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I've noticed that my daughter, despite being an engineering student, isn't nearly as comfortable with the properties of logarithms as I am. Of course, she studi

by todd8 8y ago

I've noticed that my daughter, despite being an engineering student, isn't nearly as comfortable with the properties of logarithms as I am. Of course, she studied them in Calculus classes, but they were just abstract functions to her since she always had computers or calculators to perform calculations. For me, they were a part of the standard education for technical or science related fields. Even in high school we were expected to use slide rules or tables of logarithms to perform calculations. I bought my first slide rule around 1964 (with money I made delivering the Detroit Free Press newspaper every morning before school). It was a bright yellow Pickett like those available on EBay[1]. It was possible to do multiplication, division, roots, trig, exponentials, etc. to just less than 3 significant digits of accuracy. If this wasn't enough accuracy, I had to recast the computation as addition or subtraction of logs from log tables, which could with some interpolation yield around 6 significant digits of accuracy. I just recently pulled out my old slide rule to show my accountant how they worked. At MIT I saw circular slide rules, and some of my fellow students used them (more accuracy on the outer scales, less on the inner most scales). The most interesting slide rules I've seen are cylindrical. The scales wrap around the cylinder in a helix and are much longer giving an extra digit or two of accuracy (but requiring more mental work on the user to figure out which reading of the cursor to use because the cursor was parallel to the axis of the cylinder). See [2] By the time I was finished using my slide rule, I'd started working with computers. Even today, I have a fancy overpriced TI calculator that just sits in a drawer. I'd much rather fire up a Python REPL to do most calculations. [1] https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLIDE-RULE-MODEL-N4-ES-WITH-LEATHER-CASE/113321672651?hash=item1a627f7fcb:g:tCMAAOSwWotbwn12:rk:10:pf:0 https://www.ebay.com/itm/VINTAGE-1959-PICKETT-DUAL-BASE-SLID... [2] https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-experiments-from-history-inform-the-future-from-the-past-galileo-january-iap-2010/image-galleries/slide-rule/ https://ocw.mit.edu/courses/edgerton-center/ec-050-recreate-...

rmason 8y ago
I bring out the slide rule pretty much these days to give history lessons to young folks. Last time I showed how it worked to a pair of GenZ kids they looked at me with a healthy bit of skepticism. Like somehow this was some sort of fake contraption. I felt a bit like my late father explaining what it was like to crank a car to start it.
- todd8 8y ago
  I know what you mean. I borrowed a car from a fraternity brother to pick up a date once. Before departing he explained that if it didn't start I might have to use the crank! It was a Citroën if I remember correctly. I'm sure it really impressed my date.
  - blattimwind 8y ago
    Extra battery (the one you take inside where it's warm over night) and starter cables in the footwell :)
kqr 8y ago
I do think the first encounter people have with logarithms ought to be doing reverse lookups in exponentiation tables, by ocular linear search. It's not convenient at all, but it should give a good grasp of the concept.
jacobolus 8y ago
Yes, everyone should learn to use a slide rule in high school, and should spend at least a couple months regularly using it for calculations in math/science class. As you say, they not only build strong intuition about logarithms, but also help teach about working precision, etc. Handheld electronic calculators should be banned as having almost no pedagogical value. In general assigned problems should be conceptually more challenging but should have simpler numerical values. Anything that needs more calculation than that should be done on a computer with a real keyboard and a real programming language. In primary/middle school, counting boards (like those used in ancient civilizations or medieval Europe) should be used much more than they currently are. Experimenting with these tools is great preparation for thinking about how computers store and manipulate data.

by todd8 8y ago

rmason 8y ago

I bring out the slide rule pretty much these days to give history lessons to young folks. Last time I showed how it worked to a pair of GenZ kids they looked at me with a healthy bit of skepticism. Like somehow this was some sort of fake contraption. I felt a bit like my late father explaining what it was like to crank a car to start it.

todd8 8y ago
I know what you mean. I borrowed a car from a fraternity brother to pick up a date once. Before departing he explained that if it didn't start I might have to use the crank! It was a Citroën if I remember correctly. I'm sure it really impressed my date.
- blattimwind 8y ago
  Extra battery (the one you take inside where it's warm over night) and starter cables in the footwell :)

kqr 8y ago

I do think the first encounter people have with logarithms ought to be doing reverse lookups in exponentiation tables, by ocular linear search. It's not convenient at all, but it should give a good grasp of the concept.

jacobolus 8y ago

Yes, everyone should learn to use a slide rule in high school, and should spend at least a couple months regularly using it for calculations in math/science class. As you say, they not only build strong intuition about logarithms, but also help teach about working precision, etc. Handheld electronic calculators should be banned as having almost no pedagogical value. In general assigned problems should be conceptually more challenging but should have simpler numerical values. Anything that needs more calculation than that should be done on a computer with a real keyboard and a real programming language. In primary/middle school, counting boards (like those used in ancient civilizations or medieval Europe) should be used much more than they currently are. Experimenting with these tools is great preparation for thinking about how computers store and manipulate data.