Hammers are pretty useful objects around the house. This is a photograph of a claw hammer - it can be used to bang nails in things like sheets of wood and plastic, and then remove the nails later. A hammer is a tool. But the hammer pushes back because by using it, I now have to think about what certain materials are made of and what it means to layer objects on top of one another. Computers, and the mathematics that drives them, are like hammers--you cannot use a computer without being fundamentally changed. You think differently when you interact with computers and add numbers together when paying the bill at a restaurant. And since almost everything has a computer in it these days, that means that your philosophy, well-being, and way of knowing the world are all rapidly evolving. It doesn't seem like that should be so. Why can't we just use something that interfaces with a computer and treat the computer tool as, essentially, invisible? Because using a tool is a two-way street. Now that I know my hammer is talking back to me, I am a little worried.
When I was a kid in Pennsylvania, we lived for many years right next to a railroad track, which ran behind my back yard. The trains on that particular track were infrequent, but we'd go down to the tracks and then wave and shout at the engineer in the caboose. He'd toot his horn. Trains, rails, and rail yards, where trains are stored and come together, are information flows--that is how a computer scientist sees them: information moving around, being processed, being controlled. That is how we see everything--admittedly somewhat of an unusual way of seeing. There are numerous information controls and structures such queues when train cars move through stations, and stacks when a train reaches a terminus at the rail yard, and the locomotive may need to be attached to the other end. A "stack" is a mental concept. Stacks implemented in written software are ways of reifying the stack concept using typography--seeing it with the naked eye. Trains at rail yards are another way of seeing stacks. The train's behavior is not a visualization of a stack. It is a stack. As much as anything else is one. Then, there are the track switches, merging, selection, sorting - just about everything you need to make a data flow computer. If we can observe trains as information then we can use this as a metaphor to recreate data flow in the image of trains. The trains, or slight simplifications of them, become models for computation--creative automata.
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.
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.
I recall first seeing this image in a science museum - the Boston Museum of Science if I recall, in their wonderful Model Section. The image is Fritz Kahn's mechanical model of digestion. The National Institutes of Health (NIH) has a special exhibit celebrating the different views and perspectives of the body in an exhibit called Dream Anatomy. This design belongs to the history of automata, and adds some new twists in its detailed anatomical representation. Fritz Kahn, the designer, produced a variety of creative infographics for the relationship of man to machine-- "Maschine Mensch"
Machines as art. It seems a bit odd to ponder it in today's world. But, that is because as a society, we have lost touch with the past. It is only very recently in our history that we have come to associate art with art museums and with the business of buying and selling art for outrageous prices. The Greek word techné, meaning "skill" or "craft" in modern parlance, originally captured art's meaning. Artists were craftspeople, and through their intense labor, they made beautiful objects of enduring cultural and historical value. Now, we have fine art. What does that mean? As pointed out in the fine art Wiki, "The separation of arts and crafts that exists in Europe and the United States is not shared by other cultures." So, there is an apparent schism between those who produce something useful and those who, according to the Wiki, produce something that "has been created primarily for aesthetic and intellectual purposes and judged for its beauty and meaningfulness..." The problem with fine art and this division is that it doesn't mesh well with our society as it presently exists. I am not suggesting an end to art museums---they serve an invaluable purpose in preserving culture and, more importantly, in guiding people in how to perceive. However, we need to bring back the concept of artisan, craft, and utility as natural extensions to how we define art, so that fine art does not represent the sole authority on "art." Due to technology, we live in world where "making" and "sensing" are made infinitely possible through inventions such as 3D printing, computer-aided design, games, and virtual reality. The time is ripe to slowly erode this pointless distinction between that which is done only for itself and that which may be useful. I find the Computer History Museum's Lesson Plan "Perceptions of Technology: Its Hidden Art and Beauty" both timely and appropriate. We are all artists now.
Representations of automata bring together the arts with technology, and computing with modeling and simulation. A broader topic is the structure of the academy (i.e., our present system of education) and how this system supports areas such as automata. George Bugliarello, former president of Sigma Xi and Polytechnic Institute of New York University, wrote a very good article on what sometimes divides us and what might help unite us as we improve integration of the arts and humanities with engineering. I particularly like this passage:
"Recently, with structural art—e.g., the view of a bridge also as a work of art (Billington)—and with the growing commercial importance of aesthetics in automobiles and other functional artifacts, the time is ripe in engineering for a renewed appreciation of aesthetics. Unfortunately, in the required curriculum of our engineering schools, not a single course deals with taste, aesthetics or style. Neither, for that matter, do arts curricula focus on the kinship of art and engineering as modifiers of nature. The consequence is, much too often, human-made environments with no emotional impact, that can benumb, rather than inspire."
Automata are, after all, machines whether they are made out of virtual or physical materials. They can be beautiful works of art regardless of their capacity to play a functional, utilitarian role.