The best thing here at OAC is that anyone can write a blog post or a comment or a discussion topic about anything as long as there's a discernible anthropology in it. Other anthropology sites are too academic and formal; thus the posts and the comments seemed restrained, awfully familiar, and vanilla--that's not out of the box. It makes me wonder if anthropologists in those sites are really sharing their best or if they are being careful not to sound unprofessional or come out unacademic. The tone of their discussions and the depth of their arguments are no different to what one experiences in a graduate seminar run by a boring professor. I don't see passion, intensity, raw ideas, fresh thinking in their pages. If these forums were films, I would consider OAC an alternative or indie film. I hope Keith will continue running this site with such spirit.
I'm not being dismissive of other sites without basis. Last night I could not sleep and continue working on my latest project: a clay sculpture of a distorted face, an ashtray. So, I read the old posts I missed during my long hiatus from OAC. One blogger consumed most of my time. I went to bed full of thoughts, one of which was my newfound appreciation for OAC. If decades from now (and I'll still be alive) future anthropologists (if there will be) will apply mathematics in anthropology the way most do now with French theories, I'll be able to say: "A guy named Michael Alexeevich Popov bombarded us with mathematical and computational anthropology at OAC before you were born."
Although I seldom see a comment under his posts, I appreciate his intensity and passion towards his difficult subject. His post under discussion, P vs NP Problem, made me browse Wikipedia all night and write this blog post. P vs NP asks "whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer." "Quickly" means "the existence of an algorithm for the task that runs in polynomial time." Can we apply the concepts in this problem in our analyses of how long it will take us to know the death or failure of a culture or a community and how long it will take us to save it? It's interesting how "polynomial time" is qualitatively understood in Cobham's thesis. It is synonymous to "tractable", "feasible", "efficient", or "fast"--qualities we can use in time and efficiency-based problems in socio-cultural studies. My understanding of P vs NP is shallow and very little, but I already see concepts that are applicable in anthropology. I can't help but ask if algorithm for culture change is possible.
When I started here maybe three years ago, I was addicted to systems and models. I also wrote about Social Physics and my wishful statement about the possibility of applying the Laws of Physics in the study of culture. I still have the same questions now but not necessarily laws like the ones in Thermodynamics. So let me start. Can we apply Stress Terms from Mechanics of Materials or the simple formula for pressure (force/area) from high school Physics in analyzing economic stress or cultural pressure? Force can be poverty or religious fundamentalism or gangsterism, and area can be a community, a village or a city. Can we quantify economic stress and cultural pressure? I doubt a simple formula will do the job. Will the mathematics for complex systems work?
Anthropologists can be too wordy, repetitive, and long-winded especially if they are filling a required number of pages. Can Foundations of Mathematics be used as another language that simplifies concepts and clarifies logic? Maybe an Euler Diagram (imagine a small circle--subset--within a big circle--superset) from Set Theory can be a precise representation of a marginalized group within a marginalized community or a moderate group within a conservative political party. I know this is basic and has been done before in social sciences, but can we use the advance, complex stuff? For sure, culture is a complex system that controls chaos with groupings and categories. There are variables and constants in culture too. Can they be expressed mathematically?
I don't pretend to know all the answers, and I'm too old to go back to my high school dream of solving one of the prized conjectures. The thought that maybe anthropology students in the future will have the chance to choose Theoretical Anthropology as a field of expertise or even an undergraduate course, where they will study Physical Anthropology (not the biological one), Computational Anthropology, Mathematical Anthropology, and Systems Anthropology, tickles my dreamy mind. Maybe this will be the cutting edge in anthropological theories that will replace and bury Postmodernism, Poststructuralisn, and Postcolonialism for good.
