There is something interesting about the Steampunk movement. Steampunk takes inspiration from the past to reinvent the future. I am reminded of the fictional worlds created by H. G. Wells and Jules Verne. The above image is from Indulgy and is an example of Steampunk and fashion. There are subtle connections to 19th century engineering where scientists such as Maxwell and Kelvin did modeling of mathematics that was touchable, where cause and effect were clear and visible. We see the raw elements of computing (e.g., information flows) everywhere we look and yet it is with classic machines from the past that we find information-rich experiences as indicated in Organum Hydraulicum. Steampunk, and its inroads into theatre, fiction, and fashion may be partially a result of our deep human need to touch, see, and hear information. To model, Steampunk style.
Physics sandbox programs such as PowderToy create an entertaining environment for playing with mechanics. Sometimes, the physics is a bit surreal, as with MineCraft, but that is fine as long as the rules are uniform, repeatable, and easy to understand. I worked on a design with Scott Easum here in our lab, and he produced a nice sand integrator inside of Powdertoy using a digital counter thats someone else had developed within the Powdertoy community. The learning theory is simple: if a student likes PowderToy, then deliver content such as calculus to that student through PowderToy. The goal of this machine is to measure the area of the circle. Note the digital counter with some very small multi-colored pixels beneath it. These pixels form a structure that represents a digital circuit required to make the counter work. The count begins once the sand starts pouring into the circle. The circle's area can then be measured mechanically using a feedback mechanism so that when the container is full, the overflow sand triggers the digital display to stop counting. The final count is read off to yield the area (an adjustment coefficient is required to obtain the area in common metric units). The operating principle is similar to the hourglass. Unlike the hourglass, though, we can quickly create any geometry we like in PowderToy and use our sand calculus machine to determine the area of an arbitrary shape.
Da Vinci's cam hammer was covered briefly here. This object was the "object of the day" during the Creative Automata class at UT Dallas (Jan 22, 2014). At the start of each class, students are shown an object from real life in a photograph or perhaps from an illustration. In this case, the object is a picture of a kit model that I made and later stained. The physical model was handed out during class for handling and observation. The driving question is "What information do you see?" This question elicited a wide number of expected and completely unexpected responses, all of which were welcome since this exploration is how we communicate and learn about computing. The first comment was that there was a conditional branch on the snail cam. You can see the cam driving the follower (the rigid linkage that connects to the hammer on the right side). When the follower makes contact with this discontinuity in the cam, the rising hammer falls, causing a change in state (another type of information flow---of control). Someone said that there was a stack (a type of data structure similar to a stack of plates), but when we went looking for the stack, it was not clear that one existed. The support structures for the cam shaft are inverted ternary trees of height one. Seeing information--in an ancient machine. However, the technology goes much further back than Da Vinci in what were called trip hammers written about by the Chinese in 40BC in the Ji Jiu Pian dictionary. So, foundations for computing were were alive and kicking early on with hammers.
This is Da Vinci's design for a cam-driven hammer. Here is a model that I built out of wood using a hand Dremel tool, glue, and wood from this kit. The hammer can be also interpreted as an information machine, and there are ways of using this as an analog model to investigate mathematical and computing principles. We can ask system theoretic questions and pose challenges: (1) How would you use Da Vinci's hammer to capture the concept of number? (2) Define the states, state space, inputs, events, and outputs for this mechanism. (3) What is the cause-effect chain of the machine? (4) Map the continuum of state space to make it a finite state machine. (5) Is there a control loop in this machine? If so, what are the beginning and ending loop values? (6) Define a mathematical function being dynamically represented, and (7) define the mechanical advantage using the lever concept. Answering these questions and addresses the resulting challenges can be more interesting than having students move alphabetic symbols around, plus they can learn a little bit about history.
Volvelles are primitive paper computers and they were found in books in astronomy. Volvelles were printed as part of a book and served as interactive devices long before the world wide web and browser. The one pictured above is from Petrus Apianus' Cosmographia published in 1524. Volvelles were also called "Apian Wheels." The purpose of these devices was to compute something such as the time of sunrise or sunset at a specific latitude. This computation is a form of simulation--of the motion of the sun or moon. How can one simulate anything with paper? Think of the volvelle as a radial look up function table. Suppose you wanted to create something to determine y=sin(x). The volvelle creator will pre-compute sines for different values of x in making the device. Then as the user/reader, you rotate the disc to x and read off y. If you have ever used a circular slide rule, this works on a similar principle where the scale is logarithmic.
What is it? Looks like a hair comb and a strange cylinder with small bumps. This is a 3D printed music box. I've been thinking quite a lot lately about 3D printing ever since I opened up my lab to show posters and research last Thursday, and then realized that everyone was, instead, taking a bee-line to our 2 Makerbot 3D printers. "Is this the room where the 3d printers are?" Sure! Why not? It seems that there is a new 3D printer company on KickStarter every day. So, clearly, this represents a technology that is only going to get better and cheaper. Lots of things can be fabricated with a 3D printer, including the music box. Our interest is a bit beyond music, though, to the point where we are looking at objects like the music box and thinking about how we can use these quick-print objects for math and computing education. There are many possibilities -- people are drawn towards the tangible, the touchable, and that which can be forged immediately from plastic. I am reminded of a toy when I was young, where we had a kit for making plastic insects. What ever happened to it?
The verge and foliot escapement. The first mechanical clocks, building on the older principle of water flow for energy, employed a solid weight to yield the computation of time. If we just tied a weight and let it drop, we would not have to wait long, and we would be able to measure time only in seconds. So the trick for a mechanical clock without water, but instead using a weight, is to delay the time of the weight drop. This was done with an escapement. The verge is the vertical post and the foliot, the horizontally rotating bar. This animation (which can be viewed by clicking on the above image) is from Peter Ceperley who has a good explanation of the gear train powered via the escapement control. Think of this escapement is the medieval equivalent of a square wave--a mechanism to achieve an oscillating signal.
You can make anything out of paper. This flying pig is an example of making a crank-based automaton from paper. You cut out the pieces and glue them together to create a machine. No 3D printing required. There are also gears that can be made from paper - it is recommended to get a thick stock of paper (cards, cardboard) otherwise, the mechanism may not have enough rigid parts to operate. For electronics, one can use cheap inkjet printers to create circuits. To make circuits by printing them requires special ink containing silver nanoparticles. I didn't see a discussion of how one would make a switch (e.g., transistor) but research on thin-film transistors has been ongoing, so it should eventually be possible for the average consumer. Then, we can mix our own ink, or buy it ready-made with reusable print cartridges.
In MIT's curation of 5000 Moving Parts, Laura Knott asks questions on why kinetic art is not as well represented as it could be in art history. Kinetic art has a relationship with computing. Artworks that are driven by complex chains of power transmission through levers, gears, and cams are isomorphic to data flow graphs found in computer science. Can kinetic art be viewed not only on its own aesthetic merits, but also as means toward understanding data flow? Here is a piece from Arthur Ganson's web site called "The Dream":
Here is another exhibit by John Douglas Powers with accompanying video. A simulation of waves of grain?
This is the creative automata blog for the Creative Automata Laboratory at the University of Texas at Dallas. The goal of the lab is to explore representation of process abstractions used in mathematics and computing starting with historical automata up to theoretical automata, code, and data in present day technology. Representation is informed by areas outside of computer science such as design, the arts, and humanities. The purpose of the representation is enhanced mass communications, education, and training in the arts of computing. Paul Fishwick serves as Director of the Laboratory.