1

"EMAG III, a Checker-playing Digital Computer," was the name of the project presented by finalist David S. Ecklein, Cedar Falls, Iowa, at the Tenth National Science Fair.    ,.;

"Introduction ,

My project, a digital computer programed to play a reason­able game of checkers with a human as its adversary, is the logical culmination of a previous active interest in electronics and symbolic logic. Its conception dates back to the summer of 1957 and since then has been the focal point of my efforts and aspirations. The project has in its entirety been developed in my home laboratory.

Indicative of the physical scope of this endeavor are the 3200 vacuum tubes, over 3000 sockets, 200 germanium diodes, thousands of resistors and miles of soldered wire circuitry which in part comprise its material aspect.

The design and construction demanded rigorous scheduling and utilization of time. Semi-mass-production methods were adopted to make practical and feasible what initially appeared to be a tremendously complex, if not impossible, task.

The procurement of components posed a very real chal­lenge because of my limited resources. Careful choice of materials from war and industrial outlets coupled with some ingenuity of circuit design and construction parameters ac­complished the necessary economies.

Past savings plus part-time and vacation earnings provided a budget. Employment during the past summer at the IBM Poughkeepsie Research Laboratory not only helped financially but provided valuable and encouraging experience through associations with outstanding computer scientists and engin­eers.

Theory

Checkers being a relatively complex game characterized by many variables, disillusionment can result from the wrong approach to its logical analysis. My analysis regards the main game as consisting of thirty-two simple subgames wherein only one elect square of their fields can contain a piece to be moved. The merit of a move is a result of a Boolean function involving conditions in the elect square and in its adjacent squares as variables. Hence the checkerboard is considered to consist of thirty-two fields. Switching attention from subgame to subgame, the computer searches for a move. Several scans of the thirty-two subgames are made, the first being condi­tioned to effect a move from an elect square only under the most optimum conditions. If the first fails to produce a result, the next scan looks for a move of less merit. Thus the possible moves are ranked into categories as in the following list, inversely as to merit.

I.          Multiple jump using single man

II.         Multiple jump using king

III.       Single jump involving no risk

IV.       Exchange using single man

V.        Exchange using king

VI.       Dangerous or undesirable jumps using single man

VII.      Dangerous or undesirable jumps using king

VIII.     Defend a man in danger, or escape being jumped

IX.       Traps, including two for one shots, breeches and forks

X.        Back men to build strong positions

XI.       Mediocre moves that do not immediately affect the position

XII.      Moves using single man involving risk of trap

XIII.     Moves using king involving risk of trap

Moves definitely losing single man

XV.      Moves definitely losing king

In addition to those previously listed, two transient cate­gories are recognized and are shifted as to relative merit in accordance with the stage of the game and the possession of the move or opposition, to be explained later: T1—force ex­change, and T2—challenge the enemy.

My analysis incorporates a number of general principles which in theory produce a consistent strategy of play. Au­thorities consider the game as divided into three consecutive stages: opening, midgame and endgame.1 The first of these

1. Louis C. Ginsberg, "Principles of Strategy in the Game of Checkers" (New York,  1945), pp.  10-11. includes the initial moves which must be made with considera­tion to avoid subsequent forfeit. Following this stage the second or body of the game is reached.2 When play has pro­gressed to the point where six or less pieces remain on the board for each adversary, it is recognized that the endgame has been reached.3

Inasmuch as the opening consists of eight or fewer moves,4 I have combined it and the midgame into a single phase. The separate strategies of the opening-midgame and the endgame phases encompass two areas: first, the order of selection of subgames for consideration of the actual piece to be moved; and second, the relative importance of the transient cate­gories."

The paper then analyzes the opening-midgame strategy, the strategy for the endgame phase and the importance of choosing the proper direction of motion. Because the computer lacks the faculty to memorize proper endgame forcing techniques, it is inadequate to cope with an average to good human opponent.

The next section describes how the computer was built.

"Components

Circuit components were chosen after rigorous experimen­tation. Suitability and availability made the 7193 surplus tube my choice for application throughout. Repeated trials indicated the choice of resistor values for the Eccles-Jordan trigger circuits and the inverter circuits. Zip-in type sockets were selected to expedite construction. Office shelving pro­vided inexpensive and flexible chassis material. Perforated masonite served as paneling. Discarded pinball machines contributed some parts, including the field selector switch and stepping switches.

Input-Output Console

The input-output console comprises a display panel as well as the power supply and control panel. The display panel incorporates two functions, the board display and the move display.

• Ibid., p.  11.
  
• Ibid.
  
• Ibid., p. 10.
  

Ninety-six Eccles-Jordan trigger circuits, incorporating neon indicators arranged in checkerboard design, three in each of thirty-two squares, are the basis for the board display. The human player manipulates these indicators by means of a test-prod and screw-stud arrangement. The move display is an array of thirty-nine neon indicators and trigger circuits. This display indicates the square containing the piece to be moved for the machine, and also the direction and type of move to be made.

