Monday, October 25, 2010

How much information is stored in a lapchart?

If your sleep was somewhat disturbed over the weekend, it may have been a consequence of getting up in the middle of the night to watch the latest round of the Ryanair Formula 1 World Championship, hosted, it appears, at a South Korean fishing village. Equally likely, however, your mind may have been immedicably troubled by the question of how much information is encoded in a typical Grand Prix lapchart.

So, to soothe your passage Lethewards tonight, let us endeavour to address the latter source of vexation, at least.

Begin by supposing that there are 24 cars, and that a Grand Prix consists of 70 laps. For simplicity, let us also suppose that all 24 cars complete all 70 laps. There are 24! (twenty-four factorial) permutations of ('ways of ordering') the 24 cars on each lap. Assuming that the permutations on each lap are independent, (even if the reality is that they are highly correlated), gives us the following number of possible lapcharts:

(24!)70 ≈ 101665 .

Now, to find the amount of information, in bits, stored by a particular lapchart one merely has to take the log to the base 2 of the total number of possible lapcharts:

log2 (101665) ≈ 5,000 bits .

Dividing by the number of bits in a byte (eight), gives the number of bytes as approximately 625. In other words, there is, at most, about half a kilo-byte of information in a typical Grand Prix lapchart. Taking into account the average degree of correlation between the order on successive laps in modern Grand Prix racing would reduce this quantity quite considerably.

Sleep well.

Wednesday, October 20, 2010

Many Worlds and quantum fungibility

This image, by Joakim Berglund, graces the cover of Many Worlds? Everett, Quantum Theory, & Reality. The photo, taken by Berglund from a Cessna, depicts the damage wrought to a section of Swedish pine-forest by hurricane Gudrun in January 2005. The dendritic pattern is created by logging trucks, employed to remove the fallen dendritic growths...

The book itself contains a decent collection of papers, based upon the contributions delivered by various philosophers and physicists at a pair of conferences hosted in 2007 to commemorate the 50th anniversary of Hugh Everett's famously dendritic Many-Worlds Interpretation (MWI) of quantum theory.

Whilst most of the papers are highly technical, David Deutsch expounds a manifesto for the MWI which is more accessible to the non-specialist. Deutsch, it should be emphasised, is something of an extremist when it comes to the MWI. As explained previously on this blog, there are various strains of the MWI. One version of the MWI claims that a measurement conducted on a particle in a superposed state, literally causes the universe to split into different branches, so that each possible measurement outcome is recorded in at least one branch. In this version, there is one copy of the particle prior to the measurement, but multiple copies afterwards of both the particle, and its associated space-time.

A different version of the MWI claims that quantum theory is a theory of interfering classical universes, and that a particle in a superposed state is composed of numerous interfering branches even before it is subjected to a measurement. On this account, the measurement does not create any more branches than were already present. Rather, it is claimed that the measurement causes two things to happen: (i) the state of the measurement device becomes correlated with the respective state of the particle in each of the branches; and (ii) because the measurement device is macroscopic, a decoherence process subsequently suppresses the interference between the different branches, thereby ensuring the absence of macroscopically-detectable superpositions.

This latter version of the MWI provides not only an interpretation of the dynamics of quantum theory, but a radical compositional metaphysics, and one might imagine the wave-function splitting into decohered branches in the same way that a prism splits white light into the colours of which it is composed.

The radical formulation of the MWI is the version which I take David Deutsch to be the principal exponent of. This much is clear from the following excerpt, (where Deutsch refers to the branches as 'universes', and the interfering collection of branches as the 'multiverse'):

"Consider a single, free particle in empty space. It's described by a wave-packet...Which means that, as far as universes go, it's at different positions in different universes. You might think that a non-interacting particle, at least, is something that happens in each universe independently of the others, so that we can forget about the multiverse when describing it. But no. Again because of the uncertainty principle, and because of the linearity of quantum mechanics, there is no region of the multiverse in which both the position and velocity are behaving independently of what's happening elsewhere in the multiverse. That means that there are no autonomous information flows that would be universes. So in fine detail, even a free particle is an irreducibly multiversal object, not just a parallel-universes' one.

Furthermore, at a later time, the shape of the wavepacket will have changed. The instances of the particle in the multiverse will be at different positions. But none of them, individually, will have moved to where it is - because there is no such thing as one of them individually. When the universe approximation breaks down, the autonomy of the instances of a single particle in the multiverse breaks down too. They are then fungible,"

In other words, the branches of a quantum state possess an identity consisting entirely of their interference relationships to the other branches, rather than any self-sufficient existence.

Tuesday, October 12, 2010

The Many Worlds of Hugh Everett III

Investigative reporter Peter Byrne has written a fabulous book which traces the life and career of Hugh Everett III, the inventor of the Many Worlds Interpretation of quantum theory.

Everett devised the Many-Worlds Interpretation for his 1957 PhD thesis, but the interpretation was neglected and derided at the time, and Everett himself never returned to academia. Charting Everett's intellectual and personal adventure, Byrne has uncovered some priceless material. Historians and sociologists of science will be particularly interested to note the pressure exerted by John Wheeler, Everett's thesis supervisor, for Everett to retract and rewrite much of the thesis, so that it would avoid antagonising Wheeler's scientific hero and mentor, Niels Bohr.

