Spontaneous symmetry breaking in F1

Team-mates crashing into each other; team-management revealing a hitherto covert favouritism for one of their drivers; and a Grand Prix winner who appears indifferent to the rituals of victory, nurturing a belief that he was tricked by his team-mate: yes, Sunday's Turkish Grand Prix was a proper race.

Both Red Bull and McLaren purport to provide their drivers with equality of opportunity, but this intra-team driver symmetry will always be broken under racing conditions, for equality of outcome is neither possible, nor desirable. In the case of the Turkish Grand Prix, the root cause of the symmetry-breaking was the 2010 sporting regulations, which prohibit refuelling during a race. As Mark Hughes explains, filling up with 10kg less fuel gives a lap-time benefit of around 0.33s. From the evidence of Sunday's race, the top teams are therefore trimming their fuel loads to the absolute minimum, and giving themselves very little margin for error.

Hence, fuel consumption was an issue for both Red Bull and McLaren. It was this fact which created the opportunity for a momentary performance disparity between Webber and Vettel, and a similar disparity between Hamilton and Button a few laps later.

Whilst Hamilton and Webber fought tooth-and-nail in the first stint, Vettel and Button were able to watch from a convenient distance, staying within range, but conserving their brakes and fuel. Thus, when Mark Webber was forced to turn his engine settings down at mid-race, Sebastian Vettel was able to continue running his at a higher level for three vital laps, taking 0.3 secs out of Webber on two consecutive laps, and then using his superior power to catch Webber's slipstream on the run to Turn 12.

It is possible that there was no team favouritism here, for Vettel may genuinely have been able to conserve his fuel in the first part of the race, and the power discrepancy between the drivers at this point may be attributable to the differing circumstances they faced in the race. However, there can be no doubt that the ensuing accident was caused by Sebastian Vettel. Webber was perfectly within his rights to squeeze his team-mate onto the dirty part of the track, and Vettel was perfectly within his rights to go for the gap. At this point, however, team-principal Christian Horner could reportedly be seen mouthing "Move! move!" on the pitwall. Given that Webber was squeezing Vettel, rather than vice-versa, this can only be interpreted as an expostulation directed towards Webber.

Horner's bias became rather more overt after the race, when he argued that the principal cause of the accident had been the fact that [Webber] hadn't given Vettel sufficient room. Both Horner and Helmut Marko, (Red Bull owner Dietrich Mateschitz's representative within the team), voiced the opinion afterwards that Vettel needed to pass Webber at this stage, otherwise Hamilton would have passed Vettel. Although Vettel himself had only another lap available at the higher engine setting, it seems that the Red Bull team-management believed that he offered them their best chance of victory on this occasion.

Circumstances, then, have conspired to expose and amplify the Red Bull team's underlying favouritism towards Sebastian Vettel. It is difficult to imagine that Mark Webber will wish to remain with the team in these circumstances, hence the individual who suffers most from the collision between the Red Bull cars may ultimately be Felipe Massa...

Meanwhile, over at McLaren, Lewis Hamilton may feel that he can no longer trust his team-mate. In this respect, there was an interesting tell-tale conversation between Hamilton, Button and Webber, caught by the TV cameras, just before the post-race podium ceremony. Webber briefly recounted his accident with Vettel, and when Hamilton responded that "Yeah, he did the same to me," Button jumped to the conclusion that Lewis was referring to their own intra-team battle. "All they told me was..." Button immediately began to protest, before Hamilton interjected "No, no, no," and explained that he was complaining about Vettel's behaviour when Lewis attempted to overtake the Red Bull. This exchange suggests that Button felt he had done something about which Lewis could be expected to complain, and duly had his defence prepared.

So what was the problem? Well, Button it seems had been saving fuel from lap 20, and while Lewis took the fight to the Red Bulls, thereby triggering the very collision which put the McLarens first and second, Jenson had been able to sit back, watching it unfold, ready to pounce. After the Red Bulls had taken themselves out, McLaren told both drivers to save fuel, and according to Chief Engineer Tim Goss, set a 1m31s lap-time target for both of them. It's possible that Lewis interpreted this to be an instruction that the McLaren drivers should stop racing, and coast to the finish. If so, then it's equally clear that Button didn't share this interpretation. In fact, Jenson also claimed afterwards that he had not received a target lap-time instruction from the team.

