Site Section Links
KRONOS Vol V, No. 1
SECTION II: THE ARTIFICIAL INSERTION
LYNN E. ROSE AND RAYMOND C. VAUGHAN
Copyright (C) 1980 by Lynn E. Rose and Raymond C. Vaughan
K. 160. the best known of the Ninsianna or Venus fragments, contains an "artificial insertion" that has intrigued commentators for over a century. Inserted after Year 17 and before Year 19 are twelve paragraphs or verses, each of which gives a date and direction of appearance of Ninsianna, a forecast, a date and direction of last visibility, a date of disappearance (the next day), an interval of invisibility, a date and direction of reappearance, and another forecast. The dates of initial appearance are I 2, II 3, III 4, and so on, down to XII 13.
Reiner and Pingree call this artificial insertion Section II, and they refer to Years 1-17 as Section I and Years 19-21b as Section III. (These year numbers are not in the text, but have been supplied by modern scholars.) After Section III on some fragments-(but not on K. 160) comes what Reiner and Pingree call Section IV, where all except two – they would say three – of the entries in Sections I and III are listed in order of the month of disappearance, rather than in chronological order. After Section IV there is sometimes a rather short part of the text that we propose to call Section V, though Reiner and Pingree do not do so. Each of the five Sections ends with a "footing", which serves the same purpose as would a modern "heading", and the entire text is then ended with a colophon. Some versions of the text lack Section IV or Section V, and some put Sections IV and V on a separate tablet.
Calling Section II an insertion may reinforce the questionable but seldom questioned thesis that the years have been properly numbered and that Years 19-21b really do follow immediately after Years 1-17, with Year 18 omitted. But it is still in some sense an insertion, for it is indeed placed between two groups of observational reports (Sections I and III).
See the accompanying translation (Table I) of the reconstructed and conflated text of the artificial insertion. There may be disagreement (as between Langdon and Reiner, for example) about what the correct translation is, especially where the forecasts are concerned. Usually we have followed Langdon, but sometimes Reiner. It will be seen later that how a forecast is to be translated is far less important than where that forecast occurs. It is also unimportant to us what the tenses are: as long as Sections I, III, IV, and V are based on observational material, and as long as Section II really is artificial, it does not matter which tenses were used by the astrologer-scribes who gave these texts their present format. We do not even care whether the introductory symbol in each paragraph is an "If" or simply a paragraph marker (though we have taken them in the latter sense). What does count is whether the material contained in such paragraphs is observational or artificial; we need not be overly concerned about the style of the astrologically-oriented versions that happen to have survived.
One of the important features of the artificial insertion is that it makes it clear that disappearance means first invisibility, rather than last visibility. The day of last visibility is here distinguished from the following day, which is the actual day of disappearance or first invisibility. From the other Sections there is no way to determine which is meant.
For us, the major value of the artificial insertion is that it provides a way to test our reconstruction of the observational material in Section I. That reconstruction has been accomplished independently of Section II, and is defended in our Commentary (not included here). In many cases, there are no problems at all, and we simply report what the fragments say. Our most speculative interpretations are those for Years 8b and 16b, which we would reconstruct as XI 25 (3m9d) III 4 and as XII 25 (2m7d) III 2, and for Years 13b and 14, which we take as IX 20 (2m1d) XI 21 and as VII 21 (1m7d) VIII 28. The main purpose of this paper is to argue that Section II is based upon and is strictly tied to the various intervals of invisibility and implied periods of visibility that we established in our reconstruction of Section I.
Reiner recently found three other fragments – B.M. 36758 + B.M. 37496; K. 12344 + K. 12758; and K. 3105 – that supplement some of the Section II information from K. 160 (which still remains our most complete source for Section II). She also located some Section II material on the reverse of K. 3170 + K. 11719 + K. 14551;such material seems sometimes to have been included as part of the astrological series known as Iqqur ipus.
