My daughter’s math class is working on logarithms. I have a special enthusiasm for logarithms. Every single thing about them appears to be overwhelmingly opaque and indecipherable. Everything. And the most awesome thing about them being so completely crushingly incomprehensible is that Mr. John Napier (1550 – 1617) invented this system was to make life exponentially easier for us. And he succeeded.

Now here’s another cool thing about logarithms. The spelling. No one confidently remembers how to spell this word. But there’s a trick to remembering.

The trick is to spelling logarithm is to notice that it starts with L O G (that’s the easy part) and ends with the most of arithmetic. No pun intended.

I’ve been experiencing something that I mistook for an internal tug-of-war: I like blogging about book arts, but my mind of late has been drawn to playing with ideas that seem to have more to do with math than with books. It’s been a dilemma, how to keep writing about book arts when my mind is elsewhere. Finally I’ve had an ah-ha moment: I had forgotten that what brought me to book arts in the first place was wanting to make visual sequences of images that were related to a simple equation.

The equation that drew me into making books is the one which starts with the number 2 and doubles, then doubles again, then doubles again and again. It takes eight pages of doubling to get from 2 to 256. I’m infatuated by the slow measured way the numbers increase until there’s this tipping point, when the quantities then erupt into unmanageable largeness. I had created maybe a dozen of these books, experimenting with using lines, circles, overlapping lines, droplets of paint ect. I bound these books in a most inefficient and cumbersome way. Eventually a friend pointed me in the direction of The Center for Book Arts in NYC and new part of my education began. I found the geometry of constructing books to be a satisfying, even sublime experience. And, since I didn’t really know any other intoxicating mathematical equations I just kept making books.

Now, many years later, my daughter is coming home with problems like the one pictured above. My son offered an insight on this kind of problem, one that I hadn’t thought of before. He said that the answer to this problem made no more sense to him that the problem itself. It’s tough to remember that these functions have a look to them, and that solving for x *looks* like something. A day or two after having this problem as part of a long, mind numbing homework assignment, my daughter came home and bemoaned that her teacher had just that day told them that the point of logarithms was to find exponents. She wanted to know why they weren’t told that in the first place, and what was the point of doing all those numerical gymnastics? We had quite the discussion about that. And it keeps me thinking about pictures.

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I still don’t understand that answer. LOL! I used to be really good at math and tutored people in it, no it makes my eyes cross a lot of times, like that example. I’ve never been able to do Sudoku for instance, but I appreciate the math in origami and other book forms, like the blizzard book

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Yes, isn’t that funny how the answer is just as unfamiliar looking as the question! So you used to tutor people in math? This totally makes sense to me, as it does seem to me that people who like to make books have mathematical minds.

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Your example of doubling a number shows just how cool exponential functions really are. Exponential growth crops up all the time in science, business and everyday life, and is one of the truly useful things people can take away for use in later life. A logarithm is simply the inverse of an exponential function. It’s not so useful in the real world 😦

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What interests me about logarithms is trying to figure out why they are so good at repelling students. I’m thinking about how students are introduced tolog as part of a function that contains an equal sign. Now, think about this: by the time students see logs, they have been seeing the equal sign in equations for more than a decade, and generally the equal sign is a signal for a student to do an actual calculation. With Logs, to find a final numerical solution, there are no actual calculations to do: one needs to reference a table or a calculator, and I think that this is such a disorientating proposition that students just can’t easily make the shift in thinking.

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It’s not so useful in the real world? This comment shows your youth. I went to high school BC (before calculators). Logarithms were essential to do calculations. Slide rules worked because they are built using a logarithmic scale. Slide rules used to be so important. Today noise (decibels), earthquakes (Richter scale), and the heat in peppers (Scoville scale) are among the items measured using logarithmic scales. By the way, Paula, I’m a little late, but I really enjoyed this post.

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Ha! I had log books at school too! So glad they are no longer in use 🙂 I had forgotten about logarithmic scales though – that’s a good example. Most people probably don’t understand the Richter scale.

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Oh, I bet you were a whiz at doing them at the time. But, like everyone else, I’ll bet you didn’t have a clue as to why you were doing them. Hey, though, didn’t you study physics? Isn’t the natural log a major player in the world of physics? Enlighten me!

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ooo! I didn’t know about the Scoville scale for hot peppers!!! What a great detail to know! Logarithms are, to me, so intriguing because what they do is make otherwise impenetrable calculations doable. On the other hand, they are (nearly) universally thought of as being too difficult to comprehend…until you understand them, in which case one can only feel grateful that someone figured them out.

Thanks for checking in.

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