The Invention That Saved Science: How a numerical table with 5,400 entries became the world's calculator for the next 350 years.
That invention was logarithms and the story starts with Johannes Kepler having to complete a massive project requiring many years of long laborious calculations (by hand, of course) and which he was only able to complete because of the recent invention of logarithms.
What I really liked about this video (aside from spotting all the foreshadowing -- "Kepler!" "Tycho Brahe!" "Kepler's First Law!" "Second Law!" "Third Law!" "Napier's bones!" "Slide rule!") was how it takes us through the process of developing and calculating the entries of the first tables. A little nerdy, but utterly fascinating. My grandsons won't be ready for it for several years (the elder being in Kindergarten, he's only gotten to multiplication), so I hope I can find it again to show them.
I stumbled upon this last night and enjoyed it so I thought I would share.
In addition, it kind of addresses a recurring creationist/apologetics "dilemma" of whether mathematics (or logic or scientific laws, etc) are invented or discovered (ie, actually divinely created).
My own take is that mathematics is a form of language, a symbolic system with which we can express ideas and describe what we observe. And it does so very concisely and concretely.
Personal story: in high school algebra the hardest part was word problems and how to set them up. Then in college I saw Leonard Bernstein's series of lectures on musical linguistics, The Unanswered Question in which he inadvertently taught me how to set up word problems. He presented a spectrum for metaphor which scaled up to higher levels of metaphor with prose being least, poetry being more, and music being most highly metaphoric. So I looked to the opposite end of that spectrum where language becomes increasingly concrete with algrebraic expressions being the most concrete and concise; for example, you can describe each and every one of the infinite number of points on a line with the expression, y = mx - b and the same with all the shapes dealt with by analytic geometry.
Therefore, I realized, since the word problem expresses the problem in English, setting up the solution merely entails translating it from English to algebra. And one thing I was definitely practiced in as a foreign language major was translating from one language to another. After that, I was a wiz at word problems.
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