Table II gives the key items from Section II. Alternative readings have a slash between them; items with a question mark are incorrect, incomplete, or missing entirely. The sources of the various readings are listed in Table III. Some minor reconstruction of Section II is required, but this is by no means arbitrary: every writer who has ever discussed Section II has recognized the need for such reconstruction. On this the uniformitarians and the non-uniformitarians are in full agreement. For this reconstruction is not in order to make the text fit the present motions of Venus, but simply to make some obvious repairs in a text that is so idealized that it would not fit the actual observations (present or past) anyway.
Key Items From Section II
These repairs are dictated by the character of the text itself. For it is quite clear that the author of Section II intended for the appearances of Ninsianna to occur in the first month, the second day, in the second month, the third day, and so on, down to the twelfth month, the thirteenth day. It is also quite clear that the author recognized a period of visibility of Ninsianna lasting eight months and five days, followed either by a three-month interval of invisibility at superior conjunction or by a seven-day interval of invisibility at inferior conjunction. Thus there would be a synodic period of nineteen months and seventeen days. If the months were of 30 days, this would amount to 587 days, which is slightly longer than the present mean synodic period of 583.914 days. The situation is even worse if the present month of 29.53 days is used: the synodic period would be only 578 days. Section II is not only artificial, but so idealized as to be unrealistic. Orbital considerations aside, weather conditions alone would prevent any such pattern of appearances and disappearances that was mathematically perfect to the day.
Since we do know what Section II is supposed to say, we can assess with some confidence the effect that scribal errors, tablet damage, and all other such factors have wrought in the condition of the text, especially as far as the numbers are concerned. Of the sixteen wrong numbers, twelve have been reduced from the intended value, and only four have been increased. It is also significant that the vulnerable numbers seem to be the higher digits: one 5 has been affected, and seven 7's, four 8's, and four 9's. (See Table III.) This information may be taken as a clue as to what can be expected to have happened in other portions of the Ninsianna document, where we do not have such a reliable control.
We shall argue that Section II is based upon the data in Section I. Table IV gives the Section I intervals of invisibility and implied periods of visibility in the condition in which they probably stood at the time when Section II was derived from Section I. We do not offer these as the original readings, those that described the actual events. For example, we think that the invisibility in Year 8b actually began on XI 25, rather than on XII 25; but Section II seems to presuppose that the 8b invisibility lasted from XII 25 to III 4. Thus it is probable that Section II was invented before the interval of invisibility, the date and direction of reappearance, and the forecast of Year 8b were replaced by the 8b year-formula, but some time after the observations themselves.
Except for our handling of Year 8b – the "year of the golden throne", where some sort of reconstruction is unavoidable – and of Years 13b, 14, and 16b, our decisions about Section I can be supported in a quite straightforward way on the basis of the available readings.
The Sources Of The Variant Readings
In the matter at hand, however, the point is not what the original observations were, but rather what the best available readings were at the time when Section II was devised. That time may have been rather late, perhaps as late as the middle of the eighth century before the present era. So what we are reconstructing here is not what originally happened, but rather what was available to the author of Section II. These are two different things, and that is why we feel free to propose that the actual interval of invisibility in Year 8b was 3m9d, but that the reading available to the author of Section II was 2m9d. (See our "Ninsianna Update" in KRONOS, V, 3, pages 51-54, for further discussion of Year 8b and Year 16b. All of the other readings in Table IV are explained in our Commentary.)
The mean of the invisibilities in Table IV that last more than one month is exactly three months or ninety days, and the median of the remaining invisibilities – those of less than one month – is seven days. If the unusually short 7d period of visibility in Year 9 is disregarded, the mean of the nineteen remaining visibilities – ranging from 7m1d to 9m9d – is 244 11/19 days, or, rounded off to the nearest day, eight months and five days. (The same result emerges another way: the ten eastern visibilities – counting 14-15 – average to 240.2 days, the nine longer western visibilities – counting 13b-14 – average to 249 4/9 days, and those two figures average to 8 months 4 37/45 days. The technique is sloppy, but uniformitarian methodology tends to be bad anyway.)
