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five-day discrepancy between Oppolzer and the Olmecs is substantiated; if, on the other hand, we use Thompson's "revised" value of 584,283, then the lack of a correspondence between the two dates can no longer be explained as an error, and we would probably have to abandon any thought that the |
Olmecs were recording the eclipse after all. That, in turn, would mean discarding both the close historical "coincidence" between the two dates and the geographic "coincidence" of the passing of the eclipse's central path directly over Tres Zapotes. In effect, therefore, the inscription of Stela C, erroneous though it ... |
to be, appears to confirm the accuracy of the original Thompson correlation value between the Olmec calendar and our own. In all fairness, however, it should be noted that there is one further complication in this interpretation of Stela C's date. The bottom edge of the inscription is broken just |
at the point where the number and name of the day in the sacred almanac is recorded. If the Long Count inscription itself is accurate, the day-number and -name should be 6 Eznab, and this is the way the fragmentary glyph at the bottom of the inscription is translated by |
most scholars. If the numeral is indeed rendered by a dot and a bar, then there is no question of its being a "6," but in keeping with my hypothesis that a second bar had been mistakenly added to the inscription. Obviously, my argument is not destroyed by such a |
reading but it is substantially weakened, for to be consistent with my hypothesis, the day -number should have been a " 1 " instead. Of course, if the inscription is accurate as it stands, it would then reopen the whole issue of what it was that the Olmecs were actually |
recording on that intriguing occasion. If the blackened sun at dawn was not noteworthy enough to take cognizance of, what other event could have been so much more spectacular or important to them that they took notice of it instead? Was it the occultation of Mars by the sun that |
coincided very closely with the eclipse? Or might it have been the occultation of the bright star Regulus (magnitude 1.35) by the planet Venus that occurred during the following couple of nights? Neither of these seem very likely, for surely both of these astronomical events literally pale into insignificance when |
compared to a total solar eclipse. Thus, we are left with the very real possibility that nothing of note astronomically had prompted the carving of the inscription of Stela C but that something even more earthshaking had taken place in and around Tres Zapotes shortly after the ominous eclipse had |
occurred. Thanks to its location in the foothills of a volcanic region like the Tuxtlas, the most obvious possibilities become either a monstrous earthquake or a devastating eruption. The point of this digression has been simply to illustrate that, about the time that Edzná was coming into being, the Mesoamericans |
appear to have begun recording eclipse data on their stelae, possibly in the hope that through accurate timekeeping they would eventually solve the puzzle of when these fearsome events would recur. In the intellectual community of the Maya, therefore, this problem must have been near the top of the agenda |
as Edzná was being founded. In the flat and featureless landscape of Yucatán, it had been a rather simple matter to lay out a new city oriented to the sunset on "the day the world began" because the "summer solstice + 52 days" formula had already been developed. Nonetheless, in |
a region where the local topography presented no opportunities for calibration against a natural landmark, the "gun-sight" alignment from the courtyard of Cinco Pisos through the notch in the artificial horizon to the top of the small pyramid constituted an ingenious solution to the problem of the city's orientation. I... |
the same way, the erection of the tapered shaft surmounted by the stone disk had been an ingenious solution to calibrating the passage of the zenithal sun. The problem now at hand required some means of marking the moon's rising and setting position along the circumference of the monotonously uniform |
horizon that stretched out from Edzná in all directions. View of the western horizon as seen from the top of Cinco Pisos at Edzná. The elongated mound across the plaza served as an artificial horizon for a priest standing in the doorway of the courtyard, allowing him to sight through |
the notch in the middle of the mound to the summit of the pyramid immediately behind it to calibrate the sunset on August 13 -- an azimuth of 285º.5. The pyramid which intersects the true horizon farther to the right, or northwest, is "La Vieja," whose azimuth marks the northernmost |
stillstand of the moon (i.e., 300º). No doubt the first task was to provide the priests with a vantage point which allowed them a complete and unencumbered view of the entire 360º circuit of the horizon -- hence the need to erect what was perhaps the highest pyramid yet constructed |
in Mesoamerica. When completed, the aptly named Cinco Pisos ("Five Stories") towered more than 40 m (130 ft) above the rocky platform on which it was sited, becoming in the process a true landmark visible from 40-50 km (20-30 mi) away. Although Cinco Pisos is a Late Classic structure (i.e., |
built between A.D. 600 and 900), its situation at a focal point for the ceremonial center's canal system (which dates to the Late Preclassic period -- 300 B.C. to A.D. 300) makes it seem likely that an earlier structure previously occupied this critical position. In fact, Matheny suggests that "perhaps |
