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Today was supposed to be for grading papers. But it turned out to be a day for building astrolabes. I built four, using PDF kits I found online, cardboard left over from the Makedo challenge, and a a few sheets of paper (and an almost nicked thumb from a dull Xacto blade… curiously enough, scissors almost work better.

Why? My history classes are learning about the American Revolution. My Latin classes are studying uses of the Infinitive, and the formation of adjectives. Astrolabes don’t fit into either part of the curriculum.

Ah… but they do fit into the design lab. I think. I mean, here’s a complex medieval instrument for discerning the passage of time, the movement of the heavens, and uncovering the geometry of the worlds above the earth. It’s eminently practical — Columbus probably used one to cross the Atlantic and estimate his position day-to-day. And yet it’s a relic of an ancient age: the first was invented by Hipparchus in ancient Greece almost two thousand years ago, back when people thought planets were Gods. Building one of these even as recently as eight hundred years ago required days of a geometer’s time and the labor of several skilled craftsmen, to make sure the numbers were correct and that the lines were in the correct position… too many things could go wrong. They were slide rules and calendars, calculators and protractors, elaborate devices for knowing one’s place in the world. To use one, you had to know how to use one; to know how to use one, you had to practice with one. A bit of a catch-22, but right in line with the designer’s maxim, “build to learn.”

Here’s a video about using the Astrolabe, using a TED talk:

Although each design that I built was more complicated than the last, by the end I had a pretty good idea how each device worked, and how I could use it in the classroom, or convince a mathematics or science teacher to use it in the classroom. They’re not fantastically complex tools, but they enable one to do trigonometry fairly easily — provided you know trigonometry. Don’t know trigonometry? Don’t worry… you can be taught, with the help of an astrolabe.

Hmm. Is this a way to open up advanced mathematics to younger students?

Via Flickr:
I tried really hard during my free periods today to grade papers. But the design lab called: I’ve been thinking about stars for a whole lot of time now, and how to integrate the study of astronomy into a school program that only meets during the day. And, of course, how to include mathematics in a history class. And, of course, how to include history in a math class.

The answer is astrolabes. Of course they’re outdated technology. They were the great grandparents of slide rules when slide rules were invented. They were practically second cousins of the abacus.

Today I downloaded three basic models of them and made them.

Here they are:

• In the first photo:
  • At Left
  • At center/top
  • at Right
• the separate fourth astrolabe, in its own photo

You paste a printout onto cardboard (cereal boxes work great), and with an hour’s work you have an astrolabe similar to the one Geoffrey Chaucer described in the first technical manual in English, “treatise on the astrolabe”, written in (I think) 1391 AD.

These two are simple. They require glue, printouts, and a knife. In a classroom environment they’d need to be spread over two days — one day to glue the paper sheets down to the cardboard, and then some drying time; followed by a day to do the cutouts. The one on the left is a little more elaborate. The third one, above, is a quadrant rather than a true astrolabe… but the principle is the same. Teach a class the second day on sun sighting, or calculating the height of a flagpole. Extrapolate to sighting stars on the deck of a ship in the midst of the heaving Atlantic Ocean, and you have a seriously cool lesson about the Age of Exploration.

But only if you have willing teachers in Mathematics and history classes. You can combine it with a lesson about globes, using an icosahedron made of paper plates and a Buckminster Fuller projection of the Earth. But only if you have willing students and instructors.

Today they’re only mathematical toys. But in the late Renaissance, they were the tools of empire. And they could be the tools of a student’s modern day empire of learning if we taught students to build and use them.

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