The apparent garbling of the directions in Year 14 (more of which in a moment) would complicate the status of the visibilities before and after Year 14. But even if both visibilities were placed in the wrong group – 13b-14 with the eastern visibilities, and 14-15 with the western visibilities – the averages of the two groups would themselves still average closer to 245 days than to any other integral number of days.
There is a minor problem about the dates in Year 17. Reiner reports XII 10 and XII 14. Other scholars – see the writings of Rawlinson and Smith, Sayce, Virolleaud, and LFS, all of which are listed in our References – report a disappearance on XII 11 and an interval of 4d. All of these sources treat the date of appearance as illegible, though XII 15 would be implied by the XII 11 and the 4d. If Reiner is right, then some of the figures in the paragraph before last would be slightly different, but we would still arrive at an average visibility just short of 8m5d.
Similarly, Reiner favors month V in Year 16a, rather than Langdon's more likely month IV; her reasons are not specified. (The other sources just mentioned all treat the month name as illegible.) If we were to follow Reiner rather than Langdon, we would again find some of the numbers changed, but the average visibility of 8m5d would still emerge, as would the mean of 3m for the longer invisibilities and the median of 7d for the shorter invisibilities.
The practice of rounding off to the nearest integer may not be appropriate here. Even if the average interval was only, say, 244 1/3 days, any calculation of the next disappearance, based on that figure, would actually have to use 245 days. For one could not witness the next disappearance until after sundown, 245 integral days (ignoring seasonal changes) after the first visibility, which was also witnessed just after sundown. Any number significantly over 244 days would not be rounded off to 244, but would have to be rounded up to 245.
Thus Section II does seem to be an idealization of the observational data from Section I. Like Huber, the inventor of Section II was compelled to smooth out the observational record in order "to obtain a decent alignment", and Section II stands to Section I in just about the same way that Huber's graph stands to Sections I and III.
It seems most unlikely that Section III was included along with Section I in the derivation of Section II; even if someone were to do a lot of juggling, the results would be neither as satisfactory nor as straightforward as with Section I alone. While it is possible, using alternative readings for several of the years (such as Years 20 and 14 and 15), to save the 3m and the 7d, the 8m5d is inevitably thrown off. The simple fact that Section II immediately follows Section I is also an indication that Section II is based just on Section I.
It is rather obvious why it might be tempting to group an invisibility of 9m4d with the longer invisibilities even though most of them involve disappearances in the east and reappearances in the west – what we now call superior conjunctions – while the 9m4d invisibility involved a disappearance in the west and a reappearance in the east what we now call an inferior conjunction. But what about the borderline invisibility of only 1m7d? Is there any special reason why it should have been grouped with the longer invisibilities, all of which, after all, are at least two months long? Yes, there is. The status of Year 14 in Section I is unique. It alone has both of its directions incorrectly reported. (There is another case in which one direction on one fragment is wrong – namely, the western appearance in Year 16a on K. 160 – but that incorrect direction is outweighed by four other Section I reports.) For Year 14, K. 160 reports that the disappearance was in the east and that the appearance was in the west; Rm. II 531 also reports that the appearance was in the west. Thus all three surviving reports seem to be wrong. (If B.M. 41498, Obverse, lines 3´-4´ is Year 14, as we suspect, then both directions are given correctly there. But those two correct reports would still not outweigh the three incorrect reports on the two fragments just mentioned. Besides, the scribal comment in line 5´ may report that the directions were wrong in the source but have been corrected!)
Year 14 is also special in that for some reason or reasons it was repeated at the very end of the listings, after Section IV had been concluded. Reiner and Pingree argue that this additional listing served as a "correction" of the earlier listings of Year 14. Some versions of the Ninsianna fragments – such as B.M. 42033, and/or whatever source it was from which W. 1924. 802, Reverse, line 14´ was copied – seem to have contained a "correction" for Year 5b just after the "correction" for Year 14. 5b may have needed such correction because its directions had been consistently misreported in Section IV, but it is possible also that 5b's dates needed correction, either from Section I or from Section IV, or from both. The surviving directions in these various "corrections" are themselves correct. (Reiner and Pingree have overlooked the 5b "correction".)
