This remark is inspired by Marianne de Laet ‘s anthropological comments ( Nature vol 501: 164-165,12 Sept 2013 ) on Harry Collins (2013) new book ‘Gravity’s Ghost and Big Dog : Scientific Discovery and Social Analysis in the 21^{st} Century ‘ (University Chicago Press ).
Harry Collins produced brilliant systematic sociological account of his almost 40 years (!) fieldwork among scientists in the field of gravitational ( relativistic ) astronomy.
It is important that mathematical physics of the gravitational waves is beyond of Alan Sokal’s anti-sociological scepticism because professional area of Sokal is algebra, ("physicalist") number theory and some algebraic applications of multivariative polynomials,Potts models ( 2 dimensional systems ) and even Roger-Ramanujan function in statistical mechanics and quantum field theory.Sokal is merely algebraist and not physicist. I suppose his applications of " radiculously simple generalizations " of the functions with the real and complex zeros combinatorially " defined polynomials ( of the Tuttle type )" ... to phase transitions in statistical mechanics have no real physical meaning at all. At least, I have doubts that Sokal ‘s computational algebra can have applications in real gravitational physics , correspondingly, possible Sokal’s refutation of Collins ‘work cannot be taken seriously today. Let us describe some forbidden aspects of gravitational waves history.
Gravitational waves were the first predicted by Einstein’s General Relativity in 1915 and, later, an existence of gravitational waves was rejected by Einstein ( together with N. Rosen ) in 1936 as well. Following Daniel Kennefick (1997),in his letter to Max Born, Albert Einstein reported that he arrived at the interesting result that gravitational waves do not exist at all, through they had been mathematically assumed in transitive period of formulation of General Relativity in 1915. Pure mathematically, Einstein faced with an existence of non exact solutions for nonlinear general relati-vistic equations ( described plane gravitational waves ) which cannot provide sufficient foundation for earlier prediction. Einstein and Rosen had submitted a paper entitled “Do Gravitational Waves Exist ?” to the Physical Review ( USA ) for publication (similar result with more dramatic refutation of Riemann geometry and Einstein’s time theory was published by Leningrad’s physicist Jakob Bronstein in 1935 ). However, Einstein’s paper was returned to him with … a critical referee’s report .As result, Einstein is withdrawing the paper and dismissing out the referee ‘s comments ( Einstein to Tate : July 1936, EA 19-086 ). In his letter to Editor (Konnefick 1997:2) Einstein in particular wrote :
“We ( Mr Rosen and I ) had sent you our manuscript for publication and had not authorized you to show it to specialists before it is printed. I see no reasons to address the – any case erroneous – comments of your anonymous expert .I prefer to publish the paper elsewhere “(!)
As is known, in 1937, indeed, one modified version of this paper with Rosen was accepted for publication by the Journal of the Franklin Institute in Philadelphia and another (reduced ) version was published in the USSR. In his Soviet publication, N. Rosen showed that plane gravitational waves were an impossibility due the ineradicability of singularities in the metric of General Relativity. Later, new generation of theorists had found that Rosen did not distinguish sufficiently between coordinate mathematical singularities and physical singularities, which , nevertheless, could be detected experimentally ( Bondi, Pirani, Robinson, Landau, Lifshits, and Weber) Thus, contemporary ground - based interferometers ( for instance, LIGO ) as well as ESA-NASA space - based interferometers (LISA) which built to detect gravitational waves are based on Einstein –Rosen taking unsolved mathematical dilemma seriously.
Hence, thus, Collins (2013) sociological observations on the puzzling semantics of knowing of gravitational waves, his sociological intuition that experimental evidence in gravitational wave astrophysics has gradually shifted from true observation to a social consensus and expectations of real catastrophe among experimentalists are probably have a sense in the context of our story.
However, in accordance with de Laet (2013: 165) ‘Collins defies a best practice of anthropology – to examine one’s motifs and motivations ‘ of scientists… I suppose, nevertheless, that this feature of Collins’s social analysis of gravitational waves detections cannot be achieved even within current anthropology of science and technology, in particularly, because both today’s sociologists as well as anthropologists of science do not speak in mathematical language of scientists, they, correspondingly, have limited access to understanding of scientific literature produced by members of subculture.
Being anthropologist I am doing fieldwork in some post-classical anthropological manner among quantum physicists and quantum hackers from 1996. I started my investigations with training in mathematical language ( mathematics is language of scientific subcultures )of theoretical physicists and later in order to be confident in my fieldwork, I published original mathematical result in Bulletin des Sciences Mathematiques (1999). Hence, it is quite natural that my language based ethnographic approach produced and is producing different results. In particular, I have formulated for myself some elementary rules of the fieldwork in anthropology of science which I’d like to share with readers .
