The Digi-Comp II was a toy computer invented by John "Jack" Thomas Godfrey (1924–2009) in 1965 and manufactured by

E.S.R., Inc. E.S.R., Inc. was an American manufacturer of educational toys during the 1960s. The company’s founders included William H. Duerig and Irving J. Lieberman, both involved in missile research at Kearfott Guidance in New Jersey, and C. David Hogan, an ...

in the late 1960s that used

marble Marble is a metamorphic rock composed of recrystallized carbonate minerals, most commonly calcite or Dolomite (mineral), dolomite. Marble is typically not Foliation (geology), foliated (layered), although there are exceptions. In geology, the ...

s rolling down a ramp to perform basic calculations. A two-level

masonite Masonite is a type of hardboard, a kind of engineered wood, which is made of steam-cooked and pressure-molded wood fibers in a process patented by William H. Mason. It is also called Quartrboard, Isorel, hernit, karlit, torex, treetex, and pr ...

platform with blue plastic guides served as the medium for a supply of marbles that rolled down an inclined plane moving plastic cams as they went. The red plastic cams played the part of flip-flops in an electronic computer - as a marble passed one of the cams, it would flip the cam around - in one position, the cam would allow the marble to pass in one direction, in the other position, it would cause the marble to drop through a hole and roll to the bottom of the ramp. The Digi-Comp II platform measures . The Digi-Comp II was not programmable, unlike the

Digi-Comp I The Digi-Comp I was a functioning, mechanical digital computer sold in kit form. It was originally manufactured from polystyrene parts by E.S.R., Inc. starting in 1963 and sold as an educational toy for US$4.99. A successor, the Digi-Comp II, ...

, an earlier offering in the E.S.R. product line that used an assortment of plastic slides, tubes, and bent metal wires to solve simple logic problems.

Computational power

Computer scientist

Scott Aaronson Scott Joel Aaronson (born May 21, 1981) is an American theoretical computer scientist and David J. Bruton Jr. Centennial Professor of Computer Science at the University of Texas at Austin. His primary areas of research are quantum computing a ...

analyzed the computational power of the Digi-Comp II. There are several ways to mathematically model the device's computational capabilities. A natural abstraction is a

directed acyclic graph In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called ''arcs''), with each edge directed from one ve ...

in which each internal vertex has an out-degree of 2, representing a toggle cam that routes balls to one of two other vertices. A fixed number of balls are placed at a designated source vertex, and the

decision problem In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question of the input values. An example of a decision problem is deciding by means of an algorithm wheth ...

is to determine whether any balls ever reach a designated sink vertex. Aaronson showed that this decision problem, given as inputs a description of the DAG and the number of balls to run (encoded in unary), is

complete Complete may refer to: Logic * Completeness (logic) * Completeness of a theory, the property of a theory that every formula in the theory's language or its negation is provable Mathematics * The completeness of the real numbers, which implies t ...

under

log-space reduction In computational complexity theory, a log-space reduction is a reduction computable by a deterministic Turing machine using logarithmic space. Conceptually, this means it can keep a constant number of pointers into the input, along with a logari ...

for CC, the class of problems log-space reducible to the stable marriage problem. He also showed that the variant of the problem in which the number of balls is encoded in

binary Binary may refer to: Science and technology Mathematics * Binary number, a representation of numbers using only two digits (0 and 1) * Binary function, a function that takes two arguments * Binary operation, a mathematical operation that ta ...

, allowing the machine to run for an exponentially longer time, is still in P.

Reproductions

A slightly downscaled reproduction of the Digi-Comp II, made from

plywood Plywood is a material manufactured from thin layers or "plies" of wood veneer that are glued together with adjacent layers having their wood grain rotated up to 90 degrees to one another. It is an engineered wood from the family of manufactured ...

, is available from Evil Mad Scientist since 2011. This reproduction uses steel pachinko balls, and measures . In 2011, Evil Mad Scientist also created a giant variant measuring around in size that uses

billiard ball A billiard ball is a small, hard ball used in cue sports, such as carom billiards, pool, and snooker. The number, type, diameter, color, and pattern of the balls differ depending upon the specific game being played. Various particular ball p ...

s. The

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...

's Stata Center houses one copy of the giant version.

References

External links

The Old Computer Museum
- Collection of old analog, digital and mechanical computers.
System_Source_Computer_Museum
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providing a web simulator
Extra-large recreation
video showing the multiplication of 13 × 3 on a scaled-up re-creation. * {{anchor, DIGI-TRAN
Original Instruction Manual

Digi-Comp II Replica
- Instructions and files for creating your own Digi-Comp II Mechanical computers Educational toys

Computational power

Reproductions

See also

References

External links