73 lines
3.8 KiB
Plaintext
73 lines
3.8 KiB
Plaintext
SUBJECT: THE HILL ABDUCTION CASE FILE: UFO2708
|
|
|
|
|
|
|
|
|
|
PART 7
|
|
|
|
|
|
|
|
|
|
----------------------------------------------------------------------
|
|
|
|
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.
|
|
|
|
|
|
|
|
|
|
|
|
**********************************************
|
|
* THE U.F.O. BBS - http://www.ufobbs.com/ufo *
|
|
********************************************** |