premise of the film, in which a couple delete their memories of each other after breaking up, then re-discover each other, and begin their relationship anew, is an arresting concept. However, the film is all post-modern style, and very little substance. There are basically two, rather trite observations, which the form of the film highlights:

1) We need memory to make sense of our experiences.

2) Stories are conventionally told in a chronological sequence.

The film shows how confusing things become if memories and chronological sequences are disrupted or allowed to interfere with each other. At least an hour of the film is spent playing with this single, rather facile observation. This could have been a moving and poignant film if the writer and director, Charlie Kaufman and Michel Gondry respectively, had followed through on the basic premise, but, as it stands, it's just one long gimmick.

Fermilab's 'pratfall'

The Sunday Times's Science editor, Jonathan Leake, has revealed further details of the failure suffered by the Large Hadron Collider, at CERN, on the 27th March. According to Dr Lyn Evans, who leads the accelerator construction project, "There was a hell of a bang, the tunnel housing the machine filled with helium and dust and we had to call in the fire brigade to evacuate the place...The people working on the test were frightened to death but they were all in a safe place so no-one was hurt."

The magnet assemblies responsible for the explosion were designed and manufactured by CERN's main rival, Fermilab. The director of Fermilab, Pier Oddone, has apparently written to his staff, accusing them of causing "a pratfall on the world stage". Oddone said: "We are dumb-founded that we missed some very simple balance of forces. Not only was it missed in the engineering design but also in the four engineering reviews carried out between 1998 and 2002 before launching the construction of the magnets."

An article on the Scientific American website further quotes Oddone as saying: "[E]ven though every magnet was thoroughly tested individually, they were never tested with the exact configuration that they would have when installed at CERN—thus missing the opportunity to discover the problem sooner." This means that the magnets underwent unit testing, but didn't undergo system testing. In engineering terms, this is an elementary error.

The Children of Húrin

Displaying limitless range and depth, Bryan Appleyard wrote a superb piece in yesterday's Sunday Times on the 'new' Tolkien narrative, 'The Children of Húrin', to be published on April 16th.

I have yet, however, to understand the exact provenance of this narrative. Tolkien's son, Christopher, who produced the 12-volume History of Middle-Earth, (a remarkable, but very dry work of scholarship), is also responsible for this current publication. I thought that everything Tolkien ever wrote about the children of Hurin had already been published in The Silmarillion, The Unfinished Tales, and the relevant volumes from the History of Middle Earth. The 'Narn i Chîn Húrin' in the Unfinished Tales is a lengthy, fully-fledged, and deeply poignant narrative fragment. The story is completed by joining to it 'The Wanderings of Húrin', from Volume 11 of the History of Middle Earth. I am fascinated to see what Christopher Tolkien has actually done to produce the current work. There is some extra material in verse-form also published in the History of Middle Earth. Perhaps Christopher has done some concatenation, some interpolation, some extrapolation, and some selection to arrive at a coherent and consistent final manuscript. I am not necessarily agin this, but I am interested to understand exactly what his contribution is.

Philosophers and haircuts

Charles Moore covers familiar ground here with respect to the atheism vs. religion debate, but proffers an interesting description of Professor A. C. Grayling as having "that big mane of swept-back hair which says 'philosopher' just as clearly as a pinstripe suit used until recently to say 'Tory'."

Is this really true? Certainly, Bertrand Russell also sported an interesting follicular sweep at times. With Wittgenstein it was more the look of madness which grabbed your attention; eyes which have seen into the dungeon dimensions.

Tiger Woods

Circa year 2000, Tiger Woods was dominating world golf in an unprecedented manner. He was hitting the ball further than anyone else, and by a significant margin. It was routine for Tiger to drive the ball 300 yards. In recent years, everyone else seems to have caught up. In fact, Tiger is no longer the longest driver of the ball. There seem to be two likely explanations for this:

(i) Tiger gained an advantage in club and ball technology before everyone else, and they've all now caught up.

(ii) Tiger had a pure natural ability advantage over everyone else, which the other golfers have now been able to negate by means of club and ball technology.

What is the truth here? If the latter is the case, then why hasn't Tiger been able to use technology to drive the ball further still? Gaining an advantage through technology is, of course, the very essence of Formula 1, but the golf world seems to be uncomfortable with this idea.

