Nuclear physics in other universes

The anthropic principle claims that the universe we live in is finely-tuned to permit the existence of life. According to current mathematical physics, there are many aspects of our physical universe which are contingent rather than necessary, and these include such things as the values of the numerous free parameters in the standard model of particle physics, and the parameters which specify the initial conditions in general relativistic models of the universe. The values of these parameters cannot be theoretically derived, and need to be determined by experiment and observation. The anthropic principle is based upon analysis which shows that if the values of any one of those parameters were to be changed, only slightly, then the universe would be inhospitable to life.

There is, however, some recent theoretical work which suggests that the fine-tuning claim which supports the anthropic principle may be just a little glib.

One of the favourite parameters used in anthropic arguments is the cosmological constant Λ. This appears to have a very small, but non-zero value. It is the cosmological constant which is driving the accelerated expansion of the universe discovered in 1998. If Λ were very much larger, it is argued, then the universe would have expanded far too quickly for any stars and galaxies to form. However, this argument tacitly assumes that the value of all the other parameters of physics are held constant. As Lee Smolin points out in Scientific alternatives to the anthropic principle, one can also vary the amplitude Q of the density fluctuations (which seed the formation of galaxies). If the value of Λ is increased, and the expansion of the universe is accelerated, then one can increase Q to compensate: "one can have stars and galaxies in a universe in which both Q and Λ are raised several orders of magnitude from their present value." Modern cosmologists hypothesize that the amplitude of the density fluctuations is a consequence of inflation, the short period of exponential expansion in the early universe's history, which was driven by a scalar field called the inflaton. As Smolin points out, Q therefore depends upon the parameters which define the inflaton potential energy function, parameters such as the mass and self-coupling, which are free parameters.

The existence of life in our universe is also dependent upon nuclear physics, in the sense that life appears to require the existence of hydrogen, carbon and oxygen, and these chemical elements can only exist if the nuclear physics of a universe permits the stable existence of atomic nuclei of electric charge equal to 1 (hydrogen), 6 (carbon) and 8 (oxygen), and if the nuclear physics of a universe facilitates the fusion of carbon and oxygen from primordial hydrogen.

Recent research, summarised by Alejandro Jenkins and Gilad Perez in the January issue of Scientific American, suggests that these criteria can be satisfied by universes with a nuclear physics quite different from our own.

The first case considered is a so-called 'weakless universe'. Our own universe has four forces (gravity, electromagnetism, the strong nuclear force, and the weak nuclear force). A weakless universe has only three forces, being deprived of the weak force. This is a significant omission as far as nuclear physics is concerned, because the weak force is required for neutrons to transform into protons and vice versa.

A proton consists of two up quarks and one down quark, whilst a neutron consists of one up quark and two down quarks. If one of the down quarks in a neutron emits a W^- particle, (one of the so-called gauge bosons of the weak force), it will transform into an up quark, and the neutron will transform into a proton. This is called beta-decay. The W^- gauge boson then decays into an electron and an anti-electron-neutrino, the conventional radioactive products of beta decay. Conversely, if one of the up quarks in a proton emits a W⁺ gauge boson, it will transform into a down quark, and the proton will transform into a neutron.

The latter process is required for the nuclear fusion which takes places within the stars in our own universe. The so-called PPI chain requires pairs of protons to fuse together, and for one of the protons to transform into a neutron. The result is a nucleus with one proton and one neutron, called deuterium. Further protons then fuse with such deuterium nuclei to form helium-3 nuclei, and pairs of helium 3 nuclei then fuse into helium-4, spitting out two surplus protons in the process.

Remove the weak force, then, and stellar nuclear fusion can't get started, can it? On the contrary, this conclusion only holds if all the other parameter values are held fixed. Harnik, Kribs and Perez argue in A universe without Weak Interactions, that if the level of asymmetry between matter and anti-matter in the early universe is also varied, then universes without the weak force can still synthesize the atomic nuclei required to support life. If the so-called baryon asymmetry is reduced, then a sufficient proportion of deuterium nuclei will be left over from big-bang nucleosynthesis, for the fusion of heavier elements to proceed within stars. Such stars will be colder and smaller than our own stars, but will still support a zone of habitability for planets orbiting at just the right distance.