But the inventor of Section II may have been working just with Section I, and may have been led astray by the incorrect directions for Year 14. That is, if Year 14 was recorded there as featuring an eastern disappearance and a western reappearance, that in itself might explain why it was classed with the other invisibilities that were (correctly) reported to have had eastern disappearances and western reappearances. The inventor of Section II would thus quite understandably have found himself in the position of grouping together all of the invisibilities that were longer than one month, and of grouping together all of the invisibilities that were shorter than one month. The longer ones were averaged, and the average was found to be exactly three months. The inventor may have been aware that the shorter invisibilities are much more vulnerable to bad weather (a week of cloudy weather could triple the length of an invisibility at inferior conjunction, but that same week of poor "seeing" could not produce much more than about a ten percent increase in the length of an invisibility at superior conjunction), and he may for that reason have decided to take the median of the shorter invisibilities rather than the mean, so as to minimize any undue weighting by any of the invisibilities that might have been stretched out by bad weather. The median, of course, is seven days.
(No great sophistication is required in taking a median. Just list the shorter invisibilities in order of length, and then go half way down the list. If anything, medians are easier than means, since they involve neither addition nor division.)
Once the decision had been made to group the shorter invisibilities together and to group the longer invisibilities together, it would have seemed inappropriate to group the short seven-day visibility (between 8b and 9) with all the other periods of visibility, each of which is thirty to forty times longer than it. The seven-day visibility could have seemed to be an anomaly, and could thus have been disregarded. The average of the remaining periods of visibility would then have yielded the figure of eight months and five days that is used in Section II.
(If the 9m4d was averaged in with the longer intervals of invisibility, shouldn't the 7d be averaged in with the periods of visibility, especially since the length of the one is the reason for the shortness of the other? Yes, it should. But we are not defending what was done; we are simply trying to discover what was done. And it seems clear that the 9m4d was counted and that the 7d was not counted.)
If we are correct in explaining Section II as an idealization of the observations recorded in Section I, then it would follow that the author of Section II did not recognize any intercalary months from the time of the Section I observations (whenever he thought that time was), other than the second Ulul recorded in Year 11. Any of the uniformitarians' postulated intercalations, such as 4A, 5U, 13U, 13A, or 14U, or, for that matter, any other intercalations that might be proposed, would stretch out the periods of visibility to significantly more than the average of eight months and five days. Nor will it work to lengthen an invisibility and shorten a visibility, with the idea of making room in the visibility for an extra intercalary month. The longer invisibilities are already maximal; none can be lengthened by even one month without spoiling the three month average.
Section I implies a mean synodic period of 581.65 days. The artificial insertion or Section II implies a synodic period (the "mean" is unnecessary, so idealized is Section II) of 587 days. If the author of Section II had taken the mean of all invisibilities at superior conjunction, and the mean of all invisibilities at inferior conjunction, and the mean of all periods of visibility, then Section II would not conflict with Section I. Instead, the author took the mean of the longer invisibilities (including Years 9 and 14, which occurred at inferior conjunction), the median of the remaining shorter invisibilities (excluding Years 9 and 14), and the mean of all visibilities (excluding the anomalous seven-day visibility in Year 9), and then proceeded to use these derived values throughout Section II for all invisibilities at superior conjunction, all invisibilities at inferior conjunction, and all visibilities, respectively.
The resulting scheme may have been intended as a rough guide to what might have been expected whenever Ninsianna appeared, but it gives us no empirical information beyond what we have from Section I. (It does, however, serve as a check on our reconstruction of Section I.) The 587 days comes from a bad statistician's attempt to smooth out accurate but displeasing data, in the manner of a Huber. Even the use of medians is similar to Huber, who properly calls them "more robust" than means, but then reveals a typical uniformitarian compulsion "to obtain a decent alignment", even at the expense of clearly irregular observational facts. As far back as twenty-seven centuries ago, there were students of the heavens who would go to any lengths to make the celestial phenomena uniform and regular and "decent" and predictable, whatever the facts, just as there are today.
