The controversial interpretation of the Hill "star map" conducted by Marjorie Fish includes the sun and 15 nearby stars. These stars make an ideal case study for stellar age determination as described in this article. For further details specifically about this map, see in Focus and the December issue.

 

Commentary Editor's Preface The lead article in the December 1974 issue of ASTRONOMY, entitled "The Zeta Reticuli Incident", centered on interpretation of a map allegedly seen inside an extraterrestrial spacecraft. The intent of the article was to expose to our readers a rare instance where astronomical techniques have been used to analyze a key element in a so-called "close encounter" UFO incident. While not claiming that the analysis of the map was proof of a visit by extraterrestrials, we feel the astronomical aspects of the case are sufficiently intriguing to warrant wide dissemination and further study. The following notes contain detailed follow-up commentary and information directly related to that article. The age of our own sun is known with some accuracy largely because we live on one of its planets. Examination of Earth rocks -- and, more recently, rocks and soil from the moon -- has conclusively shown that these two worlds went through their initial formation 4.6 billion years ago. The formation of the sun and planets is believed to have been virtually simultaneous, with the sun's birth producing the planetary offspring. But we have yet to travel to any other planet -- and certainly a flight to the surface of a planet of a nearby star is an event no one reading this will live to witness. So direct measurement of the ages of nearby stars -- as a by-product of extrasolar planetary exploration -- is a distant future enterprise. We are left with information obtained from our vantage point here near Earth. There is lots of it -- so let's find out what it is and what it can tell us.

 

When we scan the myriad stars of the night sky, are we looking at suns that have just ignited their nuclear fires -- or have they been flooding the galaxy with light for billions of years? The ages of the stars are among the most elusive stellar characteristics. Now, new interpretation of data collected over the past half century is shedding some light on this question. Computer models of stellar evolution reveal that stars have definite lifespans; thus, a certain type of star cannot be older than its maximum predicted lifespan. Solar type stars of spectral class F5 or higher (hotter) cannot be older than our sun is today. These stars' nuclear fires burn too rapidly to sustain them for a longer period, and they meet an early death. All main sequence stars cooler than F5 can be as old or older than the sun. Additionally, these stars are also much more likely to have planets than the hotter suns. There are several exciting reasons why the age of a star should be tracked down. Suppose we have a star similar to the sun (below class F5). If we determine how old the star is, we can assume its planets are the same age -- a fascinating piece of information that suggests a host of questions: Would older Earthlike planets harbor life more advanced than us? Is there anything about older or younger stars and planets that would make them fundamentally different from the sun and Earth? Of course we don't know the answer to the first question, but it is provocative. The answer to the second question seems to be yes (according to the evidence that follows). To best illustrate the methods of star age determination and their implications, let's select a specific problem. "The Zeta Reticuli Incident" sparked more interest among our readers than any other single article in ASTRONOMY's history. Essentially, that article drew attention to a star map allegedly seen inside an extraterrestrial spacecraft. The map was later deciphered by Marjorie Fish, now a research assistant at Oak Ridge National Laboratory in Tennessee. In her analysis, Ms. Fish linked all 16 prominent stars in the original map (which we'll call the Hill map since it was drawn by Betty Hill in 1966) to 15 real stars in the southern sky. The congruence was remarkable. The 15 stars -- for convenience we will call them the Fish-Hill pattern stars -- are listed on the accompanying table. Since these stars have been a focus of attention due to Ms. Fish's work and the article mentioned above, we will examine them specifically to see if enough information is available to pin down their ages and (possibly) other characteristics. This will be our case study star group.     The Fish-Hill Pattern Stars Gliese Cat. No. Alternate Name Spectral Type W - Velocity Total Space Velocity Galactic Orbit Eccentricity Galactic Orbit Incl. 17 Zeta Tucanae G2 -38 70 .1575 .0529 27 54 Piscium K0 10 45 .1475 .0260 59 HD 9540 G8 1 26 .0436 .0133 67 HD 10307 G2 0 45 .1057 .0092 68 107 Piscium K1 3 43 .1437 .0134 71 Tau Ceti G8 12 36 .2152 .0287 86 HD 13445 K0 -25 129 .3492 .0269 86.1 HD 13435 K2 -37 41 undetermined undetermined 95 HD 14412 G5 -10 33 .1545 .0025 97 Kappa Fornax G1 -13 35 .0186 .0078 111 Tau 1 Eridani F6 14 81 .0544 .0078 136 Zeta 1 Reticuli G2 15 79 .2077 .0321 138 Zeta 2 Reticuli G1 -27 127 .2075 .0340 139 82 Eridani G5 -12 37 .3602 .0310 231 Alpha Mensae G5 13 22 .1156 .0065 Sun Sol G5 0 0 .0559 .0091 All the stars listed here are main sequence or spectral group V stars. Tau Ceti has a slight peculiarity in its spectrum as explained in the text. W- velocity is the star's motion in km/sec in a direction above or below (-) in the galactic plane. Total space velocity relative to the sun is also in km/sec. Data is from the Gliese Catalog of Nearby Stars (1969 edition). Consider, for example, the velocities of these stars in space. It is now known that the composition and the age of a star shows a reasonably close correlation with that star's galactic orbit. The understanding of this correlation demands a little knowledge of galactic structure. Our galaxy, as far as we are concerned, consists essentially of two parts -- the halo, and the disk. Apparently when the galaxy first took shape about 10 billion years ago, it was a colossal sphere in which the first generation of stars emerged. These stars -- those that remain today, anyway -- define a spherical or halolike cloud around the disk shaped Milky Way galaxy. Early in the galaxy's history, it is believed that the interstellar medium had a very low metal content because most of the heavy elements (astronomers call any element heavier than helium "heavy" or a "metal") are created in the cores of massive stars which then get released into the interstellar medium by stellar winds, novae and supernovae explosions. Few such massive stars had "died" to release their newly made heavy elements. Thus, the stars which formed early (called Population II stars) tend to have a spherical distribution about the center of the galaxy and are generally metal-poor. A further gravitational collapse occurred as the galaxy flattened out into a disk, and a new burst of star formation took place. Since this occurred later and generations of stars had been born and died to enrich the interstellar medium with heavy elements, these disk stars have a metal-rich composition compared to the halo stars. Being in the disk, these Population I stars (the sun, for example) tended to have motions around the galactic core in a limited plane -- something like the planets of the solar system. Population II stars -- with their halo distribution -- usually have more random orbits which cut through the Population I hoards in the galactic plane. A star's space velocity perpendicular to the galactic plane is called its W-velocity. Knowing the significance of the W-velocity, one can apply this information to find out about the population classification and hence the ages and compositions of stars in the solar neighborhood -- the Fish-Hill stars in particular. High W-velocity suggests a Population II star, and we find that six of the 16 stars are so classified while the remaining majority are of Population I. A further subdivision can be made using the W-velocity data (the results are shown in the table below.     