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Appendix B: Patterns
An Induction Game
Method of Scoring:
Scientists:
+1 for
every correct prediction
-1 for every incorrect prediction
0 for every experiment or
observation
Designer :
two times the difference between the best and worst
scientist
-5 for the first dropout
-10 for every additional dropout
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The induction game of Patterns was devised by
Sidney Sackson and popularized by Martin Gardner in his "Mathematical Games"
column in Scientific American. The analogue between the use of induction in the
scientific method and the game is remarkable. One player, called "the Designer"
or "Nature," secretly constructs a Master Patterna design composed of four
different symbols in a six-by-six grid. The design can be simply
or complexly ordered, but the method of scoring encourages the Designer to be clever. The
other players, called "Scientists," request information about any cell
("the experiment" or "observation of nature") at any time and ask for
as much information and they want.
When a scientist believes she has guessed the Master Pattern, she draws
the inferred symbols in the untested cells (marked somehow in order to identify which
symbols are the inductions) and now is ready to "publish." Scientists need not
take turns, and they might choose not to play. |
When the scientists publish, they check their theories with the
Master Pattern. If a scientist drops out of the game, she has a score of zero, but
dropping out could save her from a minus score. Dropping out also penalizes the
Designers score. The overcautious scientist who prefers not to publish will often
dropout. High scorers often look for symmetry, ordered arrangements, or mathematical
patterns. Low scorers often use intuition, guesses, and hunches.
Designers are rewarded for constructing patterns which can be solved by
only some of the scientists. In the following game, suppose a Scientist has requested the
experiments shown in Grid 1. At this point many hypotheses are possible, as shown
by the Hypotheses 1-3.
Grid 1: The experiments shown to
the right suggest the hypotheses 1-3 shown below.
(Experiments shown are
B-1,
C-2,
C-4,
E-3,
E-5,
E-6,
F-1, and
F-5) |
1 |
|
O |
|
|
|
* |
2 |
|
|
D |
|
|
|
3 |
|
|
|
|
D |
|
4 |
|
|
* |
|
|
|
5 |
|
|
|
|
* |
O |
6 |
|
|
|
|
O |
|
|
A |
B |
C |
D |
E |
F |
Hypothesis 1
|
1 |
* |
O |
O |
O |
O |
* |
2 |
O |
* |
D |
D |
* |
O |
3 |
O |
D |
* |
* |
D |
O |
4 |
O |
D |
* |
* |
D |
O |
5 |
O |
* |
D |
D |
* |
O |
6 |
* |
O |
O |
O |
O |
* |
|
A |
B |
C |
D |
E |
F |
Hypothesis 2 |
1 |
* |
O |
* |
* |
O |
* |
2 |
O |
* |
D |
D |
* |
O |
3 |
* |
D |
* |
* |
D |
* |
4 |
* |
D |
* |
* |
D |
* |
5 |
O |
* |
D |
D |
* |
O |
6 |
* |
O |
* |
* |
O |
* |
|
A |
B |
C |
D |
E |
F |
Hypotheses 3 |
1 |
* |
O |
D |
D |
O |
* |
2 |
O |
* |
D |
D |
* |
O |
3 |
D |
D |
* |
* |
D |
D |
4 |
D |
D |
* |
* |
D |
D |
5 |
O |
* |
D |
D |
* |
O |
6 |
* |
O |
D |
D |
O |
* |
|
A |
B |
C |
D |
E |
F |
The next experiment done should be a "crucial"
one-- namely, you would want to choose a cell exhibiting a different entry in each
of the three hypotheses. Any of the following experiments would select the
best hypothesis: A-3, A-4, C-1, C-6, D-1, D-6, F-3, and F-4.
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