Sources page biographical material

5.V. THINK A DOT, ETC.
I managed to acquire one of these without instructions or packaging some years ago. Michael Keller provided an example complete with instructions and packaging. I have recently seen Dockhorn's article on variations of the idea. This is related to Binary Recreations, 7.M.

The device was produced by E.S.R., Inc. The box or instructions give an address of 34 Label St., Montclair, New Jersey, 07042, USA, but the company has long been closed. In Feb 2000, Jim McArdle wrote that he believed that this became the well known Edmund Scientific Co. (101 East Gloucester Pike, Barrington, New Jersey, 08007, USA; tel: [phone]; email: [e-mail]; web: http://www.edmundscientific.com). But he later wrote that investigation of the manuals of DifiComp, one of their other products, reveals that there appears to be no connection. E.S.R. = Education Science Research. The inventors of DigiComp, as listed in the patent for it, are: Irving J. Lieberman, William H, Duerig and Charles D. Hogan, all of Montclair, and they were the founders of the company. The DigiComp manuals say Think A Dot was later invented by John Weisbacker. There is a website devoted to DigiComp which contains this material and/or pointers to related sites and has a DigiComp emulator: http://members.aol.com/digicomp1/DigiComp.html . www.yahoo.com has a Yahoo club called Friends of DigiComp. There is another website with the DigiComp manual: http://galena.tj.edu.inter.net/digicomp/ .

E.S.R. Instructions, 8pp, nd -- but box says ©1965. No patent number anywhere but leaflet says the name Think-A-Dot is trademarked.

E.S.R., Inc. Corporation. US trademark registration no. 822,770. Filed: 8 Dec 1965; registered: 24 Jan 1967. First used 23 Aug 1965. Expired. The US Patent and Trademark Office website entry says the owner is the company and gives no information about the inventor(s). The name has been registered for a computer game on 23 Jul 2002.

Benjamin L. Schwartz. Mathematical theory of Think A Dot. MM 40:4 (Sep 1967) 187 193. Shows there are two classes of patterns and that one can transform any pattern into any other pattern in the same class in at most 15 drops.

Ray Hemmings. Apparatus Review: Think a Dot. MTg 40 (1967) 45.

Sidney Kravitz. Additional mathematical theory of Think A Dot. JRM 1:4 (Oct 1968) 247 250. Considers problems of making ball emerge from one side and of viewing only the back of the game.

Owen Storer. A think about Think a dot. MTg 45 (Winter 1968) 50 55. Gives an exercise to show that any possible transformation can be achieved in at most 9 drops.

T. H. O'Beirne. Letter: Think a dot. MTg 48 (Autumn 1969) 13. Proves Steiner's (Storer?? - check) assertion about 9 drops and gives an optimal algorithm.

John A. Beidler. Think-A-Dot revisited. MM 46:3 (May 1973) 128-136. Answers a question of Schwarz by use of automata theory. Characterizes all minimal sequences. Suggests some generalized versions of the puzzle.

Hans Dockhorn. Bob's binary boxes. CFF 32 (Aug 1993) 4-6. Bob Kootstra makes boxes with the same sort of T-shaped switch present in Think-A-Dot, but with just one entrance. One switch with two exits is the simplest case. Kootstra makes a box with three switches and four exits along the bottom, and the successive balls come out of the exits in cyclic sequence. Using a reset connection between switches, he also makes a two switch, three exit, box.

Boob Kootstra. Box seven. CFF 32 (Aug 1993) 7. Says he has managed to design and make boxes with 5, 6, 7, 8 exits, again with successive balls coming out the exits in cyclic order, but he cannot see any general method nor a way to obtain solutions with a minimal number of movable parts (switches and reset levers). Further his design for 7 exits is awkward and the design of an optimal box for seven is posed as a contest problem.