Population Classification of the Fish-Hill Stars Old Population I (1 to 4 Billion Years Old) Gliese 59 Gliese 67 107 Piscium Older Population I (4 to 6 BillionYears Old) Tau 1 Eridani Tau Ceti Alpha Mensae Gliese 95 Kappa Fornax 54 Piscium Sun Disk Population II (6 to 8 Billion Years Old) Zeta 1 Reticuli Zeta 2 Reticuli Intermediate Population II (About 10 Billion Years Old) Zeta Tucanae Gliese 86 Gliese 86.1 82 Eridani According to this classification system (based on one by A. Blaauw), most of the 16 stars are in the same class as the sun -- implying that they are roughly of the same composition and age as the sun. The sun would seem to be a natural unit for use in comparing the chemical compositions and ages of the stars of the Fish-Hill pattern because it is, after all, the standard upon which we base our selection of stars capable of supporting life. Three stars (Gliese 59, 67 and 68) are known as Old Population I and are almost certainly younger than the sun. They also probably have a higher metal content than the sun, although specific data is not available. The Disk Population II stars are perhaps two to four billion years older than the sun, while the Intermediate Population II are believed to be a billion or two years older still. For main sequence stars like the sun, as all these stars are, it is generally believed that after the star is formed and settled on the main sequence no mixing between the outer layers and the thermo-nuclear core occurs. Thus the composition of the outer layers of a star, (from which we receive the star's light) must have essentially the same composition as the interstellar medium out of which the star and its planets were formed. Terrestrial planets are composed primarily of heavy elements. The problem is: If there is a shortage of heavy elements in the primeval nebula, would terrestrial planets be able to form? At present, theories of planetary formation are unable to state for certain what the composition of the cloud must be in order for terrestrial planets to materialize, although it is agreed to be unlikely that Population II stars should have terrestrial planets. But for objects somewhere between Population I and II -- especially Disk Population II -- no one really knows. Although we can't be certain of determining whether a star of intermediate metal deficiencies can have planets or not, we can make certain of the existence of metal deficiencies in those stars. The eccentricities and inclinations of the galactic orbits of the Fish-Hill stars provide the next step in the information sequence. The table above also shows that the stars Gliese 136, 138, 139, 86 and 71 have the highest eccentricities and inclinations in their galactic orbits. This further supports the Population II nature of these four stars. According to B.E.J. Pagel of the Royal Greenwich Observatory in England, the correlation between eccentricity and the metal/hydrogen ratio is better than that between the W-velocity and the metal/hydrogen ratio. It is interesting to see how closely the values of eccentricity seem to correspond with Population type as derived from W-velocity -- Old Population I objects having the lowest values. Since the two methods give similar results, we can lend added weight to our classification. So far all the evidence for metal deficiencies has been suggestive; no direct evidence has been given. However, specific data can be obtained from spectroscopic analysis. The system for which the best set of data exists also happens to be one of the most important stars of the pattern, Zeta 1 Reticuli. In 1966, J.D. Danziger of Harvard University published results of work he had done on Zeta 1 Reticuli using wide-scan spectroscopy. He did indeed find metal deficiencies in the star: carbon, 0.2, compared to our sun; magnesium, 0.4; calcium, 0.5; titanium, 0.4; chromium, 0.3; manganese, 0.4; iron, 0.4; cobalt, 0.4; nickel, 0.2, and so on. In spite of the possible error range of about 25 percent, there is a consistent trend of metal deficiencies -- with Zeta 1 Reticuli having less than half the heavy elements per unit mass that the sun does. Because Zeta 1 Reticuli has common proper motion and parallax with Zeta 2 Reticuli, it probably also has the same composition. Work done by M.E. Dixon of the University of Edinburgh showing the two stars to have virtually identical characteristics tends to support this. The evidence that the Zeta Reticuli system is metal deficient is definite. From this knowledge of metal deficiency and the velocities and eccentricities, we can safely conclude that the Zeta Reticuli system is older than the sun. The question of terrestrial planets being able to form remains open. The other two stars which have high velocities and eccentricities are 82 Eridani (Gliese 139) and Gliese 86. Because the velocities of these stars are higher than those of Zeta Reticuli, larger metal deficiencies might be expected. For the case of Gliese 86, no additional information is presently available. However, some theoretical work has been done on 82 Eridani concerning metal abundances by J. Hearnshaw of France's Meudon Observatory. Although 82 Eridani is a high velocity star, its orbit lies largely within the galactic plane, and also within the solar orbit. Its orbit is characteristic of the Old Disk Population, and an ultraviolet excess indicates only a mild metal deficiency compared to the sun. Hearnshaw's conclusions indicate that the metal deficiency does not appear to be any worse than that of the Zeta Reticuli pair. Because Gliese 86 has a velocity, eccentricity and inclination similar to 82 Eridani, it seems likely that its chemical composition may also not have severe metal deficiencies, but be similar to those of 82 Eridani. Tau Ceti appears to be very much like the sun except for slight deficiencies of most metals in rarely seen abnormal abundances of magnesium, titanium, silicon and calcium. Stars in this class are known as alpha-rich stars, but such properties do not appear to make Tau Ceti unlikely to have planets