The second case considered is that in which the masses of the quarks are varied. In our own universe, only the two lightest quarks, the up and the down quark, combine to form stable baryons: the proton and the neutron. The other quarks are too massive to form such baryons, hence they do not participate in the physics of atomic nuclei. The down quark in our universe is heavier than the up quark, hence the neutron is slightly heavier than the proton. Jaffe, Jenkins and Kimichi argue in Quark Masses: An Environmental Impact Statement, that universes with other combinations of quark masses could support the existence of life.

If, for example, the up quark is set to be heavier than the down quark, and protons are therefore set to be heavier than neutrons, then whilst hydrogen itself would be become unstable, the heavier isotopes of hydrogen, such as deuterium and tritium, would act as stable substitutes.

Another potential life-supporting universe is one in which the mass of the strange quark is reduced to a value close to that of the up quark, and the down quark is given a much lower mass than either of them. In such a universe, the sigma minus baryon Σ^-, consisting of two down quarks and one strange quark, functions as a substitute for the proton, and can combine with neutrons to form stable isotopes of hydrogen, carbon and oxygen.

As Perez and Jenkins comment, "Physicists in such a universe might be puzzled by the fact that the up and strange quarks would have almost identical masses. They might even imagine that this amazing coincidence has an anthropic explanation, based on the need for organic chemistry. We know, however, that such an explanation would be wrong, because our world has organic chemistry even though the masses of the [up] and strange quarks are quite different."

Pitot-booms

Formula One's meagrely rationed series of pre-season tests resumed at Jerez on Wednesday this week, and, as scheduled, Red Bull took the opportunity to unveil their much-anticipated RB6. In fact, the RB6 superficially resembles the RB5, even down to the extent of possessing the same pull-rod rear suspension featured on the 2009 vehicle. In contrast, every other team this year has opted for push-rod rear suspension.

Push-rod suspension places the rockers and spring-dampers up top, and therefore potentially compromises the dorsal airflow between the rear wheels, over the beam wing, and over the top of the diffuser. In contrast, pull-rod suspension places the rockers down low, thereby potentially compromising the volumetric capacity of a double-diffuser. By opting for the latter solution, one presumes that Red Bull designer Adrian Newey has discovered that the greatest net effect comes from maximising the airflow over the top of a moderately-sized double diffuser.

McLaren have opted for a huge double-diffuser on the MP4-25, and turned up at Jerez with an interesting Meccano-like device behind the left-side front-wheel. At first sight, this lateral boom appeared to be a mechanism for spraying rivals with DDT. Closer inspection, however, suggested it was equipped with pitot-static tubes, to measure airspeed and static air pressure.

Of particular interest was just how far out this contraption projected. The airflow in this region is both crucial and complex. The front wing of the car, and the rotating front wheel, both generate a turbulent wake, and these wakes interact with each other in a complex manner, albeit a manner which can be heavily influenced by the design of front-wing endplate. The interaction between these wakes partially determines the dorsal airflow between the rear wheels, and thence partially determines the performance of the diffuser. Getting this part of the airflow correct is therefore paramount, hence McLaren's use of their pitot-boom.

Whether the use of such a diagnostic tool indicates that McLaren have problems again, is another matter...

Rendez-vous on the Riviera

Beneath a cerulean sky lie glinting golden sands and the shimmering Mediterranean. A sinuous, black corniche bakes in the Sun as it winds between pines and poplars to the semi-decadent splendour of the Cote d’Azur. The merest zephyr of a wind induces gentle whorls in the heat haze clinging to the landscape. We are equidistant in time from the mechanised slaughter of two world wars, in a period framed on one side by cold muddy trenches, and on the other by Hadean orange fireballs and genocidal concentration camps. Alive now is a generation born under imperial conflict, which will survive to see the growth of fascist totalitarianism. It is a generation haunted by the memory of mass tragedy, attempting to snatch some life in this brief respite, but developing a growing awareness of a new, and altogether more sinister threat.

