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| My Pickett N901-T, set to show 1.5 x 4 = 6 |
The earliest instrument designed to aid in these endeavors was the counting board, which later developed into the abacus. This tool simplified and facilitated the addition and subtraction of large sums, and underwent several revisions both in Western culture and in the Far East.
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| Salamis tablet, earliest known counting board, c. 300 B.C. Image from the National Museum of Epigraphy, Athens. (I got it from this excellent history of the abacus) |
Still, our earliest record of a counting board is the Salamis tablet. Abacuses as we think of them did not show up until 1200 A.D. in China, and have undergone significant improvements well into the 1900s.
No easy method of multiplication existed until 1614 with the invention of logarithms, as those interested in math could afford to pay others to do the gruntwork (obligatory pre-Renaissance reference, thanks to the Discover article reference below). The principle is fairly simple, though not intuitive. With a bit of algebraic manipulation, one can see that
log(a)+log(b) = log(a * b)
which means that mathematicians were able to look up the logarithms of two numbers, add them, and do a reverse lookup to find the product of the two numbers. This was faster, especially for three- and four-digit numbers. Pretty soon, someone got the idea to mark off the logarithms on a stick and to then physically add and look up the values. This system, embodied in what is called a slide rule, slipstick, or slide ruler, was refined and added to so that slide rules in the 1960s could do exponentials, logarithms, roots, and trigonometric functions in addition to simple multiplication. Discover Magazine, HP, and a fella named Eric host excellent galleries and articles. The Oughtred Society is an excellent resource as well, with lots of links.
This is the kind of history is what I hoped to introduce Ted to. He's not terribly fond of math, but he was curious about this relic of a previous generation and so was willing to learn.
I also noticed that curiosity is enough to start with a skill--knitting and slide rules--yet it is not enough to really get "into" a piece of folk knowledge. Growing up among computer-savvy brothers led me to develop my technical expertise (a large part of it arguably folk knowledge in my case), as watching them work fascinated me. Rachel's family's involvement with knitting helped motivate her to get into it. Also, a certain need is fulfilled by folk knowledge, for example Jared bonding with his nephews or me chatting with Rachel as we knitted. While entirely practical, all of the folk knowledge we've discussed so far has had the mother-tongue tendency to bring individuals together.
interesting! I'm scared now, though - if all the calculators in all the world exploded simultaneously, i wouldn't know how to do math :(
ReplyDeletewell, it is interesting how it seems as though the knowledge of mathematics, though very father-tongue ish, didn't really advance from Adam to the mid 1900's when the computer was invented. i feel like the father tongue knowledge is more ephemeral than mother tongue knowledge. discoveries of new knowledge in father tongue pursuits seem to account for a continual shift in the message of the father tongue, though the tone stays the same, whereas the mother tongue seems to vary significantly less
Very interesting. It's definitely different to think of how we learn in mother vs. father tongue. Maybe we learn it in different ways based on how or where we grew up. For example, if I was to learn science from a tutor, I feel like it would be very father tongueish but if I had learned it from an older brother, where the setting was informal I can see it being more mother tongueish. Not because the information is different but because of the way it is presented.
ReplyDeleteHeh--I wouldn't be too worried. You learned long division and multi-digit multiplication in elementary school, no? ;)
ReplyDeleteWell, I would say arithmetic aides didn't change much. Sextants usually include some impressive trigonometric aides, but they're usually as useful as a sailor needs them to be. Portions of mathematics were developed by the ancient Egyptians, Babylonians, and others. Mathematics underwent some unification and a great deal of development during Pythagoras' time and through Greek history. It veritably exploded during the Renaissance, and theory progressed by leaps and bounds up through the 1900s.
Interestingly, the Discover article has a few things to say about these very recent changes you mentioned having a sort of democratizing effect on math. While all the progress before was limited to a fairly small stratosphere of society, the slide rule (and abacus) permitted anyone with some training to do the gruntwork of math quickly.
my 2c
As the student in this experiment, I guess I should add my two cents. Learning the slide rule was definitely an interesting experience that made me think about the father and mother tongue. While I was being taught via mother tongue, I realized that I have never really been taught math via mother tongue. . .I think I have almost always learned math in an academic setting. Therefore, I never really had a big connection to it.
ReplyDeleteLeGuin talks about how the mother tongue unites while the father tongue dichotomizes. I realized that although my math knowledge is mostly father tongue, learning it in this new mother tongue way made me actually think log and multiplying and math were actually. . .interesting. I still don't know everything about slide rules, but I'm pretty sure I will never think of it without remembering the stories of how Jon learned to use it, or the things we talked about while he taught me. That must be where the unification comes from.