similar to the sun's. Tau 1 Eridani, an F6V star, has a life expectancy of 4.5 billion years -- so it cannot be older than the sun. The low eccentricities and low moderate velocity support an age and composition near that of the sun. Gliese 67 is a young star of at least solar metal abundances, considering its low velocity and eccentricity. Having covered most of the stars either directly or simply by classifying them among the different Population classes, it is apparent that there is a wide age range among different stars of this group as well as a range of compositions. It is curious that the stars connected by the alleged "trade routes" (solid lines) are the older and occasionally metal deficient ones -- while the stars connected by dotted lines seem to be younger Population I objects. A final point concerning the metal deficiencies is rather disturbing. Even though terrestrial planets might form about either star in the Zeta Reticuli system, there is a specific deficiency in carbon to well within the error range. This is disturbing because carbon is the building block of organic molecule chains. There is no way of knowing whether life on Earth would have emerged and evolved as far as it has if carbon were not as common here. Another problem: If planets formed but lacked large quantities of useful industrial elements, could a technical civilization arise? If the essential elements were scarce or locked up in chemical compounds, then an advanced technology would be required to extract them. But the very shortage of these elements in the first place might prevent this technology from being realized. The dolphins are an example of an intelligent but nontechnical race. They do not have the means to develop technology. Perhaps some land creatures on another planet are in a comparable position by not having the essential elements for technological development. (This theme is explored in detail in "What Chariots of Which Gods?", August 1974.) This whole speculation certainly is not strong enough to rule out the Fish interpretation of the Hill map given our present state of knowledge. Actually in some respects, the metal deficiencies support the Fish hypothesis because they support an advanced age for several of the stars -- suggesting that if cultures exist in these star systems, they might well be advanced over our own. The fact that none of the stars in the pattern is seriously metal deficient (especially the vital branch high velocity stars 82 Eridani and Gliese 86) is an encouragement to the Fish interpretation -- if terrestrial planets can form in the first place and give rise to technical civilizations. Once again we are confronted with evidence which seems to raise as many questions as it answers. But the search for answers to such questions certainly can only advance knowledge of our cosmic environment. Jeffrey L. Kretsch is an astronomy student at Northwestern University working under the advisement of Dr. J. Allen Hynek. For more than a year Kretsch has been actively pursuing follow-up studies to the astronomical aspects of the Fish-Hill map. More of his studies and comment s appear in In Focus. Pattern Recognition & Zeta Reticuli by Carl Sagan & Steven Soter "The Zeta Reticuli Incident" is very provocative. It claims that a map, allegedly shown on board a landed extraterrestrial spacecraft to Betty Hill in 1961, later drawn by her from memory and published in 1966, corresponds well to similar maps of the closest stars resembling the sun based on stellar positions in the 1969 Gliese Catalog of Nearby Stars. The comparison maps were made by Marjorie Fish using a three dimensional physical model and later by a group of Ohio State University students using a presumably more accurate (i.e., less subjective) computer generated projection. The argument rests on how well the maps agree and on the statistical significance of the comparison. Figure 1 [not available here] show the Hill map and the Ohio State computer map with connecting lines as given in the ASTRONOMY article. The inclusion of these lines (said to represent trade or navigation routes) to establish a resemblance between the maps is what a lawyer would call "leading the witness". We could just as well have drawn lines as in the bottom of Figure 1 to lead the other way. A less biased comparison of the two data sets, without connecting lines as in Figure 2, shows little similarity. Any residual resemblance is enhanced by there being the same number of points in each map, and can be accounted for by the manner in which these points were selected. The computer star map includes the sun and 14 stars selected from a list of the 46 nearest stars similar to the sun, derived from the Gliese catalog. It is not clear what criteria were used to select precisely these 14 stars from the list, other than the desire to find a resemblance to the Hill map. However, we can always pick and choose from a large random data set some subset that resembles a preconceived pattern. If we are free also to select the vantage point (from all possible directions for viewing the projection of a three dimensional pattern), it is a simple matter to optimize the desired resemblance. Of course such a resemblance in the case of selection from a random set is a contrivance -- an example of the statistical fallacy known as "the enumeration of favorable circumstances". The presence of such a fallacy in this case appears even more likely when we examine the original Hill drawing, published in The Interrupted Journey by John Fuller. In addition to the prominent points that Betty Hill connected by lines, her map also includes a number of apparently random dots scattered about -- evidently to represent the presence of background stars but not meant to suggest actual positions. However, three of these dots appear in the version of the Hill map used in the comparison, while the others are absent. Thus some selection was made even from the original Hill map, although not to the same extent as from the Gliese catalog. This allow even greater freedom to contrive a resemblance. Finally, we lear from The Interrupted Journey that Betty Hill first thought she saw a remarkable similarity between her UFO star map and a map of the constellation Pegasus published in the New York Times in 1965 to show the position of the quasar CTA-102. How many star maps, derived from the Gliese catalog or elsewhere, have been compared with Betty Hill's before a supposed agreement was found? If we suppress information on such comparisons we also overestimate the significance of the result. The argument on "The Zeta Reticuli Incident" demonstrates only that if we set out to find a pattern correlation between two nearly random data sets by selecting at will certain elements from each and ignoring others, we will always be successful. The argument cannot serve even to suggest a verification of the Hill story -- which in any case is well known to be riddled with internal and external contradictions, and which is amenable to interpretations which do not invoke extraterrestrial intelligence. Those of us concerned with the possibility of extraterrestrial intelligence must take care to demand adequately rigorous standards of evidence. It is all too easy, as the old Chinese proverb says, for the imprisoned maiden to mistake the beating of her own heart for the hoof beats of her rescuer's horse. Steven Soter is a research associate working under the advisement of Carl Sagan, director of Cornell University's laboratory for Planetary Studies.     