When Jenson overtook Lewis, he came from a long way back, and didn't even need to use the full benefit of Lewis's slipstream as he zoomed down the outside. It's difficult to reach a conclusion other than that Button had a higher engine setting at this moment in time. Jenson presumably thought that he was entitled to do this by virtue of the fact that he had been saving fuel from an earlier point in the race. Lewis, therefore, was "surprised" to see Jenson come past him, and clearly thought that Button had tried to trick him out of victory.

Perhaps McLaren will be able to smooth over this mis-understanding in the days to come, and one duly expects some form of words to be issued to that effect. Nevertheless, in Lewis's mind, it's likely that an irreversible switch has been thrown. For both Red Bull and McLaren in 2010, things will never be the same again.

The Earwax Guy

It's a sunny Saturday morning in Krakow, and escorted by the delightful Ola, myself, James Ladyman, and Sir Roger Penrose, are climbing into the taxi which will take us to the airport, where we will catch an EasyJet flight back home to Gatwick.

Sir Roger climbs into the front, and I clamber into the middle of the back seat alongside James. Ola is about to fill the remaining spot, when, spying my longer legs, she offers to occupy the middle berth instead. "Er,...Ok," I say. At which point, with the back door still open, and Ola standing on the pavement, the taxi driver takes off.

Ola is desperately running alongside the accelerating car, and momentarily seems to contemplate making a Hollywood-style dive for the back seat, before deciding better of it. Despite the urgent "Whoa! Stop! Stop!" exclamations from Ola and the other backseat passengers, the taxi driver carries on for some yards, before his finely-tuned sense of spatial awareness eventually enables him to recognize that he's left one of his passengers behind.

It was a suitably entertaining end to a remarkable week.

The 'Road to Reality' conference was hosted by the Stefan Banach Institute of Mathematics on the Monday and Tuesday in Warsaw, and the Copernicus Center in Krakow on the Thursday and Friday. The hospitality throughout was superb, with the quality of the food and wine in Krakow (all gratis) particularly memorable. Roger Penrose himself is a fabulous ambassador for science. He spoke to large audiences of students and members of the public in Warsaw and Krakow, who were hanging on his every word, totally captivated for 90 minutes, as he used his multicoloured hand-drawn slides to explain black holes, the big bang, and his cyclic cosmology theory. He was totally accessible, friendly, patient and good-humoured with everyone.

The week began, however, in a less promising fashion...

Monday evening in Warsaw. It's been raining all day, and I can't hear out of my left ear. I wander out of my accommodation on the first floor of the Stefan Banach Mathematical Institute, and splash through the puddles to a fish-and-chip shop on the other side of the pl. Konstytucji, which James has spotted earlier in the day. As I wait inside for my chips to be cooked, the young English-speaking Pole behind the counter engages me in conversation, and I discover that he has recently spent some time in the UK, living in Brighton to be precise.

"That's an exciting place to live isn't it?" I suggest. "Oh yes," he confirms, "LOTS of pussy." I conclude that he has a fine grasp of colloquial English, take my chips, and return to the Institute.

The problem with my hearing arises from the fact that on my first night in Warsaw, I decided to use some ear plugs to block out the mysterious nocturnal thumping noise coming from the plumbing. Unfortunately, this conspired to compress the wax in my left ear, and on Monday I have great difficulty hearing what people are saying to me. I spend much of Monday morning trying to communicate that I need eardrops, and am guided through the rain-sodden streets of Warsaw to an Apteka (chemist), where it duly transpires that they have nothing useful at all. Back in the Institute, an incredibly kind lady from the admin team helps me to track down a brand of eardrops available in Poland, and gets on a bus to purchase them for me.

Sadly, the drops are ineffective, and on the Tuesday morning I agree that I need to see a doctor. A conference delegate generously steps into the fray, and drives me through the streets of Warsaw to see his own doctor, a lady who apparently serviced the communist regime when they were entrenched in power. En route, I gaze up at one stage to see an alarming image of Robert Kubica grinning back at me, with a can of N-gine in his hand. "Polecam (recommended by) Robert Kubica," claims the billboard poster.

The lady doctor unblocks my auditory system with a variety of hoses and scarily sharp objects that she sticks into my ear, and then tests my hearing by slapping a tuning fork on her knee, before holding the reverberating object in various positions around my head. An American mathematician at the conference, C. Denson Hill, later declares that I will hereafter be remembered to him as 'the earwax guy'!