Peep Show

The excellent 'Peep Show' returns this Friday, and there's a perceptive interview with David Mitchell and Robert Webb in today's Daily Telegraph. Mitchell and Webb have recently enjoyed a high profile from Apple's latest UK advertising campaign. They've also been accused of selling-out on this, to which Robert Webb responds: "I'm an actor. So when someone asks, 'Do you want to do some funny ads for not many days in the year and be paid more than you would be for an entire series of Peep Show?' the answer, obviously, is, 'Yeah, that's fine.' "

Uncertainty and imagination

Bryan Appleyard recently advocated, as a personal ethic, the combination of uncertainty and empathic imagaination: "I believe in uncertainty...and the imagination, not least because the combination of the two makes killing people almost impossible."

Whilst it may not have been Bryan's intention, might one be able to use this as the fundamental principle for a fully-fledged ethical theory? As an ethical principle, it is methodological rather than substantive, but I see no reason why one couldn't apply this principle to a variety of moral issues to arrive at substantive principles. I do see two possible problems though:

(i) Moral dilemmas. These tend to be used by moral philosophers to test, and often to break, moral principles. Now, uncertainty entails the hedging of bets, and moral dilemmas are often framed in a manner which prevents such hedging. For example, should a pregnant teenage girl, who has been the victim of rape, have an abortion or not?

(ii) Game theoretic situations. These are situations where the decision one takes is dependent upon one's belief about the decisions that other people will take. If the morally uncertain and imaginative individual or society is faced with potentially threatening agents, individual or societal, who possess high levels of certainty and low levels of empathic imagination, how should the former respond? This, of course, is a question of high contemporary relevance, given the Islamist threat to Western societies. It is a question which always applies in times of war, when uncertain and imaginative individuals may still choose to kill other humans.

I don't necessarily regard these problems as irresolvable, but I certainly think they need to be grappled with.

The Mathematical Universe

After 11 years, the brilliant Swedish cosmologist Max Tegmark, has produced a follow-up to his seminal paper, Is 'the theory of everything' merely the ultimate ensemble theory? His latest paper, entitled The Mathemaical Universe, concludes with the following crescendo:

Since our earliest ancestors admired the stars, our human egos have suffered a series of blows. For starters,we are smaller than we thought. Eratosthenes showed that Earth was larger than millions of humans, and his Hellenic compatriots realized that the solar system was thousands of times larger still. Yet for all its grandeur, our Sun turned out to be merely one rather ordinary star among hundreds of billions in a galaxy that in turn is merely one of billions in our observable universe, the spherical region from which light has had time to reach us during the 14 billion years since our big bang. Then there are more (perhaps infinitely many) such regions. Our lives are small temporally as well as spatially: if this 14 billion year cosmic history were scaled to one year, then 100,000 years of human history would be 4 minutes and a 100 year life would be 0.2 seconds. Further deflating our hubris, we have learned that we are not that special either. Darwin taught us that we are animals, Freud taught us that we are irrational, machines now outpower us, and just last year, Deep Fritz outsmarted our Chess champion Vladimir Kramnik. Adding insult to injury, cosmologists have found that we are not even made out of the majority substance. The [Mathematical Universe Hypothesis] brings this human demotion to its logical extreme: not only is the...Multiverse larger still, but even the languages, the notions and the common cultural heritage that we have evolved is dismissed as `baggage', stripped of any fundamental status for describing the ultimate reality.

On voting

There's no getting away from it: I'm definitely on the electoral roll now. The local district council sent me a letter and a form to fill-in last year. I ignored it for a couple of months, hoping that it would go away. Sadly, they sent me another missive, stating that it was a legal requirement to register on the electoral roll. It was simply less bother to fill in the form than it was to take the matter to the European Court of Human Rights, so I filled it in. And now, through the letter box, comes an envelope, with my name and address hand-written upon it, and leaflets inside from two local worthies, Vicki Black and Leslie Phillips, seeking my vote as Independent candidates.

Reading these leaflets, I get no real sense that either candidate has any policies as such. Vicki says that "were there a Common Sense Party, I should be more than willing to join." Leslie, however, does say that "My main interest is Social Housing and I am committed to providing accomodation, training and support for homeless young people." Well, as a Wikipedia entry puts it, "Governments since the early 1990s have...encouraged 'mixed tenure' in regeneration areas and on 'new-build' housing estates, offering a range of ownership and rental options, with a view to engineering social harmony through including 'social housing' and 'affordable housing' options. Recent research by Dr. Rebecca Tunstall has argued that the evidence base for tenure mixing remains thin." The article by Dr Tunstall points out that "It is notable that there is little explicit evidence of the views of housing consumers, whether housebuyers, potential buyers or tenants, on mixed tenure." So I'm not really sure I want to vote for someone who supports a Social Housing policy. And by 'accomodation, training and support for homeless young people,' does that mean that money is taken away from hard-working people, via taxation, and given in the form of hand-outs to alcoholic layabouts? I think it does.

