This is a card in Dave's Virtual Box of Cards.

Logarithms

Page created: 2025-06-30
Draft!
 This page is a draft and may be incomplete, incorrect, or just a stub or outline. I've decided to allow myself to put draft pages on my website as an experiment. I'm hoping they will:
  • Help me address my backlog of article ideas.
  • Serve as a "living" TODO list of things to work on.
  • Be useful to myself or others in their incomplete forms.
As always, I'm happy to accept feedback on anything I publish including draft content.

In Richard Hamming’s The Art of Doing Science and Engineering: Learning to Learn (link goes to my book notes), Chapter 3: History of Computers - Hardware, he writes:

"The invention of logarithms by Napier (1550–1617) was the next great step. From it came the slide rule, which has the numbers on the parts as lengths proportional to the logs of the numbers, hence adding two lengths means multiplying the two numbers. This analog device, the slide rule, was another significant step forward, but in the area of analog not digital computers. I once used a very elaborate slide rule in the form of a (6–8”) diameter cylinder and about two feet long, with many, many suitable scales on both the outer and inner cylinders, and equipped with a magnifying glass to make the reading of the scales more accurate."

The Napier’s logarithms

TODO

Modern logarithms

TODO

and natural logarithms (I have a 3blue1brown video bookmarked for this, "What makes the natural log "natural"? | Ep. 7 Lockdown live math")

And e (the 3blue1brown vid covers this as well?)

Also the history of mathematics book I’ve got probably does a great job covering this.

The slide rule

In the paragraph that follows the first one I quote above, Richard Hamming writes:

"Slide rules in the 1930s and 1940s were standard equipment of the engineer, usually carried in a leather case fastened to the belt as a badge of one’s group on the campus. The standard engineer’s slide rule was a “10 inch loglog decitrig slide rule” meaning the scales were 10” long, included loglog scales, square and cubing scales, as well as numerous trigonometric scales in decimal parts of the degree. They are no longer manufactured!"

In my Circular Slide Rule Watch Tutorial page, I explain some of the basic usage of a "pilot’s computer" watch with a slide rule dial you can turn using a little knob on the outside of the watch. I think it’s a fun, geeky thing. But I’ve never really understood why the slide rule works. I mean, I understand that a slide rule is a lookup table and it works because of the way logarithms describe the relationship between numbers…​but I have no intuition for that at all beyond the sentences I just typed.

I’ve also inherited my father-in-law’s slide rules and the instruction books that came with them. I’d like to learn those properly.

TODO: do that