Tiger Woods and Lewis Hamilton

"My overriding feeling about Lewis is one of sadness for a young man who has, one way or another, let himself down very badly and done something which will never be erased from the record...The Tiger Woods parallel has always been a frame of reference with Lewis but for different reasons now. You see him everywhere in those big posters at the airport (with dotted white lines and percentage ratings of this or that) or on television. He was so close to imposing his will on all those boring golfers at the top of the leaderboard at the Masters this weekend. I can imagine Lewis watching him and feeling the same sadness that I do. Here is the guy Lewis wanted to be. A worldwide icon and superstar, leading by example and unsullied by ill-deeds, a sponsor's dream and someone who can make an impact - the right impact - almost anywhere he goes and whatever he does." (Edward Gorman, April 13th 2009).

PISN into the stellar wind

Whilst the lighter chemical elements found on the Earth, such as carbon and oxygen, are produced by nuclear fusion inside stars, the heavier elements from the far end of the periodic table are produced in supernovae, the explosive events by which high-mass stars end their lives.

The type of supernova described in most textbooks is a core-collapse supernova, in which the core of the star is transformed into iron by nuclear fusion, and fusion then ceases. The weight of the core is supported by a pressure gradient ultimately created by the energy released from fusion, hence when fusion ceases, the core collapses, triggering a supernova.

However, this type of supernova only occurs to stars in the range 10-140 solar masses. For stars more massive than this, their lives will actually end with a Pair Instability Supernova (PISN). Such an event occurs before the stage at which the fusion of oxygen would otherwise begin in the core. The temperatures in the core of such massive stars are so high at this stage, that the photons produced are effectively high-energy gamma rays. By virtue of their high-energy, these photons will tend to interact with the nuclei in the core by means of a mechanism called electron-positron pair production. The consequence of this is that the radiation pressure in the core plummets, leading to the collapse of the core, and a PISN supernova.

Nature for 3rd December reports that a supernova first detected in 2007, has now been verified as the first ever observational PISN. Such supernovae are difficult to observe because stars lose mass during their lifetime due to radiation-driven stellar winds, and the threshold mass for a PISN supernova increases for stars with a higher proportion of heavy elements. Each generation of stars forms from interstellar matter created by the supernovae of preceding generations, hence each successive generation of stars in a galaxy possesses ever higher proportions of heavy elements. PISN were therefore most frequent in the early universe, when stars had lower fractions of heavy elements, and when stellar winds were weaker. In fact, it is claimed that a single PISN can release more heavy elements than an entire generation of core-collapse supernovae. It is calculated, for example, that the 2007 supernova released 22 solar masses of silicon alone!

Hence, the heavy elements utilised by much of our technology on Earth, may owe their existence to the production of electron-positron pairs from high-energy gamma rays.

How to survive Christmas

That grim spectacle of familial strife and forced collegiate jollity, Christmas is barely more than a couple of weeks away. So how to endure it for another year?

One possible recourse may be Michael Heller's new book, Ultimate Explanations of the Universe. Polish physicist, philosopher and priest, Heller offers a critical guide to all the big philosophical issues in cosmology: eternal universes, cyclic universes, the heath death of the universe, quantum creation out of nothing, inflation, the anthropic principle, cosmological natural selection, theories of everything, and multiverses. Whether Springer Verlag will get around to publishing this book before Christmas, however, is another matter.

Speaking of slipping publication dates naturally brings us to Autocourse 2009-2010, the glossy annual review of the Formula One year. This publication was at its peak in the 1970s and 1980s, when it combined lengthy and informative Grand Prix reports with superb photography. Sadly, in the years since it degenerated into a rather insipid publication, low on information, and padded with the most average of photography. Last year's annual, however, was a significant improvement, with excellent and detailed team-by-team assessments provided by Mark Hughes, and Simon Arron taking over responsibility for the race reports. If the word-counts haven't been hacked again, this should be well worth reading over the fetid period.

The Large Hadron Collider Pop-up book

Those worried about falling education standards, diminishing attention spans, and the debauched culture of modern liberal capitalist democracies, can rest easy in their beds tonight. Two physics books published this year eschew the modern habit of teaching science with the aid of visual gimmicks, and revert to old school methods, gripping the attention of the reader with the clarity of the prose and the innate fascination of the subject matter.