Reply: by Terence Dickinson The question raised by Steven Soter and Carl Sagan concerning the pattern resemblance of the Hill map and the computer generated projection of the Fish pattern stars is certainly a key question worthy of discussion. Next month two authors will make specific comments on this point. Briefly, there is more to discounting the Fish interpretation than pattern resemblance. We would have discounted the Fish interpretation immediately on pattern resemblance alone. The fact that all the connecting lines join stars in a logical distance progression, and that all the stars are solar type stars, is significant. Ms. Fish tried to fit hundreds of other viewpoints and this one was the only one that even marginally fit and made sense in three dimensions and contained solar type stars. in this context, you could not "have just as well drawn the lines...to lead the other way". Naturally there was a desire to find a resemblance between a group of nearby stars and the Hill pattern! That's why Marjorie Fish built six models of the solar neighborhood containing the relative positions of up to 256 nearby stars. The fact that she came up with a pattern that fits as well as it does is a tribute to her perseverance and the accuracy of the models. Stars cannot be moved around "to optimize the desired resemblance". Indeed Marjorie Fish first tried models using nearby stars of other than strictly solar type as defined in the article. She found no resemblances. The three triangle dots selected from the background dots in the Hill map were selected because Mrs. Hill said they were more prominent than the other background stars. Such testimony was the basis of the original map so we either accept Mrs. Hill's observations and attempt to analyze them or reject the whole incident. We feel there is sufficient evidence compelling us not to reject the whole incident at this time. We too are demanding rigorous standards of evidence to establish the reality of extraterrestrial intelligence. If there is even the slightest possibility that the Hills' encounter can provide information about such life, we feel it is worth pursuing. The map is worthy of examination by as many critical minds as possible. Reply: by David R. Saunders Last month, Steven Soter and Carl Sagan offered two counterarguments relating to Terence Dickinson's article, "The Zeta Reticuli Incident" (ASTRONOMY, December 1974). Their first argument was to observe that the inclusion of connecting lines in certain maps "is what a lawyer would call 'leading the witness'." This was used as the minor premise in a syllogism for which the major premise was never stated. Whether we should consider "leading the witness" a sin or not will depend on how we conceive the purpose of the original article. The implied analogy between ASTRONOMYmagazine and a court of law is tenuous at best; an expository article written for a nonprofessional audience is entitled, in my opinion, to do all it can to facilitate communication -- assuming that the underlying message is honest. Much of what we call formal education is really little more than "leading the witness", and no one who accepts the educational goals objects very strongly to this process. In this context, we may also observe that Soter's and Sagan's first argument provides another illustrative example of "leading the witness"; the argument attacks procedure, not substance -- and serves only to blunt the reader's possible criticism of the forthcoming second argument. This paragraph may also be construed as an effort to lead the witness. Once we have been sensitized to the possibilities, none of us needs to be further misled! The second argument offered by Soter and Sagan does attack a substance. Indeed, the editorial decision to publish the original article was a responsible decision only if the issues raised by this second line of possible argument were fully considered. Whenever a statistical inference is made from selected data, it is crucial to determine the strenuousness of that selection and then to appropriately discount the apparent clarity of the inference. By raising the issue of the possible effects of selection, Soter and Sagan are right on target. However, by failing to treat the matter with quantitative objectivity ( by failing to weigh the evidence in each direction numerically, for example), they might easily perform a net disservice. In some situations, the weight of the appropriate discount will suffice to cancel the clarity of a proposed inference -- and we will properly dismiss the proposal as a mere capitalization on chance, or a lucky outcome. (It is abundantly clear that Soter and Sagan regard the star map results as just such a fortuitous outcome.) In some other situations, the weight of the appropriate discount may be fully applied without accounting for the clarity of the inference as a potentially valid discovery. For example, if I proposed to infer from four consecutive coin tosses observed as heads that the coin would always yield heads, you would properly dismiss this proposal as unwarranted by the data. However, if I proposed exactly the same inference based on 40 similar consecutive observations of heads, you would almost certainly accept the inference and begin looking with me for a more systematic explanation of the data. The crucial difference here is the purely quantitative distinction between 4 and 40; the two situations are otherwise identical and cannot be distinguished by any purely qualitative argument. When Soter and Sagan use phrases such as "some subset that resembles", "free also to select the vantage point", "simple matter to optimize", and "freedom to contrive a resemblance", they are speaking qualitatively about matters that should (and can) be treated quantitatively. Being based only on this level of argument, Soter's and Sagan's conclusions can only be regarded as inconclusive. A complete quantitative examination of this problem will require the numerical estimation of at least three factors, and their expression in a uniform metric so that wee can see which way the weight of the evidence is leaning. The most convenient common metric will be that of "bits of information", which is equivalent to counting consecutive heads in the previous example. One key factor is the degree of resemblance between the Hill map and the optimally similar computer-drawn map. Precisely how many consecutive heads is this resemblance equivalent to? A second key factor is the precise size of the population of stars from which the computer was allowed to make its selection. And a third key factor is the precise dimensionality of the space in which the computer