[T]hose researchers at high levels to whom prizes like the Crafoord Prize are given, have already attained such a level of eminence in society, that they have more than they need of material benefits and prestige among their colleagues, as well as the authority and perks that accompany these things. Is it not obvious, however, that these excessive rewards to the few must come at the expense of the many?

Those labors which now earn me the approbation of the Royal Academy were carried out 25 years ago, at a time when I was still integrated into the scientific milieu and shared both its worldview and its values. But I departed from this milieu in 1970. Since then, while not in the least renouncing my passion for scientific research, I have continued to put some distance between myself and scientific circles.

In the two decades that have intervened the ethical standards of the sciences ( certainly in mathematics) have been degraded to such an extent that the most bare-faced plagiarism between colleagues ( often at the expense of those who can’t defend themselves), seems to have become the norm. At least it is generally tolerated, even in exceptionally flagrant instances.

Given this situation, were I to agree to enter into the game of prizes and rewards, it would be equivalent to my giving stamp of approval to a state of affairs in today’s sciences that I see as being profoundly unhealthy. Their spiritual state, even their intellectual and material states, are nothing less than suicidal, hence they are destined to vanish in the near future.

Alexandre Grothendieck, rejecting the Crafoord prize

(Source: fermentmagazine.org)




women working in a tannery in the United States in 1932

hi-res







One young man’s experience of being homeless.

  • age 23
  • from Connecticut
  • moved to Santa Cruz, CA 5 years ago
  • worked in construction, got laid off (due to seniority) when demand lapsed
  • $3/hr is what you can earn by begging













Watch out people! This is Serious Mathematics for Seriously Smart People only … also it’s on the level of Kindergarten.

(Source: ams.org)
















how is anthropological knowledge of the way natives think, feel, and perceive possible? The issue [Bronislaw Malinowski’s] Diary presents, with a force perhaps only a working ethnographer can fully appreciate, is not moral. (The moral idealization of fieldworkers is a mere sentimentality in the first place, when it is not self-congratulation or a guild pretense.) The issue is epistemological. If we are going to cling—as, in my opinion, we must—to the injunction to see things from the native’s point of view, where are we when we can no longer claim some unique form of psychological closeness, a sort of transcultural identification, with our subjects? What happens to verstehen when einfühlen disappears?

As a matter of fact, this general problem has been exercising methodological discussion in anthropology for the last ten or fifteen years; Malinowski’s voice from the grave merely dramatizes it as a human dilemma over and above a professional one. The formulations have been various: “inside” versus “outside,” or “first person” versus “third person” descriptions; “phenomenological” versus “objectivist,” or “cognitive” versus “behavioral” theories; or, perhaps most commonly “emic” versus “etic” analyses […]. But perhaps the simplest and most directly appreciable way to put the matter is in terms of a distinction formulated, for his own purposes, by the psychoanalyst Heinz Kohut, between what he calls “experience-near” and “experience-distant” concepts.

An experience-near concept is, roughly, one that someone—a patient, a subject, in our case an informant—might himself naturally and effortlessly use to define what he or his fellows see, feel, think, imagine, and so on, and which he would readily understand when similarly applied by others. An experience-distant concept is one that specialists of one sort or another–an analyst, an experimenter, an ethnographer, even a priest or an ideologist—employ to forward their scientific, philosophical, or practical aims. […]

Clearly, the matter is one of degree, not polar opposition—"fear" is experience-nearer than “phobia,” and “phobia” experience-nearer than “ego dyssyntonic.” […] Confinement to experience-near concepts leaves an ethnographer awash in immediacies, as well as entangled in vernacular. Confinement to experience-distant ones leaves him stranded in abstractions and smothered in jargon. The real question, and the one Malinowski raised by demonstrating that, in the case of “natives,” you don’t have to be one to know one, is what roles the two sorts of concepts play in anthropological analysis. Or, more exactly, how, in each case, ought one to deploy them so as to produce an interpretation of the way a people lives which is neither imprisoned within their mental horizons, an ethnography of witchcraft as written by a witch, nor systematically deaf to the distinctive tonalities of their existence, an ethnography of witchcraft as written by a geometer.

Putting the matter this way—in terms of how anthropological analysis is to be conducted and its results framed, rather than what psychic constitution anthropologists need to have—reduces the mystery of what “seeing things from the native’s point of view” means. […] To grasp concepts that, for another people, are experience-near, and to do so well enough to place them in illuminating connection with experience-distant concepts theorists have fashioned to capture the general features of social life, is … a task at least as delicate, if a bit less magical, as putting oneself into someone else’s skin. The trick is not to get yourself into some inner correspondence of spirit with your informants. Preferring, like the rest of us, to call their souls their own, they are not going to be altogether keen about such an effort anyhow. The trick is to figure out what the devil they think they are up to.

In one sense, of course, no one knows this better than they do themselves; hence the passion to swim in the stream of their experience, and the illusion afterward that one somehow has. But in another sense, that simple truism is simply not true. People use experience-near concepts spontaneously, unself-consciously, as it were colloquially; they do not, except fleetingly and on occasion, recognize that there are any “concepts” involved at all. That is what experience-near means—that ideas and the realities they inform are naturally and indissolubly bound up together. What else could you call a hippopotamus? Of course the gods are powerful, why else would we fear them? The ethnographer does not, and, in my opinion, largely cannot, perceive what his informants perceive. What he perceives, and that uncertainly enough, is what they perceive “with"—or “by means of,” or “through” … or whatever the word should be. In the country of the blind, who are not as unobservant as they look, the one-eyed is not king, he is spectator.

Clifford Geertz, From the Native’s Point of View

(Source: hypergeertz.jku.at)




a couple different views on associativity.


Sources:

Marius Buliga says that an interesting mathematical paper should use ideas from at least 3 fields of mathematics. That’s great when it happens, however crossovers of 2 are quite good!

  • algebraic combinatorics – view combinatorics as clever counting tricks, and use classic isomorphisms of modern-algebra so one style of thinking can inform the other. For example Lagrange’s theorem is a “real result” in group-theory which is about counting. (It yields results in algebra.)
  • lie theory – view it as continuity (analysis) plus algebra (groups )
  • algebraic topology – the pentagonator comes from the swirlibund world of (non-pathological) topology, which speaks to my own pro-Seussical esthetics. But its content is somewhat algebraic—the “loop-deformation” rules biject nicely to tensors, so the “loose geometry” part of your brain can talk to the “move formal symbols around” part of your brain.

as well as some more familiar ones like analytic combinatorics, algebraic geometry, and algebraic topology, and some exotic stuff I saw recently: arithmetic topology and some papers of Benson Farb.