The power supply is of two parts, the B+ plate supply, and the C- bias supply. The plate supply operates directly from the power line and utilizes a half-wave bank of selenium rectifiers giving an output of 150 volts D.C. at 10 amperes. Filtering is accomplished by a bank of electrolytic capacitors totaling 1750 microfarads. Bias voltages of 25 volts at 5 amperes is derived from a transformer and full-wave rectifier arrangement with 10,000 microfarads of filtering. Tube heat­ers are connected in series-parallel to operate directly from the power line. This was attempted after experiments to establish the heater-cathode breakdown voltages of the tubes.

The control panel includes five fuse-box switches, which control the five blocks of heaters. Each block draws 5 to 15 amperes. Other fuse boxes handle the plate and bias voltage supplies. Meters keep vigil on the power supply voltages and amperages.

The Matrix Section

The matrices in this computer are of two types: triode and diode. The triode matrices comprise about 1500 tubes and are used in the field selection switching. They are nothing more than aggregates of inverters with common cathodes, plates and grids to economize on resistors. The diode matrices serve to build up off-board conditions for the field and to activate trigger-circuit aggregates.

The Logic Section

This is the decision-making organ. It contains the inverters, diodes and resistors necessary to simulate the category logic. It is the heart of the computer.

The Executive Section

This section encompasses the field scanning selector switch and motor, the category selector, the direction of move selector and other sequence of play apparatus

Conclusion

This project is my most valued and significant scientific experiment. While EMAG III was developed as a mere game-playing device, the processes of solution and strategy involved are related to all machine decision making as applied to scientific or commercial problems. It has expanded my knowledge, developed my creative skills and definitely di­rected my interest into a field in which I hope to have a future career.

Acknowledgment

I wish to express appreciation for the encouragement re­ceived from my parents, teachers and friends. Most especially do I value the inspiration and guidance contributed by Dr. Arthur L. Samuel of the IBM Poughkeepsie Laboratory and by Dr. C. W. Farr of the Lincoln Laboratory at the Massa­chusetts Institute of Technology. I am grateful to the IBM Corporation for the experience provided me while employed at the Poughkeepsie Research Laboratory during my summer vacation

Bibliography

Call, W.T. Vocabulary of Checkers. New York:  Schlueter, 1909.

Doran, Peter. Doran's Old 14th. Chicago: Frank R. Wendemuth, 1936.

Duffy,   J.M.   Duffy's   Single   Corner.   Chicago:   Frank   R.

Wendemuth, 1934. Elementary Checkers. Buffalo, New York:  Wales Checker System, 1950.

Friel,  Leonard  G.   Checkers.  Chicago:   Leonard  G.   Friel, 1940.

Ginsberg, Louis C. "Principles of Strategy in the Game of
Checkers." New York:  The American  Checkerist maga­zine, 1945.

Hill, James. Hill's Manual. London: E. Marlborough, N.D.

Hopper, Millard. How to Win at Checkers. Buffalo, New
York: Wales Checker System, 1956.

Lees, James. Lees' Guide. London:  E. Marlborough,  1893.

McKay,  Paul.  Easy  Lessons  in  Checkers  reprint.   Buffalo,
New York: Wales Checker System, N.D.

Patterson, W. How to Play Checkers. Girard, Kansas: Haldeman Julius, N.D.

Pickering, S.J. Modern Magic reprint. Buffalo, New York:
Wales Checker System, N.D.

Sivetts, B. Frank. Sivetts' Original and Infallible Method.

Oberlin, Ohio: Pearce and Randolph, 1894.

Spayth,   Henry.   Checkers   for   Beginners.   Chicago:   Stein,

N.D."

2

"The Logical Mouse" was a project done by Roger Roberts, Baltimore, Maryland, finalist at the Ninth and Tenth National Science Fairs, and member of the Honors Group of the Eighteenth Science Talent Search.

"For many years the mouse has been the subject of condi­tioning experiments using shock and drugs. He has learned to remember sequences of problems, such as which path to traverse to reach his food. Since my project concerns the logical thought processes for working out a similar problem, I decided to use the mouse as a subject. However, my mouse is not a living organism, but merely an indicator of a trans­port mechanism. And to replace the mouse's brain I use a computer.

Background

The first high-speed computer, the Mark I, was introduced in 1944. It was developed as a means of performing complex mathematical computations rapidly. The first true electronic computer, ENIAC, was capable of speeds several thousand times as fast, and calculations which would have taken many man-months to perform were completed in minutes.

These first computers were digital, solving problems by simple binary counting. Many functions could be more ef­ficiently handled by analog means, and complete or partial analog computers were designed.

The next stage of computer design was its application to the generating and maintaining of business records. This type of computer does not have to be a genius at solving problems. It must be able to perform many simple operations, store a large volume of data, change records rapidly and print out many different types of information.

There is no doubt, however, that the greatest value of the computer will be realized when its most recent application, that of logical reasoning, is fully developed. The Logical Mouse is a demonstration of this type of computer.

Design

For a system to be considered a computer it must have four basic elements: input, control, memory and output. Without these elements, it could not perform its basic func­tions of solving problems.

