PART 1
Oxford’s oral tradition, at least, suggests that E.E. Evans-Pritchard (Oxford’s “EP”) 1902-1973 ( “strangest” ethnographer who believed that social anthropology could be a part of natural sciences ) made the first historical attempt to introduce Quantum Mechanics for social anthropologists in the last century. Presently, Vice –Chancellor of Oxford University and experimental quantum physicist realized the second one at Humanities and Science panel discussion ( Randomness and Order , 10 February , www.torch.ox.ac.uk/humsciox ). In his presentation Jan Walmsley reduced the best scientific tradition of the 21^{st} century to the problem of non-classical or quantum probability, correspondingly , he used quantum card game and quantum notion superposition in order to explain real and dramatic challenge of quantum mechanics for humanities and “social sciences”. Definitely Jan used some sort of simplification, because there is a general ignorance in official and educational circles of what quantum mechanics is. In particularly, real drama is that all Western systems of education for humanities and so called “social sciences” are based on non-quantum ( more exactly – anti-quantum ) principles of classical materialism and classical physics of the 18^{th} century. Even Albert Einstein in 1930s considered “quantum revolution “ in physics as return of “wrong idealism “ in science. He famously asked quantum theorists :” the Moon exists when nobody is looking at it ?” And in 1935 Einstein, Podolsky and Rosen published scientific paper where they described seriously impossible experiment which must stop development of “wrong “ idealistic foundations of quantum mechanics.
We may describe today such “EPR-experiment” (in later David Bohm's terms ) as an impossible experiment where a particle with no spin ( with no magnetic circular movements described by “imaginary numbers “), while at rest, decays into two identical particles ( labelled 1 and 2), each with spin 1/2. Since momentum is conserved, the particles fly out in opposite directions. And since spin is conserved, the two spins must add up to zero. Therefore, in good agreement with “right “science, if
the spin of particle 1 is measured to be “up” along some specific direction, then the spin of particle 2 must be “down'” along some specific direction and there is no such thing as “observer dependent spin” at all. Following the results of such sort of EPR experiment, it became obvious that any observer dependent reality, predicted by quantum theorists in 1920 - 1930s, is simply a nonsense.
In the mid-1960s, however, mathematician and experimentalist John Bell ( CERN ) showed that it was actually quite possible to realize the EPR-experiment, when the two particles are emitted with definite spin directions, which are locally fixed at the decay. These directions, according to Bell,nevertheless, might be Unknown to the experimentalist. He then showed that if we measure the spin of particle 1 along one direction, and the spin of particle 2 along another direction, the results will be correlated. For instance, if we measure the spin of both particles along the same direction, particle 2 will always have the spin down when particle 1 has the spin up.
Thus, a nonsense, described by Einstein - Podolsky - Rosen in 1935 ( in which strong correlations are observed between presently no interacting particles, even if they are detected arbitrarily far away from each other ) became a part of experimental physics !
Since Bell's discovery, a number of physical tests have been performed successfully (by J Clauser and S Freedman (1972), A Aspect, J Dalibard, and G Roger (1982), and G . Weihs, Ch Simon, T Jennewein, H Weinfurter, and A Zeilinger (1998)] etc.etc
Moreover, in 21st century whole new non-nonsensical physics with their ideas of quantum computers, quantum telepathy, quantum internet , quantum teleportation, quantum cryptography, quantum credit cards, quantum markets, quantum elections, quantum space communications and even new quantum anthropology are emerging…
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Lee Drummond said:
" Here I must confess that the appeal quantum mechanics, complexity theory, and cellular automata have for me is at the level of analogy or metaphor"
Lee, I think it is exact observation. Indeed, some modern mathematicians doing applications ( calculations ) in theoretical physics consider mathematics as metaphor. Later I'd like to describe such sort of quantum mathematics.
Keith, thank you for
The social meaning of the power law. Your paper suggests that some anthropologists nevertheless use probability theory and famous theorem of "the small worlds" in very productive way... I suppose that you used Classical Statistics and Classical Probability ( based on Kolmogorov axiomatics ). However, Quantum Probability cannot be reduced to Classical- it is non-Kolmogorovian axiomatic system.In particularly,this is reason why the best phisical labs of the world work under quantum control, quantum memory and quantum computing now. Quantum player ( player equipped with quantum device ) in classical market will be winner . ALWAYS. Competition is very strong, because winner will take all during first few hours...There are also developments in continental mathematics in context of the small worlds theorem as well.
Huon,
Thank you - probably you had found the first professionally formulated definition of Godel's theorem ( and Godel's problem ) in history of social anthropology !
John McCreery said:
Consider, for example, Daniel Lende's piece Culture Like Relativity. I may not agree with everything Lende says, but the direction in which he is thinking strikes me as having great potential.
John, if you have thoughts about Relativity and Anthropology, I'd like to offer my sketch
http://dx.doi.org/10.6084/m9.figshare.769222
( which I used in my Satellite Navigation project , ESA )
Part 4.
