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
Interesting, John. I will just write a blog post, if I have time as I'm back to work, about Mauss, Gibson, gift exchange, participation shift, and the application of sociological theory and method in anthropology.
Also for your information:
Hi, Mark. You are indeed correct: the P-shift terms relate to the next event in the sequence, while the R* terms reflect overall recency in terms of events ever received (RRec) or sent (RSnd) by the focal actor.
The statistics associated with these terms are described formally in:
Butts, C.T. (2008). "A Relational Event Framework for Social Action." Sociological Methodology, 38(1), 155-200.
Note that, as a general matter, RRecSnd and PSAB-BA involve distinct types of reciprocity, and both can be active within the same exchange. The former reflects the tendency of ego to send to alters who have most recently directed events to him or her (relative to other alters who have directed events towards ego); this depends only on ego's incoming event history, and not on other activity within the event sequence. By contrast, the latter reflects temporally local turn-taking dynamics (the tendency of the next event to be a response from the last receiver to the last sender), and is not egocentric in character. If you are dealing with a small-group setting, you will probably find P-shift effects (including the AB-BA shift) to be quite important; in a setting where actions are not globally observable (e.g., email), such effects are typically contraindicated.
The author of the email and the article cited is Carter Butts, who is usually the smartest guy in the room at Network Analysis Conferences. Note what he's doing here, talking about reciprocity but not just in generic Maussian terms. He's thinking about the sequence and timing and choice of partners, all questions blurred by the generic assumption that reciprocity implies a gift, acceptance, and giving back, with no specification of who reciprocates to whom and when.
Those interested in this topic and especially in developing simulations may find it interesting to take a look at Insight Maker, a free, Web-based tool for doing simple simulations.
I suppose that the best strategy is to continue where Malinowski and Levi-Strauss were successful in their applications of mathematics in anthropology.It could be understandable for all ethnographers, it could have historical logic and it can provide an introduction into universal language of science (and ideas ) - mathematics. There exist different forms of such introductions - new history of ethnography (with some mathematical refinements ),new ,say, "Anthropology - Foundational Mathematics -Foundational Physics " kind of programme, fusion(holistic) workshops and new methods courses and knowledge exchange seminars, etc..? My experience also suggests that contemporary mathematics, physics, life sciences are needed a special vision of anthropologist as scientists as well.
Ananlogy .The best results in scientific economics are connected with good applications of mathematics ( in fact all Noble prizers in economics are applied mathematicians ). Einstein's Relativity is applied Riemannian geometry, best known interpretation of quantum mechanics is applied complex analysis etc etc. Thus,this is a kind of algorithm of success... which can help to define the field of actions.
Thank you.
P.S. Lest someone think that I could have just spent years going through the data manually, let me add that the result is a recipe that works regardless of the data in question. I can, for example, now do the same sort of analysis using media or years as the attributes, to see how many creators work in multiple media or win prizes in multiple years. To me that is what makes the math so valuable. Once you know it, you can reuse it in all sorts of ways.
M, I would say that I am getting serious about studying complex systems and networks; but the direction my seriousness is taking is not some new contribution to mathematics or algorithms. I am resigned to the fact that others (our Michael Popov is, I suspect a good example) are way ahead of me in that direction, and at my age I am not likely to catch up. My own particular interest is in integrating social network analysis with historical and ethnographic research.
So far the chief virtue of the social network analysis is enabling me to work with archival data on a vastly larger scale than anything I have tried before. I think of what I am doing as resembling field geology as described by John McPhee. The industry I am studying is like a mountain range. From a distance I can see the peaks and foothills. What I want to know more about is the underlying structures and how they got that way. On my own I can't examine every inch of those mountains and, in any case, a lot of what I want to know is buried deep below the surface. I have discovered a body of data that is sampled from a space near the peaks and my analytical tools help me map the samples in a way that suggests new ways to look at the other material I've collected. I can ask basic questions like
I have more than enough to keep me busy and not nearly enough time to learn ERGM modeling or other hot shot techniques. Just as it was back in Taiwan, there are numerous possible paths to pursue. I will not get around to pursuing them all.
What I can do for people who do similar research is share some of my recipes, procedures that fill the gap between toy examples like the five households you studied and the serious mathematics that like beyond my capabilities. The example I described in my previous message falls into this category. If someone else who is working on project team or other 2-mode network data comes across it, they can save a lot of time by not having to work it out for themselves. A modest contribution, but I think a useful one. I can feel good about that.