Neither candidate mentions the anti-social effects of the lengthened opening hours of the pubs and clubs in town. I can't sleep on Friday and Saturday nights for the endless train of drunk people yelling their way down my street. It used to finish by 1:15am; now it goes on to 3am, and sometimes 4am. I guess the council generates extra revenue from the pubs and clubs, so this is one policy which isn't about to change.

Jebus was an environmentalist!

Happy crucifixion day everyone! Now, I think the Bible has been somewhat mis-interpreted on the subject of the crucifixion. The key point to note is that Jebus died to atone for all the sins of mankind. This means not only those which had been committed up to that point, but the future sins of mankind as well. This must have included man's future greenhouse gas emissions, hence the crucifixion is simply a metaphor to represent all the various carbon offsetting schemes that Jebus established around Judaea and Galilee. This is why the Bible says that at the time of the crucifixion, the sun darkened and the earth shook. This is clearly a metaphor to represent climate change. It's also a little known fact that the journey of the Magi created more greenhouse gas emissions than a 747 trans-Atlantic flight. The Magi travelled by camel, and camels release an astonishing amount of methane, the equivalent of 1000g of CO2 per passenger kilometre. Jebus had to plant a small copse in Nazareth to offset these emissions alone.

Aviation health warnings and talking cameras

The left-wing 'think tank', the Institute for Public Policy Research, has suggested today that "the Government should introduce cigarette-style health warnings on all advertising for air travel, holidays that include flights, and at airports." We have, of course, also learnt this week that 'talking' CCTV camera schemes' are to be extended across the country. Perhaps, then, the government could combine the two ideas, and publicly berate people, via loudspeakers, at all UK airports and petrol filling stations.

These sorts of environmental issues seem to reveal a vestigial socialist desire to tell people how to lead their lives, and to plan the nature of society from the top-down.

Faggots

What ever happened to faggots? When I was a lad, you could get a fantastic faggot and chips from the Bake 'n' Take, down the Wokingham Road. There were braised faggots on the menu in the NATS' canteen at Hurn, but that's the last I've heard of them. And gimmicks like National Faggot Week, and a cheap play on words from those McCabism favourites, Somerfield supermarket, will do nothing to help the cause.

"Life is too fun to take things the wrong way"

Now, I'm a busy fellow, but I recently found time to graduate from Ole Miss with a degree in chemical engineering. As you can see, I've also built up a large group of admirers. I really should find the time to return their calls though. And yes, Breezy, it has been WAY too long.

Easter

It would clearly be impractical to celebrate the auditory and visual hallucinations of every schizophrenic in society. However, as a token reparation, we celebrate, on an annual basis, the 'resurrection' of an ancient Middle-Eastern David Icke figure, by consuming chocolate confections shaped to resemble the fertilised egg cells of birds. This has clearly confused Somerfield supermarket, who claimed yesterday that Easter was a celebration of the 'birth' of this ancient David Icke character. Somerfield claimed just before Christmas that the mean time at which family arguments break out on Christmas Day is 4:17pm. Yesterday, their latest survey suggested that "Brits are set to spend a massive £520 million on Easter eggs this year — but many young people don’t even know what Easter’s all about."

Singularities on the surface of the sea

One Sunday in the Summer of '98, I drove down to Alum Chine, parked my car at the top of the headland, and walked down to the beach. As I strode down the hill, the entire expanse of Poole Bay was before me, stretching from Hengistbury Head to the left, and Sandbanks to the right. The sky was pure azure, the sun was bright and hot, and the surface of the sea was a billion glittering points of reflected sunlight, criss-crossed by a seething foment of multi-coloured yachts, motorboats, speedboats, water-skiers, and jet-skis.
In the popular imagination, singularities are primordial or destructive things, found either at the beginning of the universe, or within the interiors of black holes. These, however, are merely singularities of space-time. There is a quite distinct type of singularity, which belongs to a mathematical discipline called singularity theory, and the sparkling points of light upon the surface of the sea are singularities in this sense of the term.

To understand this, freeze the surface of sea at a moment in time, and fix the position of the Sun (an extended light source) and the eye of the observer. According to Fermat's principle, the light rays between a source and an observer must be extrema of something called the optical length. (Extrema are either maxima or minima). The optical length of a path in space is determined by its geometrical length, and the index of refraction of any media through which it passes. In the case of interest to us here, the only medium is the air, so we can equate the optical length with the geometrical length.

