the Astrolabe, part 1

or, I’ve got your computation right here, right now

stereographic projection
of the sky and horizon
at 45° N
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plus hour lines for three different systems

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I’ll explain later.

I’m designing my own astrolabe. I’m doing it in a hyper-modern way - by writing software a for a modern digital computer (e.g. my laptop), and computer-controlled processes to embed my computations into physical matter (via laser-cutters, 3D printers, printed circuit board manufacturing, etc) to make an analog computer.

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What do I mean by analog computer?

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Have you ever used a slide rule?

People my age or younger probably haven’t, they were quickly displaced by the pocket calculator.

The thing I love about analog computers, is that the picture of the thing is still the thing. The same way that a picture of a map is still a useful map. So I can show you some pictures that actually work for doing analog computing.

Slide rule basics are surprisingly straightforward. You start with two number lines:

standard slide rule “C” and “D” scales

but it’s set up so they can slide by each other and change the relationship (I’m not going to make moving parts here, but other people have). And due to the geometry embedded in the layout, the relationship between the two defines a mathematical operation.

close-up of “times two”

once you add more scales, it starts getting hard to see what’s going on, so they added a sort of sliding window with a red line down the middle to help you see the relationships - this is the pre-digital meaning of “cursor"

(source)

The astrolabe is suprisingly similar, except that the mathematical relationships it embeds are related to the celestial sphere and the visible sky.

The “rule” is equivalent to a cursor, but it can also be thought of as the hour hand of a clock - when you’re thinking about the rotation of the Earth, space and time start to look interchangeable.

image from
Whipple Museum
of the History of Science
(source)

The alidade, on the back, is for actually taking measurements. I can talk about that later.

“Rete” means “net” in Latin — somehow there was never an English word for the concept (Chaucer described it as looking like a spider’s web). It’s a map of the fixed stars, with holes cut out so you can see the grid lines on the plate underneath. Modern people tend to use transparencies for this sort of thing, but apparently, in ancient times, glass was not practical for this purpose.

The important part, though, is that the rete spins freely while the plate below holds still. This is all it takes to compute a relationship between the stars and spacetime.

I’ll show you some example calculations, next time.