The problem that I undertook to solve was the tracing of an unknown maze by a mouse in the search for food.

The input element permits data to be read into the system. Input information can be delivered by punched tape, punched cards, special typewriters, magnetic tape, impulses or con­trol positions.

The input of my Mouse is the impulses generated by a photoelectric eye seeing barriers which are set up to form the maze.

The control function establishes the program for the proper manipulation of the input data. It can be built into the computer, established by push buttons or patch cards, inserted as  additional  input  or any combination of these.

My control stops the Mouse when it sees a barrier, turns it to find a clear path and signals the memory bank as to the correct direction.

The memory element provides a repository for information so that it can be obtained when needed. Memory can be internal or external. Forms of memory are punched tape, punched cards, magnetic tapes, magnetic drums, magnetic disks, magnetic cores, relays, vacuum tubes, sonic delay lines, electrical delay lines and cathode-ray tubes. The selec­tion of the type of memory depends upon the amount of information to be stored, the desired speed of access, require­ments for random access, the size of the computer and the economic factor.

Since I had a relatively small amount of information to store, I decided to use a relay system. Relays offer direct control, efficiency, low cost, and can be reset by turning the power switch off and on.

The output, or the end product of a computer system, can take many forms. To name a few: punched tape, punched cards, magnetic tape, high-speed printing, cathode-ray dis­play and control signals.

The output of my Mouse directs it through the maze, signaling the correct turn each time a barrier is reached.

Operation

The Mouse's movements are carried out by a transport mechanism beneath the maze. This mechanism moves a car­riage horizontally and vertically. A magnet on the carriage is rotated by a motor. The Mouse is thus joined magnetically to the carriage and any motion of the magnet is repeated by the Mouse.

The photoelectric sensing unit consists of two parts, one in the Mouse and one in the carriage. The Mouse has two eyes, one of which contains a light source and the other the photoelectric cell. The light and cell are aimed so that when their paths converge on a barrier the Mouse will be positioned correctly before it rotates. There is a second light source on the underside of the Mouse which is directed at a photoelectric cell on the carriage. When the cell in the Mouse receives the reflected light from the barrier, it completes a circuit to the second light source. When this second light is energized, it signals the cell on the carriage and a relay is energized which causes the Mouse to stop moving.

Another relay is energized and the Mouse rotates 90° in a counterclockwise direction, searching for an unobstructed path. If there is no barrier, the Mouse will proceed until it is halted by another barrier farther on. But, if it senses a bar­rier in the same box after its first turn, the Mouse will rotate 180° in a clockwise direction by means of an energized relay before it starts moving horizontally or vertically along the maze after its rotation. This procedure continues until it reaches its destination (food), the lower left-hand box. Each time the Mouse encounters a barrier and only makes a left turn, the memory relay for that barrier retains that informa­tion by not being energized. But if the opening is on the right, the memory relay is energized and thus "remembers" that the correct path is to the right.

A TYPICAL PROBLEM

A—Mouse starts

B—Sees barrier, turns left

C—Sees barrier, turns left, sees barrier, turns right

D—Sees barrier, turns left

E—Sees barrier, turns left

F—Sees barrier, turns left, sees barrier, turns right

G—Sees barrier, turns left

H—Sees barrier, turns left

I—Sees barrier, turns left, sees barrier, turns right

J—Sees barrier, turns left, sees barrier, turns right

K—Sees barrier, turns left

L—Mouse reaches food

On second run Mouse will not make incorrect turns. When the correct path is to the left, it will turn left; when the correct path is to the right, it will turn right.

When the Mouse makes its second trip through the maze, it again stops as it sees each barrier. The memory is searched for the correct turn, and the Mouse will then move either right or left, depending upon the setting of the memory relay for that barrier. After the Mouse completes its turn it starts to move again, stops again at the next barrier, turns as the memory indicates and then moves on. It continues this pro­cedure until it again reaches its destination.

Inspiration

The inspiration for my project came from reading an article describing a mechanical mouse that learned its way through a maze. Further investigation disclosed that it operated on the principle of stopping in each box and investigating all exit possibilities before proceeding. I felt it would be more meaningful to design one operating on principles that would simulate logical thinking, that is, not stopping until a barrier is encountered.

Conclusion

I call this the "Logical Mouse" because it’s actions are made in a logical manner. It follows a pattern of "looking" first left and then right, and remembers only the correct informa­tion. Computers, working on similar reasoning principles, can, by examining all pertinent information, predict weather or elections, navigate ships or missiles, control factory pro­duction, direct traffic patterns and perform many other tasks.

The potential of this type of computer is limited only by human imagination. For example, an apartment house could be designed for maximum efficiency, or an entire city could be planned. A master control could handle all municipal serv­ices automatically. A new product could be completely en­gineered, and then built directly by output signals controlling automatic production equipment. I hope someday to design one of these computers."

See also "Some Investigations into the Relationship be­tween Symbolic Logic and Electronic Switching Networks," Chapter 8, Mathematics, 2.

Are You Ready To Move Onto The Next Lesson? Click Here….