The Schrodinger equation
▼²ψ + 2m/ һ² ( E – V )ψ = 0 ( 1 )
( where E is total energy, V – the potential energy of the particle (electron, for example ), ψ is mysterious wave function and һ – Plank constant or number )
represents the most beautiful as well as the most heuristic foundation of quantum mechanics . This equation expresses general principle of Atomism : Continuous could be produced from Discrete and, it replaces Newton’s equation of motion of a particle.
Whilst Newton’s equation of motion allows one to calculate the orbit of a particles accurately, the Schrodinger equation is more precise and it allows one to calculate ψ , i.e. the probability for finding the particle at a certain position. This replacement is the main logical step in the Classical- Quantum transition . It is accepted that such replacement is due to the double nature of quantum particles ( particles – and - waves at the same time - as is known , Feynman used taking term “wavicle “ seriously for this kind of hybrid symbolic construction )
For physicists it is very important to prove such classical – quantum transition. At the fist approximation, it looks like a mathematical trick, however, it is seen to have a deep meaning…
Namely :
1^{st} Step. They try to rewrite the general wave equation ▼²ψ + 2m E/ һ² × ψ = 0 ( pre- assumption for (1) ) for a free particle in the form :
Eψ = һ² / 2m▼²ψ = - һ² / 2m ( δ²/ δx² + δ²/ δy² + δ²/ δz² )ψ ( 2 )
2^{nd} Step. They try to compare this equation with the corresponding expression for E in Classical theory , i.e. with
E = m/2 × ( υ²x + υ²y + υ²z ).
3d Step. Simply introducing mυx = px as the momentum, they automatically have new expression for classical E :
E = 1 / 2m ( p²x + p²y + p²z ) ( 3 )
Hence, it is easy to see that a great similarity exists between the classical and quantum equations ! Thus, in order to pass from the classical expression ( 3 ) to the quantum equation ( 2 ) theorists use pure symbolic trick – they try to substitute for p²x the operator “- һ² (δ²/ δx²). In this context they say that “operator acts on the wave function “. In other words, in order to pass from our “sin “ Classical world to the world of Quantum Complexity, we have to replace px itself by the operator.
In some sense, such sort of symbolic replacement could be understood as Mathematical Symbolic Experiment which has decided in favour of the quantum reality.
Remark
It is the most difficult part of quantum mechanics, but if you understand it , I am sure, you can easy understand such anthropological equations as Shirokogoroff ‘s equation of “cultural unconscious impulses for ethnic changes” ( 1923 )
± ί² = δ/ ST × T/∆ T = ώ T/∆ T
in his Ethnoscience, and famous Levy-Strauss’s “ canonical formula “ ( 1954 )
( a : b :: c : a ¯¹ )
his Science of Mythology as well…
Michael, this description is nice. It reminds me, however, of when I was working with computer geeks in the Yale Artificial Intelligence Laboratory a long, long time ago. As a newbie, I would ask a geek how to do something. He would sit down at the keyboard. His fingers would flash over the keys. "See, that's how you do it," he'd say. But, of course, I didn't. I had about as much chance of understanding as I did of playing a concerto having heard a professional pianist play it one time.
I note, for example, that when you introduce the Schrodinger equation, you indicate the significance of E, V, ψ, and h, but do not account for m. Is that mass, momentum, meters or mulligatawny soup? I don't know. Ditto for the u and p in the second and third step. And then there is the fact that neither Shirokogoroff's nor Levi-Strauss' equations have the same form as those that you have been playing with previously (there are, at a glance, no squared terms, for example). To you, all this is obvious, hardly worth fussing about. To your intended audience, the majority of whom are at least as ignorant of math and physics as I am, all this is speaking Greek to a native speaker of Cantonese whose acquaintance with Indo-European languages is confined to a smattering of Old-Church Slavonic.
Even I, in my ignorance, can see some potential here for enlightening anthropological thinking. The notion of substituting the probability of a human being's occupying a certain social position for the assumption that her position is precisely fixed by the forces impinging on her at the moment that we are describing her behavior is provocative. It forces us to consider how she reached the position in which we find her and the likelihood of various directions in which it might be changing.
But without further development, we are left with nothing more useful than a maxim familiar to students of history, that you need to understand both what came before and what might have been to understand whatever it is that you are attempting to explain. Without some further explanation of how the formulas make it possible to follow that reasoning more precisely to unanticipated insights, the mathematical bubble simply bursts.
Michael, Keith, John,
Let me respond to your Comments, in no particular order.
Michael,
Again, I must come with a confession. As a science groupie of long-standing (but definitely not a scientist and most definitely not a mathematician), I can’t participate in your sense of wonder at the beauty of Schrödinger’s wave function equation – but I have long been deeply intrigued by Schrödinger’s cat. In fact, reading John Gribbin’s 1984 In Search of Schrödinger’s Cat was crucial to the theory of culture I’ve tried to develop over the years. That we can’t know whether the cat is alive or dead without opening the box containing it – and thus collapsing the wave function -- captures the indeterminacy of the virtual cultures each of us inhabits, enclosed as we are in our Schrödinger’s box of cultural space.