was free to choose the best vantage point. If the first factor exceeds the sum of the other two by a sufficient margin, we are justified in insisting on a systematic explanation for the data. The third factor is the easiest to deal with. The dimensionality of the vantage-point space is not more than three. A property of the metric system for weighing evidence is that each independent dimension of freedom leads us to expect the equivalent of one more consecutive head in the observed data. Three dimensions of freedom are worth exactly 3.0 bits. In the end, even three bits will be seen as relatively minor. The second factor might be much larger than this, and deserve relatively more discussion. The appropriate discount for this selection will be log2C, where C is the number of distinct combinations of stars "available" to the computer. If we were to agree that C must represent the possible combinations of 46 stars taken 14 at a time, then log2C would be 37.8 bits; this would be far more than enough to kill the proposed inference. However, not all these combinations are equally plausible. We really should consider only combinations that are adjacent to one another and to the sun, but it is awkward to try to specify exactly which combinations these are. The really exciting moment in working with these data came with the realization that in the real universe, our sun belongs to a closed cluster together with just six of the other admissible stars -- Tau Ceti, 82 Eridani, Zeta Tucanae, Alpha Mensae, and Zeta 1 and Zeta 2 Reticuli. The real configuration of interstellar distances is such that an explorer starting from any of the seven should visit all of them before venturing outside. If the Hill map is assumed to include the sun, then it should include the other members of this cluster within an unbroken network of connections, and the other connected stars should be relatively adjacent in the real universe. Zeta Reticuli occupies a central position in all of the relatively few combinations that now remain plausible. However, in my opinion, the adjacency criteria do leave some remnant ambiguity concerning the combination of real stars to be matched against the Hill map -- but only with respect to the region farthest from the sun. The stars in the closed cluster and those in the chain leading to Gliese 67 must be included, as well as Gliese 86 and two others from a set of five candidates. Log2C for this remnant selection is 3.9 bits. we must also notice that the constraint that Zeta Tucanae be occulted by Zeta Reticuli reduces the dimensionality of the vantage-point space from 3.0 to 1.0. Thus, the sum of factors two and three is now estimated as only 4.9 bits. The first factor is also awkward to evaluate -- simply because there is no standard statistical technique for comparing points on two maps. Using an approximation based on rank-order correlation, I've guessed that the number we seek here is between 11 and 16. (This is the result cited by Dickinson on page 15 of the original article.) Deducting the second and third factors, this rough analysis leaves us with an empirical result whose net meaning is equivalent to observing at least 6 to 11 consecutive heads. (I say "at least", because there are other factors contributing to the total picture -- not discussed either by Dickinson or by Soter and Sagan -- that could be adduced to enhance this figure. For example, the computed vantage point is in good agreement with Betty Hill's reported position when observing the map, and the coordinate system implicit in the boundaries of the map is in good agreement with a natural galactic coordinate system. Neither have we discussed any quantitative use of the connections drawn on the Hill map, which were put there in advance of any of these analyses.) In the final interpretation, it will always be possible to argue that 5 or 10 or even 15 bits of remarkable information simply isn't enough. However, this is a matter for each of us to decide independently. In deciding this matter, it is more important that we be consistent with ourselves (as we review a large number of uncertain interpretations of data that we have made) than that we be in agreement with some external authority. I do believe, though, that relatively few individuals will continue a coin-tossing match in which their total experience is equivalent to even six consecutive losses. In scientific matters, my own standard is that I'm interested in any result that has five or more bits of information supporting it -- though I prefer not to stick my neck out publicly on the basis of less than 10. Adhering to this standard, I continue to find the star map results exceedingly interesting. Dr. David R. Saunders is a Research Associate at the University of Chicago's Industrial Relations Center. 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.     Rebuttal: To David Saunders and Michael Peck by Carl Sagan and Steven Soter Dr. David Saunders last month claimed to have demonstrated the statistical significance of the Hill map, which was allegedly found on board a landed UFO and supposedly depicted the sun and 14 nearby sunlike stars. The Hill map was said to resemble the Fish map -- the latter being an optimal two-dimensional projection of a three-dimensional model prepared by selecting 14 stars from a positional list of the 46 nearest known sunlike stars. Saunders' argument can be expressed by the equation SS = Dr -(SF + VP), in which all quantities are in information bits. SS is the statistical significance of the correlation between the two maps, DR is the degree of resemblance between them, SF is a selection factor depending on the number of stars chosen and the size of the list, and VP is the information content provided by a free choice in three dimensions of the vantage point for projecting the map. Saunders finds SS = 6 to 11 bits, meaning that the correlation is equivalent to between 6 and 11 consecutive heads in a coin toss and therefore probably not accidental. The procedure is acceptable in principle, but the result depends entirely on how the quantities on the right-hand side of the equation were chosen. For the degree of resemblance between the two maps, Saunders claims that DR = 11 to 16 bits, which he admits is only a guess -- but we will let it stand. For the selection factor, he at first takes SF = log2C = 37.8 bits, where C represents the combinations of 46 things taken 14 at a time. Realizing that the size of this factor alone will cause SS to be negative and wipe out his argument, he makes a number of ad hoc adjustments based essentially on his interpretation of the internal logic of the Hill map, and SF somehow gets reduced to only 3.9 bits. For the present, we will let even that stand in order to avoid becoming embroiled in a discussion of how an explorer from the star Zeta Reticuli would choose to arrange his/her/its travel itinerary -- a matter about which we can claim no particular knowledge. However, we must bear in mind that a truly unprejudiced examination of the data with no a priori interpretations would give SF = 37.8 bits. It