First up is Voyage to the Heart of Matter, which sounds like some dreadful confessional book by Joan Bakewell, but is otherwise known as the Large Hadron Collider Pop-up book.

Actually, this does look like a clever and original piece of work from 'paper engineer' Anton Radevsky. However, whether it is "Perfect for: teenagers who have studied the LHC at school or been lucky enough to visit CERN," is debatable.

Consider the following question: Why does the Large Hadron Collider accelerate two counter-rotating beams around a circle before colliding them into each other? Why not simply accelerate one beam, and smash it into a target which is at rest in the laboratory frame of reference? If the single beam is accelerated to twice the energy of each beam in the double-collider, then surely the energy of the collision will be the same?

If students of physics cannot answer this question, then they haven't grasped the most fundamental and important concept about particle accelerators. The answer to the question above depends upon the fact that the energy for creating new particles comes from the energy of the colliding particles in the centre of mass reference frame.

If one particle is at rest, and another particle is accelerated towards it, then the centre of mass of the joint system moves in the laboratory reference frame. (If the two particles have the same mass, the centre of mass will be the point equidistant between the moving particle and the target particle). Some of the energy of the accelerated particle goes into moving the centre of mass of the joint system, and it is only the remaining energy in the centre of mass reference frame which is available for creating reaction products. In this case, one needs to quadruple the energy of the accelerated particle to double the energy in the centre of mass reference frame.

However, in the case of two counter-rotating particles, the centre of mass remains fixed in the laboratory reference frame, so the laboratory reference frame coincides with the centre of mass reference frame, and the energy in the centre of mass reference frame is simply twice the energy of each particle.

A pop-up book clearly isn't going to communicate this type of crucial understanding, and that's obviously not the intention. It would be nice, however, if this type of book could ultimately inspire some students to develop a more sophisticated understanding in later years.

Next up is The Manga Guide to Physics, in which doe-eyed female teenagers learn about physics via the medium of tennis:

Megumi is an all-star athlete, but she's a failure when it comes to physics class. And she can't concentrate on her tennis matches when she's worried about the questions she missed on the big test! Luckily for her, she befriends Ryota, a patient physics geek who uses real-world examples to help her understand classical mechanics-and improve her tennis game in the process!

Perfect, then, for uncles as well as teenagers.

The Systems Engineering delusion

"Division of labour or economic specialisation is the specialisation of cooperative labour in specific, circumscribed tasks and roles, intended to increase the productivity of labour. Historically the growth of a more and more complex division of labour is closely associated with the growth of total output and trade, the rise of capitalism, and of the complexity of industrialisation processes."(Wikipedia, Division of labour).

Systems Engineering is an attempt to uplift engineering into the information economy. It is predicated on the notion that because complex engineering projects are really 'systems of systems', it is necessary to create a separate discipline, with its own group of practitioners, which specialises in the abstract, top-down analysis of such systems of systems.

As John Morton, Chief Executive of the Engineering and Technology Board, asserted in 2007, "projects are increasingly complex and some climate-change solutions will cross the traditional branches of engineering. If you wanted to extract carbon dioxide from the atmosphere you’d need aerospace, IT, electronical, mechanical and civil engineers." The solution to this complexity, however, does not reside in the creation of "systems engineers who can coordinate big, complex projects like the building of Heathrow Terminal 5," as the subsequent debacle of Terminal 5 demonstrated.

The alternative ethos, the default attitude before the rise of Systems Engineering, and the philosophy which naturally follows from the principle of economic specialisation, is that the productivity and efficiency of an engineering project or company, is maximised by engineers specialising in concrete disciplines, and by those specialist engineers cooperating on complex projects. Such cooperation requires a combination of bottom-up and top-down methods, depending upon the circumstances. There is no need for Systems Engineers, just specialist mechanical engineers, aerodynamic engineers, electronic engineers etc, organised in hierarchies with heads of department, and coordinated by project managers and technical directors, who cooperate with business managers, accountants etc.

The need for complex interaction between different specialists is not a new economic phenomenon, and in engineering it does indeed require project managers and technical directors who can take a multi-disciplinary overview. This, however, is quite distinct from the Systems Engineering ethos, which attempts to legitimise the creation of a separate discipline which specialises in the top-down analysis of engineering projects in terms of requirements, capabilities and stakeholders, abstracted from concrete engineering issues.