the remains of the Late Preclassic structure still exist within Cinco Pisos" (1983, 81). In any case, from the top of this key structure one could look out in any direction in a clear sight-line to the far horizon. The real problem was to keep track of the places along |
the horizon where the moon either rose or set. That Cinco Pisos faced slightly to the northwest to begin with -- having been oriented along with the rest of Edzná to an azimuth of 285º.5 -- meant that the moon's setting position was the one the priests chose to calibrate. |
But with a horizon so distant and so featureless, one is tempted to conclude that most of the initial record keeping may have been done by marking lines in the appropriate directions on the top platform of Cinco Pisos itself. Only after the observations had narrowed in on a distinct |
enough point to erect some structure against the horizon at the required azimuth would that have been done. Conceptually, the Maya already had the model of the sun's behavior on which to predicate their observations. Its northernmost stopping point marked the summer solstice, which in turn established the beginning dat... |
for the 52-day count which fixed "the day the world began" -- i.e., August 13. If they could locate a similar position for the moon -- its northernmost setting point -- perhaps that would allow them to begin the count which would eventually reveal the secrets of the eclipse cycle. |
Deciding what the northernmost setting point of the moon really was must have been a tedious and frequently altered judgment in itself. Each time the moon reached what appeared to be an even more extreme setting position, the count for the eclipse cycle would have to be started again. One |
can well imagine that sometimes years of patient counting and record keeping might have gone on before the moon unexpectedly pushed its setting position even farther north along the horizon and literally wiped out the whole exhaustive tally in one fell swoop. When this process actually began and how long |
it took to yield any kind of meaningful results has to be pure conjecture. It is probably safe to say that the idea for launching the count may already have been formulated shortly after Edzná was founded, and may well have been under way when the calendar reform fixing the |
new new year's day was adopted. What we do know for certain is that the first time that mention is made of the phase of the moon corresponding to a given Long Count date is in an inscription dating from A.D . 357 (Coe, 1980, 159). This does not mean, |
of course, that the problem had been solved by then, but only that from that time forward this seemingly important fact was now to be regularly recorded along with the date itself. Indeed, this may be evidence that the lunar cycle had not yet been worked out, and that the |
priests felt the additional bit of information regarding the phase of the moon might actually be useful in finally establishing the cycle -- once they could examine the records in retrospect. This is not to say that the eclipse cycle could not have been worked out within the first half |
century that the quest was initiated. What the Maya were ultimately to learn was that the cycle required a full 6797 days, or 18.61 years, to complete, so if they had actually recognized the moon's northernmost stillstand on one occasion, they would have had to count that long to find |
the moon once more back at the same setting position. Of course, to confirm the accuracy of their count would require the completion of at least one more full cycle, so by this time more than 37 years would have elapsed. Thus, to postulate even the minimum time span necessary |
for such an achievement makes one appreciate the care and continuity which the Maya priests exercised in keeping a constant, running tally over the equivalent of more than an entire generation. Although less than a half dozen of the original Maya manuscripts appear to have escaped the flames of the |
fanatic Spaniards, one of those that did survive is the so-called Dresden Codex, which has subsequently been recognized as an elaborate eclipse warning table. Thompson, among other scholars, assigns a twelfth-century origin to it, but concedes that its three base dates go back to the middle of the eighth century. |
(My suggestion that the Stela C inscription may have involved a five-day error owing to a stone carver's failure to understand the date he was carving finds an ironic parallel in the Dresden Codex. Thompson's study of the manuscript revealed that no fewer than 92 errors of transcription have been |
made in recording its dates [1972, 115-116], but no one, least of all Thompson, has ever suggested discounting the validity of the tables on that account.) The three base dates of the Dresden Codex occur in the latter part of the year 755 and define two 15-day intervals. For this |
reason, Maud Makemson suggested, in 1943, that they most likely represent two solar eclipses bracketing a lunar eclipse (Makemson, 1943). While not disputing such an interpretation, Floyd Lounsbury, writing in 1978, argues that if this is correct, then these dates must have been arrived at by calculation rather than th... |
observation, because no such celestial events took place in Yucatán in that year (Lounsbury, 1978, 816). The three dates in question would equate to November 8, November 23, and December 8, 755, if the original correlation value of Thompson (namely, 584,285) is employed. (Naturally, if his "revised" version is used, |
