*Squares and Sticks

James LYONSW at UCONNVM.UCONN.EDU
Wed Jun 15 20:16:01 EST 1994


Bill Tavol queried on the length of the sticks.

RELATIVE APPARENT SYNAPOMORPHY = the number of times a pairs
                                  of squares shares any given stick
                                  to the exclusion of a third.

Assume that the sticks are all the same length (21 cm) and cannot be
so that four squares in diagonal share the same stick (A1, B2, C4, C5).

For short sticks, three squares can share a stick like this:

   ______ ______ ______
   |   ***|******|*    |
   |      |      |     |
   ______ ______ ______

or like this:
       ______ ______
       |      *     |
       |     *|     |
       _____* ______
       |   *  |
       |      |
       ______


 If two squares uniquely share a stick, the RAP score for that stick
 is N-2 (N= number of squares), or the number of times that pair of
 squares share a stick to the exclusion of any third.

 My colleague knows the length of the sticks.  My question is are the scores
I send independent?  For some sticks they clearly are, but sometimes
(like a perfect diagonal) a stick will be found within a square juxtaposed
 between two other squares.  I say that the fact that _I_ know
 a particular stick has to be found in a certain square while I'm counting
 RAP scores does not matter to my colleague because the conditions
 which brought about the observation was proximity, which is
 observer-independent.

 More HELP!

 James



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