Can any program be implemented mechanically?

Question

Is it possible to build a single purpose (non Turing complete) mechanical implementation of say, Microsoft Word? Is it possible to implement such things as iterators, first-order functions, the whole gamut of programming techniques? Could gears and other mechanical parts represent data structures or even program objects? At a certain point does this necessitate building a general purpose Turing-equivalent machine, or can each function, variable, etc, have its own unique mechanical construct in the form of flywheels and/or gears, ratchets, what have you? In summary I wonder if any given piece of software on a standard computer could be compiled to a mechanical blueprint.

Answer 1

Yes, it is. Here's how you do it:

You can compile basically any program you like to circuits. See for instance the work of Dan Ghica and his collaborators on the Geometry of Synthesis, which shows how to compile programs into circuits.

1. Dan R. Ghica. Geometry of Synthesis: A structured approach to VLSI design
2. Dan R. Ghica, Alex Smith. Geometry of Synthesis II: From Games to Delay-Insensitive Circuits
3. Dan R. Ghica, Alex Smith. Geometry of Synthesis III: Resource management through type inference.
4. Dan R. Ghica, Alex Smith, Satnam Singh. Geometry of synthesis IV: compiling affine recursion into static hardware.

Circuits then turn out to reappear over and over in engineering. John Baez gives a big table of analogies of concepts, and works out a lot of connections, in This Week's Finds 288-296. So the circuit diagrams Dan's compiler generates could be instantiated as mechanical or hydraulic systems, if you really wanted to!

╔══════════════════════════════════════════════════════════════╗
║                 displacement  flow      momentum     effort  ║
╠══════════════════════════════════════════════════════════════╣
║ Mechanics      position      velocity  momentum     force    ║
║ (translation)                                                ║
║                                                              ║
║ Mechanics      angle         angular   angular      torque   ║
║ (rotation)                   velocity  momentum              ║
║                                                              ║
║ Electronics    charge        current   flux         voltage  ║
║                                        linkage               ║
║                                                              ║
║ Hydraulics     volume        flow      pressure     pressure ║
║                                        momentum              ║
╚══════════════════════════════════════════════════════════════╝

1. http://math.ucr.edu/home/baez/week288.html
2. http://math.ucr.edu/home/baez/week289.html
3. http://math.ucr.edu/home/baez/week290.html
4. http://math.ucr.edu/home/baez/week291.html
5. http://math.ucr.edu/home/baez/week294.html
6. http://math.ucr.edu/home/baez/week296.html

Answer 2

A practical example of this is the Tic Tac Toe computer made out of Tinker Toys at the Boston Science Museum (originally made by a team of MIT students). Of course, this is much simpler than Microsoft Word.

Here is a 1989 article from Scientific American describing it.

There have also been Turing machines made out of legos (this cheats a bit because it uses electricity---indeed a computer---for movement, but I think the design could be modified to avoid this) scrap metal, and more.

Answer 3

Trying to address specifically your example of creating an editor in hardware, there was an early experimental computer built which implemented both the operating system and the editor entirely in hardware. Later the editor was replaced with software, which substantially reduced the hardware needed. This was described in a book on computer architecture and history. Unfortunately I've forgotten the name and haven't found the keywords to track down the original source.