A cobalt-blue, open-top Bugatti Type 35C travels at speed between the low walls of the coastal road, its primordial bark reverberating intermittently from the granite cliffs, the chassis rolling and dipping with elegant alacrity through the myriad hairpins and corkscrew bends. At its wheel is a tall, attractive, thirty year-old woman. Her hair is long and blonde, her skin delicately tanned, and her cheeks are flush with passion and adrenalin. She is Helle Nice, erstwhile model and dancer, and now racing driver and socialite. And she is racing to a rendez-vous in Monte Carlo with her new consort, Baron Philippe de Rothschild.


Two men sit brooding as they dine at a table in Monaco’s Hotel de Paris. One of these men is Enzo Ferrari, the nascent Godfather of Formula One. His hair is swept back from a broad, square forehead, hinting at the burgeoning ambitions which circle within. His eyes are hooded, and he conceals as many secrets as he harbours aspirations. The other man is driving genius Tazio Nuvolari, a neat but diminutive character, with a charismatically extended chin. Tazio’s body-language is undemonstrative, but his eyes twinkle with percipience and audacity.

Tazio breaks the silence. “Steak was good,” he asserts without inflection, pushing his plate to one side. Ferrari nods his assent, chewing on the last mouthful of his duck a l’orange.

“So Enzo,” asks Tazio, sipping on a glass of red wine, “if a man dies in a Scuderia Ferrari Alfa, and his death is undoubtedly caused by a mechanical failure, do you not feel guilt? Do you not feel that you have robbed a wife of her dearest love, a son and a daughter of the father they idolised?”

Enzo’s forehead creases with momentary but suppressed irritation, and he glances out the window, his eyes darting back and forth in thought. He carefully wipes his lips on a napkin before responding. “Guilt? Should I feel guilt for giving a man the opportunity to pursue his dreams until he catches them and makes them real? Are you suggesting that I would deliberately cause a man’s death?”

“No, of course I am not. But in the absence of engineering perfection, mechanical failures are inevitable, are they not?”

“Yes, but these failures are as unpredictable as they are inevitable,” declares Enzo with a shrug. “Should I then feel guilt at providence itself? Would you not agree that providence is within God’s remit alone?”

“Ummm, what one man calls providence is often under another man’s control, but yes, ultimately I suppose I have to concede that.”

“Well, then it follows that if I felt guilt at the operation of providence, I would be presuming to wrest responsibility from the hands of the Almighty himself. Now, I am no cardinal or pontiff, Tazio, and my grasp of theology is poor, but as I understand it, God Does Not Share Responsibility.”

A shallow smile creeps like metal fatigue across Enzo’s lips. “But let me ask you something, Tazio. Let us agree that your virtuoso gifts in a racing car are greater than those of any mortal man, and let us consider that when other men strive to beat you on the racetrack, they therefore push themselves to the very limit of their abilities. If such a man’s will-to-win transcends his judgement, then is it not likely that he will crash attempting to match you? If, in a vain attempt to beat the Great Tazio Nuvolari, he thence perishes within a tangled mass of steel and rubber by the roadside, are you not, perhaps indirectly, responsible for that man’s death? Do you not have his blood on your hands, the tears of his widow and children on your conscience?”

Tazio glances down at his glass of wine, and shifts uncomfortably in his chair. “Yes, it’s a thought.”

“Well, then.” For a brief moment, Enzo Ferrari holds Nuvolari’s eyes intently, assessing his reaction. Reciprocal respect and mutual suspicion reflects across the table, until Ferrari turns aside and snaps his fingers. “Garcon!”

To be continued...

Jerry Fodor and natural selection

Philosopher and cognitive scientist, Jerry Fodor has co-written an article with Massimo Piattelli-Palmarini in New Scientist this week, which argues that natural selection "overestimates the contribution the environment makes in shaping the phenotype of a species and correspondingly underestimates the effects of endogenous variables."

