Wednesday, February 24, 2010

Czy mowisz po angielsku?

"Chee MOO-veesh poh ang-yell-skoo?" Polish for "Do you speak English?"

The last time I went to Krakow, in 2007, I stayed, with a friend, in a hostel at the end of Florianska street, a matter of yards from the al fresco cafed Market Square, and the gothically-tipped St Mary's Basilica. From a high window of the church, the poignant notes of the Hejnal Mariacki would drift on the warm air, on the hour, every hour, into the inner courtyards and shuttered windows of the hostel and adjoining apartments.

It was in the hostel that we met a Polish chap, who, it transpired, was having an affair with the female receptionist. In fact, this chap had three girlfriends, one of whom was, in turn, having an affair with the receptionist. Now this fella was the first to acknowledge that "Me, no speak Engleesh," yet this excusable disadvantage was more than compensated for by the fact that, as he declared, "me [spinning a finger in front of his forehead]: IQ 156!"

Later on he would confide in us his trenchant judgement that, "Snoop-Dog,...nothing! But me [making a sniffing gesture, covering up one nostril]: crack." A frank admission, which he duly complemented by plucking his fingers from his lips in delight.

We called him Mike.

Anyway, after something of a hiatus, I'm due to return again this May to deliver a presentation at The Road to Reality with Roger Penrose - mathematics, physics and philosophy. Perhaps I'll catch up with Mike again.

Monday, February 22, 2010

Nuvolari - the legend lives on

Tazio Nuvolari once sent a bundle of straw bales to Scuderia Ferrari, ("scuderia" having the literal meaning of "stable" in Italian), enclosing a note to Enzo Ferrari which read:

"For your horses."

Now that's style. In contrast, to the best of our knowledge, Michael Schumacher did not send a box of woolly jumpers to Flavio Briatore after leaving Benetton.

The straw bale story comes from Cesare de Agostini's book, Nuvolari - The Legend Lives on. It certainly can't be described as a dull book, for de Agostini seems to have intended this to be an impressionistic, lyrical work, rather than a comprehensive biography. In fact, some of the similes are quite brilliant. Defying all rational expectation in the 1935 German Grand Prix, to beat nine technologically superior Mercedes and Auto Unions, driven by Caracciola and Rosemeyer, amongst others, "Nuvolari drove with a slight twisting of the upper body and dramatic movements of his arms, as if they were swinging trapezes...As he took the chequered flag, Tazio grimaced and uncovered his long teeth, strong as a constellation of gears."

One thus has the sense of a talent expressed with the acrobatic grace of the trapezist, but driven by a will as implacable as the interlocking grind of steel gears.

Elsewhere, however, the metaphors and similes appear forced, and sometimes quite bizarre, at least in translation from the original Italian: "While just about all cars consumed space, the Auto Union created it. A seductive and mysterious car, because skirting science fiction, it knew how to remain untouched by time. The long tail, fascinating with those sharp and shaped air vents at its 12-cylinder lungs, seemed like the fin of a cetacean, immersed in a heaving marine abyss."

There's an excellent collection of photographs, however, including one of the start of the 1936 Monaco Grand Prix, which makes the principality look rather like Torquay on a damp Sunday. Overall, though, a little less contrived poetry, and a little more information and explanation, would have gone a long way to making this a better book.

The Non-unique Universe

"Against the palpably sophistical proofs of Leibniz that this is the best of all possible worlds, we may even oppose seriously and honestly the proof that it is the worst of all possible worlds. For possible means not what we may picture in our imagination, but what can actually exist and last. Now this world is arranged as it had to be if it were to be capable of continuing with great difficulty to exist; if it were a little worse, it would be no longer capable of continuing to exist. Consequently, since a worse world could not continue to exist, it is absolutely impossible; and so this world itself is the worst of all possible worlds." (Schopenhauer, The World as Will and Representation).

Last June, McCabism featured a couple of posts on Mathematical logic and Multiverses, and Theories of Everything and Godel's theorem. These posts inspired the submission of a paper, The Non-Unique Universe, to Foundations of Physics, which has just been accepted for publication.

You read it here first. Literally.

Sunday, February 21, 2010

Formula One and random processes

"There is still a desire to introduce mechanisms that create even greater abnormality to the grid, even more random processes." Ron Dennis, March 2003.

In the eyes of a statistician, a Formula One lapchart graphically represents a sample from twenty inter-dependent stochastic processes, (colloquially referred to as random processes).

Mathematicians define a stochastic process as a time-ordered family of random variables Xt upon a probability space Ω. This is a rather recondite definition, but the basic idea is that Ω is the space of histories for the system under consideration. In other words, each point in this probability space, ω ∈ Ω, represents a possible history of the system.

This space could be the space of possible share-price histories of a company, or it could be the space of possible lap-by-lap positions of a Formula One car starting from a particular grid position in a Grand Prix. Each actual share-price history, and each actual lap-by-lap history, is a sample from such a probability space. Run the process again, from the same starting point, and you'd get a different history. In the case of a Grand Prix, each different starting grid position generates a different random process. Run a Grand Prix again, with all the cars in the same starting grid positions, and you'd get a different sample of 20 histories from the joint probability space of these inter-dependent random processes.

By definition, a random variable X is a function on a probability space Ω, which possesses a probability distribution over its range of possible values by virtue of the probability measure on the subsets of the probability space Ω. In the case of a stochastic process, Xt is a function on the path-space of the system, which represents the position of the system at time t. The probability measure on Ω, the space of histories, determines the probability distribution over the range of each random variable Xt, and thereby determines a probability distribution over position at each time t. Different positions at time t have different probabilities because different histories have different probabilities.

In the case of a Grand Prix, there are twenty such inter-dependent random variables, corresponding to the number of different starting grid positions:

Xnt: n = 1,...,20.

Xnt is the random variable which represents the position on lap t of the car which started in the nth grid position. The probability distribution over the range of possible values of Xnt, specifies the probability of a car being in position x on lap t after starting nth on the grid.

Each different track on the Grand Prix calendar will define its own unique probability measure on the joint space of possible lap-by-lap histories. Thus, the probability distribution over the range of possible values of Xnt, will vary from one track to another. For example, the probability of being in 6th position on lap 40 at Monaco, after starting 16th on the grid, is different from the probability of being in 6th position on lap 40 at Monza, after starting 16th on the grid.

Randomicity, and the unpredictability which follows from it, is one of the ingredients which makes a sport exciting. Back in 2003, Ron Dennis was complaining about new qualifying regulations which introduced a degree of randomicity into the starting grid positions. The cars were forced to start a race with the fuel load they qualified with, and different cars would choose to start a race with different fuel loads. Hence, for the past seven years, qualifying grid positions have not necessarily been a reflection of true pace. For 2010, however, Formula One returns to low-fuel qualifying, hence that particular random element of the sport has been eliminated.

Anticipation is high for the 2010 season, with Michael Schumacher's return, and Jenson Button paired with Lewis Hamilton at McLaren. However, with overtaking as difficult as it has been for the past decade, and with the ban on re-fuelling removing another strategic dimension, one wonders if the resurgence of deterministic processes in Formula One might provoke a mid-season revision to the sporting regulations...

Saturday, February 13, 2010

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."

Wednesday, February 10, 2010


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...

Sunday, February 07, 2010

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...

Thursday, February 04, 2010

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.

Tuesday, February 02, 2010

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.