176 lines
11 KiB
Plaintext
176 lines
11 KiB
Plaintext
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SUBJECT: THE HILL ABDUCTION CASE FILE: UFO 2707
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PART 6
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REPLY: By David R. Saunders
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Last month, Steven Soter and Carl Sagan offered two counterarguments
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relating to Terence Dickinson's article, "The Zeta Reticuli Incident"
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(ASTRONOMY, December 1974).
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Their first argument was to observe that the inclusion of connecting
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lines in certain maps "is what a lawyer would call 'leading the
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witness'." This was used as the minor premise in a syllogism for which
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the major premise was never stated. Whether we should consider "leading
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the witness" a sin or not will depend on how we conceive the purpose of
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the original article. The implied analogy between ASTRONOMY magazine
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and a court of law is tenuous at best; an expository article written
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for a nonprofessional audience is entitled, in my opinion, to do all it
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can to facilitate communication -- assuming that the underlying message
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is honest. Much of what we call formal education is really little more
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than "leading the witness", and no one who accepts the educational
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goals objects very strongly to this process. In this context, we may
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also observe that Soter's and Sagan's first argument provides another
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illustrative example of "leading the witness"; the argument attacks
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procedure, not substance -- and serves only to blunt the reader's
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possible criticism of the forthcoming second argument. This paragraph
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may also be construed as an effort to lead the witness. Once we have
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been sensitized to the possibilities, none of us needs to be further
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misled!
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The second argument offered by Soter and Sagan does attack a
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substance. Indeed, the editorial decision to publish the original
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article was a responsible decision only if the issues raised by this
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second line of possible argument were fully considered. Whenever a
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statistical inference is made from selected data, it is crucial to
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determine the strenuousness of that selection and then to appropriately
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discount the apparent clarity of the inference. By raising the issue of
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the possible effects of selection, Soter and Sagan are right on target.
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However, by failing to treat the matter with quantitative objectivity (
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by failing to weigh the evidence in each direction numerically, for
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example), they might easily perform a net disservice.
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In some situations, the weight of the appropriate discount will
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suffice to cancel the clarity of a proposed inference -- and we will
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properly dismiss the proposal as a mere capitalization on chance, or a
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lucky outcome. (It is abundantly clear that Soter and Sagan regard the
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star map results as just such a fortuitous outcome.) In some other
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situations, the weight of the appropriate discount may be fully applied
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without accounting for the clarity of the inference as a potentially
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valid discovery. For example, if I proposed to infer from four
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consecutive coin tosses observed as heads that the coin would always
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yield heads, you would properly dismiss this proposal as unwarranted by
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the data. However, if I proposed exactly the same inference based on 40
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similar consecutive observations of heads, you would almost certainly
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accept the inference and begin looking with me for a more systematic
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explanation of the data. The crucial difference here is the purely
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quantitative distinction between 4 and 40; the two situations are
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otherwise identical and cannot be distinguished by any purely
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qualitative argument.
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When Soter and Sagan use phrases such as "some subset that
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resembles", "free also to select the vantage point", "simple matter to
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optimize", and "freedom to contrive a resemblance", they are speaking
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qualitatively about matters that should (and can) be treated
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quantitatively. Being based only on this level of argument, Soter's and
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Sagan's conclusions can only be regarded as inconclusive.
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A complete quantitative examination of this problem will require the
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numerical estimation of at least three factors, and their expression in
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a uniform metric so that wee can see which way the weight of the
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evidence is leaning. The most convenient common metric will be that of
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"bits of information", which is equivalent to counting consecutive
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heads in the previous example.
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One key factor is the degree of resemblance between the Hill map and
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the optimally similar computer-drawn map. Precisely how many
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consecutive heads is this resemblance equivalent to? A second key
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factor is the precise size of the population of stars from which the
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computer was allowed to make its selection. And a third key factor is
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the precise dimensionality of the space in which the computer was free
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to choose the best vantage point. If the first factor exceeds the sum
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of the other two by a sufficient margin, we are justified in insisting
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on a systematic explanation for the data.