The future of the universe

All of the complexity and structure we see in the world around us will ultimately be degraded and eradicated.

Consider first the fate of gravitationally bound systems, such as galaxies and galaxy clusters. Let us first recall some concepts from Newtonian gravity. Because gravitation is an attractive force, the potential energy U of a system of gravitating objects is negative; the kinetic energy K of the system, the energy of motion of the objects, is positive; and the total energy is E = U + K. A gravitating system is said to be bound if the total energy E is negative. In other words, if the magnitude of the potential energy exceeds the magnitude of the kinetic energy, the system is bound. The more negative the total energy, the more tightly bound the system is.

Each gravitating system has associated with it an escape velocity, which is the speed a constituent object must attain if the distance between it and the other objects in the system is to become unbounded. A bound system is such that the average velocity of the objects in the system is less than the escape velocity. However, after the objects in the system have interacted for a period of time, there will be a distribution of velocities, and some will exceed the escape velocity. These objects will thence depart the system, never to return. This evaporation of objects from the system will remove positive kinetic energy from the system, hence the total energy of the system will become more negative, making the system more tightly bound. Nevertheless, the system will continue to evaporate.

Contemporary spiral galaxies are bright and vibrant star cities, evolving through multiple generations of star formation, and possessing an ecological structure in which material is cycled between the population of stars, and the gas and dust of the interstellar medium. Eventually, however, star formation will cease, all the stars in a galaxy will expend their nuclear fuel, and galaxies will be populated by black holes and the dead cinders of stars. These cold, dark galaxies will then evaporate, as Iain Nicolson explains:

"Although close encounters between stars are extremely rare, given sufficient time, many encounters between dead stars will take place. In each encounter, one star will gain energy and the other will lose energy. Even without any encounters of this kind, an orbiting star will gradually lose energy by radiating gravitational waves and so, very slowly, will migrate closer to the centre of its galaxy. Close encounters will accelerate this process. Over extremely long periods of time, most dead stars will evaporate from their host galaxies and the remainder will coalesce into gigantic 'galactic' black holes at their centres. A similar process is likely to happen to clusters and superclusters of galaxies, with dead galaxies merging at their centres to form 'supergalactic' black holes, and others being ejected into intercluster space." (The End of the Universe, 1998 Yearbook of Astronomy, pp220-232).

Smaller bound systems, such as molecules and atoms will also evaporate, but the reason for this is quite subtle. As John C.Baez explains, any system in thermal equilibrium will minimise its so-called free energy, the amount of energy which is available to perform work. The free energy can be defined to be E - TS, where E is the total (internal) energy, T is the temperature of the system, and S is the entropy of the system. The restriction to internal energy here simply means that one ignores the potential energy a system might possess in an external field, and one ignores any bulk energy of motion; internal energy includes the internal potential energy of the system, and its internal kinetic energy. The entropy S of a system can be seen in this context as the amount of unusable energy in the system, per unit of system temperature; hence, multiply the entropy by the temperature, and one obtains the total amount of unusable energy in the system. Subtract the amount of unusable energy from the total energy, and one obtains the free energy.

The free energy of a system E - TS can clearly be reduced either by reducing E, or by increasing TS. As Baez points out, an ionised gas (a so-called plasma) has more energy than a gas made from atoms or molecules of the same substance. When those atoms or molecules form, electromagnetic radiation is released, decreasing the total energy of the matter in the system. However, the atoms or molecules have less entropy than the ionised system. At high temperatures, the free energy is minimised by the high entropy plasma state. However, at lower temperatures, the free energy of a matter system can be minimised by reducing the total internal energy of the system. (Note, however, that although the atomic or molecular state is a lower entropy state for the matter, the total entropy still increases because of the entropy of the electromagnetic radiation released when the atomic or molecular state is formed).

This assumes, however, that the system occupies a fixed volume. If the volume available to the constituents of the system is constantly increasing, as is the case in an expanding universe, then the maximum available entropy S of the system will be constantly increasing, and eventually, even at very low temperatures, the free energy of a gas will be minimised in the ionised, plasma state, the state which maximizes the entropy of the system.

Black holes, of course, are also capable of evaporating into radiation, but only do so if their temperature is lower than that of their surroundings. Crucially, some theorists currently argue that the presence of the dark energy, responsible for the acceleratory expansion of the universe, equips the universe with a minimum temperature. The temperature of a black hole is inversely proportional to its size, hence if sufficiently large black holes form from the merger of smaller black holes (and they would have to be as large as the currently observable universe), then such black holes would never evaporate.