it would put each of these dates two days earlier.) When the first of these dates was checked against a planetarium programmed to duplicate celestial events as seen from Edzná on that day, it was found that the sun and moon did in fact rise just eight minutes apart on |
that morning over the Yucatán, with an angular separation of less than 2º.5. In other words, there had been a "near miss" to a solar eclipse visible in the Maya area on that date. For the second date, we once again employ the calculations of Oppolzer (1887). Fifteen days after |
the near solar eclipse over the Yucatán -- i.e., on November 23 -- he records a total lunar eclipse as having taken place, but ironically, his data demonstrate that it was visible only in the half of the world centered on the Indian subcontinent. On the third date, again using |
Oppolzer as our source, we find that a partial solar eclipse did indeed take place on December 8, 755, but its central path lay over the ocean between South Africa and Antarctica, where probably not a single human being witnessed it. From this data we can draw two very important |
conclusions. First, by the year 755 the Maya had apparently worked out the motions of the moon with such precision that they knew when an eclipse should occur, but they still could not be sure if it actually would occur, in the sense of being visible to them. Second, the |
original Thompson correlation value of 584,285 is clearly the correct one, for an acknowledged eclipse warning table such as the Dresden Codex could certainly not have been based upon a foundation two days out of phase with the realities of the celestial sphere. In this map view of Edzná, we |
see the features shown photographically in Figure 37. The astronomical importance of Edzná may be gauged from these facts: (1) only at its specific latitude could the beginning of the Maya new year be calibrated, here with the assistance of a remarkable gnomon; (2) the "day the world began" was |
commemorated in the "gun-sight" orientation between the doorway of Cinco Pisos and the small pyramid across the plaza; and (3) lunar cycles were measured by using the line of sight between Cinco Pisos and "La Vieja" on the northwestern horizon. Although we cannot be certain when the Maya finally succeeded |
in working out the lunar eclipse cycle, it would seem that most of the basic "research" on the problem was carried out at Edzná. Located some 300 m (1000 ft) to the northwest of Cinco Pisos is the ruin of a lofty pyramid which Matheny has termed "La Vieja," or |
the "Old One." The "La Vieja" complex appears to date to the Late Classic period as well, but has not experienced the "urban renewal" from which Cinco Pisos subsequently benefited (Matheny, 1983, 109). Even in its dilapidated condition it is still high enough to intersect the horizon as seen from |
the top of Cinco Pisos; indeed, it is the only manmade construction which does so. This fact immediately prompted me to measure its azimuth as seen from Edzná's commanding edifice, and the value I obtained was 300º. This means that the summit of the pyramid lies exactly 5º beyond the |
sun's northernmost setting position at the summer solstice. Because the moon's orbit is just a hair over 5º off that of the sun, it seems very likely that the Northwest Pyramid, or "La Vieja," had been erected as a horizon marker to commemorate the moon's northernmost stillstand. Not only is |
"La Vieja" an eloquent testimonial to the patience and accuracy of Maya "science," but because of its specialized function, it is also probably worthy of being designated as the oldest lunar observatory in the New World. (Indeed, if Matheny's dating of "La Vieja" is accurate, then it is apparent that |
Translated by W. D. Ross. WE have treated of that which is primarily and to which all the other categories of being are referred—i.e. of substance. For it is in virtue of the concept of substance that the others also are said to be—quantity and quality and the like; for |
all will be found to involve the concept of substance, as we said in the first part of our work. And since ‘being’ is in one way divided into individual thing, quality, and quantity, and is in another way distinguished in respect of potency and complete reality, and of function, |
let us now add a discussion of potency and complete reality. And first let us explain potency in the strictest sense, which is, however, not the most useful for our present purpose. For potency and actuality extend beyond the cases that involve a reference to motion. But when we have |
spoken of this first kind, we shall in our discussions of actuality’ explain the other kinds of potency as well. We have pointed out elsewhere that ‘potency’ and the word ‘can’ have several senses. Of these we may neglect all the potencies that are so called by an equivocation. For |
some are called so by analogy, as in geometry we say one thing is or is not a ‘power’ of another by virtue of the presence or absence of some relation between them. But all potencies that conform to the same type are originative sources of some kind, and are |
called potencies in reference to one primary kind of potency, which is an originative source of change in another thing or in the thing itself qua other. For one kind is a potency of being acted on, i.e. the originative source, in the very thing acted on, of its being |
passively changed by another thing or by itself qua other; and another kind is a state of insusceptibility to change for the worse and to destruction by another thing or by the thing itself qua other by virtue of an originative source of change. In all these definitions is implied |
