There are two different anthropologies – anthropology by historians and anthropology by physicists and mathematicians. The first is academically recognized social science ,whereas , the second is just emerging discipline inspired by results of cosmology of antropic (anthropological ) principle, space life sciences, computational theory of human limits, gravitational and quantum biology, mathematical evolution, experimental econophysics, quantum games applications,applied mathematics and digital formalisms in anthropology.
Lack of formal training in physics and mathematics (correspondingly, a kind of ignorance ) in current anthropological education produces, unfortunately, a substantial gap between anthropologies. Mathematics is language of scientists, hence, misunderstanding of such tool of communication and experimental imagination by anthropologists may isolate anthropological community speaking in some ancient scientific language of the 19^{th} century from brilliant achievements of modern sciences.
Some attempts of Levi-Strauss of 1940s to incorporate elements of modern mathematics ( category mathematics ) became forgotten today and feeling of uselessness of social anthropology became now predominant.
Some analogies with economics, perhaps, can help us to find some balanced approach in anthropology as well.
There exist two economics now - traditional economics used mathematical methods and statistics in political discourse and econophysics - "physical economics" used advance mathematics of quantum physics and relativity’s mathematical imagination. Now they are coexisting worlds, however, numerical economics rapidly evolves now towards econophysics. Similarly, anthropology 1 ( as a social science ) and anthropology 2 ( existing as applications of physical and mathematical methods in anthropology , i.e applications of antropic principle in astrophysics, human -oriented area of gravitational and quantum biology , mathematical theology, artificial intellect anthropology, game theoretical anthropology etc ) can co-exist as diifirent worlds and different imaginations. Their competition can help to develop a new scientific vision of future anthropology.
Generally, thus, sooner or later, economics as well as anthropology could become full scale experimental sciences. We may await, that Solipsism by anthropologists cannot be tolerated always . Scientific ignorance could be reduced However , we also can expect, that anti-scientific attitudes of modern politicians can produce merely another wave of Economic Catastrophes. In particular in EU, where trivial problem of mathematical algorithm of numerical analysis of budget and its provable presentation for public consciousness are usually understood as pure political or historical legacy problem…
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Keith, thank you.
Let us imagine science where "borrowing from other disciplines " became impossible. This means we must use own anthropological,own biological, own poetical etc scientific standards to develop original own science. However, history of science may suggest that, for example, discovery DNA is merely application of physics in biology, modern neuroscience is based on nuclear imaginary technology , Levi-Strauss theory of myth is based on Weil catagory algebra's associations, etc. Thus, we cannot use such sort of strange assumption at all. There is high scientific standard presented by modern physics and mathematics,and our attempts to relocate our discipline beyond or into another universe must have serious arguments...
intuitions
In case you haven't seen it, I think you would appreciate BBC documentary filmmaker Adam Curtis' new three-part series "All Watched Over By the Machines of Loving Grace," in particular episode two titled "The Use and Abuse of Vegetational Concepts." (Hat tip, yet again, to The Memory Bank.)
I have two thoughts really. The first is that I am suspicious of attempts to incorporate models from one domain to another without really thinking it through. Case in point: memetic theory was popular for a while at least in part because it seemed to promise that existing population genetics models might be immediately applicable... except that they were not, because the underlying systems are quite different in most of the ways that matter.
The truth is that fields like physics, chemistry and computer science have driven a great deal of mathematical innovation, because existing mathematics were insufficient for their respective needs. The networks (or graphs) that John McCreery mentions is I think an excellent example of precisely this sort of need-based innovation. Rather than another tired attempt at making social science another physics or biology, the focus needs to be on developing a mathematics, or body of mathematical models, appropriate for the domain of inquiry.
Naturally, that mathematics does not need to be all new. Algebraic approaches, for example, have been quite successfully used in modeling certain conceptual systems (e.g. kinship terminologies, see work of Dwight Read, or take a look at http://csufresno.academia.edu/JacobLee/Talks/13570/An_algebraic_ana...). And of course, there are the various social network and agent-based simulation methods that have been employed... I might also mention the various ontological theories of information (e.g. situation theory and situation semantics, channel theory, and so on) that in one way or another attempt to formalize meaning in natural language, etc..
My second thought is that although I see myself as an advocate for mathematical anthropology, a fair amount of the work that are self-described as belonging to that category of inquiry is too light on the anthropology and heavy on the mathematics. The complaint is not that the math is difficult--I've gotten used to the difficulty of papers in mathematics--but that their authors seem to have lost sight of the fact that they are studying people. I've read entire papers in the category that failed to mention a single ethnographic example, or if an example was cited, no rigorous attempt was made to actually connect the mathematical model to the ethnographic reality in a way that would allow one to evaluate the use of the mathematics. Mathematical anthropology is not an excuse to do mathematics, but an application of mathematics to anthropological problems.
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