Thus, (neglecting some questions over the fate of protons) the future of the universe is a future in which all galaxies, stars, planets, complex molecules and atoms eventually evaporate, and all that remains will be gravitational radiation, electromagnetic radiation, black holes, and isolated elementary particles.

Lewis Hamilton and instability

The Eurofighter-Typhoon jet aircraft is so unstable, that it cannot be controlled by a pilot alone, and requires the intervention of electronic control systems to prevent it from stalling in flight. Hold that thought in your head as you read the description of Lewis Hamilton's raw driving ability, which McLaren director of engineering, Paddy Lowe, gave to Autosport's Mark Hughes in 2008:

"He's tremendously good at controlling a car in oversteer. We saw that from the first moment he got in our car. We saw the data, and on every entry we could see there was a massive correction on the steering, and our normal drivers would have been bitching like hell that the car was undriveable, yet he didn't even pass comment. So with a driver like that, you're better equipped to push the boundaries to new levels. Speaking generically of that characteristic, a lot of the performance limit of a car is set by stability; if you can't hang on to it, you will have to introduce understeer in that zone. But if you have a driver better able to deal with oversteer in those zones that induce it, then you will have a less-understeery car elsewhere and therefore more total grip over the lap. The great drivers over the years - Senna, Schumacher, Mansell - have all had that ability. Like for like compared to other drivers, they want more front end."

There are two particular concepts in Lowe's analysis which need to be distinguished: corner entry oversteer, and entry instability. To understand Hamilton's unique capabilities, we therefore need to briefly introduce some definitions from stability theory.

If a car (or aircraft) is initially in an equilibrium state, and there is a transitory control input (or external disturbance), a stable vehicle will return towards its initial equilibrium state of its own accord, whilst an unstable vehicle, in the absence of any further control inputs, will diverge even further from the initial state. To be precise, the first condition is sometimes called static stability, and the latter condition is called static instability. Whether a vehicle is stable or not can be speed dependent. For example, a bicycle is stable at higher speeds, but is unstable at low speed, requiring continuous corrective inputs from the rider to remain vertical.

In the case of an F1 car, an initial steering input induces an initial slip-angle in the front tyres, which induces an initial direction change (a rotation about the vertical axis, called a yaw motion). If an F1 car is statically stable, the car will then return towards a state of zero yaw. If an F1 car is statically unstable, an initial steering input would not just induce an initial slip-angle and change of direction, but an ever greater change of direction (in the absence of corrective action from the driver), giving the vehicle a tendency to spin on entry to every corner. In particular, if an initial steering input provokes the car into oversteer, then that oversteer will increase the initial direction-change. Hence, the driver must supply opposite-lock steering corrections to reduce the direction-change. Oversteer and instability are therefore related. To be precise, turn-in oversteer is a statically unstable handling characteristic, albeit one which Lewis Hamilton is clearly capable of dealing with.

There is a further nuance here, however, because even statically stable vehicles can be either dynamically stable or dynamically unstable. After an initial input, the attitude of a dynamically stable vehicle will oscillate with simple harmonic motion of decreasing amplitude about the initial attitude. In contrast, in the case of a dynamically unstable vehicle, whilst its attitude will at first return towards the initial state, it will then oscillate with increasing amplitude about that initial attitude, leading to a loss of control (in the absence of corrective inputs). These two behavioural characteristics are also sometimes dubbed positive stability, and relaxed stability, respectively. The Eurofighter Typhoon possesses dynamic instability (relaxed stability).

If an F1 car was statically stable, but dynamically stable on turn-in, an intial steering input would create an initial direction-change, and the direction-change would then oscillate with decreasing amplitude. If, however, an F1 car was dynamically unstable on entry to a corner, then the direction-change would oscillate with increasing amplitude, (in the absence of corrective action), giving the vehicle a tendency to spin.

Rear-end instability on corner entry is reportedly the handling characteristic which Jenson Button struggles most to deal with, but as his Brawn team-mate, Rubens Barrichello, demonstrated this year, it is a characteristic which different drivers can cope with to different degrees. Perhaps, then, the type of instability exhibited at times by the Brawn in the second half of the 2009 season, was merely the dynamic instability of a statically stable car.