the formula if potency in the primary sense.—And again these so-called potencies are potencies either of merely acting or being acted on, or of acting or being acted on well, so that even in the formulae of the latter the formulae of the prior kinds of potency are somehow implied. |
Obviously, then, in a sense the potency of acting and of being acted on is one (for a thing may be ‘capable’ either because it can itself be acted on or because something else can be acted on by it), but in a sense the potencies are different. For the |
one is in the thing acted on; it is because it contains a certain originative source, and because even the matter is an originative source, that the thing acted on is acted on, and one thing by one, another by another; for that which is oily can be burnt, and |
that which yields in a particular way can be crushed; and similarly in all other cases. But the other potency is in the agent, e.g. heat and the art of building are present, one in that which can produce heat and the other in the man who can build. And |
so, in so far as a thing is an organic unity, it cannot be acted on by itself; for it is one and not two different things. And ‘impotence'and ‘impotent’ stand for the privation which is contrary to potency of this sort, so that every potency belongs to the same |
subject and refers to the same process as a corresponding impotence. Privation has several senses; for it means (1) that which has not a certain quality and (2) that which might naturally have it but has not it, either (a) in general or (b) when it might naturally have it, |
and either (a) in some particular way, e.g. when it has not it completely, or (b) when it has not it at all. And in certain cases if things which naturally have a quality lose it by violence, we say they have suffered privation. Since some such originative sources are |
present in soulless things, and others in things possessed of soul, and in soul, and in the rational part of the soul, clearly some potencies will, be non-rational and some will be non-rational and some will be accompanied by a rational formula. This is why all arts, i.e. all productive |
forms of knowledge, are potencies; they are originative sources of change in another thing or in the artist himself considered as other. And each of those which are accompanied by a rational formula is alike capable of contrary effects, but one non-rational power produces one effect; e.g. the hot is |
capable only of heating, but the medical art can produce both disease and health. The reason is that science is a rational formula, and the same rational formula explains a thing and its privation, only not in the same way; and in a sense it applies to both, but in |
a sense it applies rather to the positive fact. Therefore such sciences must deal with contraries, but with one in virtue of their own nature and with the other not in virtue of their nature; for the rational formula applies to one object in virtue of that object’s nature, and |
to the other, in a sense, accidentally. For it is by denial and removal that it exhibits the contrary; for the contrary is the primary privation, and this is the removal of the positive term. Now since contraries do not occur in the same thing, but science is a potency |
which depends on the possession of a rational formula, and the soul possesses an originative source of movement; therefore, while the wholesome produces only health and the calorific only heat and the frigorific only cold, the scientific man produces both the contrary effects. For the rational formula is one which |
applies to both, though not in the same way, and it is in a soul which possesses an originative source of movement; so that the soul will start both processes from the same originative source, having linked them up with the same thing. And so the things whose potency is |
according to a rational formula act contrariwise to the things whose potency is non-rational; for the products of the former are included under one originative source, the rational formula. It is obvious also that the potency of merely doing a thing or having it done to one is implied in |
that of doing it or having it done well, but the latter is not always implied in the former: for he who does a thing well must also do it, but he who does it merely need not also do it well. There are some who say, as the Megaric |
school does, that a thing ‘can’ act only when it is acting, and when it is not acting it ‘cannot’ act, e.g. that he who is not building cannot build, but only he who is building, when he is building; and so in all other cases. It is not hard |
to see the absurdities that attend this view. For it is clear that on this view a man will not be a builder unless he is building (for to be a builder is to be able to build), and so with the other arts. If, then, it is impossible to |
have such arts if one has not at some time learnt and acquired them, and it is then impossible not to have them if one has not sometime lost them (either by forgetfulness or by some accident or by time; for it cannot be by the destruction of the object, |
for that lasts for ever), a man will not have the art when he has ceased to use it, and yet he may immediately build again; how then will he have got the art? And similarly with regard to lifeless things; nothing will be either cold or hot or sweet |
or perceptible at all if people are not perceiving it; so that the upholders of this view will have to maintain the doctrine of Protagoras. But, indeed, nothing will even have perception if it is not perceiving, i.e. exercising its perception. If, then, that is blind which has not sight |
