Machinamenta in Old English

Reading a little about the etymology in Lord of the Rings, I came across the word that they used in Old English to translate the Latin word "machinamenta." It was Orþanc, and that p/b shaped letter (called thorn) is pronounced 'th.' This meaning of ingenious devices and siege engines was the reason Tolkein picked the name Orthanc for the tower of Saruman (whose name similarly means 'cunning mind.')

Gödel and Leibniz

Leibniz gets a whole chapter in Machinamenta; I love the story of how he imagined the potential of computers so early. I had thought the rediscovery of Leibniz's digital aspirations (Gregory Chaitin, for example, speaks highly of him in this context) was a recent phenomenon, though-- Charles Babbage was certainly inspired by Leibniz's writings, but as far as I knew his influence on the first electronic computers was pretty far removed. However, I now think that there may have been some influence by way of Kurt Gödel.

Gödel was fascinated by Leibniz's ideas, to the point that others felt he was obsessed: he checked out every book on Leibniz from his university library. He believed (correctly, I would say) that Leibniz's most important ideas (the characteristica universalis) had been nearly forgotten by society; but he also believed that this was due to a shadowy conspiracy meant to prevent the intellectual advancement of mankind. While one could make up a marvelous conspiracy theory about this, involving Newton, the Illuminati, the Invisible College, and so forth, it was more likely due to the fact that many of Leibniz's writings have never been published, and that Leibniz himself never completed the project.

At any rate, Gödel wanted to achieve Leibniz's dream of an exact, computational philosophy, able to come to provable conclusions. Gödel wrote, "There are systematic methods for the solution of all problems (also art, etc.)" Leibniz believed that the natural world arose out of a network of binary relations.  This idea of a mathematical world underlying the world we see, a kind of Platonic realism, was appealing to Gödel as well, and he saw his work as pointing in that direction. Gödel  like Leibniz, believed that the study of mathematics could tell us ultimate truths about the nature of reality. Since, as he proved, it is impossible to prove certain true facts about the mathematical universe, those truths must exist, he thought, somewhere outside of proof.

Gödel's more mathematical ideas were very important to people like Alan Turing, Stanislaw Ulam, and John Von Neumann. Gödel's famous proof of the incompleteness theorem needs to be able to make statements about mathematics using mathematics itself, and this required the invention of something very much like a programming language. Turing's key paper "On Computable Numbers, with an Application to the Entscheidungsproblem" uses the incompleteness theorem, proved five years before, to prove that it is impossible to decide algorithmically whether a given Turing machine will ever halt.

There are two main ideas I tried to get across in Machinamenta, that I laid out in the introduction. One is the idea of the kaleidoscope pattern, which I'm not going to go into here. The other is that the history of computers is not just the history of the development of mechanical math machines. There has also been, for a long, long time, a desire to make machines that can take ideas, and combine them with other ideas, to come up with new ideas. You see this in divination machines, which inspired Ramon Llull. Lllull's own devices inspired Leibniz to develop a much more ambitious and realistic plan. This in turn was taken up by Babbage and Gödel, who were direct influences on the people who built the first electronic computers. The dream of machine intelligence was already fully present through this chain of influence at the birth of the computer.

AI and children's drawings

I've been reading about attempts to write software that approximates the steps that children go through when they create drawings. This gets at some of the fundamental differences between how machine currently generate images in "artistic" styles (using brushstroke filters in Photoshop, for example) and  how an artist paints. By trying to shortcut past the early representational stages, we have failed to capture some of the important things about what it means for a person to create a painting.
One of the best papers I've found is called Thoughtful Drawings: A Computational Model of the Cognitive Nature of Children’s Drawing. It describes a piece of software called Rose (Representation Of Spatial Experience). The author states, "Rose is not intended to be a model of any part of a child’s mind. Rose is a representation of personal ideas about just a few vital elements of the human experience of drawing."
Rose takes as input a 3D form, composed of triangular surfaces.

From this form, it recognizes certain parts that are joined together-- the legs, the neck, and the tail all joined to the body, and the head joined to the neck. Each of these body parts is fit with a cylinder.

Then the program attempts to draw the shape. It attempts to create closed curves (by moving a "pen" around with an imperfect control algorithm) whose length and width are determined by the proportions of the cylindrical body parts, and are connected in the same way.

This projection doesn't take into account perspective, viewpoint or occlusion: it simply copies the connectivity of the graph of how the body parts join together. This seems to me to be how children begin to draw. We could test this by giving children an unfamiliar shape and seeing if the drawings tend to follow this rule. I would also like to know when a child will use a closed curve and when they will simply use a line to represent a part.
I would like to do something similar to this, but add in an extra step. I would like to give the program a computer vision capability that allows it to look at its own drawings and see how much they resemble realistic line drawings of the same subjects (or, more practically, semantic contour detection on photos of the same subjects). Depending on how good the resemblance is, it could choose what lines to keep and what lines to erase and try again. This extra judgement step is an important aspect of how people create art.