Fodor and Piattelli-Palmarini claim that more attention should be devoted to "non-environmental constraints on trait transmission. [These] include constraints imposed 'from below' by physics and chemistry, that is, from molecular interactions upwards, through genes, chromosomes, cells, tissues and organisms. And constraints imposed 'from above' by universal principles of phenotypic form and self-organisation - that is, through the minimum energy expenditure, shortest paths, optimal packing and so on, down to the morphology and structure of organisms."

Unfortunately, Fodor and Piattelli-Palmarini make two crucial conceptual errors:

(i) They conflate natural selection with adaptation to an environment.

(ii) They conflate evolutionary fitness with adaptivity to an environment.

In fact, natural selection and evolutionary fitness can be defined in abstraction from adaptation to an environment. As John Barrow puts it, natural selection "has just three requirements:

(1) The existence of variations among the members of a population. These can be in structure, in function, or in behaviour.

(2) The likelihood of survival, or of reproduction, depends upon those variations.

(3) A means of inheriting characteristics must exist, so that there is some correlation between the nature of parents and their offspring. Those variations that contribute to the likelihood of the parents' survival will thus most probably be inherited.

It should be stressed that under these conditions evolution is not an option. If any population has these properties then it must evolve," (The Artful Universe, p21).

There is no need to refer to the existence of an environment, or adaptation to an environment, in the definition of natural selection. As Lee Smolin points out, "at this formal level, concepts like 'survival of the fittest' or 'competition for resources' play no role...What is responsible for that variation, and what goes into the differential survival rates, is not relevant for how the basic mechanisms of natural selection work," (The Life of the Cosmos, p104).

As a demonstration of this, Smolin's theory of cosmological natural selection requires no environment for the evolution of its hypothetical population of universes.

In fact, the conceptual errors made by Fodor and Piattelli-Palmarini are probably shared by many evolutionary biologists, who probably do conflate natural selection with adaptation to an environment. The endogeneous constraints which Fodor and Piattelli-Palmarini refer to may well play an important role in biological evolution, and they might well demonstrate that biological evolution involves far more than adaptation to an environment. Nevertheless, such endogeneous constraints are consistent with evolution by natural selection.

Equally, this doesn't entail that natural selection is the only process operating within biological evolution. Far from it, it seems that horizontal gene transfer plays a huge role in microbial evolution, and processes such as genetic drift also play a role under specific circumstances. The fact remains, however, that the concept of natural selection is neutral with respect to the importance of the environment.

Aerodynamics in Valencia

There are many reasons for thinking that Formula 1 aerodynamicists have it easy. For a start, this particular guild of tradesmen are only compelled to consider the dynamics of a single fluid (namely air), and perforce have no need to take into account the turbulent mixing which occurs at the boundary between fluids of different densities, due to Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Moreover, at Formula 1 speeds, the airflows under consideration are almost exclusively subsonic, and these conditions permit the simplifying idealisation of incompressible fluid flow. Formula 1 aerodynamicists are thereby deprived of such complex beauty as the hourglass cavities, and supersonic jets produced when small objects, such as mere pebbles, are thrown into water. One can go even further afield, and consider the exotica of radiation hydrodynamics, typical in the astrophysical realm, where the fluids in question absorb and emit radiation, and the humble theoretician must solve both the Boltzmann equation for radiation transport, and the entwined equations of fluid flow.

Despite the ultimately parochial nature of the field, however, Formula 1 aerodynamics remains capable of generating a creative cornucopia in the early months of the year, when a flotilla of new cars are unveiled and testing resumes. Only two days of testing have been completed at Valencia, but already the most exciting development is the new McLaren MP4-25, and to be precise, the diffuser on the McLaren.

It appears that McLaren are using the beam wing, rather than the rear crash structure, as the ceiling for the upper-storey of a triple-diffuser, thereby utilising the entire area between the rear wing endplates. McLaren director of engineering, Paddy Lowe, commented at the unveiling of the car in Newbury last week: "This is the first car in which we have had a clean sheet of paper to really exploit the interpretation [of diffusers] that was developed last year...You will see we have produced a fairly extreme incarnation of that but we won't be alone in that...In certain aspects we have sought guidance from the FIA and they have come out with very clear interpretation, understanding and guidance - and we think that has been made available to all the teams." The question, however, is whether McLaren can feed the upper storey of their diffuser with sufficient airflow to prevent it from stalling.

