Denis, your story strikes a Romanian chord. The situation around here is even worse, from what I can tell. But it is quite a fascinating question, with different answers from different points of view.
For an economist, it is a matter of price formation. In the state system, Romanian doctors are paid a fixed (and miserable) wage, largely unrelated to quality or effort. The incentive to pocket bribes is huge, and patients know it so well. In the private sector (with transparent and varied prices for medical services), bribes are almost unheard of. Also, there is a more or less efficient market for bribes. Patients find out how much a doctor expects, usually from past patients, or from other doctors. Surgeons receive more than GPs, professors more than debutants, etc.
But I think there is something more about "medical envelopes", from a cognitive point of view. First of all, there is a vast asymmetry of competence between doctors and patients, which gives the former a large freedom of action. Is this pill better, or another one? Surgery or not? Home treatment or hospitalisation? To make things worse, the post-hoc reckoning is not very helpful, since most decisions may be medically justified, but you might also end up dead. The patient is at the mercy of the practitioner since she does not know what choices are better. The best way to make sure one gets the proper treatment is to insure the benevolence of the doctor, and a bribe is the simplest path to gain the doctor's amity.
Second, there is something special about this particular social exchange: the patient is dealing in an ultimate value - her health. Something everyone in Romania says is that there is no price too high to be healthy. (Paradoxically, giving up smoking somehow does not make the list - self-hint-hint-nudge-nudge). If people would risk not bribing a policeman to avoid a fine, they are extremely unlikely to jeopardise their health in this manner. One cannot afford to stick to abstract principles (like discouraging corruption) when her life is at stake.
Finally, there is something like a Maussian gift in the affair: one passes a fat envelope even without the explicit mention of an economic exchange. It is not that the surgeon would not operate without being bribed - the patient just shows gratitude without visible economic reckoning. Of course, under the veil of generosity stands the solid self-interest of the patient. The fat envelope is meant to make sure that no scalpel is lost in her belly. But no-one says it out loud. It's a "I know that you know that I know etc" which makes sure that the transaction is smooth and polite.
To end with a personal anecdote: I was (and to some extent I still am) very wary of giving out envelopes to doctors. A little bit of moral prudishness, a little bit of fear (what if he feels insulted?), a bit of monetary unsaviness. Those who are more competent in these matters reassured me: "just put the envelope on his desk - he knows what to do next" After all, he is the expert, and I am not.
Azzouni certainly has the bona fides to weigh in on this. But it seems to me that the pure sociology of it isn't quite so simple.
Take Wiles' first proof of Taniyama-Shimura. It had an error, but it took concerted efforts by extreme experts to locate it. But that's not the end of the story. It turns out that he and Richard Taylor were able to ascertain that piecing together two parts of the theory that didn't quite seem to work on their own was in fact enough to 'patch' the proof together (Wiles himself says as much).
So, Yes, the original proof was wrong. To a much lesser extent, Perelman didn't fill in all the blanks in his landmark proof of Poincare, leading to a (minor scandal) where two other mathematicians claimed to give the "first" proof based on the "ideas of" Perelman and Hamilton.
The question is this: if someone had done the patching of Wiles' proof for him, would THEY be the prover? How large does the hole have to be? When an error is found, who gets to decide whether it is trivial, whether it wrecks the proof entirely, and who will be the one credited with the insight that makes the whole thing work?
These are not trivial matters, and the issue isn't apportioning credit, but deciding what an error truly is. Typos don't count. Proving incorrect results certainly do. But what about "generally correct" ideas that eventually lead to a proof? How loose do those ideas have to be?
I don't think there's ANY argument about when large, demonstrable errors have been found in published proofs. But there are many other cases -- like de Branges' purported proof of the Riemann Hypothesis -- that fall through these neat cracks.