is Saunders' choice of the vantage point factor VP with which we must take strongest issue, for this is a matter of geometry and simple pattern recognition. Saunders assumes that free choice of the vantage point for viewing a three-dimensional model of 15 stars is worth only VP = 3 bits. He then reduces the information content of directionality to one bit by introducing the "constraint" that the star Zeta Tucanae be occulted by Zeta Reticuli (with no special notation on the Hill map to mark this peculiarity). This ad hoc device is invoked to explain the absence of Zeta Tucanae from the Hill map, but it reveals the circular reasoning involved. After all, why bother to calculate the statistical significance of the supposed map correlation if one has already decided which points represent which stars? Certainly the selection of vantage point is worth more than three bits (not to mention one bit). Probably the easiest circumstance to recognize and remember about random projections of the model in question are the cases in which two stars appear to be immediately adjacent. By viewing the model from all possible directions, there are 14 distinct ways in which any given star can be seen in projection as adjacent to some other star. This can be done for each of the 15 stars, giving 210 projected configurations -- each of which would be recognized as substantially different from the others in information content. And of course there are many additional distinct recognizable projections of the 15 stars not involving any two being immediately adjacent. (For example, three stars nearly equidistant in a straight line are easily recognized, as in Orion's belt.) Thus for a very conservative lower bound, the information content determined by choice of vantage point (that is, by being allowed to rotate the model about three axes) can be taken as at least equal to VP = log2(210) = 7.7 bits. Using the rest of Saunders' analysis, this would at best yield SS = zero to 4.4 bits -- not a very impressive correlation. There is another way to understand the large number of bits involved in the choice of the vantage point. The stars in question are separated by distances of order 10 parsecs. If the vantage point is situated above or not too far from the 15 stars, it need only be shifted by about 0.17 parsecs to cause a change of one degree in the angle subtended by some pair of stars. Now one degree is a very modest resolution, corresponding to twice the full moon and is easily detected by anyone. For three degrees of freedom, the number of vantage points corresponding to this resolution is of order (10/0.17) cubed ~ (60) cubed ~ 2 X 10 to the fifth power, corresponding to VP = 17.6 bits. This factor alone is sufficient to make SS negative, and to wipe out any validity to the supposed correlation. Even if we were to accept Saunders' claim that SS = 6 to 11 bits (which we obviously do not, particularly in view of the proper value for SF), it is not at all clear that this would be statistically significant because we are not told how many other possible correlations were tried and failed before the Fish map was devised. For comparison, there is the well-known correlation between the incidence of Andean earthquakes and oppositions of the planet Uranus. It is unlikely in the extreme that there is a physical causal mechanism operating here -- among other reasons, because there is no correlation with oppositions of Jupiter, Saturn or Neptune. But to have found such a correlation the investigator must have sought a wide variety of correlations of seismic events in many parts of the world with oppositions and conjunctions of many astronomical objects. If enough correlations are sought, statistics requires that eventually one will be found, valid to any level of significance that we wish. Before we can determine whether a claimed correlation implies a causal connection, we must convince ourselves that the number of correlations sought has not been so large as to make the claimed correlation meaningless. This point can be further illustrated by Saunders' example of flipping coins. Suppose we flip a coin once per second for several hours. Now let us consider three cases: two heads in a row, 10 heads in a row, and 40 heads in a row. We would, of course, think there is nothing extraordinary about the first case. Only four attempts at flipping two coins are required to have a reasonable expectation value of two heads in a row. Ten heads in a row, however, will occur only once in every 2 to the tenth power = 1,024 trials, and 40 heads in a row will occur only once every 2 to the fortieth ~ 10 to the twelfth power trials. At a flip rate of one coin per second, a toss of 10 coins requires 10 seconds; 1,024 trials of 10 coins each requires just under three hours. But 40 heads in a row at the same rate requires 4 X 10 to the thirteenth power seconds or a little over a million years. A run of 40 consecutive heads in a few hours of coin tossing would certainly be strong prima facie evidence of the ability to control the fall of the coin. Ten heads in a row under the circumstances we have described would provide no convincing evidence at all. It is expected by the law of probability. The Hill map correlation is at best claimed by Saunders to be in the category of 10 heads in a row, but with no clear statement as to the number of unsuccessful trials previously attempted. Michael Peck finds a high degree of correlation between the Hill map and the Fish map, and thereby also misses the central point of our original criticism: that the stars in the Fish map were already preselected in order to maximize that very correlation. Peck finds one chance in 10 to the fifteenth power that 15 random points will correlate with the Fish map as well as the Hill map does. However, had he selected 15 out of a random sample of, say, 46 points in space, and had he simultaneously selected the optimal vantage point in three dimensions in order to maximize the resemblance, he could have achieved an apparent correlation comparable to that which he claims between the Hill and Fish maps. Indeed, the statistical fallacy involved in "the enumeration of favorable circumstances" leads necessarily to large, but spurious correlations. We again conclude that the Zeta Reticuli argument and the entire Hill story do not survive critical scrutiny.  