NIM Playing Machine from Tinkertoy
Colour images from 1978-9 to supplement this paper
H.A. Cohen, Modelling Boolean Algebra with Tinkertoy or Meccano: How to Construct a NIM Playing Machine, in P.Williamson (Editor), Learn to Love Mathematics, Mathematics Association of Victoria, Melbourne, 1980, pp 253-265. Download by clicking on PDF token to the left



The NIM Playing machine constructed out of Tinkertoy.
The player and the machine (aided by a human) make moves alternatively, dislodging 1, 2 or 3 tokens from the verucal stack. Neither player nor the machine can cheat. But which one will win? Making the player's move -- David can stroke to remove 1, 2 ,or 3 orange plastic pieces from the stack. The machine's (human) slave will then make a complete stroke with the machine's input arm, and using wooden logic the machine removes the (legal) number of pieces it deems appropriate.

The Overlord of the system decides just which of player or machine makes the first move. TheOverlord then reloads the stack with an arbitary (or is it ) number of pieces.





This devise is really a special purpose computer. A far more impressive wooden computer - developed at about the same time - is the Tic-Tac-Toe Playing Machine described at the bottomof this web page.
Related Papers on Introducing Number and Computer Concepts in Primary School
H.A. Cohen, Making Algebra Concrete using a Microcomputer: An Algebraic Programming Language for the Control of Robots, in P. Williamson (Editor), Learn to Love Mathematics, Mathematics Association of Victoria, Melbourne, 1980, pp 336-350. Download by clicking on PDF token to the left
H.A. Cohen, Modelling Boolean Algebra with Tinkertoy or Meccano: How to Construct a NIM Playing Machine, in P.Williamson (Editor), Learn to Love Mathematics, Mathematics Association of Victoria, Melbourne, 1980, pp 253-265. Download by clicking on PDF token to the left
H.A. Cohen, Expanding the Child's Concept of Number, Space and Operation, in M. Poole (Editor), From Creativity to Curriculum, Allen and Unwin, Sydney, 1980, pp 147-162. Download by clicking on PDF token to the left
TIC-TAC-TOE Playing Machine
from Tinkertoy






The Tic-Tac-Toe playing machine shown above is a special purpose computer built by Danny Hillis, Danny Silverman (*), and others at MIT circa 1980. The only such model constructed is on display at the Boston Museum of Science.
Like the NIM playing machine, a slave - human (or android) - is needed to supply the muscle power utilised (and controlled) by the machine in making its moves. The slave cranks the read head up and down and supervises input. After the computerís opponent makes a move, the slave walks to the front of the machine to adjust the core piece inside the read head, registering the contestantís move. The slave then pulls on a string to cock the core piece for its impending whirl of recognition. When it discovers a memory that matches the current state of the game, the core piece spins, and the computer indicates its move.
When first assembled, this specialised computer worked perfectly. All joints had been glued together. However it had to partly assembled for transport purposes, and its this witer's impression that it has never been able to function since. It is notable that it is displayed enclosed in a glass case.
This story indicates the limitation of the original variety of Tinker Toy for such constructions.

Last Thoughts on the NIM Playing Machine
The NIM Playing machine illustrated here can be constructed in a couple of hours. It works OK without gluing. The design COULD in principle be readily extended to have multiple columns of tokens. I never did this -- as I believed that it would become very unreliable. ( Certainly one would need to glue the components together. ) But I may be wrong ! If you meet this challenge -- please inform by email to AboutDragonsATtpgDOTcomDOTau.

About Danny Hillis
Inn 1980 Danny Hillis was about to enter graduate school at MIT. His PhD on the Connection Machine contained the design of a computer which was massively parallel, every (small) memory unit was connected/interconnected with millions of others. It was believed that such a design was especially suitable for Articial Intelligence Calculations -- as its extreme parallellism mimics the modst notable design feature of the human brain -- huge numbers of slow biological elements neurally interconnected. Hillis hoped that the Connection Machine -- once constructed -- would be proud of him and his design. In fact Thinking Machines Inc, the company he founded shortly after completing his PhD, built several Connection Machines over the next few years before the company went bankrupt.
DIRECTORY
Publications Since 89 By Year
This is a collection of papers in image engineering and visual information systems, including image processing generally including numberplate recognition and speed-up issues, image restoration, (IFS and) fractal image coding, issues in image retrieval using thumbnails, and parallel processing techniques, together with some papers devoted to the design of image codecs, to aspects of satellite systems and to the education of engineers.
Publications Prior to 89 By Topic excluding Physics Papers
These papers are grouped by topic. Topic titles include qualitative physics, mathematics education, OZNAKI - a pioneering educational robotics project, the La Trobe Talking Communicator ( developed for severely disabled non-speech students ).
Papers on Physics and Geophysics
This directory of papers in theoretical particle physics and quantum electrodynamics includes the abstracts for each paper.
Primers on VIS and Image Engineering
VIS = Visual Information Systems.Topics: Edges. Interesting points. Image restoration. Image access via thumbnails. Texture analysis, identification, segmentation. Fuzzy image processing. Using fractals to encode images. The perceptron images.
Dragons are formidable problems in qualitative physics, challenging, and yet solvable using little or even no algebra or calculus.
e.g. Which direction does the yo-yo roll?
What if the table were greased?
     Buy a yoyo to check !! are you a Newtonian ?
Personal Home Page of Dr Harvey A. Cohen of Melbourne Australia