Comment
Well, M, having you around is a powerful justification for the OAC. I have recently suggested to my colleagues that I should quit when the OAC turns 4 this May. I may be wrong, but I think a site like this needs active leadership and, for too long now, I have felt that mine is unrequited. You don't see much presence of the other members of the Admin team, some of whom justify their own lack of enthusiasm in terms of alienation from the commercialism of Ning. My proposal to quit has led immediately to a renewal of the idea that we should move from Ning to some other private, non-commercial site. So expect a discussion before long about the future direction and form of the OAC. Perhaps it might lead to a change of personnel, perhaps to the decision to leave things as they are (minus me). Obviously I have begun this discussion in repsonse to your generous post. You at least have never stinted with your contributions to this place. I wish I could say the same of a few more than our handful of regulars.
I started life as a mathematician and have taught statistics (which is not the same thing) for several decades, so I can't be said to be a numerophobe, like the majority of anthropologists. You probably have in mind a sequence like pure maths, applied maths, theoretical physics, physics.
Let me start with a Kantian question. If we meet extraterrestrials, would we expect them to have the same maths as us? The positivists would say yes, since maths is a set of abstract principles derived from how the universe objectively is. Kant had a different view. He believed that theories are recipes that help us to achieve the results we want within an acceptable degree of error. When the error is too great, we have to change the theory. He thought that the origin of science was in cooking -- metallurgy and brewing after the urban revolution. The fact that our theories work only for a time suggests that they are cultural, not natural. So there is no reason to suppose that ET's maths would be like ours.
I am a Kantian or perhaps a neo-Kantian (the latter don't rely on the categorical imperative to hold together a fragmented empirical world). He supposed that we bring preformed ideas to our experience of the world (the synthetic a priori) where they interact with our material sensations of it (the analytical a priori). Theory and fact join in an elaborate dance in which neither predominates.
I am interested in how number is instituted in our societies. The three dominant categories for this are money, time and energy. If you observe middle class conversation, you will notice that people often evoke how long, how much, how old etc in quite precise ways. It seems to me legitimate to apply formal reasoning to stocks and shares, household composition, time series, energy consumption etc since the theoretical approach is mirrored to some extent by the social substance being analysed. I baulk, however, at the extension of such approaches to fields of human expereince which are rarely or not at all organized by number. So I reject Gary Becker's claim that a neoclassical economist has the theoretical tools to explain family love.
I realise that maths is not just a question of number, but of logical propositions and relations. I have become convinced that the physicists and mathematicians, fondly assuming that their objects of study have nothing to do with human experience, are in fact a better guide than the social scientists to how ideas about the world are influenced by society. For this reason, I have avoided biological subjects since these lend themselves so readily to ideology, preferring rather to glean what I can from the study of stars, earthquakes, clouds, metals and elementary particles. But that is a whole other story.
Whether mathematics can be used productively in anthropology is a good question. But first more anthropologists would have to learn more math. For many of us that will mean overcoming math phobia. If I were starting over, this is the way I'd do it.
I'd begin with Kalid Azad's Math, Better Explained. Let me give you a taste by quoting a bit from Chapter 1, "Developing Math Intuition."
Our initial exposure to an idea shapes our intuition. And our intuition impacts how much we enjoy a subject. What do I mean?
Suppose we want to define a "cat":
- Caveman definition: A furry animal with claws, teeth, a tail, 4 legs, that purrs when happy and hisses when angry.
- Evolutionary definition: Mammalian descendants of a certain species (F. catus) sharing certain characteristics.
- Modern definition: You call those definitions? Cats are animals sharing the following DNA:ACATACATACATACAT....
The modern definition is precise, sure. But is it the best? Is it what you'd teach a child learning the word? Does it give better insight into the "catness" of the animal? Not really. The modern definition is useful, but after getting an understanding of what a cat is. It shouldn't be our starting point.
Unfortunately, math understanding seems to follow the DNA pattern. We're taught the modern, rigorous definition and not the insights that led up to it. We're left with arcane formulas (DNA) but little understanding of what the idea is.
Let's approach ideas from a different angle. I imagine a circle: the center is the idea you're studying, and along the outside are the facts describing it. We start in one corner, with one fact or insight, and work our way around to develop our understanding.....
It's an interesting trip, and you will wind up with a knowledge where important mathematical ideas come from and why they might be good to think about—even when doing anthropology.
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