Just saw an article describing an unusual computer that reminded me of two previous articles I’ve seen in the past.  Not many pictures today, but there were a lot the past few days, and the links have plenty of nice pictures.

1. The first article is from a landscape architecture blog, and describes a hydraulic computer, which is specifically used to solve partial differential equations:

“Built in 1936, this machine was “the world’s first computer for solving [partial] differential equations,” which “for half a century has been the only means of calculations of a wide range of problems in mathematical physics.” Absolutely its most amazing aspect is that solving such complex mathematical equations meant playing around with a series of interconnected, water-filled glass tubes. You “calculated” with plumbing.”

I would venture a guess that the system was built around the idea that there aren’t that many really important PDE (in particular, Lawrence Evans’ classic 660page PDE text lists 32), and that by applying the right sort of pressure to water, you can exhibit many of these PDE.

This would be sort of a neat trick: we describe scientific phenomena (i.e., how water moves) using math, but then calculate values of a different phenomena using the first.  It would be like noticing that your car is making a noise that sounds like a distressed cat, and then looking at what distresses your cat to diagnose your car.  Only maybe adding “…in a mathematically rigorous manner” after the words “distressed cat”.  And then realizing that in fact most car troubles can be mimicked by distressed cats.  This analogy has gone too far.

2.

Xiaoji Chen at MIT (now Microsoft, apparently) designed a mechanical computer, and the videos are definitely worth a watch.  I guess really all you need is a way of linking elements together to get a certain amount of logic, but I really liked this project.

3. Wang Tiles are a way of computing, again by just putting together enough logic, but they work in an interesting way.  In particular, you start with a set of square-ish tiles, but some marking on each edge.  Then by placing a certain number of tiles in the first row, there will be a unique way of filling out the tiling, and the pattern may bounce back in a way that conveys some information.  Branko Grunbaum and G.C. Shephard have a fantastic text on general tilings, and how to, for example, add two numbers with Wang tiles.

Below is an example of a calculation.  The 16 Wang tiles are shown top left, and instead of an edge marking, there is an edge coloring.  I don’t know what the top center and top right images refer to, but the bottom image shows the calculation of 5+9=14.  It is not hard to convince yourself that if you require the “outside” of the tiling to be black, then once you place the two pieces with the black circles in the center (at the positions 5 and 9), the rest of the tiling is determined.  The tile with the green circle in the center is the answer.  There are similar ways of multiplying, etc.

Computing with Wang tiles. From http://seemanlab4.chem.nyu.edu/XOR.html