Judging from Paddy Lowe's remarks, one can speculate that not only is Lewis Hamilton able to cope with such dynamic instability on corner entry, but to a degree unique amongst his peers, he is able to supply the corrective inputs necessary to prevent a statically unstable car from spinning on corner entry.

Why did Jenson Button leave Brawn?

On Friday, Eddie Jordan announced to the world that Michael Schumacher will be making a comeback with the Mercedes Formula 1 team. Generally speaking, Eddie Jordan is a reliable source of motorsport information in the same sense that Gillian McKeith is a qualified authority on diet and nutrition. In this case, however, Jordan's prediction makes a lot of sense, for Michael is clearly directionless without the opiate of Formula 1, and Mercedes have conspired to lose their World Champion driver, Jenson Button, to erstwhile partners McLaren.

And here's an interesting thing: Jordan claims that Mercedes's attempts to woo Michael "started with a meeting between Michael, Ross Brawn and Daimler chief executive officer Dieter Zetsche at the Abu Dhabi Grand Prix." This claim was corroborated on Sunday by Willi Weber, latterly Schumacher's manager, who said he was "sure that Schumacher had had talks with Dr Dieter Zetsche, head of Mercedes-Benz and Norbert Haug, who runs the company’s motor-sport division, at the Abu Dhabi Grand Prix."

At Abu Dhabi? Reports that Button could be lured to McLaren had surfaced in the week after he secured the World Championship in Brazil, but still it seemed that an agreement between Button and Brawn/Mercedes was a mere formality. As Ross Brawn commented at the time, "We are working with Jenson to find a balance between what we can afford and what he feels is fair for his status and what he can contribute in the future...You are never 100% but I would say 99% [certain it will happen]."

The possibility of Button switching to McLaren was interpreted as a mutually convenient negotiating ploy: it let Brawn/Mercedes know that Button had another option, and it let McLaren candidate Kimi Raikkonen know that McLaren too had other options. Mercedes motorsport boss Norbert Haug, for one, was rather dismissive of the possibility that Jenson Button and Lewis Hamilton could end up in the same team: "I do understand that people in England are dreaming of an English team with two world champions in the cockpits... However, dreams don't always come true."

By Abu Dhabi, however, Haug and Mercedes were apparently considering the loss of Button as a serious prospect, and began exploring the Schumacher option before Button put pen to paper with McLaren.

Both Mercedes and McLaren now claim that money was not an issue, that Mercedes offered Button the £8 million a year salary he was seeking, and that McLaren ultimately granted Jenson a deal worth less than Mercedes were offering. This, however, is not the point. Whilst Mercedes's final offer matched Button's salary requirements, the initial deal which Brawn/Mercedes offered to Jenson was only £4 million. This constituted little advance on the reduced salary which Jenson had voluntarily accepted to keep the team afloat when Honda pulled out at the end of 2008, and Jenson probably perceived this as something of a slight. By the time that Jenson was escorted on a tour of the Sir Norman Foster-designed McLaren Technology Centre (MTC) at Woking, the damage may already have been done.

To understand the effect this may have had on Jenson, it's worth recalling the words of Ron Dennis, speaking to Nigel Roebuck in late 2001 (Autosport, December 20-27, p23) before the opening of the MTC:

We were looking for perfection, so we didn't want [MTC] to look out over any buildings. When people are working there, all they'll see out of the windows is fields and trees...I believe that good technical resources attract the best people like a magnet...OK, they want money - and money becomes like a rate card...You measure yourself in financial terms - yes, it affects your lifestyle, but primarily it's a reflection of how good or bad you are. The best people get the most money - that should just be common sense. And once you've satisfied that desire, you've got to give them the best facilities.

So perhaps, then, the picture is as follows: Brawn/Mercedes made an offer which undervalued Button's services, at which point Jenson's management team made contact with McLaren to develop some negotiating leverage; in response, Brawn/Mercedes tried to cover the possibility of losing their new World Champion by developing an interest in Michael Schumacher; already offended by the comparatively low nature of the salary on offer, Button possibly became aware of Mercedes's apparent attempt to seduce Schumacher out of retirement, and decided to take the McLaren offer seriously; Jenson's eyes were then opened by the yin and the yang of the McLaren Technology Centre, and he reciprocated the interest of his new suitor, irrespective of salary.

