A Black Box is a theoretical object that can only be examined indirectly. Black Box, however, is an excellent 2-player logic game invented by Eric Solomon in 1976
The 'Black Box' in this case is a molecule, represented as an 8x8 grid. Somewhere inside the molecule is a number of atoms - up to five. Each atom takes up one square in the grid.
The first player marks the positions of the atoms on a small grid that only she can see. The second player is the experimenter. It's his job to determine the positions of the atoms.
The experimenter can only examine the molecule by firing rays at it. These can be fired from any point on the outside of the grid - 32 places in all. The rays interact with the atoms in the molecule according to simple rules:
- If a ray hits an atom, it is absorbed
- If a ray enters a space diagonal to an atom, it is deflected through 90 degrees
- If a ray enters a space diagonal to 2 different atoms, it is reflected 180 degrees
Now, all the experimenter does is call an entry point for his ray. The other player follows through all the moves of the ray, and calls , 'absorbed' if the ray is absorbed at some point on its journey, 'reflected' if it emerges from the grid at the point it entered, or, if it exists the grid elsewhere, the exit point.
Some examples of a ray entering at 'd':
_ _ _ _ _ _ _ _
|_|_|_|_|_|_|_|_|a
|_|_|_|_|_|_|_|_|b
|_|_|_|o|_|_|_|_|c
|_|_|_|_|-|-|-|-|d <-
|_|_|_|_|||_|_|_|e
|_|_|_|_|||_|_|_|f
|_|_|_|_|o|_|_|_|g
|_|_|_|_|_|_|_|_|h
ABSORBED
_ _ _ _ _ _ _ _
|_|_|_|_|_|_|_|_|a
|_|_|_|_|_|_|_|_|b
|_|_|_|o|_|_|_|_|c
|_|_|_|_|-|-|-|-|d <-
|_|_|_|_|||_|_|_|e
|_|_|_|_|||_|_|_|f
|_|_|_|o|_|o|_|_|g
|_|_|_|_|_|_|_|_|h
REFLECTED
_ _ _ _ _ _ _ _
|_|_|_|_|_|_|_|_|a
|_|_|_|_|_|_|_|_|b
|_|_|_|o|_|_|_|_|c
|_|_|_|_|-|-|-|-|d <-
|_|_|_|_|||_|_|_|e
|_|_|_|_|||_|_|_|f
|_|_|_|_|-|-|-|-|g ->
|_|_|_|o|_|_|_|_|h
DEFLECTED to g
The experimenter has an empty grid with five marbles that he can place to indicate where he thinks the atoms are. He also has coloured pegs which represent rays. When a ray is absorbed, he puts a black peg on the entry point (like 'd', above). When it is reflected, he uses a white peg. For deflections, pairs of coloured pegs are used to indicate the exit and entry points of the ray.
At a certain point, the experimenter will think he has enough data to infer where all the atoms must be to give the results he's obtained. He'll put the marbles where he thinks the atoms are, and will ask if he has it right. The other player checks, and if the setup is right, he wins. If not, he loses. The object is to win in as few moves as possible - kind of like Mastermind. The players then swap over.
The main problem with this game is that there are certain arrangements of atoms where the result is
ambiguous, and no possible experiment can give 100% certainty of the right answer. The game's creator thinks that deliberately setting up a grid like this is
cheating. Those of us
in the know realise that this state
corresponds to a superposition of all possible states
.
Black Box variants are available online, where the computer can set up the game and will never 'cheat'. The board game itself is still available from Franjos in Germany. This game kept me amused for hours as a kid - I'd recommend it as a good tool for teaching inferences.
http://www.ericsolomon.co.uk/ The creator's website
http://www.franjos.de/spiele/bbe.htm Order the game