[etrautmann]

A key idea is that addition for logs is equivalent to multiplication. To multiply two numbers you line them up on a log scale and then read out the sum, which is equivalent to the product. There is much more they can do but that was one aha moment when my dad showed me his.

[sanjayjc]

I've never used a slide rule but recently developed an interest in them (and also in nomograms [1])

My fascination stems from a belief: that slide rule usage helps users develop a certain intuition for numbers whereas the calculator doesn't. To illustrate, suppose someone tries to multiply 123 and 987 with a calculator but incorrectly punches in 123 and 187. My hypothesis is they'll look at the result but won't suspect any problem. The equivalent operation on a slide rule requires fewer physical actions and hence, is less error prone.

Do you think there's anything to this hypothesis?

[1] https://news.ycombinator.com/item?id=28690298

[quotemstr]

> nomograms

Me too!

Nomograms are cool. They're little charts that let you compute a function physically, e.g. by lining up a ruler. A nomogram isn't a picture of a function: it is the function. If you're clever, you can make a nomogram that encodes complicated nonlinear mappings or even complex-valued relationships on a 2D plane.

Occasionally nomograms are just better too: because they're continuous and analog, they can naturally express things digital logic people can do only awkwardly, just like Rust people can only awkward approximate things natural in Verilog (e.g. truly parallel CAM search).

Nomograms are basically the tabletop gaming of math. Like a good tabletop game, a good nomogram requires a special kind of cleverness. Sure, coding something like Factorio is also hard: but it runs on a CPU. Something as rich and complex as Power Grid and High Frontier? Running on cardboard? Whole other level.

I recall one tabletop two-player game that featured a single-player mode in which you played against an "AI" that you ran by hand by moving cardboard pieces around on a game-provided template under pseudocode-ish rules from the game manual. It's hard enough to code a decent game AI with all the resources of a CPU at your disposal. It's an OOM harder to do it when you're limited to physically-realized lookup tables, a literal handful of registers, and a scant few clock cycles of logic per turn.

Coming full circle, some of these tabletop game "AI"s incorporate nomograms to help them fit their logic within the constraints.

Example of a cool nomogram: https://en.wikipedia.org/wiki/Smith_chart. Smith charts let you compute complex (pun intended) relationships in RF signal processing with just a compass and straightedge.

Also: part of the fun in making nomograms is that there's no general procedure you can follow to make a good one, just like there's no general compiler from computer game to tabletop game. They're art: specifically, one of those forms of art that, like architecture, has to meet functional requirements while tickling our aesthetic sense. It's kind of funny how when you optimize this kind of art for aesthetics under their functional constraints, you end up supercharging the functional part by side effect somehow.

[jonjacky]

With a slide rule you always have to estimate the expected answer in your head before you begin any calculation. So you develop a feel for how quantities scale with multiplication.

With a slide rule you can only multiply the significant digits, not the magnitudes -- which you have to do in your head. So you do exactly the same thing with the slide rule to multiply 123 and 987, 1.23 and 9.87, and 1,230 and 9,870. In all three cases, you get exactly the same answer: 121 or maybe just 120 (you only get 3 digits of precision at best). You still have to multiply the powers of ten in your head, to get the answers 121,000, 12.1, and 12,100,000.

I am just old enough to belong to the last generation of slide rule users. I used them in high school and college, then scientific calculators came along.

[litoE]

You don't have to multiply the powers of ten in your head. In your examples, the slider of the slide rule must be moved to the left of the body of the rule. This means the number of digits left of the decimal point in the answer is the sum of the number of digits left of the decimal point in the two multiplicands.

If the slider had been to the right of the body, the number of digits left of the decimal point in the answer is the sum of the number of digits left of the decimal point in the two multiplicands MINUS 1. .

[jonjacky]

Yes. I don't recall doing this, though. Maybe because in scientific and engineering calculations we often worked in scientific notation so 'digits to the left of the decimal point' wasn't meaningful - we had to keep track of the exponents.

[jonjacky]

It's not the number of actions, it's because the slide rule is analog and physical. The smaller numbers are to the left, the larger to the right, and you have to slide the rule to the first number, then the hairline cursor to the second number. There's no way you could mix up a large number like 987 with a small number like 187.

[realo]

Exactly. Using a slide rule shows how some complex operations in one domain can be made much easier in another.

One you understand slide rules and logarithms, it is easier to understand convolutions in the FFT (frequency) domain...

Almost like programming in APL, where you can solve a problem by expanding it in extra dimensions and getting the answer by re-compacting the complex object using a different view.