In respect to kinship terminologies, Levinson's question, "What constrains this exuberant diversity of systems?", is not answered by Kemp and Regier's analysis for one simple reason: Terminologies have a structure and logic, like grammars for language, that determine the possible range of kinship terminologies. Kemp and Regier assume any partition of the space of genealogical relations is a potential terminology and then show that existing terminologies occupy only a small portion of this space due, they assert, to a tradeoff between simplicity and usefulness. This would be like saying a sentence can be any subset of all possible vocabulary words, then asserting that the realized languages have sentences that are a tradeoff between simplicity and usefulness, but ignoring the fact that the simplicity and usefulness of sentences is created through the grammar of the language that constrains what are admissible sentences. The same is true for kinship terminologies, and the answer to Levinson's question has already been made by showing that kinship terminologies have a generative structure that determines the corpus of kinship terms, starting from the primary kin terms of a terminology, along with kinship concepts that are expressed in the terminology (such as reciprocity of kin terms), and the kinship structural properties embedded in a particular terminology (Read 1984, 2001, 2007, 2009; Read and Behrens 1990; Leaf and Read 2012, among others). For example, the difference giving rise to the fundamental division of terminologies into descriptive versus classificatory (bifurcate merging) terminologies derives from two different ways that sibling relations are conceptualized in different societies: (1) a sibling is the child of my parent other than myself (descriptive terminologies) or (2) siblings are those persons who have parents in common (classificatory terminologies) (Bennardo and Read 2007; Read, Fischer and Leaf 2013). Trying to understand kinship terminologies (and hence kinship systems) without first working out the generative logic of a terminology is like trying to understand languages without working out the grammar of a language. Extensive work has already been published on the generative logic of kinship terminologies and this work makes evident what constrains the variability in kinship terminologies that Levinson asks about.
Bennardo, G. and D. Read 2007. Cognition, Algebra, and Culture in the Tongan Kinship Terminology. Journal of Cognition and Culture 7: 49-88.
Leaf, M. and D. Read. (2012) Human Thought and Social Organization: Anthropology on a New Plane. Lanham: Lexington Press
Read, D. l984. An algebraic account of the American kinship terminology. Current Anthropology 25: 4l7-440
Read, D. 2001 What is Kinship? In The Cultural Analysis of Kinship: The Legacy of David Schneider and Its Implications for Anthropological Relativism, R. Feinberg and M. Ottenheimer eds. University of Illinois Press, Urbana. Pp. 78-117.
Read, D. 2007. Kinship Theory: A Paradigm Shift. Ethnology 46(4):329-364
Read, D. 2009. Another Look at Kinship: Reasons Why a Paradigm Shift is Needed. Algebra Rodtsva 12:42-69.
Read, D. and C. Behrens. 1990. KAES: An expert system for the algebraic analysis of kinship terminologies. J. of Quantitative Anthropology 2:353-393.
Read, D., Fischer, M. and M. Leaf. 2013. What are kinship terminologies, and why do we care? A computational approach to analyzing symbolic domains. Social Science Computer Review 31(1): 16-44.
Yes, kinship is back -- or more accurately, it is reclaiming its original vigor. Haven't you heard of the Kinship Circle? For each of the past three years, and as part of this year's annual meeting of the Amerian Anthropological Association as well, we have had highly successful sessions on kinship. The sessions have been integrated with the themes of each of the meetings. We have had an international group of scholars from Australia, Brazil, Canada, China, England, France, Germany, Italy, Qatar and the United States, presenting a wide range of papers, ranging from more "classic" questions about kinship systems to current research that is challenging some of our theoretical ideas about what constitutes kinship. The papers from the first two sessions will be published shortly. Dwight ReadFadwa El Guindi
Dear learned scholar of mathematicians, I disagree with your premise that mathematicians do not disagree, and, being wonderful souls, are easily converted to consensus. No less a scholar, intellectual and role model than Von Neumann (1961), the founder of game theory, argued against your premise. In fact, he bemoaned that unlike physicists, mathematicians who don't agree behave in an unsocial manner by striking out in new directions, leaving their conflicts unresolved. In his article, the first in his collected works, Von Neumann wished that mathematicians disagreed as physicists did. Whenever conflict arose between two physicists (e.g., Bohr and Einstein), physicists refused to ignore it, often bringing their field to a standstill until a resolution was found (i.e., consensus via debate, unlike your fanciful example of consensus without debate). I have long cherished Von Neumann's insight, and his remarkable paper on mathematicians. BTW, in my research, I too have found that consensus without conflict is indeed possible, except that none of the participants can agree on the result.
Von Neumann, J. (1961). The mathematician. Collected works, Pergamon.
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