My God, John, you are this technical. Why don't you get serious in studying complex systems and networks?
My knowledge of graph theory is high school introductory, but I think it is already applicable in ethnography especially when it involves connection, relationship, kinship, influence, participation.
The best experiment we did then involved five households (K5) in a block, we checked if they had close relationships or if the block was peaceful. We were told that if each of the five vertices had the same number of edges (in this case, four) or had the same degree, it was a complete graph as K5 is, and indeed the five households were peaceful and friendly to each other. They were all connected to each other. The stuff I learned were mostly applicable in data organization and representation. Forgive me if I mismatched the terms.
Regarding the data you shared, let's invite our resident mathematical anthropologist. Hi, Mr. Popov.
@M "The question is: can we make a flowchart, for example, of steps or rules that will help us come up with a meaningful, if not general, definition?"
Azad's advice for getting to grips with mathematical ideas is to realize that there are many angles from which to approach them. Pick one that looks promising. Try working with it. If that doesn't work for you, try a different one. Keep changing angles until you finally get the idea. When you get the idea right, you should be able to see how it works from all of the different angles you've tried. That is, it suddenly occurs to me, the way a Roomba robot vacuum cleaner works. It bounces around at random, acquiring information about where obstacles are and how to get around them. It will never get into some corners of the room but has it travels back and forth it does quite a respectable job of cleaning up the room. Where it gets stuck is when it traps itself in a place that it can't bounce out of.
@Keith
""I am interested in how number is instituted in our societies. The three dominant categories for this are money, time and energy."
I, too, am intrigued by this suggestion.Serendipitously, I am currently reading Keith Devin's The Man of Numbers: Fibonacci's Arithmetic Revolution. As I am sure you know, Fibonacci did not invent the Arabic numerals we use today; but his books, showing how hundreds of different problems could be solved using them, set the stage for the rise of both modern commerce and modern science. He was the son of an Italian merchant who traded with the Levant and became fascinated by the way in which Arabs calculated prices and other measurements and thought that they would be useful for Europeans, too.
The most difficult and also intriguing part of the book is trying to follow Fibonnaci's examples. Without modern algebraic notation and the rules we learn in school, he had to work them out one step at a time and write out what he was doing in words instead of formulas. Without the conventions we take for granted, he employed approaches that now seem both strange and very cumbersome, not at all easy for me at least to get my head around.
@M and Keith
Indulge me for a moment, while I talk about my own application of mathematics to anthropology. I am talking about graph theory and matrix algebra, which lie at the heart of network analysis. My understanding of both these topics is rudimentary, but I am in the fortunate position of being able to use software developed by people who understand them very well, indeed. My problems have been working out how to use the software to answer particular research questions.
When I began my research on the social networks formed by the members of the creative teams who produce award winning advertising, I was curious about how many worked on projects for more than one advertising agency. On the one hand, I had the keiretsu model of Japanese industry, in which a large company, its suppliers and distributors, form a vertically integrated group modeled on the han (roughly "feudal domains") into which Japan was divided during the Tokugawa era. Keiretsu ideology prohibited group members from working for rival groups, an act that would be seen as a betrayal. On the other hand, I knew from personal experience that there are freelancers and employees of production companies that sometimes worked for both Hakuhodo, the agency that employed me, and our arch-rival Dentsu. What I didn't know was how common these people were, i.e., what proportion they formed of all of those who worked on the award-winning ads in my data set.
Since I am working with credits data on over 7,000 creatives linked to nearly 4,000 ads by roughly 30,000 roles (copywriter, creative director, art director, etc.), manually checking that data would have been an enormous task. But I noticed something. Each ad is produced by a single agency. Agency is thus what network analysts call an attribute, a property with a 1-to-1 mapping to the nodes to which it applies. Thus, if I simplified the agency codes, reducing several hundred shops large and small to four categories (Dentsu, Hakuhodo, ADK [the no. 3 agency] and other) and replaced ads with agencies, I would be left with a 2-mode network of several hundred (or thousand) creatives linked to only four nodes on the agency side. I had noticed, too, that by definition a 2-mode network is one in which nodes in one mode (here creators) are linked to each other only via paths that pass through nodes in the other mode (here agencies replacing ads). Since creatives would then have only agencies as immediate neighbors, the degree distribution (the number of immediate neighbors per node) would tell me precisely how many creatives worked for 1, 2, 3 or 4 agencies, with those who worked for 2 or more being precisely the the multi-agency creators I wanted to identify.
