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REPLY: By Michael Peck

Carl Sagan and Steven Soter, in challenging the possibilities
discussed in "The Zeta Reticuli Incident", suggest that without the
connecting lines drawn into the Hill map and the Fish interpretation
there is little resemblance between the two. This statement can be
tested using only X and Y coordinates of the points in the Hill map and
a projection of the stars in the Fish pattern. The method used for the
comparison can be visualized this way:

Suppose points of the Hill map and the Fish map are plotted on
separate glass plates. These plates are held parallel (one behind the
other), and are moved back and forth and rotated until the patterns
appear as nearly as possible to match. A systematic way of comparing
the patterns would be to adjust the plates until corresponding pairs of
points match exactly. Then the other points in the patterns can be
compared. Repeating this process for all the possible pairs of points
(there are 105 in this case), the best fit can be found.
Mathematically, this involves a change of scale and a simple coordinate
transformation. A computer program was written which, using X and Y
coordinates measured from a copy of the Hill map and a projection of
the Fish stars, and using the Hill map as the standard, computed new X
and Y coordinates for the Fish stars using the process described. From
these two sets of coordinates, six quantities were calculated: the
average difference in X and Y; the standard deviation of the
differences in X and Y, a measure of the amount of variation of the
differences; and correlation coefficients in X and Y. The coefficient
of correlation is a quantity used by statisticians to test a suspected
relation between two sets of data. In this case, for instance, we
suspect that the X and Y coordinates computed from the Fish map should
equal the X and Y coordinates of the Hill map. If they matched exactly,
the correlation coefficients would be one. If there were no correlation
at all, the value would be near zero. We found that, for the best
fitting orientation of the Fish stars, there was a correlation
coefficient in X of 0.95 and in Y of 0.91. In addition, the average
difference and the standard deviation of the differences were both
small -- about 1/10 the total range in X and Y. As a comparison, the
same program was run for a set of random points, with resulting
correlation coefficients of 1/10 or less (as was expected). We can
conclude, therefore, that the degree of resemblance between the two
maps is fairly high.

From another point of view, it is possible to compute the probability
that a random set of points will coincide with the Hill map to the
degree of accuracy observed here. The probability that 15 points chosen
at random will fall on the points of the Hill map within an error range
which would make them as close as the Fish map is about one chance in
10 to the fifteenth power (one million billion). It is 1,000 times more
probable that a person could predict a bridge hand dealt from a fair
deck.

Michael Peck is an astronomy student at Northwestern University in
Illinois.

Jerry
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