Monday, December 27, 2010

Identity criteria for Formula 1 teams

The ongoing controversy over the right to use the Lotus brand-name in Formula 1, highlights some subtle questions concerning the identity criteria for a Formula 1 team.

Companies, like people, are able to remain the same entity, despite changing substantially over time. Whilst philosophical discussions of personal identity revolve around bodily and psychological continuity, the identity of a company seems to hinge upon a combination of location, key personnel, name and ownership.

It seems fairly uncontroversial to propose that continuity of location, personnel, name and ownership, are jointly sufficient to preserve the identity of a Formula 1 team. Conversely, if all four of these conditions are violated, then it seems impossible to justify any claim for the preservation of identity; a team located in a different place, employing different people, bearing a different name, and possessing different ownership, must simply be a different team. Equally, however, none of these four conditions is individually necessary to preserve identity. Let us look at some examples to demonstrate this.

For a start, continuity of name and ownership is unnecessary to preserve identity, as clearly illustrated by the case of the 'Brackley-based team', which has, within the past decade, evolved from BAR into Honda, from Honda into Brawn, and from Brawn into Mercedes. The successive changes of name and ownership have not prevented this being considered to be a continuation of the same team. Hence, continuity of location and personnel alone are sufficient to preserve the identity of a team.

Continuity of location is also unnecessary to preserve identity, as exemplified by the Williams team, which in its current location at Grove is still clearly a continuation of the same team which was once located at Didcot. This case proves that continuity of personnel, name and ownership, is jointly sufficient to preserve the identity of a team.

The history of McLaren, meanwhile, provides another interesting case study. The merger between McLaren and Project 4 in the early 1980s effectively resulted in a change of ownership (from Teddy Mayer and Tyler Alexander to Ron Dennis and partners), and a change of location from Colnbrook to Woking. In this case, there was only continuity of name and personnel, yet it seems to be accepted that McLaren in the 1980s was a continuation of McLaren in the 1970s. It appears, then, that continuity of name and personnel alone are also sufficient to preserve the identity of a team.

Another interesting case is provided by the creation of the Arrows team from the key personnel within the Shadow team. (In fact, this is almost an example of fission, exactly the type of phenomenon which poses such difficulties in philosophical discussions of personal identity). On the basis of continuity of location, name and ownership, the Shadow team remained identifiable as the same team which existed prior to the departure of Alan Rees, Jackie Oliver, Dave Wass and Tony Southgate, even if the team had been fatally weakened in the process.

Abstracting from such cases, it might be proposed that the identity of a Formula 1 team is preserved if and only if the following criterion is satisfied:

There is continuity of: Either (location and personnel) Or (personnel and name) Or (location, name and ownership).

Irrespective of these complications, the preservation of identity seems to be impossible without some form of continuity. Setting up a new team with the same name as a famous, but defunct team, isn't sufficient to ensure preservation of identity. As the case of the Lotus name in F1 demonstrates, breaking all forms of continuity opens up the possibility of multiple entities, each claiming to be the modern representative of a famous historical team. And if there's one thing which the criteria for identitiy must ensure, it is the preservation of initial uniqueness.

Monday, December 20, 2010

Vorticity and helicity

There seem to be at least two types of vortex relevant to racing car aerodynamics: transverse vortices and longitudinal vortices. The former spin along axes which lie orthogonal to the direction of travel (as seen in the diagram on the left here), whilst the latter spin along axes parallel to the direction of travel.

Whilst transverse vortices just create drag, a longitudinal vortex can be rather useful, because the centre of such a vortex is a high velocity, low pressure region, which can be used to accelerate or direct airflow in certain directions. The Renault F1 team, for example, used a V-shaped cut in the front wing at Monza this year to create a vortex which accelerated the airflow under the car.