Keith,
About power laws: Another major inspiration for me has been Per Bak’s classic piece on self-organized criticality. Lots of little things happen, fewer larger things happen, very few enormous things happen – and these events conform nicely to increasing magnitudes of a power law. The problem for human experience and social life is that the very events that affect us most dramatically – earthquakes, volcanic eruptions, stock market crashes, rebellions, revolutions, population extinctions – are spread over such a long time frame that knowing the power laws describing those phenomena does little or nothing for our ability to deal with them.
Take earthquakes, for example. These are a subject of some interest to me, since I live a few hundred yards away from the San Andreas fault (I imagine they are for John as well, sitting on the other side of the Pacific Rim). We know that every day there will be an average of a few hundred (imperceptible) tremors below 2.0 on the Richter Scale, and that as we move up the scale that number diminishes, following a nice power law. But when we get to quakes of The Big One proportions – 8.0 or above – these supposedly occur every few hundred years on the southern portion of the San Andreas, again following a power law. Now were I a sapient California sequoia tree that’s been around for a couple thousand years, I could observe the regularity of those giant quakes and see that they indeed conform to the mathematical pattern. But I’m not. The best the CalTech seismologists can tell me is that The Big One may hit tomorrow, or in a couple hundred years. Either way, averaged out over millennia their frequency is that spread of a few hundred years. But that mathematical truth doesn’t affect a lot of human behavior; it’s certainly not the first thing on my mind when I wake up in the morning.
Yet when The Big One does hit it will be hugely important, and its coming is inscribed in the power law for earthquakes. This is basically what I’m getting at in suggesting that our lives are lived in the context of “a logic of things that just happen.” Things don’t just happen higgledy piggledy, but neither do they present any sort of determinacy we can rely on in going about our daily lives.
John,
Thanks very much for your reference to the Complexity Explorer; I’ll certainly check it out. Quite a while back I did try to keep track of what the Santa Fe crowd was up to, even followed Christopher Langton’s lead and designed a few primitive cellular automata. What really fascinates me about their project – as a big fan of schismogenesis – is that they offer (what seem to me) utterly contradictory models of reality. One model is self-organized criticality (see above) which posits that any system large and complex enough to be interesting (a society, the transportation or electric grid, the global economy, etc) is so finely organized that the slightest event can produce disaster. In other words, “equilibrium” is really a bomb ready to explode. What a marvelous irony this serves up to that old nag, functionalism: the institutions of a society fit together so nicely only because they are on the point of self-destructing. The other model, diametrically opposed to SOC may be summarized by the complexity crowd’s mantra, “order for free.” While we tend to think of organization as an aspect of matter wrested at great expenditure of energy from the jaws of entropy, it actually “just happens” (that phrase again). A random selection of elements set in motion generate orderly arrangements (those cellular automata, especially Conway’s Game of Life).
How can we even begin to reconcile these fundamentally different takes on the nature of reality? My suggestion, in a nutshell: The Universe is ambivalent about itself. And, not coincidentally, so is humanity.
Remark
It is the most difficult part of quantum mechanics, but if you understand it , I am sure, you can easy understand such anthropological equations as Shirokogoroff ‘s equation of “cultural unconscious impulses for ethnic changes” ( 1923 )
± ί² = δ/ ST × T/∆ T = ώ T/∆ T
in his Ethnoscience, and famous Levy-Strauss’s “ canonical formula “ ( 1954 )
( a : b :: c : a ¯¹ )
his Science of Mythology as well…
You will have to tell everyone about Shirokogoroff's theory, but here is a paper by Peter Gow about "mythic transformation... caused by the presence of thresholds, whether cultural or linguistic" based on Levi-Strauss' formula:
http://aotcpress.com/articles/lvistrausss-double-twist-controlled-c...
Huon, thanks so much for the link to Peter Gow's paper. It is, indeed, a fine example of anthropology in the classic style, informed by ethnographic detail but using that detail to enlarge a conversation and address the need for new theory. Lke Tim Ingold's recent Hau paper arguing for the importance of participant-observation, it would make a terrific topic for an OAC seminar. Can we get one organized?
I think there is an fine awareness in Gow's article of the relativity in the relation between 'smallness' (ethnographic analysis of threshold relationships in a given setting) and 'largeness' (grand cultural 'ensembles', the pan-human conversation).
I take it that it is this difficult relative scale that Michael is drawing attention to in talking about quantum effects and chaos theory--perhaps we need to study the 'small', 'smallness' with more analytical rigour because it contains crucial structural principles for understanding/predicting 'bigness', the 'big'.
I am not sure I have the same sympathy for Ingold's paper which seems to sit on the old fallaciously concrete dichotomy where ethnography is an absolutely small activity and too much attention to this little arena must impede our capacity for thinking about really big important issues. Maybe I misunderstood; I have to admit I found it hard to grasp what kind of bee was under the bonnet (or whether Bee was ≤ Alive).
Either might make thought-provoking seminars topics, though.
You have my support for this. I should say that Tim was my first ever student at Cambridge (writing up PhD gving one on one tutorials to a second year undergraduate). He probably taught me more than the other way round. This was memorable for me, but probably not for him. We were colleagues in Manchester and Aberdeen, but he was never "my student" in any strong sense of the phrase.
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