RULE 1. Mathematical language of scientists is essential.
It is well known principle of the field anthropology. Perhaps, Edmund Leach ( after Bronislav Malinowski) was the first mathematically speaking and mathematically educated ( Cambridge University ,1^{St} Honour Degree ) anthropologist of science within British social anthropological tradition. Some his works on experimental “ethnographic algebra”(1945), binominal arithmetic of Jakobson–Levi-Strauss’s structuralism and symbolic logic of communication in social anthropology can, certainly, help to realize that understanding of the scientific subject and communications with scientists are almost impossible without mathematical language, indeed. Another story about Bruno Lotour can demonstrate an importance of mathematical language as well. Anthropologist Latour published results of his semiotic analysis of theory of Relativity where he expressed some doubts on logical justification of Lorentz transformations in Einstein theory and attempted to describe some sort of absurdity he had found in Relativity . In accordance with Latour, both Special and General Relativity “are accepted, more frames of reference with less privilege can be accepted, reduced, accumulated and combined, observers can delegated to a few more places in the infinitely large ( the cosmos ) and the infinitely small ( electrons ), and the readings they send will be understandable “(Latour, Bruno 1988 .A Relativistic Account of Einstein’s Relativity “ Social Studies of Science 18 :3-44)
As is known, number theorist Alan Sokal ( 2008 ), rejected B. Latour’s finding as ‘an example of nonsense ‘and had defined 40 pages of Latour’s article as typical ‘comical misunderstanding’ of real physics. He suggested that Latour ‘doesn’t understand what the term “ frame of reference” means in physics – he confuses it with “actor” in semiotics – he claims that relativity cannot deals with transformations laws between two frames of reference, but needs at least three [frames of references ]( Sokal, 2008.Beyond the Hoax. Science, Philosophy and Culture. Oxford : Oxford University Press p.155 ) Thus, old ethnographic rule about language training is also essential in modern anthropology.
RULE 2. Participant – observation of scientific subcultures can include such sort of integration as observer’s scientific publications.
This means that in comparison with sociologist, anthropologist can be completely integrated in scientific community, however, here, there is the risk of losing some levels of objectivity of observation. In my own fieldwork, I used this rule and have published physical article on quantum physics (2003) and have presented, recently, cryptographic paper at the first conference on Quantum Cryptography (QCRYPT 2011) in Zurich ETH (2011) in order to change a focus of acceptance and understanding of rapidly evolving subculture.
RULE 3. Anthropological Analysis of physical and even mathematical assumptions can discover something new indeed.
Comment
John, Thank you.
In contrast with popular “Fashionable Nonsense” that Einstein’s General Relativity predicts an existence of gravitational waves, our anthropological historical analysis is assuming quite different picture:
- Einstein had sufficient foundation to reject an existence of gravitational waves in 1936, even if it can destroy General Relativity ;
- Einstein accepted that chemistry, size and form of bodies are not important in gravitational physics ( Galileo‘s discovery ), hence, as is known Einstein made conclusion that gravity is effect of pure geometry (non – Euclideanness or curvature of spacetime ).Thus, if such thing as gravitational waves (purely geometrical effect ) cannot exist, then nevertheless gravitational movements as stable and well predicted transformations of our spacetimes must be in some sense “programmed” ?
- Thus, “general relativistic gravitational waves – 1915” as current social agreeing among physicists,may be, can have more sophisticated mathematical definition ( to include some unknown non Riemann geometries and non Einstein’s time theory ),
- current experimental installations built to detect the ripples in curvature of spacetime are not, probably, justifiable ( beyond trick with gravitational radiation at the large distances for very big masses), hence, such multi-billion experiment as LISA could be, perhaps, rejected by A. Einstein in 2013 as “ in any case erroneous “ test.
Michael, what you describe here sounds very impressive, indeed. Your remarks about social scientists who study sciences that are heavily dependent on mathematics without knowing the mathematics are very much on point. They also, from my perspective, point to a larger problem, which mathematical sciences are only a special case. One could say similar things, for example, about anthropologists who study Chinese religion with only the feeblest grasp of classical Chinese or, a less lofty example, anthropologists who study advertising without a firm grasp of marketing strategy and media planning. The days when the anthropologist was "the expert" on "his people" are long gone — especially so when the people in question may think in sophisticated ways that the anthropologist only dimly comprehends.
Best of luck with your research.
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