For light to reach the eye via a reflective surface, such as the surface of the sea, it must follow an extremum of the optical length L. If we let x denote an arbitrary point on the surface of the sea, then, of all the possible paths from the Sun to the eye via point x, the actual path taken by the light is typically the one which minimizes the geometrical length.

Whilst reflected light will reach the eye from all the points upon the surface of the sea, only some points reflect a bright image of the Sun. If one treats the optical length as a function defined upon the surface of the sea, then these bright points are (i) singularities of the optical length, in the sense that the gradient vanishes, ∂ L(x)/∂ x = 0; and (ii) caustics, in the sense that the Hessian of the optical length is singular. (The Hessian, ∂² L(x)/∂ x_i ∂ x_j, is the matrix of second-order derivatives, and if a matrix has a zero determinant, then it is deemed to be singular).

The caustic singularities upon the surface of the reflective medium, relative to the fixed observer, are responsible for focusing the light rays for that fixed observer. Each momentary bright image of the Sun upon the surface of the sea, is responsible for a focal plane which intersects the eye of the observer for that brief moment of time. As the surface of the sea chops and shifts, the caustic singularities change for a fixed observer, and if the surface of the sea is frozen, the caustic singularities will be different for different observers.

Did Fermilab sabotage CERN?

The Large Hadron Collider at CERN suffered a serious setback on March 27th, when the structure supporting some of the superconducting magnets collapsed. The assembly was made by Fermilab, CERN's main rival for the discovery of elementary particles. This seems rather like Airbus getting Boeing to manufacture the wings for the new Airbus A380, but perhaps CERN had no other option. It might also have been an assembly problem, a bit like flat-pack furniture.

Is The Kop a metaphysical idea?

It was announced yesterday that work on the replacement stadium for Anfield will begin in Stanley Park, Liverpool, next month. Liverpool fans, of course, are legitimately concerned that the atmosphere of Anfield, and, in particular, the atmosphere of The Kop end will be lost. Tony Evans raises the question in today's Times that The Kop may just be "a metaphysical idea, merely being a manifestation of the intensity of purpose Liverpool fans bring to their support."

On the contrary, I would suggest that the atmosphere produced by Anfield and The Kop end, has a lot to do with physics. It is the quality of the sound at Anfield which makes it so special, and this is a consequence of the fact that Anfield is so compact and enclosed. A new, more open stadium, designed for architectural appearance rather than quality of sound, will lose the acoustic quality which makes Anfield special.

The quality of sound heard by an audience in a building is largely a function of that building's reverberation time, the time taken for reflected sound to decay to inaudibility. Now, three-quarters of the intensity of a sound will lost in one-tenth of the reverberation time. After this length of time, the human ear and brain is capable of distinguishing a new sound. In a good concert hall, for example, the reverberation time is 2 seconds, and this means that a new sound can be distinguished every 0.2 seconds. That makes for 5 new sounds each second, which is approximately the rate at which notes are performed in many forms of music. In contrast, a good lecture theatre has a reverberation time of 0.5 seconds, given that a human speaker produces new sounds every 0.05 seconds.

The reverberation time for a building is determined by both the size and shape of the building. If the reverberation time is too long for the type of sound being produced, then different sounds become confused. Conversely, if the reverberation time is too short, then the smooth flow of sound is lost. It is also important that the intensity of the sound decays smoothly with time. (Info. on reverberation times from John Barrow, 'The Artful Universe', p227-229)

I can personally attest to the fact that the reverberation time at Anfield is just right. 'You'll never walk alone' seems to reverberate very pleasantly off the roof of the Anfield Road grandstand, and the roof over The Kop. The design of the new stadium needs to pay very careful attention to the physics of acoustics, and moreso than the aesthetic sweep of the grandstands.

Steps - Last thing on my mind

Ok, let's crank the irony and premature nostalgia up to galactic proportions. While Bryan Appleyard is charting the triumphant return of 'Take That', let's also pay tribute to another 1990s pop phenomenon: Steps. Are they due for a re-union as well? Well, Lisa has pointed out that Steps have only been separated for a few years, while 'Take That' have been separated for a decade. Faye claims that "the record companies have been asking us for years. But because we are all busy, it hasn't happened. We meet up regularly and the connection between us is still thriving. I think we will come around to reforming at some stage, but it will happen when everyone has time."

When it happens, I can only hope that Bryan Appleyard will be there to record the event for posterity.

