One of the projects I’m working on at the moment is a series of articles for an upcoming encyclopedia of world history; I’m writing a set of short pieces for them about various aspects of science and technology in the ancient and early medieval periods. Two of my assigned articles deal with Indian mathematics in various periods. All of the research I’ve done on this so far, both for my courses and for these articles, has been in books devoted specifically to Indian science and technology. I decided this week that it couldn’t hurt to see how these topics are portrayed in more general texts, surveys of the history of math in general.
What I found in these general histories was… not surprising, I think, so much as disappointing. When I was first assembling the materials for my ancient science survey course, a couple of years ago, I was struck by how many of the “general” histories completely discounted the work done by any non-Greek and non-European culture. I had started to think, though, that my memory of that was exaggerated, but I don’t think it was.
One of the books I looked at this week was Carl Boyer’s History of Mathematics. It’s a pretty standard general survey, and one that (as far as I can tell) is well-respected and fairly standard in the field. It has one chapter covering mathematics contributions from China and India, and it’s extremely dismissive of Indian contributions.
(Since I don’t assume that y’all know a lot about the history of math: a lot of major mathematical concepts were either invented or developed by scholars working in the Indian subcontinent. The first systematic development of algebra comes out of India, as does the place-value notation system and the first real use of zero as a number that can be used in mathematical calculations. Some of this filtered into European intellectual consciousness as attributed to Islamic influences–algebra (al-jabr) and “Arabic numerals” in particular–but the Islamic scholars credited the Indians with the real innovations. That cultural transmission process is interesting in its own right, but also a little beside the point here.)
In describing all of this, Boyer basically goes out of his way to avoid having to credit Indian mathematicians with any real discoveries. Like this:
“It appears from the extant evidence that the change took place in India, but the source of the inspiration for the change is uncertain. Possibly the so-called Hindu numerals were the result of internal development alone; perhaps they first developed along the western interface between India and Persia, where remembrance of the Babylonian positional notation may have led to modification of the Brahmi system.”
“It is quite possible that zero originated in the Greek world, perhaps at Alexandria, and that it was transmitted to India after the decimal positional system had been established there. The history of the zero placeholder in positional notation is further complicated by the fact that the concept appeared independently, well before the days of Columbus, in the western as well as eastern hemisphere.”
In both of these examples, it’s a case of misdirection. Sure, it’s -possible- that the concept of zero (as a mathematical operator, not just a blank placeholder) originated in Alexandria. It’s equally possible that it originated in Beijing or Prague or on the coast of southern Maine, or any number of other places in the world for which there’s no evidence whatsoever for the discovery of zero. I’m all in favor of giving Alexandria more credit for fascinating discoveries and accomplishments–the story of Alexandria is one of my favorites in the whole history of premodern science–but I’ve never seen any hint that they should get credit for this one, and Boyer doesn’t provide any evidence in support of this. He just suggests it, you know, as a possibility. The historical evidence points clearly in one direction, and the only reason one might need to suggest that Hindu numerals actually originated in Persia, or that zero actually originated in Alexandria, is if there’s some reason it’s implausible for it to have happened in India. It’s hard for me to justify that sense of implausibility, since Indian mathematicians were renowned throughout the ancient world for their advanced calculation skills and their sophisticated understanding of number concepts.
This is as good a time as any to point to one of the most brilliant pieces of writing I’ve seen on an academic blog lately: New Kid’s explanation of what “bias” means. The cloth analogy is great, not just because it’s etymologically valid, but because it’s gorgeously concrete and also flexible. Everyone has a bias, which makes it easier for them to believe certain things. Boyer’s bias seems to have led him to have trouble believing that Hindu numerals actually originated in India; my bias leads me in a different direction. (A couple of points, in the interest of fairness: the book in question was written, as far as I can tell, about fifty years ago, when his kind of approach was much more common. Also, I can’t presume to speak to Carl Boyer’s attitudes more generally, since all I know of his work is this particular book. And, finally, there is always the possibility that his position is right and mine is wrong–when you’re dealing with history that old, a lot of it is reconstruction and extrapolation anyway.)
One of the guiding principles behind my ancient science survey course was that scientific activity is one of the most basic human functions. The forms of scientific work have varied from culture to culture, but every human civilization that’s gotten beyond a certain baseline of stability and prosperity has developed some form of scientific culture. The fact that the forms vary is key to understanding the historiography–not all types of scientific work have looked, to modern Western historians, like real intellectual work. But if you approach the historical record with the right mindset (with the right bias?), you can’t help but see that there’s an enormous amount of creativity, vitality, and intellectual sophistication throughout the ancient world.
Posted Friday, April 25th, 2008 at 5:08 pm. Filed under: academic > writing and editing.
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I loved that post by New Kid, too. I may have to steal it for teaching–especially since I’ll be working with students who have been taught that it is possible, and desirable, to avoid any bias at all.
[...] Joe McKeever wrote an interesting post today on indian math.Here’s a quick excerpt…ago, I was struck by how many of the “general” histories completely discounted the work done by any non-Greek and non-European culture. [...]