Can Jenson beat Lewis?

It seems to be a week for unusual and inexplicable combinations. Erstwhile Toyota F1 driver Jarno Trulli revealed at the weekend that he was seriously considering an eventual move to NASCAR, the American stock-car racing series. On the face of it, this would be as appropriate as Brian Sewell playing centre-forward for Caledonian Thistle.

Jarno, of course, was so indignant at being hung out to dry by Adrian Sutil in the Brazilian Grand Prix, that he turned up at the next race in Abu Dhabi with a portfolio of photographs and video evidence to prosecute his case. Sadly, however, the driving tactics in NASCAR hardly constitute the Queensberry Rules either...

This is completely overshadowed, however, by Jenson Button's apparently counter-intuitive decision to join Lewis Hamilton at McLaren next year. Many pundits have advised Jenson against this because McLaren appears to be very much Lewis's team, and many have predicted that Lewis would blow Jenson away if the two were partnered in the same car.

There is, however, at least one factor in Jenson's favour. Next year's cars will have narrower front tyres, and the presence of larger fuel tanks will shift the centre of mass, and therefore the centre of aerodynamic pressure, further towards the rear of the car. This is potentially very much to the favour of Jenson, and to the detriment of Lewis. A centre of pressure further towards the rear potentially alleviates the possibility of rear instability under braking, a handling trait which Jenson struggles to deal with. Furthermore, Lewis notoriously favours a car with a strong front-end, and the narrowing of the front tyres and the shift in the centre of aerodynamic pressure will both contribute towards making next year's cars more liable to understeer. Perhaps Jenson, then, fancies his chances against Lewis...

The primary solecism of quantum theory

Last night, the BBC's popular science series, Horizon, once again featured the popular comedian Alan Davies, in a programme entitled How long is a piece of string? Like virtually every other popular science book or programme, it is also reiterated the following interpretation of quantum theory:

A particle can be in two different places, A & B, at the same time.

This is a claim repeated not just by many science journalists and popularisers, but also by many working physicists, yet it is completely wrong. Instead, the weirdness of quantum theory arises from the fact that either-or statements of the following form,

Either particle x is at position A or particle x is at position B,

can be true, even though quantum theory doesn't represent either of the constituent disjuncts to be true:

Particle x is at position A.

Particle x is at position B.

Thus, a disjunction can be true in quantum theory without either of the disjuncts being true. In technical terms, the logic of quantum theory is said to be non-distributive. This is the problem which any successful interpretation of quantum theory must deal with, and, in particular, this is why one of the possible approaches is the so-called hidden variables interpretation, which claims that quantum theory provides an incomplete specification of the actual state of a physical system.

For an excellent summary of the issues involved, one could do worse than this excellent review from Oxford philosopher of physics, David Wallace: The quantum measurement problem: state of play.

Paradoxes, however, are good press, and physicists are trying to sell their products to an increasingly ill-educated public, so don't expect the solecisms to abate.

Shell V-power and journalism

Being not disinterested in the world of motoring journalism, I was intrigued the other day to find what, at first sight, appeared to be a competition for aspiring journalists, jointly organised by Shell and Auto Express magazine.*

Sounds good, I thought.

But how, exactly, would the applicants demonstrate their journalistic flair and investigative powers to the competition judges? Well, here's how:

Please now share your thoughts in a written statement of 75 words or fewer in response to the question: "What do you think about Shell V-Power and the difference it makes to you and your car?"

What I like about this is the brazen assumption that there really is no difference at all between a journalist and a PR or press officer. Personally speaking, I was hoping to sell my soul after 5 years of fruitless struggle in journalism, not cave-in at the very outset.

Still, have to be in it to win it, I suppose, so here goes:

As the latest premium brand of fuel from the type of company which Robert Mugabe refuses to deal with on ethical grounds, Shell V-power is designed to fool affluent and the poorly-informed Western motorists, that a higher octane 'quality' will improve power, irrespective of an engine's compression ratio. Manufactured from the pituitary glands of Ugandan infants, and blended with the tears of Filipino child prostitutes, Shell V-power is now able to scrub CO2 from the atmosphere, and is increasingly used as a cure for syphilis and pancreatic cancer.

I look forward to my trip to Shell Global Solutions in Thornton, Cheshire.

*Many thanks to Patrick's Motorsports Ramblings for this link.