I'll bet you didn't expect a post on this site to start out with that. But coming upon something unexpected is just how I felt when I recently learned about the origin of logarithms. Apparently, many math teachers have neither time nor inclination to pass on the why of logarithms, and I wish this wasn't so. I am one of those people that really like to know the origins of things, because I'm stubborn about what I pay attention to. I have only ever felt a bit grateful for knowing algebra, slightly appreciative of geometry, grumpy toward trigonometry, and downright indifferent to calculus.
The other day I was trying to figure out interest rates and principals, but realized that I had too many variables to solve my problem. I wondered, how has anyone ever solved these problems? and thus I got my answer in a very rudimentary explanation on logarithms. Usually, any phrase such as "nominal interest rate" or "linear approximations" makes me want to curl up with a stomach ache and weep. But I resisted the curl, and held on to my curiosity.
My reasons for math anxiety are probably the same as anyone else's. I do believe that educators are valiantly trying to get math out of cloudy theory and into the hands of students grasping at the concepts. I believe this because of a day I was volunteering in my child's first grade class and the teacher said, "All right, it's time to put away the manipulatives." Startled, I looked around for a group of shell-shocked survivors of some terrible mind experiment, trapped in a diabolically created mathematical Stockholm Syndrome. An instant later, I saw several multi-colored wooden shapes scattered on a table and thought, "Oh, right. Shapes."
I'm not at all sure that referring to shapes with their pedagogical term, "manipulatives" did much to make all the necessary synaptic connections fire in those little brains. But its multi-syllabic mysteriousness might have at least brought the brightly colored bits out of kindergarten babyishness long enough to be paid attention to by these more sophisticated first graders.
If that term was surprising to me then, I was further unprepared for even more blatant and suspiciously sounding human behavioral terms in Mathematics. There are inverse relationships, conjugate pairs, arguments, degenerates, end behavior, restricted domains, indeterminate expressions and imaginary numbers. It sounds like a dysfunctional family coping the best it can. If only I had been teased long ago with this array of more juicy trouble-makers, I might have stayed with Math a bit longer. Who knew?
Back to the Logarithm, which sounds more solidly earthbound and kind of "groovy". As I saw this term being applied to the calculation of interest rates, which seems like something only a human would need to know, I wondered if logarithms had been discovered as a principle, or invented as a device. A quick google search showed me that my question is a common one; the answer is "both" which is my favorite answer to anything, and many sites that will explain this duality with the story of John Napier, Lord of Merchiston. If not groovy, he was considered "marvy", as his nickname was "Marvelous Merchiston".
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| John Napier (1550–1617) |
A Scottish nobleman, Napier was around other scholars who were contemplating the planets and working out pages upon pages of computations by hand, in order to calculate the planetary orbital pathways. It seems as if Napier had a moment of resolve inspired by pity, and spent the next twenty years working on his idea of a logarithmic table to replace all of that labor. The astronomers must have felt like they had been handed the moon. With nothing else to do aside from being the laird of a castle with twelve children, and working on this table, he also made a set of wooden rods displaying the multiplication table that became known as "Napier's Bones." With a few spare brain cells, he also tossed around the idea of using a decimal point to distinguish fractions after a large number.
In his own words:
"Seeing there is nothing (right well-beloved Students of the Mathematics) that is so troublesome to mathematical practice, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers, which besides the tedious expense of time are for the most part subject to many slippery errors, I began therefore to consider in my mind by what certain and ready art I might remove those hindrances."-- Mirifici logarithmorum canonis descriptio, 1614.
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| Set of Napier's calculating tables circa 1680 |
Poor Joost Bürgi. Over in Switzerland in 1588, he invented his own table of logarithms (from the Greek "logos" meaning 'word', 'reckoning' or 'ratio' + "arithmos" meaning 'number') six years before Napier completed his, but published six years after Napier's, at the insistence of Johannes Kepler, astronomer extraordinaire. Luckily, however, Joost was recognized for his genius, and became a right hand man to Kepler, in the service of three successive emperors.
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| Astronomical clock, invented by Bürgi, 1585 |
A little personal glory didn't hurt either man, and today they both have lunar craters Byrgius and Neper named after them.
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