Lewis Hamilton tested the car on Tuesday, and reported "a night and day difference and feeling compared to the first lap and the first test day in 2009." The latter, however, constitutes a very low baseline for comparison, and Hamilton was half a second slower than Felipe Massa's Ferrari. Moreover, McLaren instantly resorted to using the same fluorescent paint used in 2009 when grappling to understand the MP4-24's intransigent behaviour.

Ferrari, meanwhile, also have a triple diffuser, but appear to be using the rear crash structure
as the upper ceiling, as per the 2009 convention.

The other expected championship contender, Mercedes, seem to currently possess a simple double-diffuser. Whilst the word is that an updated version will appear before the first race in Bahrain, such a device will clearly have less testing time than those on the McLaren and Ferrari. Plenty of fluid flow for thought, then.

Dendritic diffusers

The next few days in Formula 1 herald a flurry of new car launches, with Ferrari revealing their 2010 contender on Thursday, McLaren unveiling the MP4-25 at Vodafone's Newbury headquarters on Friday, and Mercedes displaying their silver Schumi-wagen on Monday. The major design novelties are likely to stem from the new requirement to accommodate a race-distance capacity fuel-tank, and a reduction in front tyre widths. Apart from that, there is an expectation in some quarters that many teams will pay Red Bull designer Adrian Newey the ultimate compliment, and effectively copy his RB5 design, the fastest car of last year.

However, whilst almost all the teams may imitate the protrusions on the front nose that Newey used to satisfy the letter of the dimensional regulations in 2009, it is far from certain that the other teams will adopt the pull-rod rear suspension, used to such fine effect on the RB5. The purpose of the pull-rod solution was to remove the suspension rockers, springs and dampers from the top of the car, where they otherwise restrict the flow of air over the top of the diffuser. As Newey himself explained to Alan Henry, the unexpected introduction of double-diffusers severely detracts from the advantages of pull-rod suspension:

"I thought it was an elegant solution to the single-diffuser car, but given the rule changes, it is much more difficult to make the pull-rod layout work satisfactorily in conjunction with a double diffuser.

"We took the decision to use the pull-rods because the start of the diffuser had moved from the front of the rear wheel to the rear axle centre-line. What the double diffuser does is, in effect, to completely circumvent that rule. So certainly the shape of the double diffuser we had latterly on the RB5 was compromised slightly by the pull-rod layout." (Autocourse 2009-2010, p35)

It may be that to maximise the effect of a double-diffuser, push-rod suspension still offers the best solution. The question is whether one can both maximise the flow through a double-diffuser, and use pull-rod suspension to maximise the flow between the rear wheels, and over the top of the diffuser. When the Red Bull RB6 debuts on February 10th, it will be fascinating to see if Newey's fertile mind has responded to this challenge with an exotic multi-storey diffuser, replete with multiple slots, channels, and branching points. A dendritic diffuser perchance...

The Motorsport Magazine podcast

Podcast chemistry: it's a black art.

Motorsport Magazine's foray into the podcast market has been running now for six months or so, and is somewhat beginning to hit its stride. Introduced by the strangely charismatic Rob Widdows, and featuring Nigel Roebuck, Damien Smith and Ed Foster, it may not have the alchemy of Mayo and Kermode, but it's rapidly developing into an unmissable monthly download.

Highlights so far have included Nigel Roebuck's uncanny impersonation of Niki Lauda, some forthright opinions from Jody Scheckter, and a profanity-laden appearance from John Watson, in which he seemed to suggest that Kimi Raikkonen might prefer to spend the rest of his life getting inebriated.