At first sight, there seems to be a particularly simple way to mathematically characterise the distinction between transverse and longitudinal vortices.
Given the fluid flow velocity vector field u, the vorticity vector field ω is the curl of the velocity field:

Basically, the vorticity vector points along the axis of spin, and the magnitude of the vorticity vector encodes the rate of spin. Given the vorticity vector field, mathematicians introduce several useful additional concepts: vortex lines, vortex sheets and vortex tubes. Technically speaking, vortex lines are the integral curves of the vorticity vector field; this simply means that vortex lines are curves which are tangent to the vorticity field at each point. Vortex sheets, meanwhile, are surfaces which are tangent to the vorticity field at all points. Vortex tubes are three-dimensional regions obtained by taking a 2-dimensional area orthogonal to the vorticity field, and then taking all the vortex lines through that area.

Now, the helicity h is simply defined as the inner product of the velocity and the vorticity:

h = u • ω

Thus, if the streamlines of the fluid are orthogonal to the vorticity, then the helicity is zero. This is the case with a tranverse vortex. In the case of a longitudinal vortex, the helicity is non-zero, and measures how tightly the streamlines corkscrew along a vortex tube. In fact, the helicity of a vortex tube can be defined by integrating the helicity field:

It is a theorem of inviscid fluid mechanics that the helicity of a vortex tube is preserved over time. However, if a vortex tube is stretched, (as I presume it must be when it is sucked underneath the floor of a racing car), then its cross-sectional area decreases, and the magnitude of the vorticity ω increases, lowering the pressure at the centre of the vortex.

One might therefore conclude that the stretching of longitudinal vortex tubes should be a principal objective of all racing car aerodynamicists.

Sunday, December 19, 2010

King of the galaxy

"Bernie, who is the king of the world – more than the world, he is king of the galaxy." Luca di Montezemolo.

I knew it!

Thursday, December 16, 2010

The Minotaur and the Monopole

In a moonlit glade of an enchanted wood, the Minotaur of Sirius-A sat and mourned the loss of his beloved Medusa, caustic tears burning a crater in the mossy ground betwixt his feet. The last survivor of a dying species, it was centuries since Daedalus-A's labyrinth had crumbled to ruin, and millennia since the Minotaur had feasted on the final consignment of virgins from Athens-A.

Such was the solitary intensity of his grief, the Minotaur resolved to be re-united with his partner by any means possible, and began furiously researching cosmology in the deserted library of Athens-A. There, he discovered that a universe just like our own - and therefore containing his dearest, alive again - could be created, without the need for an initial singularity, if one could only find a magnetic monopole.

The Minotaur, however, had no idea where to begin searching for such an item, and immediately lapsed into a pit of mythological depression, hurling himself out of the colonnaded library, and back to his friendless forest dell. There he lay forlorn in supine agony, and many days passed until, by providence, he descried above a lofty flock of migrating birds, and pondered anew the basis for such navigational feats. Thus it was that the Minotaur commenced a five-year effort, harvesting the magnetite from a billion birds, slowly implanting the precious ferrimagnetic mineral within his bovine skull.

Eventually, the harvest complete, the Minotaur tuned his magnetoreception to the faint magnetic fields which permeate the galaxy, and embarked on a thousand-year odyssey, pursuing hidden Teslatic paths between sparkling spiral arms and gigantic dust lanes, seeking hints and traces of the fabled monopole.

Finally, the grieving beast alighted upon a dark, brooding planet where magnetic field lines converged in densely-packed radial spokes. There, in a dark sulphuric cavern, between rivers of roiling magma, the Minotaur cleaved his monopole from an obsidian peninsula.

Summoning forth his cumulative, concentrated sorrow, he crushed the pulsing topological defect within his hand, compressing it until a black hole was formed. At once, a Reissner-Nordstrom space-time effloresced within, and a bubble universe blossomed with false vacuum energy inside the double black hole horizons.