Dr. Steven Soter is a research associate in astronomy and Dr. Carl Sagan is director of the Laboratory for Planetary Studies, both at Cornell University in Ithaca, N.Y. Is the Fish Interpretation Unique? by Robert Sheaffer The story of Marjorie Fish's attempts at identifying the star patterns sketched by Betty Hill was told in "The Zeta Reticuli Incident" by Terence Dickinson in the December 1974 issue. This pattern of solar type stars unquestionably bears a striking resemblance to the map that Betty Hill says she saw while she was being examined aboard a flying saucer. But how significant is this resemblance? Is there only one pattern of stars which will match the sketch convincingly? Betty Hill herself discovered an impressive resemblance in a star map published in the New York Times. In 1965 a map of the stars of the constellation Pegasus appeared in that newspaper, accompanying the announcement by a Russian radio astronomer (Comrade Sholomitsky) the radio source CTA-102, depicted in the map, may be sending out intelligent radio signals. Intrigued by this remarkable claim, Betty Hill studied the map, and added the corresponding star names to her sketch. As you can see, the Pegasus map -- while not exactly like the sketch -- is impressively similar. If CTA-102 -- appearing near the "globes" in her sketch -- was in reality an artificial radio source, that would give the Pegasus map much additional credibility. However, the case for the artificial origin of quasar CTA- 102 soon fell flat. Other scientists were unable to observe these reported strange variations which had caused Sholomitsky to suggest that CTA-102 might be pulsing intelligently. In 1966, when Marjorie Fish was just beginning her work, Charles W. Atterberg (employed by an aeronautical communications firm in Illinois) also set out to attempt to identify this star pattern. "I began my search by perusing a star atlas I had on hand," Atterberg explained. "I soon realized that this was a pointless and futile project." Any star pattern useful for interstellar navigation, he reasoned, would not be Earth-centered as are the familiar constellation figures. Thus Atterberg began to look in three dimensions for a pattern of stars that would approximate the Hill sketch. Working from a list of the nearest stars, Atterberg "began plotting these stars as they would be seen from various directions. I did this by drawing the celestial position of a star, I would draw a straight line penetrating the sphere at a known position, and measure out to the distance of the star...It at first took me hours to plot this out from any one particular direction." When plotting the stars as seen from a position indefinitely far away on the celestial equator at 17 hours right ascension, Atterberg found a pattern of stars conspicuously similar to the Hill sketch. After much work he refined this position to 17 hours 30 minutes right ascension, -10 degrees declination. The resulting map resembles the Hill sketch even more strongly than does the Fish map, and it contains a greater number of stars. Furthermore, all of the stars depicted in the Atterberg map lie within 18.2 light-years of the sun. The Fish map reaches out 53 light-years, where our knowledge of stellar distances is much less certain. Carl Sagan states in Intelligent Life in the Universe that, excluding multiple star systems, "the three nearest stars of potential biological interest are Epsilon Eridani, Epsilon Indi and Tau Ceti." These three stars from the heart of the Atterberg map, defining the two spheres in the very center of the heavy lines that supposedly represent the major "trade routes" of the "UFOnauts". Epsilon Eridani and Tau Ceti were the two stars listened to by Project Ozma, the pioneering radio search for intelligent civilization in space. Other heavy lines connect the spheres with the sun, which we know has at least one habitable planet. Thinner lines, supposedly representing places visited less frequently, connect with Groombridge 1618, Groombridge 34, 61 Cygni and Sigma Draconis, which are designated as stars "that could have habitable planets" in Stephen H. Dole's Rand Corporation study, Habitable Planets for Man. Of the 11 stars (not counting the sun) that have allegedly been visited by the aliens, seven of them appear on Dole's list. Three of the four stars which are not included are stopping points on the trip to Sigma Draconis, which Dole considered to have even better prospects than Epsilon Eridani or Epsilon Indi for harboring a habitable planet. Another remarkable aspect of the Atterberg map is the fact that its orientation, unlike the Fish map, is not purely arbitrary. Gould's belt -- a concentration of the sky's brightest stars -- is exactly perpendicular to the plane of the Atterberg map. Furthermore, it is vertical in orientation; it does not cut obliquely across the map, but runs exactly up and down. A third curious coincidence: The southpole of the Atterberg map points toward the brightest part of Gould's belt, in the constellation Carina. The bright stars comprising Gould's belt might well serve as a useful reference frame for interstellar travelers, and it is quite plausible that they might base a navigational coordinate system upon it. No other map interpreting the Hill sketch offers any rationale for its choice of perspectives. The problem with trying to interpret Betty Hill's sketch is that it simply fits too many star patterns. Three such patterns have been documented to date. How many more exist undiscovered? Robert Sheaffer is a computer systems programmer currently working at NASA's Goddard Space Flight Center in Greenbelt, MD. Reply: by Marjorie Fish Basically, Robert Sheaffer's contention is that at least three patterns can be found that are similar to Betty Hill's map, and therefore, more such interpretations are likely. If one stipulates that any stars from any vantage point can be used, then I agree that many patterns can be found similar to the map. However, if one uses restrictions on the type of stars, according to their probability of having planets and also on the logic of the apparent travel paths, then it is much more difficult. The three maps were: (1) Betty Hill's interpretation of the constellation Pegasus as being similar to her map, (2) Charles Atterberg's work, and (3) my work. When I started the search, I made a number of restrictions including: The sun had to be part of the pattern with a line connected to it, since the leader of the aliens indicated this to Betty. Since they came to our solar system, they should also be interested in solar type stars (single main sequence G, probably also late single main sequence F and early single main sequence K). These stars should not be bypassed if they are in the same general volume of space. Since there are a number of the above stars relatively near the sun and the pattern shows only 12 stars, the pattern would have to be relatively close to us (or else they would be bypassing sunlike stars, which is illogical). The travel pattern itself should be logical. That is, they would not zip out 300 light-years, back to 10 light-years, then out 1,000, etc. The moves should make a logical progression. Large young main sequence stars (O, B, A, early F) which are unlikely to have planets and/or life would not be likely to be visited. Stars off the main sequence with the possible exception of those just starting off the main sequence would probably be avoided as they are unsuitable for life and, due to their variability, could be dangerous. If they go to one star of a given type, it shows interest in that type star -- so they should go to other stars of that type if they are in the same volume of space. An exception to this might be the closest stars to the base star, which they might investigate out of curiosity in the early stages of stellar