Byrne's account of the philosophical issues surrounding quantum theory is amongst the best to be found outside of the professional literature. The author has made a massive effort to understand and explain the concepts involved, and, crucially, has extensively consulted philosophers of physics such as Jeffrey Barrett, Simon Saunders and David Wallace. This level of scholarship is reflected in the final product, which puts most popular science accounts of quantum theory to shame. Byrne should receive huge plaudits for the diligence of his work here.

Everett is a particularly fascinating individual because after completing his PhD thesis, he disappeared into the world of US military research, initially working on the optimisation problems surrounding nuclear warfare. However, the reader seeking an informative, sober, impartial analysis of Cold War politics and strategy will be sorely disappointed here. What we get instead is an unbalanced, sub-Michael Moore, caricature of the era. As just one illustration of this, consider the following claims made by Byrne:

"During much of the 1950s, the de facto strategy of the Strategic Air Command under General Curtis LeMay was to 'preventatively' launch everything in its nuclear arsenal," (p74). "During the 1950s, the operating nuclear war plan of the United States was all or nothing. General Curtis LeMay, head of the Strategic Air Command, told a Gaither commissioner that a surprise attack by Soviet bombers would destroy the bulk of his B-52 bombers on the ground. He said that the official doctrine of deterrence by threatening a 'second-strike', or 'massive retaliation', was an improbable dream. He announced that SAC airplanes flew over the Soviet Union 24 hours a day picking up radio transmissions, and, 'If I see that the Russians are amassing their planes for an attack, I'm going to knock the shit out of them before they take off the ground.' And he intended to do this under his own recognizance, regardless of the opinions of civilian leaders, such as the president. Deterrence, for LeMay meant striking first and without warning," (p195).

Other historical analyses suggest, however, that US Strategy in the early stages of the Cold War was one of preemption rather than prevention, and there is a crucial distinction here which Byrne fails to emphasise:

"A first strike can take three forms. A preemptive attack is one made in immediate anticipation of enemy attack. A surprise attack against an enemy who is not yet preparing his own attack is either simply aggressive, or if undertaken from fear of an eventual threat posed by the enemy, preventive...the difference between the preemptive and preventive variants has often been confused, even by professional strategists." (Nuclear blackmail and nuclear balance, Richard K.Betts, p161). "NSC 68 [a 1950 document which formed the basis of US Cold War strategy for twenty years] rejected preventive war but tentatively embraced preemption," (ibid., p162).

Whether General Curtis LeMay privately endorsed a preventive strategy at various times is a moot point. The quote used by Byrne, however, is merely evidence that he supported a strategy of preemption, not one of prevention. Moreover, in a briefing given by SAC in March 1954 concerning its war plans, General LeMay explicitly stated: "I want to make it clear that I am not advocating a preventive war; however, I believe that if the US is pushed in a corner far enough, we would not hesitate to strike first." (Preventive attack and weapons of mass destruction, A comparative historical analysis, Lyle J.Goldstein, p43)

To claim, as Byrne does, that the US Strategic Air Command had a de facto strategy of preventive nuclear war, is therefore quite misleading. On recognising this, one might begin to doubt the veracity of other claims made by Byrne, and that would be unfortunate, because this is otherwise a great book.

As an investigative reporter, Byrne "specializes in uncovering government and corporate corruption." This is an important duty to society, but it is also crucial not to begin with the assumption that all government activity is corrupt. Byrne, sadly, lapses into a simplistic worldview in which most US Cold War politicians, scientists and generals are portrayed as self-serving, war-mongering maniacs. This is a serious flaw in any work which seeks to provide a definitive historical record, rather than mere propaganda.

It also has to be said that the book is peppered with typographical errors, which include frequent misuse of the apostrophe. In a £25 book, this is unacceptable, and it is time for publishers to recognise that a book suffuse with typographical errors is quite literally a defective product.

Nevertheless, despite these reservations, on balance Byrne has written a fantastic account of the life of Hugh Everett, and the philosophical conundra posed by quantum theory.

Saturday, October 09, 2010

Return to planet Earth

With astral buoyancy, I float through interstellar space, tanning my diffuse, malefic psyche in the pleasant flow of cosmic rays. I swim upwards through delicate veils of pink and purple nebulae, then zig-zag among golden star-clusters, until I ascend above the galactic plane. There, I watch the spiral arms slowly rotating beneath me, my cold, iron will equilibrating with the solitude of space.

Off in a far corner, a red supergiant goes supernova, flaring like a nuclear match, a shockwave immediately billowing through the surrounding gas cloud. A billion stars lie beneath me, some of them providing the conditions for life and civilisation to flourish on nearby rocks. I can sense the souls on all these planets, feel their exhilaration and desperation, their love and hatred. I can hear the screams of the murdered, and detect the insatiable lust of the murderers. In time, I will harvest all these souls, good and bad; drain them of their life-force to feed my own.

I like coming up here. I can clear my head, and plot my triumph over geological and astrophysical time-scales, like an irresistible fourth law of thermodynamics. Glitches and momentary set-backs, of course, are inevitable: a necessary evil, incapable of stemming my necessary evil. All I need is a small opportunity, a platform from which I can re-insert myself into popular consciousness...

And, hullo, what's this? An invitation to appear on BBC's Question Time? Why, of course! Perfect. Now, all I need to do is re-assume corporeal form for a period of time. Let me see...this always hurts a trifle...bipedal form required rather than serpentine, remember...damn, that hurts a lot! Ah, there we go.

Planet Earth was always a favourite of mine: so much wonderful raw material to play with...