January's podcast features a remarkable revelation from Nigel Roebuck, in which he recalls being invited, along with then Autosport colleague Mark Hughes, to an audience with Max Mosley. This was three years or so ago, before the succession of scandals which ultimately led to Mosley's downfall.

Presumably looking ahead to the prospect of cars driven by electric power, Mosley posed the following question to Roebuck:

"Will the fans miss the sound of the cars?"

To which Nigel's reply was, um, yes I think they would Max!

Ron Dennis and amateur psychology

Former McLaren Racing team principal Ron Dennis has given an interview to Esquire Magazine, ('the magazine for men who mean business'), in which he provides the following insight:

"I used to go to bed with the vacuum cleaner going because my mum wanted the house immaculate when she got up. That’s the ethos I grew up with, everything had to be perfect all the time. That’s why I am such a pain to live with. I don’t want chaos; my homes are my tranquillity bases."

The description of home as a 'tranquillity base', confirms that these are indeed the words of Ron Dennis. However, the vacuum cleaner recollection may be unwise. Many magazine journalists and newspaper feature writers are fond of engaging in the amateur psychological analysis of media personalities, and those who touch on motorsport may now be inclined to suggest that Dennis's perfectionist ethos is the consequence of an inability to satisfy, or the desire to emulate, a dominant and perfectionist mother.

In fact, a perfectionist mother is one of the five 'mothering styles' defined by clinical psychologist Stephan B. Poulter, in his book The Mother Factor: How Your Mother's Emotional Legacy Impacts Your Life:

The Perfectionist Mother — whose family must look perfect in every way
The Unpredictable Mother — whose ups and downs can create lifelong anxiety and depression in her son or daughter
The "Me First" Mother — whose children come second or last
The "Best Friend" Mother — who's now in vogue but can wreak havoc
The Complete Mother — who provides guidance and shows compassion to her child

Dennis is also quoted as stating that his relationship with Ayrton Senna "edged on almost masculine love...I use the word quite deliberately. It didn’t have any homosexuality about it, it wasn’t that sort [of love]." This is touching, but with that final, Alan Partridge-like qualification, again one wonders if Dennis is simply providing his enemies with the ammunition to deride him.

Fortress Madejski

"Oi Shane! Who ate all the pies?"

It's early Saturday evening, and I sit as a Liverpool FC fan, surrounded by Reading FC fans, at the third-round FA Cup encounter between Reading and Liverpool. The heat has long since been vacuumed out of my feet by the concrete floor of the stand below, and the sartorial preferences of the crowd are wisely focused on beanie hats and ugg boots.

The undiscovered comic genius standing a couple of places to the left of me, is artfully drawing attention to the fact that Reading footballer Shane Long has been having some difficulties with his weight this year. Before the evening is out, and this gentlemen presumably wanders off to re-join his friends at the local chess club, he provides another memorable verbal contribution. A Reading defender poleaxes Fernando Torres to the ground just in front of us, and the referee is forced to brandish a yellow card: "Oh fuck off referee!" he shouts. "Is he not supposed to even touch him?"

Watching football in a stadium such as the Madejski can be a strange experience for a motorsport fan, for not only does one sit no more than 20 yards or so from one's heroes, but it's also usually possible to make one's abuse clearly audible to the heroes in question.

Anyway, Reading are playing well, stringing together some nice simple passing moves, and they're exploiting Liverpool's weakness dealing with high balls into the box. As Charlotte, a Reading fan sitting in front of me, points out at half-time: "That's the first time we haven't been booed off this season!"

The pace of the match dwindles slightly in the second half, and it seems there's an altercation occurring in the stand diagonally opposite. It appears that a Liverpool fan has infiltrated the Reading spectators, and is causing a bit of aggro. "Wanker! Wanker! Wanker! Wanker! Wanker!" comes the rhythmic refrain from that part of the ground, as a column of fluorescently-bibbed marshals ascend the stand, and haul the unfortunate scouser from their midst.