The ontological argument for Formula 1

Mark Hughes writes a fascinating piece in this week's Autosport which argues that Formula 1, defined as the pinnacle of motorsport, must necessarily exist:

"If the sport exists at all, then by definition F1 exists - and we happen since 1947 to have called it F1. If the sport...is all about going as fast as possible around a road-type circuit, then there has to be an ultimate form of it. F1 (or Grand Prix racing) thus birthed itself with the very inception of the sport...As soon as the very idea of motor racing was conceived, so there had to be an ultimate expression of it. Like a quantum quark, it magic-ed itself into existence and we eventually labelled it F1."

There appear to be two different strands to this argument. One is a reification argument: the idea of the pinnacle of motorsport, once conceived, automatically gave birth to its physical realisation. The other is formally analogous to the ontological argument for the existence of God: F1 is defined to be the pinnacle of motorsport; something cannot be the pinnacle of a profession without being realised; therefore F1 must exist. The ontological argument for the existence of God simply substitutes 'God' in the place of 'F1', defines God as the most perfect entity, asserts that something cannot be perfect without being realised, and concludes that God must exist.

The definition of F1 and God share the concept of being the maximal entity in their respective domains. Both ontological arguments attempt to derive existence from maximality, and both arguments are vulnerable to Kant's dictum that 'existence is not a predicate', and Sartre's maxim that 'existence precedes essence'. In the case of F1, however, the argument is not that F1 exists by unconditional logical necessity, but that given the existence of motorsport, the pinnacle of motorsport also necessarily exists.

Mark's argument is an argument for both the existence and uniqueness of F1, so let us now consider the uniqueness question. The collection of different motorsport formulae and categories possesses the mathematical structure of a poset (a partially ordered set). A linearly ordered set (typically called a totally ordered set by mathematicians) can be thought of as a single chain of entities, in which each element is either greater than or less than any other. In contrast, in a poset, there is a criss-crossing lattice of chains. Some elements are greater than or less than others, but other pairs are effectively parallel to each other and deemed to be non-comparable, (hence the set is only partially ordered). Thus, in motorsport terms, Formula Ford, F3, GP2 and F1, all lie on a linear chain, but rallying, Indycar racing, sportscar racing, and touring cars, are arguably neither greater than or less than each other.

Now, one thing about a poset, which potentially undermines Mark's argument, is that it can possess an arbitrary number of maximal (or minimal) elements. A maximal element in a poset is simply one which has no greater elements; there is no need for a maximal element to be greater than every element in the poset. And arguably, the presence of multiple maximal elements can be seen at times in various different professions. For example, CART and Indy League racing were, in the late 1990s at least, premier motorsport categories of equal prestige in the USA. The existence of multiple pinnacles is clearly a logical possibility, and one which is realised in the real world. However, the example of CART and Indy League racing is an interesting case in point, because the two series eventually merged, and there is good reason to postulate that the existence of multiple pinnacles is an unstable state of affairs in the real world. When multiple pinnacles exist, they do so temporarily, and ultimately collapse into one. Thus, we may formulate the following hypothesis:

There is a universal psycho-socio-economic process, operating in all human professions, which renders the existence of multiple pinnacles an unstable state of affairs.

Thus, the creation of a profession doesn't itself logically create a unique pinnacle, but there are psycho-socio-economic processes which, over time, achieve exactly that.

The art of the Formula 1 racecar

The notion that Formula One cars can attain the status of artistic creations is hardly a novel one. If nothing else, John Barnard's 1990 Ferrari 641 has been on display in New York's Museum of Modern Art for some years now.

Nevertheless, photographer James Mann and journalist Stuart Codling's recent Art of the Formula 1 RaceCar is an interesting and distinctive piece of work. Mann has photographed eighteen Formula One cars in professional photographic studios against a black background, and the results are gorgeous.

Readers, however, may be slightly puzzled by some of the cars chosen, and one suspects that Mann and Codling were constrained by which cars were available, and at what cost. For example, the Ferrari 641 is missing, Adrian Newey's Leyton House CG901 is substituted in place of his wonderful March 881, and there's no place for either the Lotus 79 or the Brabham BT52.