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The third factor is the easiest to deal with. The dimensionality of
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the vantage-point space is not more than three. A property of the
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metric system for weighing evidence is that each independent dimension
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of freedom leads us to expect the equivalent of one more consecutive
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head in the observed data. Three dimensions of freedom are worth
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exactly 3.0 bits. In the end, even three bits will be seen as
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relatively minor.
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The second factor might be much larger than this, and deserve
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relatively more discussion. The appropriate discount for this selection
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will be log2C, where C is the number of distinct combinations of stars
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"available" to the computer. If we were to agree that C must represent
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the possible combinations of 46 stars taken 14 at a time, then log2C
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would be 37.8 bits; this would be far more than enough to kill the
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proposed inference. However, not all these combinations are equally
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plausible. We really should consider only combinations that are
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adjacent to one another and to the sun, but it is awkward to try to
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specify exactly which combinations these are.
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The really exciting moment in working with these data came with the
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realization that in the real universe, our sun belongs to a closed
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cluster together with just six of the other admissible stars -- Tau
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Ceti, 82 Eridani, Zeta Tucanae, Alpha Mensae, and Zeta 1 and Zeta 2
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Reticuli. The real configuration of interstellar distances is such that
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an explorer starting from any of the seven should visit all of them
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before venturing outside. If the Hill map is assumed to include the
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sun, then it should include the other members of this cluster within an
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unbroken network of connections, and the other connected stars should
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be relatively adjacent in the real universe.
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Zeta Reticuli occupies a central position in all of the relatively
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few combinations that now remain plausible. However, in my opinion, the
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adjacency criteria do leave some remnant ambiguity concerning the
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combination of real stars to be matched against the Hill map -- but
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only with respect to the region farthest from the sun. The stars in the
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closed cluster and those in the chain leading to Gliese 67 must be
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included, as well as Gliese 86 and two others from a set of five
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candidates. Log2C for this remnant selection is 3.9 bits. we must also
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notice that the constraint that Zeta Tucanae be occulted by Zeta
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Reticuli reduces the dimensionality of the vantage-point space from 3.0
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to 1.0. Thus, the sum of factors two and three is now estimated as only
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4.9 bits.
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The first factor is also awkward to evaluate -- simply because there
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is no standard statistical technique for comparing points on two maps.
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Using an approximation based on rank-order correlation, I've guessed
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that the number we seek here is between 11 and 16. (This is the result
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cited by Dickinson on page 15 of the original article.) Deducting the
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second and third factors, this rough analysis leaves us with an
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empirical result whose net meaning is equivalent to observing at least
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6 to 11 consecutive heads. (I say "at least", because there are other
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factors contributing to the total picture -- not discussed either by
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Dickinson or by Soter and Sagan -- that could be adduced to enhance
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this figure. For example, the computed vantage point is in good
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agreement with Betty Hill's reported position when observing the map,
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and the coordinate system implicit in the boundaries of the map is in
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good agreement with a natural galactic coordinate system. Neither have
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we discussed any quantitative use of the connections drawn on the Hill
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map, which were put there in advance of any of these analyses.)
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In the final interpretation, it will always be possible to argue that
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5 or 10 or even 15 bits of remarkable information simply isn't enough.
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However, this is a matter for each of us to decide independently. In
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deciding this matter, it is more important that we be consistent with
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ourselves (as we review a large number of uncertain interpretations of
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data that we have made) than that we be in agreement with some external
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authority. I do believe, though, that relatively few individuals will
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continue a coin-tossing match in which their total experience is
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equivalent to even six consecutive losses. In scientific matters, my
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own standard is that I'm interested in any result that has five or more
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bits of information supporting it -- though I prefer not to stick my
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neck out publicly on the basis of less than 10. Adhering to this
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standard, I continue to find the star map results exceedingly
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interesting.
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Dr. David R. Saunders is a Research Associate at the University of
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Chicago's Industrial Relations Center.
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**********************************************
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* THE U.F.O. BBS - http://www.ufobbs.com/ufo *
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********************************************** |