travel. For example, they would not be likely to bypass five red dwarfs to stop at the sixth, if all six were approximately equal in size, spectra, singleness or multiplicity, etc. Or, if they go to one close G double, they would probably go to other close G doubles. The base star or stars is one or both of the large circles with the lines radiating from it. One or both of the base stars should be suitable for life -- F8 to K5 using the lowest limits given by exobiologists, or more likely, K1 given by Dole. Because the base stars are represented as such large circles, they are either intrinsically bigger or brighter than the rest or they are closer to the map's surface (the viewer) than the rest -- probably the latter. This was later confirmed by Betty Hill. Mrs. Hill's interpretation of Pegasus disregards all of these criteria. Atterberg's work is well done. His positioning of the stars is accurate. He complies with criteria 1, 2, 3, 5, 6 and 8; fairly well with 4; less well with 9, and breaks down on 7 and 10. I will discuss the last three of Atterberg's differences with my basic criteria in the following paragraphs: Relative to point 9, his base stars are Epsilon Indi and Epsilon Eridani, both of which are near the lower limit for life bearing planets -- according to most exobiologists -- and not nearly as suitable as Zeta 1 and 2 Reticuli. Concerning point 7, I had ruled out the red dwarfs fairly early because there were so many of them and there were only 12 lined points on the Hill map. If one used red dwarfs in logical consecutive order, all the lines were used up before the sun was reached. Atterberg used red dwarfs for some of his points to make the map resemble Betty Hill's but he bypassed equally good similar red dwarfs to reach them. If they were interested in red dwarfs, there should have been lines going to Gliese 65 (Luyten 76208) which lies near Tau Ceti and about the same distance from Epsilon Eridani as Tau Ceti, and Gliese 866 (Luyten 789-6) which is closer to Tau Ceti than the sun. Gliese 1 (CD-37 15492) and Gliese 887 (CD-36 15693) are relatively close to Epsilon Indi. These should have been explored first before red dwarfs farther away. Red dwarfs Gliese 406 (Wolf 359) and Gliese 411 (BD + 36 2147) were by passed to reach Groombridge 1618 and Ross 128 from the sun. Barnard's star would be the most logical first stop out from the sun, if one were to stop at red dwarfs, as it is the closest single M and is known to have planets.  Since Atterberg's pattern stars include a number of relatively close doubles (61 Cygni, Struve 2398, Groombridge 34 and Kruger 60), there should also be a line to Alpha Centauri -- but there is not. Relating to point 10, Atterberg's base stars are not the largest or brightest of his pattern stars. The sun, Tau Ceti, and Sigma Draconis are brighter. Nor are they closer to the viewer. The sun and 61 Cygni are much closer to the viewer than Epsilon Eridani. The whole orientation feels wrong because the base stars are away from the viewer and movement is along the lines toward the viewer. (Betty Hill told me that she tried to show the size and depth of the stars by the relative size of the circles she drew. This and the fact that the map was alleged to be 3-D did not come out in Interrupted Journey, so Atterberg would not have known that.) Sheaffer notes that seven of Atterberg's pattern stars appear on Dole's list as stars that could have habitable planets. These stars are Groombridge 1618 (Gliese 380, BD + 50 1725), Groombridge 34 (Gliese 15,BD +43 44), 61 Cygni, Sigma Draconis, Tau Ceti, Epsilon Eridani and Epsilon Indi. Of these seven, only Epsilon Eridani, Tau Ceti and Sigma Draconis are above Doles' absolute magnitude minimum. The others are listed in a table in his book Habitable Planets for Man, but with the designation: "Probability of habitable planet very small; less than 0.001." Epsilon Eridani was discussed earlier. Sigma Draconis appears good but is listed as a probable variable in Dorrit Hoffleit's Catalogue of Bright Stars. Variability great enough to be noticed from Earth at Sigma Draconis' distance would cause problems for life on its planets. This leaves Tau Ceti which is one of my pattern stars also. Another point Sheaffer made was that orientation of my map was arbitrary compared to Atterberg's map's orientation with Gould's belt. One of my first questions to Betty Hill was, "Did any bright band or concentration of stars show?" This would establish the galactic plane and the map's orientation, as well as indicate it was not just a local map. But there was none indicating that if the map was valid it was probably just a local one. The plane of the face of my model map is not random, as Sheaffer indicated. It has intrinsic value for the viewer since many of the pattern stars form a plane at this viewing angle. The value to the viewer is that these stars have their widest viewing separation at that angle, and their relative distances are much more easily comprehended. My final interpretation of the map was the only one I could find where all the restrictions outlined above were met. The fact that only stars most suitable for Earthlike planets remained and filled the pattern seems significant. Marjorie Fish is a research assistant at Oak Ridge National Laboratory in Tennessee. Zeta Reticuli -- A Rare System by Jeffrey L. Kretsch Zeta Reticuli is a unique system in the solar neighborhood -- a wide physically associated pair of stars almost exactly like the sun. After searching through a list of stars selected from the Gliese catalog on the basis of life criteria, only one other pair within a separation of even 0.3 light-years could be found. (This pair -- Gliese 201 and Gliese 202, a K5e and F8Ve pair separated by 0.15 light-years -- is currently being investigated.) Zeta Reticuli is indeed a rare case. Based on the Fish interpretation of the Hill map, the Zeta Reticuli pair forms the base of the pattern. If the other stars in the patter fit, it is a remarkable association with a rare star system. In order to deal with this problem, I decided to computer the three-dimensional positions of the stars and construct a three-dimensional model showing these stars positions. Speaking quantitatively, I discovered the two patterns are certainly not an exact match. However, if one considers the question of match from the standpoint of how the Hill pattern was made as opposed to the derived pattern's means of reproduction, the quantitative data may not be a complete means of determining whether the two patterns "match" or not. For example, the Hill pattern was drawn freehand -- so one would have to determine how much allowance one must give for differences in quantitative data. In such areas, I am not qualified to give an opinion. However, because the map was drawn freehand from memory, the fact that the resemblance between the Fish map and the Hill map is a striking one should be considered. In my work I was able to verify the findings of Marjorie Fish in terms of the astronomy used. Jeffrey L. Kretsch is an astronomy student at Northwestern University.