Liverpool are as insipid as ever, but then as Emiliano Insua gets the ball at the half-way line, the crowd suddenly rise around me, and begin clapping and cheering. What's this, I wonder? Bizarrely, everyone seems to be looking at a point above pitch level, and I briefly consider the possibility that the messiah has floated into the stadium. Sadly, it's not the messiah, just a very naughty Steve Coppell (Reading's erstwhile managerial hero), who's been spotted in a commentary booth across the other side of the pitch.

As the game draws to a close, I begin to watch Liverpool manager Benitez more closely, as he trundles back and forth to signal his players from the touchline, like a portly clockwork mechanism. I briefly consider shouting some abuse, but realise that "Benitez! You only play attacking football after being criticised in the Spanish press after a Champions' League game!" is probably insufficiently succinct. Instead, I settle for:

"Oi! Benitez! Who ate all the pies?"

Ayrton Senna and religious experience

In practice for the 1988 Monaco Grand Prix, Ayrton Senna was driven to a previously inaccessible level of performance by his desire not just to beat, but to destroy team-mate Alain Prost. Two seconds a lap quicker than Prost at one stage, Senna subsequently recalled attaining a mental state in which his subconscious mind had gained control, and in which he sensed the opportunity to go even faster, but feeling vulnerable, he decided to step back:

"Suddenly I realised that I was no longer driving the car consciously. I was kind of driving by instinct, only I was in a different dimension. I was way over the limit, but still I was able to find even more. It frightened me because I realised I was well beyond my conscious understanding."

There is a common suggestion that Senna believed he had a religious experience that day. One can hypothesise that as Senna concentrated with laser-like intensity on the rhythm of driving through the unwinding tunnel of barriers at Monte Carlo, he induced himself into a trance-like brain-state, and that what scared him was the feeling of an imminent loss of self-identity, the same feeling commonly induced by many shamanistic religious rituals. In particular, by looking at brain scans conducted on religious devotees engaged in meditation, one can hypothesise that the part of Senna's parietal lobe responsible for the conscious sense of self was shutting down:

Broadly speaking, the left-hemisphere side of this region deals with the individual's sense of their own body image, while its right-hemisphere equivalent handles its context — the space and time inhabited by the self. Maybe, the researchers thought, as the meditators developed the feeling of oneness, they gradually cut these areas off from the usual touch and position signals that help create the body image.

"When you look at people in meditation, they really do turn off their sensations to the outside world. Sights and sounds don't disturb them any more. That may be why the parietal lobe gets no input," says [Andrew] Newberg [a neuroscientist at the University of Pennsylvania in Philadelphia]. Deprived of their usual grist, these regions no longer function normally, and the person feels the boundary between self and other begin to dissolve. And as the spatial and temporal context also disappears, the person feels a sense of infinite space and eternity.

The mystical aura which surrounds Senna's achievements in the sport, and raise them above the achievements of Michael Schumacher in the minds of many, can be attributed in large part to what Senna believed he experienced that day at Monaco, and the vivid manner in which he was able to communicate those experiences. Whilst Senna's beliefs were in a sense delusional, those delusional beliefs may well have been directly responsible for permitting him to access levels of performance denied to other drivers.

Ronnie Peterson and roll resistance

A couple of years ago, ESPN broadcast the full fifty-minute highlights of the 1973 British Grand Prix, complete with commentary by Raymond Baxter. For the motorsport cognoscenti, this was pure manna. Whilst the Grand Prix is infamous for the multi-car accident triggered by Jody Scheckter at the end of the first lap, the re-started race is itself both exciting and interesting.

The dramatis personae consist of the iconic, John Player Special Lotus 72s of Ronnie Peterson and Emerson Fittipaldi, resplendent in their sable and or livery, Jackie Stewart's Tyrrell, and the Yardley McLarens of Denny Hulme and Peter Revson. There is also an impressive cameo from Niki Lauda's BRM, and a strong showing from James Hunt's ridiculously short-wheelbase, Hesketh-run March.

