Half Adder in Wood



Japanese Programmer/Artist Yamamiya Takashi created the above machine that represents a functional half-adder logic circuit. He was inspired after reading A. K. Dewdney's "A Tinkertoy Computer and Other Machinations". The operation in this circuit stems from Takashi's design of the AND gate. The AND gate's operation and look is seen inside his web page. At first, the half-adder design looks somewhat daunting, but it offers a certain aesthetic in puzzle-making and enjoyment in the art of logic. There is a piston-like wooden shape that represents the AND gate. The piston cannot move downward unless both L-shaped holders are also downward. This is logically equivalent to both inputs to the AND gate being 1. The downward extent of the piston is equivalent to an AND gate output of 1. This is a wonderful mechanical and artistic rendition of Boolean logic. As mentioned in the web page, the gears (3 of them) represent inverter functions. The rotating lever pinion at the top of the design is the 4th inverter. The pinions interact with the L-shaped racks to cause vertical motion, and vertical motion of the piston represents the AND gate outputs.

Classic Turing Machine with Tape Erasure


Alan Turing designed a mathematical structure to capture the essence of computation with the fewest number of elements, but so that universal computation would be possible. The result is usually referred to as the Turing Machine, and the study if this particular automaton along with many others forms the basis of automata theory taken by every computer science student. The subject is taught either in that theory class, or also sometimes in the broader area of discrete mathematics. If you are seeking to know computational thinking and the core conceptual basis for computer science, this is where you will find it.

The above physical model is by Mike Davey and is a beautiful piece of machinery. Turing Machines, in their core capability are amazingly simple devices: think of a machine having a read/write memory (you can store stuff in memory and then retrieve it later), a register (which stores the "state" of the machine), and a program that is composed of instructions to move around memory. The tape metaphor represents a linear motion along a tape (that is infinite in length). Make sure to play the video on Davey's site for a good explanation of the device and its operation. I found the erasing mechanism simple and yet elegant. Some model Turing machines use replacement of a physical artifact rather than erasure as with some Lego-based models where a small object is used to denote a bit and then "read" using an sensor capable of distinguishing between black and white objects.

The Programmable Duck



Automaton created by Jacques de Vaucanson in 1739. The program is represented by a drum that you see in the external structure. Similar to cylinders that you can find in most music boxes, the drum has protrusions that indicate positional variation (over time as the drum rotates) for the controlling rods connected to the duck. The duck has appeared in various publications. The formal equivalent of the program is a state machine. Although, in theory, this machine can be classified as infinite (because of the analog nature of the continuous drum rotation), in practice with any type of standardized size on the physical drum protrusions (i.e., cams), the formal machine could be finite. The input to the machine is not clear from the diagram but is likely either weight or spring driven. Memory as for most of these automata, is based on angular position of the cylinder down to the geometric resolution of the cams. The output is the duck, which apparently did not actually go through the details of fully digesting pellets. In some additional browsing, I happened upon Jessica Riskin's essay on artificial life where she mentions many items of historical and cultural relevance, including that weight powered the duck. These automata provide a basis for a wide range of social and philosophical connections among disciplines: mathematics, computing, engineering, arts, and the humanities.

Energy Flow and Food Consumption

I had a discussion online with Ray Winstead who recently retired from the Indiana University of Pennsylvania in Biology. Ray has a page which I came across and found a diagram which is most compelling both for its biological meaning as well as the design (created by William Standaert):


The design is a flow model which receives energy in the form of sunlight and this energy undergoes a "food chain" transformation. The transformation begins with producers (e.g., plants) which are eaten by herbivores, which are in turn eaten by carnivores, to end the chain with the top carnivores (e.g., humans). There are actually 2 sub-chains in this diagram: one for consumers of live material, and the other for detritus. These types of models can be simulated: common model types used by ecologists include Odum graphs, System Dynamics, and compartmental models. Further information with a more abstract model can be found in the Wiki link on energy flow.


A New Trivium and Quadrivium


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.

5000 Moving Parts @ MIT

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?


Introduction to Creative Automata Laboratory Archive

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.

Exploring Computing Representation

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