The Minotaur was instantly sucked inside his own creation, his mass-energy converted to surface tension in the bubble wall. The child universe expanded and cooled, stars and galaxies formed, planets coalesced, life evolved, civilisations waxed and waned, and after billions of years, in a moonlit glade of an enchanted wood, the Minotaur of Sirius-A sat and mourned the loss of his beloved Medusa, caustic tears burning a crater in the mossy ground betwixt his feet.

Saturday, December 11, 2010

F1 and the Wisdom of Crowds

The FIA's World Motorsport Council (WMSC) met on Friday this week, and, as anticipated, repealed the ban on team orders in F1. Notably, however, the following qualification was issued: "Teams will be reminded that any actions liable to bring the sport into disrepute are dealt with under Article 151c of the International Sporting Code and any other relevant provisions."

Philosophically, this is interesting, because whilst the FIA are permitting the teams to exercise discretion over the application of team orders, they're also warning them that the type of flagrant manipulation which precipitated the introduction of the original legislation in 2002, will be punished for bringing the sport into disrepute.

If we recall, Ferrari's decision to manoeuvre Michael Schumacher past Rubens Barrichello on the last lap of the 2002 Austrian Grand Prix, resulted in the drivers being loudly booed by the spectators as they ascended the podium, and in the team management being roundly condemned by the specialist and non-specialist media. Both the spectators and the media constitute a type of crowd, and their reaction to Austria 2002 was clearly damaging to the reputation of F1. This, then, was an example of the Wisdom of Crowds, the capability, under certain conditions, for collections of non-experts to make decisions, or pass judgements, of greater or equal accuracy than those which could be made by individuals.

Friday's statement from the WMSC partially transfers judgement in cases of team orders to the wisdom of such crowds. Trying to capture in legislation the exact conditions under which team orders should be punished, is way too complex, so instead the FIA are, at least partially, ceding judgement to the collective wisdom of paying spectators, television viewers, and the media.

Now, this is clearly still an arrangement open to abuse, for it is the FIA who ultimately have to decide whether the reaction of the spectators and the media is sufficient to entail a breach of Article 151c. This collapses the wisdom of crowds down to the judgement of a smaller group of individuals, whose decisions can be skewed by short-term vested interests. Moreover, Article 151c also entitles the FIA to punish actions which are merely liable to bring the sport into disrepute. Hence, any action which could be seen as setting a precedent, or instigating a trend, that might ultimately bring the sport into disrepute, could be seen to fall under the aegis of this regulation.

Whilst a repetition of Austria 2002 would unambiguously bring the sport into disrepute, and clearly render a team subject to punishment, the key question is whether a repetition of Germany 2010 would also bring the sport into disrepute. There was certainly a media outcry after Alonso was escorted past Massa in this year's race, but a large component of that reaction was attributable to the fact that Ferrari had breached a regulation banning team orders. Subtract that element of things, and Germany 2010 reduces to a borderline case.

One final point. Many commentators and analysts point out that team orders are intrinsic to the history of F1, and that F1 is a team sport. That's certainly true, but in the modern age, F1 is a commercial brand which is sold to the public as a contest between drivers, not a contest between teams. If numerous spectators and viewers are attracted to the sport on that basis, only to be disabused of their delusions mid-race, then such casual viewers have every right to complain that they haven't received the product which was sold to them.

Tuesday, December 07, 2010

2010 Season Review

It was the greatest year in the history of modern bacterial Formula 1. A five-way battle for the championship developed between Mark Meningococcus, Sebastien Clostridium, Jenson Streptococcus, Lewis Straphylococcus, and Fernando Escherichia-coli. Powered by the double-flagella motors, permitted by a loophole in the genetic code, the drivers went protein-to-protein over 19 races hosted in water, soil, rock, plant and animal, their micrometer-sized membranes specifically adapted to the low Reynolds number hydrodynamic conditions.