When the race re-starts, the cars on the front row of the grid (Peterson's Lotus, and the McLarens of Hulme and Revson) light up their rear tyres, and the noses of their cars visibly lift! Peterson's Lotus takes an immediate lead, but is hunted down first by Jackie Stewart's Tyrrell, then by Emerson Fittipaldi's similar Lotus, and finally by the McLaren M23 of Peter Revson. Revson eventually slipstreams Peterson down the Hangar straight, calmly takes the lead into Stowe, and ultimately takes the victory.

But what really grabs the attention is the extraordinary body language of the cars. Peterson's high-speed oversteer drift through Woodcote is perhaps one of the most famous images in the history of the sport, but Jackie Stewart looks similarly impressive through the same corner, the right-front wheel of his Tyrrell pawing the inside white line on one particular occasion. (There appear to be no kerbs whatsoever at either the inner or outer margins of the track). In addition, the Lotus 72s both exhibit a quite astonishing amount of chassis roll into corners such as Copse and Stowe, visibly more than all the other cars in the field, which themselves display far greater suspension travel than modern Formula One cars.

Why would this be? Well, according to Paul Fearnley's article on the Lotus 72 in Motorsport magazine (October 2002), Lotus switched from Firestone to Goodyear tyres between the 1972 and 1973 seasons, and with the waning of the erstwhile tyre war, found they were unable to generate sufficient heat in the harder Goodyear tyres. The consequence was that the Lotus 72s suffered from understeer in 1973.

One might therefore hypothesize that Lotus softened the front suspension of the Lotus 72 in an attempt to combat this understeer. To understand why doing so might reduce or eliminate understeer, we need to briefly digress into some vehicle dynamics and suspension theory.

When a car corners, the grip provided by the tyres generates a lateral (centripetal) force towards the inside of the corner. From the perspective of a reference frame in which the car is at rest (a reference frame which effectively travels around the circuit with the car; i.e., the coordinates of the car's centre of gravity remain constant in this reference frame), this induces a reaction force towards the outer wheels of the car. This reaction force is not a real force, but a fictional force, created by the use of a reference frame which is travelling around with an object undergoing acceleratory motion. Such a reference frame is called a non-inertial reference frame. The fictional reaction force is simply the result of the sprung mass of the car attempting to follow an inertial trajectory, in a straight line at a constant speed, when viewed from a reference frame undergoing centripetal acceleration.

The reaction force acts on the centre of gravity, and generates a moment around the roll centres of the front and rear suspension. (In dynamics, a moment is a force which generates a rotation about some axis). This roll moment has the effect of reducing the vertical load on the inner tyres, and increasing the vertical load on the outer tyres. The total load transfer is proportional to the height of the car's centre of gravity, and inversely proportional to the track width (the lateral distance between the wheels).

Generally speaking, this load transfer reduces cornering grip. To maximize cornering grip, one would wish to distribute vertical load equally amongst the inner and outer tyres.

The stiffness of the suspension front and rear, determines the amount of roll which the sprung mass of the car experiences for a given roll moment. The stiffness of the suspension can therefore be referred to as the amount of roll resistance. However, the stiffness of the suspension cannot really alter the total load transfer between the inner and outer pair of wheels. Rather, the relative stiffness of the front and rear suspension can alter the distribution of the total load transfer between the front and rear of the car.

The stiffer the suspension at one end of the car, the greater the load transfer at that end of the car, hence the lower the cornering grip available at that end. Conversely, the softer the suspension at one end, the less the load transfer at that end, and the greater the cornering grip available.

Hence, if a car suffers from understeer, one potential course of action is to soften the front suspension, either by softening the front spring/damper rates, or by means of softening the front anti-roll bar. Such logic might explain why the Lotus 72s wielded by Peterson and Fittipaldi at Silverstone in 1973, exhibited such a remarkable degree of roll.

Racecar suspension expert Mark Ortiz agrees, but also points out that Lotus "could have freed the cars up by stiffening the rear too, which would have reduced the roll, or stiffening the rear a bit and softening the front a bit, keeping the roll about the same.

"In other words, there is no necessary relationship between roll angle and oversteer/understeer balance. Cars that roll more don't always understeer less or oversteer more."

It's the type of speculation rarely open to modern Formula One fans.