I gotta post something, so I'll post the mechanical calculator that the flight school wanted me to get. How it works is that you can set ratios in the dial and multiply them. In this picture, it's 60:10 (or 60:1.0) so I can take any number from the inner circle in minutes and find out how many hours that is equal to on the outer circle.
There are also other things on this calculator, including a wind vector calculator, and charts. Most pilots don't use these anymore, but they still wanted me to know how to use one
Not just ANY calculator. But something that will literally save your life when the electrics on the plane are blown and you need to get to that little airport via dead reckoning.
I wonder if we’ve semi automated some way to make arbitrary slide rules. Like some kind of software that you punch your functions into, or some table of info to be interpolated, and it lines everything up.
This is how a lot of maths is already done by computers. For example, it's basically impossible to get a computer to do an integral of an arbitrary function, but there are a lot of methods to approximate the answers. And that's mostly by using "slide rule" methods of approximately getting the right answer. The computer just does it fast with smaller intervals than you'd do manually.
There's a bit of a difference though between those computer driven iterative digital numerical methods and an analog continuous geometric object. It's like comparing pixel density and film grain. At a fine enough precision they become difficult to distinguish, but they are not the same. You could definitely use iterative methods to build a "continuous" solver at an arbitrary precision. We pretty much have to do it that way for any signficantly complex function.
Sorry, this comment got away from me and feels kind of incoherent now. I'm just trying to say that analog and iterative digital methods have subtle differences that one should remain aware of.