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February 25, 2003

Yo colored-a derivative isn't authentic and true to your culture

Joanne Jacobs pointed me to this article on something called "ethnomath":

Ethnomathematics has a few parents, but most observers trace its formal birth to a speech given by the Brazilian mathematician Ubiratan D'Ambrosio in the mid-1980's. Now an emeritus professor of math at the State University of Campinas outside S-o Paulo, he explained his thinking a couple of years ago to The Chronicle of Higher Education: ''Mathematics is absolutely integrated with Western civilization, which conquered and dominated the entire world. The only possibility of building up a planetary civilization depends on restoring the dignity of the losers.'' Robert N. Proctor, who teaches the history of science at Pennsylvania State University, says he wants to counter the notion ''that the West is the be all and end all'' when it comes to mathematical studies. ''After all,'' he adds, ''all math is ethnomath -- not just African kinship numerics or Peruvian bead counting, but also the C.I.A.'s number-crunching cryptology and Reaganomics.''

I'm basically speechless.

These morons should put their well-being where their mouth is. Have a group of engineers use non-Western math, perhaps Peruvian bead counting, to figure out the parameters necessary for a bridge to safely span a river gorge. To show how strongly they believe in the validity of the ethnomath concept the researchers should cross the bridge, to actualize their teachings in the material world and break the hegemony of Euro-phallo-centric numeracy....

Posted by razib at 04:27 AM

I don't think that is the message here. In fact, you can use an abacus (or Peruvian beads, or a slide rule) to calculate just about any number. You are certainly correct to note that many abstract and essential mathematical concepts are vital to engineering, but utilizing them is not dependent on using conventional, modern, western tools. It is pretty clear that as a sociological study, it is useful to study ways that other cultures have learned and developed math. After all, it is only recently that the west developed standardized weights and measures (still not used in the most technologically advanced state in history, by the way!!). One only needs to go to the gas station to get a *gallon* of gas, derived from a *barrel* of crude oil, and then stop for a *pint* of beer on the way home, to get thinking about the vagaries of counting methods.
Incidentally, your example would be trivial, because all the hard parts would be done on paper using esoteric symbols in a gibberish language (e, pi, i, etc) anyway, and then all you have to do is enter the desired height, length, weight, etc, and calculate. You can certainly do that on a Peruvian bead counter...

Posted by: Paul_Orwin at February 25, 2003 07:34 AM

All around the world, people in all cultures (except maybe Nauroo) are writing creative papers in math and exact sciences and adding to the store of human knowledge.
It was only up to the end of the 19th century that western cultures had a monopoly on higher math. Today the content of math and physics, two fields I know about, owes much to southeast Asia, to China, Japan, and, yes, to the Islamic middle east. The ethnomathematicians are motivated by an inferiority they have no cause to feel.

Posted by: Dick Thompson at February 25, 2003 08:13 AM

yeah, but didn't India give us "Arabic" numerals?

Jeez. Not only is the concept (that math oppresses) ridiculous, but it's not even fundamentally Euro.

Posted by: David at February 25, 2003 09:19 AM

I find the inclusion of Reaganomics as a 'kind of math' quite entertaining. Anyway, if the speaker was trying to promote the study of mathematical methods and discoveries in other cultures as a field of cultural or anthropological inquiry, then I'm all for it. But if he's trying to equate them with Western mathematics in terms of usefulness (or merit) - that is he wants them promoted as mathematics as such - then he's out of touch with reality. In a big way.

Posted by: borisb at February 25, 2003 09:23 AM

I have nothing against the study of non western math/number systems. It seems to me like an interesting field of study.

Maybe cryptography is culture related, i can understand that, but what about number theory which is the under layer of it ?
It does gets silly and ridiculous when they push the math equivalent of cultural relativism.

Western math is more advanced, more useful, more systematic . In what other cultural traditions do we find a body of people thinking full time about mathematics in order to discover new problems and solve them ?
Mathematicians as we know them have probably existed in China and int he islamic world, but their contributions are already in what's called western science ( one of whose wonderful abilities is that of absorption of any useful knowledge from any source)

I'm sure that african kinship numbering is fine, but it's limited to JUST THAT, kinship numbering. It's not a system, it's not a GENERAL method. It's a special case.
Western mathematics also has the advantage of the most advanced and practical notation available (and it was humble enough to throw away roman numbers and adopt the ridiculously superior indo-arabic system).
My suggestion to those who would like to resurect other math systems : catch up with western math, take as much as you can from it and then build from that, if you wish.

Posted by: ogunsiron at February 25, 2003 11:13 AM

to PAUL :
Arithmetic may or may not be a problem. I'm sure that math systems other than the western ones "know" about arithmetic but what about trigonometry for example ? What about calculus ? Don't these "tools" make the job easier ? Are those conceptual tools available in the alternative math systems ? I think that's what really matters here.

Posted by: ogunsiron at February 25, 2003 11:38 AM


my problem is that this might give certain kids the message that the reason they aren't doing well in calculus is because it is outside the bounds of their cultural upbrining. some people just suck at calculus.