Experienced and well-liked prokaryote, Mark Meningococcus led for most of the year, but suffered a ribosome-damaging antibiotic attack with four races to go, and crashed out of the Colonic Grand Prix. Benefitting from the full attention of the Escherichia genus, Fernando E-Coli assumed the lead of the championship going into the final couple of races. There was, however, to be a further twist in the flagellum, for Adrian Lactococcus, resident design genius at Clostridium, had noted that photon pressure can be used to generate lift and downforce in micrometer-sized objects. With a photonic wing installed, Sebastien Clostridium dominated the final Grands Prix, and snatched the championship from under the nose of Fernando. The little Clostridium team had beaten the might of E-coli!

Thursday, December 02, 2010

Is space both finite and infinite?

This is an interesting diagram, for at least a couple of reasons. Firstly, as the author, cosmologist Anthony Aguirre explains in his paper Eternal Inflation, past and future, "it may well represent the current best bet for how the observable universe actually originated." Secondly, it demonstrates nicely how, according to general relativistic cosmology, the observable universe could be both spatially infinite and spatially finite.

Aguirre's diagram represents the creation of our observable universe according to a certain scenario proposed by inflationary cosmology, so let's begin by recapping the basic idea of the latter. Inflation suggests that there is a scalar field, the 'inflaton', whose 'equation of state' is such that a positive energy density corresponds to a negative pressure. In general relativity, a matter field with negative pressure generates a repulsive gravitational effect. Inflationary cosmology suggests that at some time in the early universe, the energy density of the universe came to be dominated by the non-zero energy density of the inflaton field. A region of the universe in this so-called false vacuum state would undergo exponential expansion until the inflaton field dropped into a lower energy state. This lower energy state is conventionally considered to be the 'true vacuum' state, the lowest energy state of the inflaton field.

The diagram above represents a particular type of inflationary scenario in which inflation ends locally at a 'nucleation point', by quantum tunnelling from the false vacuum value φF, to a value φW. An expanding bubble of lower-energy forms, the bubble wall expanding outwards at the speed of light. The bubble wall is duly represented on Aguirre's diagram by the vee-shape. (If one were to add an extra spatial dimension to the diagram, then one would represent the expanding bubble wall as a cone-shape).

Whilst the bubble wall possesses an inflaton field value of φW, the region inside the bubble evolves towards lower-energy inflaton field values until it reaches the true vacuum field value φT. The second diagram here simply plots the potential energy V(φ) as a function of the inflaton field value φ. (Note that Aguirre's first diagram erroneously denotes the true vacuum as φF).

Now, in general relativistic cosmology there is no preferential way of slicing up a space-time into a family of 3-dimensional spaces. If there were a preferential slicing, it would provide a basis for absolute simultaneity, contradicting the principles of relativity. Inflationary cosmology is just general relativistic cosmology with an inflaton field, so an inflationary space-time can also be sliced up in any number of ways.

If the bubble from which our observable universe arose, were nucleated at a single point, and its wall expanded at the finite speed of light, it might seem natural to think that the bubble must be finite in spatial extent, and non-uniform at each moment of time. The closer to the centre of the bubble, the smaller the value of the inflaton field φ. This would correspond to slicing up the region inside the vee-shape on the first diagram with a series of horizontal lines.

However, the conventional models of general relativistic cosmology, the Friedmann-Robertson-Walker space-times, which are purportedly preceded by the inflationary transition to a true vacuum, are considered to be spatially homogeneous and isotropic. If we carry this slicing convention back to the inflationary bubble, then we must slice it along surfaces with constant values of the inflaton field φ. These correspond to a stack of hyperboloids inside the vee-shape on the diagram, each hyperboloid being an infinite 3-dimensional space of constant negative curvature. Under this slicing, the inflaton field still evolves towards the true vacuum state, but it evolves uniformly, and blends into a spatially infinite Friedmann-Robertson-Walker space-time.

Thus, seen from this perspective, an inflationary bubble, nucleated at a single point, and growing at a finite speed, is nevertheless capable of harbouring an infinite amount of space.