Another motive of the inventor of Section II may have been astrological. Each paragraph or verse in Section II has two appearances, with a forecast following each. As can be seen from Table V, these forecasts are tied to the month of appearance: all appearances in the same month are followed by the same forecast. (The only exceptions are the second forecasts of the second and ninth entries.) Section II seems to have been intended as a schematic device for astrological forecast, a device that would be based on what was taken to be observational material (Section I), but would be smoothed out so as to form a more "decent" pattern.
Before we leave the artificial insertion, let us note some further respects in which the author of the artificial insertion has been of assistance to us. Table V indicates how the forecasts in Section II are tied to months of appearance. If a month of appearance had been lost, and the forecast immediately following it had survived, we might be able to tell what the month was supposed to be by checking the forecast. Of course we do not need this sort of clue in the case of the artificial insertion, since we already know what all of the days and months in Section II are supposed to be anyway. But the other parts of the text are different. We are not fully confident about all of the days and months in Sections I, III, IV, and V. The forecasts in those parts of the text also depend upon the month of the appearance (though apparently not in as strict or mechanical a way as in Section II), and we should keep that clue in mind whenever we attempt to determine months of appearance in those parts of the text. We do not need to be astrologers in order to exploit this clue.
Forecasts and Months of Appearance in Section II
(1) The word translated as "of the land" is missing from the second forecast of the tenth entry.
But the main value of the artificial insertion is as an independent check on the dates of appearance and disappearance in Section I that we have arrived at on the basis of alternative readings, textual analysis, and textual reconstruction. The dates that we arrived at do imply a mean of 3m for the longer invisibilities, a median of 7d for the shorter invisibilities, and a mean (to the nearest day) of 8m5d for the extended periods of visibility (excluding the 7d visibility in Year 9). The use of these same values in the artificial insertion shows that it is extremely likely that our reconstruction of the text available to the author of the artificial insertion is correct. The corroboration thus provided is perhaps the most important feature of the artificial insertion.
Now that we have a well-established reconstruction of the original readings for Section I, we are in a position to carry our investigations two further steps. (Both investigations are similar to what was done earlier for Section II.)
First, we can survey all variant readings for Section I that differ from our reconstruction, and we can see what types of errors were introduced into the text. This information may then be useful in deciding between variant readings in other parts of the text, such as Section III.
Second, we can survey all the different fragments that include parts of Section I and/or Section II, and we can evaluate or rank those fragments according to how well or poorly they correspond to our reconstruction. This information, too, may then be useful in deciding variant Section III readings from different fragments, at least in the cases of those fragments that also cover parts of Section I or Section II.
Both of these investigations could be used as a basis for judgments about Sections IV and V, as well as about Section II.
Let us now report the results of these two investigations.
The first investigation shows, as might have been expected, that symbols for ten are sometimes dropped, less often added, and that errors involving digits are clearly clustered on 6, 7, 8, and 9. Digits, like tens, are more likely to be lowered than raised.
The second investigation shows that Rm. II 531 is distinctly unreliable. It has a greater proportion of errors than any of the other Section I sources. Three of the ten errors on Rm. II 531 are month names, which suggests scribal carelessness without parallel. No other Ninsianna fragment is even half so bad. (A rival to Rm. II 531 for inaccuracy is VAT 11253, which covers parts of Section IV; but VAT 11253 is not strictly a "Ninsianna" fragment, since it refers to Venus as Dilbat rather than as Ninsianna.) Otherwise, the second investigation leads to no conclusive result. The three fragments covering Section III that can be evaluated in this way all come out about the same. Fortunately, Years 19, 21a, and 21b involve uncertainties of at most a day or two; Year 20 is the only entry in Section III – or, for that matter, in Section I – about which we have not yet taken a definite position. For the time being, we will tentatively accept K. 160's extreme dates of III 25 and VI 24, and we will assume an interval of 2m29d; this seems more likely than any alternative. Thus our reconstruction of Section III is as follows:
It should be emphasized, however, that these Section III items have not been confirmed by the various checks that the artificial insertion enabled us to provide for Section I.