Anyway, here's their video for 'Last thing on my mind', a classic from nine years ago. There's nothing not to like about this video. The girls are looking well, and there's even one of Steps' famous dance routines at the end. Watching it, I almost feel like I'm back in 1998...

Gary Lineker and sarcasm

It emerged today that the FA were upset, not so much by the criticism directed towards the England football team and their manager, Steve McClaren, by the BBC's football pundits, but by Gary Lineker's "sarcastic style". Perhaps they were hoping for a more sophisticated form of satire or parody? A well-written sketch maybe? However, whilst sarcasm is famously derided as the lowest form of humour, it is surely only those on the receiving end of it who feel this way. Sarcasm provides an efficient and effective means of responding to those endowed with both power and foolishness, and this incident exalts sarcasm to one of the highest forms of humour. Anything which could so annoy the FA has to be a good thing.

Springtime

It's the Easter holidays, the neighbour has nurtured an acrid bonfire all day, and the kids are happily playing in the Sun until the pubs open. So, to celebrate, here's a special Springtime competition: see if you can count the number of cherries on Katie Larmour's dress. Partial cherries count, the judge's decision is final, and the winner receives a special gold star.

'Half Life' and CERN

There's something deeply attractive about high-technology, industrial interiors. I noticed it playing the computer game 'Half Life' some years back. It's a world of gantries, walkways, stairs, joists, cooling pipes, trusses, fluorescent lights, ventilation ducting, fans and turbines. And sound, throbbing seismically through the floors and walls. To get a flavour of this in the real-world, visit this link for a number of 360-degree panoramas of the Large Hadron Collider at CERN. Turn the volume up as well.

Coronal mass ejection

Courtesy of John C.Baez's website, this is a NASA animation of a coronal mass ejection from the Sun, and the effect it has upon the Earth's magnetosphere. The ultimate upshot is the occurrence of the aurorae around the Earth's magnetic poles.

AA Gill on 'The Great Global Warming Swindle'

There's a very nice, and typically pithy piece by AA Gill in the Sunday Times today, on the Channel 4 programme, 'The Great Global Warming Swindle':

"It suffered from all the sins it accused the environmental lobby of enjoying: there was selective science and partial interpretation. I suspect that most of us who aren’t scientifically competent enough to make informed judgements, and therefore have to rely on the media, need to find another way of forming an opinion.

"It’s helpful to ask the oldest question in jurisprudence: Cui bono? Who benefits? Who gains from a belief global warming is not man-made or significantly influenced by man? Well, obviously, people who drill oil wells, own power stations or appear on popular motoring programmes all have an interest in global warming being none of our business.

"But don’t for a moment imagine that the bicycle-riding, organic-hedgerow-grazing, self-denying, 40-watt miserablists are in fact selfless crusaders for the common good. Never underestimate the sustaining pleasure in a hair shirt. Just look at George Monbiot, and witness a man who couldn’t be happier about the imminent demise of life as we know it. It’s given him purpose, prestige and celebrity: without global warming he’d be a geography teacher. In the end, if it is the end, I think it’s better to waste as little as possible, to live with a modest care, to mind what you eat and to have a conscience about what your life costs other people’s lives. It may or may not change the weather. It will be better for your soul and your state of mind, and make you a nicer person."

Everything must go!

I'm currently reading 'Every Thing Must Go: Metaphysics Naturalised', by James Ladyman and Don Ross (with David Spurrett and John Collier), in advance of its publication this June. Here I should declare that the authors are advocates of the same philosophy of science to which I adhere, namely 'structural realism'. I take this to mean that, beyond the empirical (detectable and observable) phenomena, the physical world objectively possesses mathematical structures, and these are the structures which physics is converging towards the identification of. Ladyman et al, however, advocate a much more radical version of structural realism, in which they argue that relational structures are the only things which exist; whilst I hold that there are individual relata, which instantiate the structures, Ladyman et al hold that relata themselves are abstractions from relational structures.

It's a fascinating book, and one to which I may return in the coming weeks. At this point, I would just like to share a fascinating observation made by the authors about the structure of money. When the physical tokens of money are considered, they obey 'classical' statistics: if Bob and Alice both have a pound note each, it makes sense to say that something has changed if they exchange pound notes; each pound note has an individual identity. However, if Bob and Alice both have a pound in respective bank accounts, it makes no sense at all to say that something has changed if those quantities are exchanged. And this is exactly the same as the quantum statistics of electrons: if you have two electrons, and one electron is in state A, and one electron is in state B, numbering the particles, and exchanging which particle has which state, does not change the quantum state of the entire system.