Posted by: razib at February 25, 2003 12:25 PM

Certainly, to the extent that this sort of thing might be used as a crutch to defend poor performance, I agree with you. My point was only that there are deep assumptions in our numbering systems that get embedded in our higher math, and it is worth studying what those are, so that we see potential holes in our logic. To this end, other number systems (using different bases, for example) can be and are studied. Incidentally, this doesn't have to be cultural, you can force yourself to work in hex, for example. But there are clear cultural pressures for and against that sort of behavior.
To ogusiron, I think that calculus, for example, is based on the notion of a continuous function v. a discrete function. This has nothing to do with numbering. All of this extends naturally, I think, from the idea of symbolic thinking. If your culture allows you to use the idea of, say, writing the number 3 on a ledger to indicate how many apples you have, then you could write "apples" at the top of the column, and then have different numbers in each row for the number of apples you had. You could then have a bunch of columns, each for different things, say apples and oranges. The total fruit would be "a+o" on a given day. That's algebra. Then you have a discrete function f(d) such that on day d you have f(d) fruit. I don't think any of this depends on the way you count fruit.
In other words, I think the numbering system does not INTRINSICALLY matter, although certainly a good base goes a long way towards simplifying the math.

Posted by: Paul Orwin at February 25, 2003 01:47 PM

paul, i think we are talking past each other. certainly the axioms that we start with matter. on the other hand, symbolic, logical & "linear" thinking are not explicitly "western" (chinese and indian philosophy is a bit garbled in my perspective, but then, so was ancient greek philosophy to some extent). certainly "western math" has non-western antecedents-on the shoulders of giants.

the problem (from what i gather, and have been told), the ethnomathists and their ilk are less interested in studying other avenues of research, as they are in deconstructing and deprivileging the logical & empirical tradition. to this end, they refashion non-western cultures in their own PoMo terminology.... (for instance, they will focus on the non-material tendencies of hinduism, but ignore the hard-headed rival caravaka philosophy that was naturalistic and explicitly anti-spiritual)

Posted by: razib at February 25, 2003 01:54 PM

Understand that there is money to be made in the social sciences to any scientist or mathematician willing to play along with the "all science and math is culturally relative" chorus. I suppose they are not hurting anyone, as long as they do not draw from the science and math budgets of their universities, and as long as potential scientists and mathematicians do not take them seriously.

Posted by: RB at February 25, 2003 02:59 PM

One nit and one comment:

Paul says "After all, it is only recently that the west developed standardized weights and measures (still not used in the most technologically advanced state in history, by the way!!)."

The US system of measurements is in fact standardized -- that's much of what NIST is all about. It's just not metric, and while that has some esthetic implications, it hardly stops the progress of science. If instead you meant "rationalized system of weights and measures", well... even though the metric system started out that way, the standards are now independent of things like the density of water and the Earth's diameter... and each other. [end pedantic rant]

As to the argument "that there are deep assumptions in our numbering systems that get embedded in our higher math, and it is worth studying what those are, so that we see potential holes in our logic." If there are in fact those "deep assumptions" embedded in our math, they're embedded just as deeply in the physical world. I think I need only point to the incredible success of such theories as quantum mechanics and the general theory of relativity to demonstrate this -- their accuracies are typically good out to the limits of our measurements, better than one part in a billion in many cases, and the fact that our technological world operates at all is testimony to the extremely close ties between math and universe.

If you're talking about things like the differences between the Schrödinger and Heisenberg formulations of quantum mechanics, I can agree to this extent: it's much easier to do QM with wave functions than with matrices (but computers and software have removed much of this difference in recent years). The mathematics of the two, on the other hand, has been demonstrated to be completely isomorphic; QM simply cannot be done, however, with Roman numerals -- regardless of the theory.

Posted by: Troy at February 26, 2003 01:45 AM

Reading the article, it seems to have little to do with the (much more interesting) argument you guys are having.

The "ethnomath" people themselves, at least as described, are pushing for inclusion of the evolutionary dead ends of mathematics to be included alongside the Egyptian->Greek->Persian-Whatever->European math that ultimately won out, out of the usual concerns for self-esteem and equal credit for all groups.

Truth is, I'd be fasscinated to learn about those things. But I'm leery about introducing them into a classroom where they'll probably confuse the kids and almost certainly confuse the teachers. Allowing ideology and math to compete for attention seems like potential bad news to me.

Posted by: Otter at February 26, 2003 06:58 PM

The whole concept is silly except from a mathematical historian's point of view. Of what possible use is it to teach all children the incredibly cumbersome methods that the Romans had to use to perform long division, or that the Babylonians had to use to calculate the hypotenus of a triangle? The fact is, the concepts are the same no matter what number system or notation one uses. As more powerful notations and methods have been developed, they've replaced older, less efficient systems. There's a very good reason why we don't use the primitive, extremely limited methods anymore -- if the math involved in designing an airliner is difficult with modern systems, what kind of horror would it be with Babylonian? "Ethnomath" is just an excuse for incompetence.

Posted by: Larry at March 1, 2003 05:44 PM