though it would naturally have it, when it would naturally have it and when it still exists, the same people will be blind many times in the day—and deaf too. Again, if that which is deprived of potency is incapable, that which is not happening will be incapable of happening; |
but he who says of that which is incapable of happening either that it is or that it will be will say what is untrue; for this is what incapacity meant. Therefore these views do away with both movement and becoming. For that which stands will always stand, and that |
which sits will always sit, since if it is sitting it will not get up; for that which, as we are told, cannot get up will be incapable of getting up. But we cannot say this, so that evidently potency and actuality are different (but these views make potency and |
actuality the same, and so it is no small thing they are seeking to annihilate), so that it is possible that a thing may be capable of being and not he, and capable of not being and yet he, and similarly with the other kinds of predicate; it may be |
capable of walking and yet not walk, or capable of not walking and yet walk. And a thing is capable of doing something if there will be nothing impossible in its having the actuality of that of which it is said to have the capacity. I mean, for instance, if |
a thing is capable of sitting and it is open to it to sit, there will be nothing impossible in its actually sitting; and similarly if it is capable of being moved or moving, or of standing or making to stand, or of being or coming to be, or of |
not being or not coming to be. The word ‘actuality’, which we connect with ‘complete reality’, has, in the main, been extended from movements to other things; for actuality in the strict sense is thought to be identical with movement. And so people do not assign movement to non-existent things, |
though they do assign some other predicates. E.g. they say that non-existent things are objects of thought and desire, but not that they are moved; and this because, while ex hypothesi they do not actually exist, they would have to exist actually if they were moved. For of non-existent things |
some exist potentially; but they do not exist, because they do not exist in complete reality. If what we have described is identical with the capable or convertible with it, evidently it cannot be true to say ‘this is capable of being but will not be’, which would imply that |
the things incapable of being would on this showing vanish. Suppose, for instance, that a man—one who did not take account of that which is incapable of being—were to say that the diagonal of the square is capable of being measured but will not be measured, because a thing may |
well be capable of being or coming to be, and yet not be or be about to be. But from the premisses this necessarily follows, that if we actually supposed that which is not, but is capable of being, to be or to have come to be, there will be |
nothing impossible in this; but the result will be impossible, for the measuring of the diagonal is impossible. For the false and the impossible are not the same; that you are standing now is false, but that you should be standing is not impossible. At the same time it is |
clear that if, when A is real, B must be real, then, when A is possible, B also must be possible. For if B need not be possible, there is nothing to prevent its not being possible. Now let A be supposed possible. Then, when A was possible, we agreed |
that nothing impossible followed if A were supposed to be real; and then B must of course be real. But we supposed B to be impossible. Let it be impossible then. If, then, B is impossible, A also must be so. But the first was supposed impossible; therefore the second |
also is impossible. If, then, A is possible, B also will be possible, if they were so related that if A,is real, B must be real. If, then, A and B being thus related, B is not possible on this condition, and B will not be related as was supposed. |
And if when A is possible, B must be possible, then if A is real, B also must be real. For to say that B must be possible, if A is possible, means this, that if A is real both at the time when and in the way in which |
it was supposed capable of being real, B also must then and in that way be real. As all potencies are either innate, like the senses, or come by practice, like the power of playing the flute, or by learning, like artistic power, those which come by practice or by |
rational formula we must acquire by previous exercise but this is not necessary with those which are not of this nature and which imply passivity. Since that which is ‘capable’ is capable of something and at some time in some way (with all the other qualifications which must be present |
in the definition), and since some things can produce change according to a rational formula and their potencies involve such a formula, while other things are nonrational and their potencies are non-rational, and the former potencies must be in a living thing, while the latter can be both in the |
living and in the lifeless; as regards potencies of the latter kind, when the agent and the patient meet in the way appropriate to the potency in question, the one must act and the other be acted on, but with the former kind of potency this is not necessary. For |
the nonrational potencies are all productive of one effect each, but the rational produce contrary effects, so that if they produced their effects necessarily they would produce contrary effects at the same time; but this is impossible. There must, then, be something else that decides; I mean by this, desire |
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