I can now perform this operation on any of the networks I work with in under a minute. But to get where I am now took an immense amount of work to get the data coded and into my Filemaker Pro database. Working out how to get it from the database into Pajek .net (for network) and .clu (for partition) formats and figuring out which sequence of Pajek commands to use to implement the process that I have described above has taken me the better part of five years.
Therein lies the rub. I don't expect you to have an easier time thinking through the process I have just described than I do trying to understand how Fibonacci solved quadratic equations. But thanks to an education that taught me enough math to follow in the footsteps of folks like Andrew Mrvar and Vladimir Bategelj, the mathematicians at the University of Llubjana in Slovenia, who wrote Pajek, the software package I use, I now have at my command tools that, for my purposes, work much like a biologist's microscope, allowing me to zoom in and out, use color to highlight structures of interest that appear at different levels of magnification, extract and dissect them to stimulate thinking about how they were formed. My friends who are still stuck with taxonomic logic chopping because they know no math will never be able to use these tools—and their anthropology will be the poorer for it.
@ Keith
I agree and like how this reads:
"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 also question the mathematicalization of something too abstract like love, hate, justice, freedom etc. I am, however, interested in the study of poverty as an economic stress, for example. Is economic stress quantifiable? I believe so. To go further, can we study racism, a kind of hate that is not too abstract since it involves government policies, using economics? Are homelessness, alcoholism, addiction caused by discrimination that's job-related and their effects to family and society quantifiable?
Let me cite what just happened at my former state university. A student who was a daughter of a taxi driver and a housewife committed suicide because basically her family could not afford to pay her tuition and she was advised by the university officials to file a leave.
http://newsinfo.inquirer.net/375869/coed-suicide-sparks-soul-search...
I have two questions related to the incident and the application of mathematics even econometrics.
1) Is the family's loss economically quantifiable considering that their daughter was their only chance to improve their lot or to get away from poverty? Can we project the future value of a person who goes to school because she wants a job later that can be a big help to her family?
2) For a developing nation that needs more scholars, do her death and other deaths of people like her affect economy and development (at least in the community level) since their families will remain poor (not productively active in economic and financial activities) and the potential that they can contribute economically in the future is gone? Can we calculate such losses?
@John
A word having many definitions is, indeed, a problem related to complexity. The question is: can we make a flowchart, for example, of steps or rules that will help us come up with a meaningful, if not general, definition?
Thanks, Keith. I think those contributors from India, Indonesia, and Korea (like Heesun) are also testaments to your inclusive mission.
Going back to the post, I like what Latour writes:
"We all know subcritical minds, that’s for sure! What would critique do
if it could be associated with more, not with less, with multiplication, not
subtraction. Critical theory died away long ago; can we become critical
again, in the sense here oﬀered by Turing? That is, generating more ideas
than we have received, inheriting from a prestigious critical tradition but
not letting it die away, or “dropping into quiescence” like a piano no longer
struck. This would require that all entities, including computers, cease to
be objects deﬁned simply by their inputs and outputs and become again
things, mediating, assembling, gathering many more folds than the “united
four.” If this were possible then we could let the critics come ever closer to
the matters of concern we cherish, and then at last we could tell them: “Yes,
please, touch them, explain them, deploy them.” Then we would have gone
for good beyond iconoclasm."
Does Latour envision critical studies to go towards the study of complexity a la Turing? Is his idea of critical studies computational, the way how logic is employed in computer studies? Is his idea of "generating more ideas than we have received" algorithmic--step by step procedures or rules of looking at things? Does his idea of "thinging" include culture? Is putting culture on paper the way how physicists reduce the universe into formulaic calculations on paper "thinging", a procedure that makes a thing we can touch and deploy?
I have so many questions related to that paragraph alone. One thing I'm sure, after iconoclasm, what is left is to study the deconstructed, the ruined, and the disordered and simplify the complex. I see mathematics and computation playing a role in that reconstruction and simplification.
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