The photos are accompanied by decent profiles from Codling, and a rather terse set of appraisals from Gordon Murray. In fact, Codling's introduction to the book is really superb, but there are also some disappointing factual inaccuracies. For example, on p108 it is suggested that Jody Scheckter was racing the Tyrrell P34 in 1976 at Spa-Francorchamps. Whilst the notion of Lauda, Hunt and Scheckter hammering flat-out through the Masta kink, is more than diverting, it is one which must sadly be relegated to universes parallel to our own.

The fact that Mann got so many historic F1 cars into photographic studios, makes one wonder if they could also be whisked into full-scale wind tunnels, and modelled in CFD, to understand exactly what their aerodynamic properties were.

For example, take the six-wheeled Tyrrell P34: the idea here was to reduce the lift and turbulence generated by the front wheels of a conventional car. However, it remains unknown to what extent this was actually achieved. Could the design have been more fully exploited with modern knowledge of front-wing aerodynamics? The nose of the P34 wasn't shaped as an inverted wing section at all; did it function as a ground-effect splitter, or was it exclusively designed to reduce drag?

Alternatively, what was the airflow regime around the front of the Lotus 72? Recall that Maurice Phillippe's iconic design had a very wide, wedge-shaped nose, with wing section spoilers protruding on either side. What was the interaction here between the front wing and the turbulent airflow generated by the tyres? Did the wedge-shape of the Lotus 72 provide any ground effect downforce at the leading edge of the nose?

So, there's plenty of opportunity here for further research, and one day, perhaps, an aesthetic appreciation of historic F1 cars will be paired with a sophisticated, retrospective aerodynamic assessment.

Marlboro Country

"Subliminal advertising is at the laughable end of the scale. This is based on an experiment in a cinema that seemed to show that frames flashed on the screen, so fleetingly that they could not consciously be seen, would make people buy more Coca-Cola and popcorn. For years, it was blithely accepted as an established truth that such subliminal ads worked. In fact, the experiment had never been done and all attempts to repeat it failed. It just doesn't work." Bryan Appleyard.

"To commemorate its 50th anniversary, the Vicary experiment was replicated at the International Branding Conference, MARKA2007...The 1,400 delegates watched the opening credits of the movie used in the original experiment, PICNIC into which subliminal messages had been placed at six second intervals. Then, the delegates were asked to choose between two fictitious brands. One brand 'Delta' had been suggested using the subliminal messages and the other 'Theta' had not. When choosing between the two brands, 81% of the audience chose 'Delta' in preference to 'Theta'." Hypnosis in advertising

Just been down the newsagents, and came back with a packet of Marlboro. Which is odd, because I only went to buy a copy of The Sunday Times. And I don't smoke.

Laser fusion and the internal combustion engine

As Formula One continues to deliberate upon the nature of the new engine formula due to commence in 2013, an international collaboration involving nuclear, plasma and laser physicists, is considering a petrol/diesel engine model of commercial fusion power.

In the interests of efficiency, Formula One is moving towards turbocharged, KERS-assisted, petrol engines, with the added possibility of direct injection to boot. However, whilst the motor industry debates the relative merits of petrol and diesel engines, no-one has yet seriously raised the dreaded prospect of introducing the D-word into Formula One.

Strangely, diesel engines and petrol engines have direct analogues in the world of laser-driven fusion. In the latter, a pellet of deuterium-tritium (D-T) fuel is compressed in a target chamber to very high pressures by blasting the outer surface with a collection of lasers. The outer surface of the pellet is transformed into a plasma, and it is the plasma pressure which compresses the D-T fuel to the temperature at which nuclear fusion can be triggered.

As explained by Mike Dunne, of the Rutherford Appleton Laboratory, in the freely-downloadable May 2010 issue of Physics World, once the D-T fuel is at the necessary high density, the fusion can either be ignited by a separate laser, which thereby functions as a sparkplug, or it can be triggered by the temperatures produced by the compression alone (p32). The former case therefore corresponds to a petrol engine model, whilst the latter corresponds to a diesel engine model.

Exploiting such laser-driven fusion as a source of commercial power, requires the design of a fuel cycle, in which multiple D-T pellets can be injected into the target chamber, ignited, and removed, every second. Dunne claims that "the high-repetition-rate technology used in the welding and machining industry" could be used to this effect.

Possible methods of improving the efficiency of the combustion in an internal combustion engine include the use of laser sparkplugs, and conversely, perhaps the power-generating capacity of laser fusion could be improved by developing some analogue of the direct injection systems used on certain modern internal combustion engines. An interesting reciprocity.