Posted: Thu Jan 21, 2016 1:14 pm
It is natural for anyone to anyone assume that, once they know that is the case. But I didn?t assume or realise that before it was explained to me, and Rhetorius talks about making this discovery for himself as if he?s made a break through.Martin wrote:But clearly Rhetorius thought (as Holden did, and Koch-Westenholz, and my humble self) that it doesn't matter whether you divide by 2? or multiply by 12, as you get the same result either way
Let me clarify that I?m not trying to lend favour to one technique or another ? that which allows us to multiply and divide to get the same result is obviously the most appealing, to me as well as anyone else. But if we strip away what Koch-Westenholz speculates, the facts reported in her work are the same as those reported by Rochberg: the Babylonians had two uses of the same term, which identifies two techniques: one generates the micro-zodiac in each sign (to which symbolic attributions are made), the other creates associations between a planet?s position, and where it would be if we multiplied its degree placement by twelve and cast that arc from its current position.
The result of the latter doesn?t correspond with the micro-zodiac, so we are left with two choices: either the Babylonians (and Paulus) expected they would, and were hopeless at maths and never figured out that what they describe gives the wrong result; or, the two techniques were developed separately and possibly used in different ways. If this possibility exists, then it may not be safe to assume that recognition of the technique that divides the signs into twelve 2?? portions (described by Ptolemy to be something similar to the use of terms), meant the astrologer expected to identify the same point by multiplication and use it in the same way.
I have been struggling with this issue a lot lately, in trying to understand a technique Valens refers to, which uses the dodekatemorion of the Sun to identify the rising sign (the association between dodekatemoria and rising signs keeps cropping up all over the place!). I am not sure if we?ll ever figure out the mechanics of this long-abandoned technique, but where Valens uses the term dodekatemorion in reference to this (I.4, Riley, p.8 ), his example leads us to assume he uses the Pauline calculation (dodekatemorion of 22 Aquarius = Scorpio). I came to this conclusion myself, as did the Project Hindsight team, with Robert Hand annotating the point in the Schmidt translation (p.24) with the comment that this "is computed by the 13th harmonic method, rather than the dwadasamsa method ...".
However, as Konrad pointed out earlier, if the Sun were between 22?30' and 23? Aquarius, its dodekatemorion would fall into Scorpio by both methods, so it is not beyond the realm of possibility that Valens used the method that Firmicus described. But this solution is messy ? why would the example he gives to illustrate a principle be complicated and require knowledge of a precise placement in the 23rd degree which he doesn?t report?
Valens uses the term ?dodekatemoria? in an entirely different way (to mean 12? increments of celestial longitude) in his first book, where he gives a handy method for determining new and full moons. The only other place he talks about the dodekatemorion of a planet is in his ninth book, chapter 8: ?Male and Female Nativities; Monstrous or Animal-like Nativities?. Here his technique uses the dodekatemorion of the Moon to establish gender and his example tells us ?? the moon in Pisces 19?. The dodekatemorion is in Libra?. This accords with the use of the micro-zodiac (as generated by the Firmicus method) ? applying the Pauline method takes us far out, landing at 7? Scorpio.
After a lot of thought and head-banging, I eventually came to conclude that, on balance, it?s more likely Valens was using the micro-zodiac/Firmicus method, and his example given in the first book is just an unfortunate one, (or has expectations in it that are not explained/ has been subject to omissions in transmission/or is mistaken). Or for some reason we'll never understand, one of the two parts of his work were effected by a "correction" from a copyist, so the knowledge of how he would have calculated himself will never be known for sure.
I felt relieved to be able to make a mental conclusion on this minor point and move my mind on to other things. But it keeps nagging away at the back of my mind. What if there is another possibility, and the mistake is to assume that the word dodekatemoria, which we know has a very broad application, has to mean the same thing for Valens in both instances? In book 9, he is making a purely symbolic reference to the signs of the micro-zodiac to establish gender in the same way that later astrologers consider the Moon?s placement by term or sign in the actual zodiac. In book one he is doing something very different: trying to establish a relationship with a point that has some kind of astronomical significance in determining the rising sign ? why would the symbolism-rich micro-zodiac be expected to do that? Valens, using Babylonian astronomical principles, knew things about the mathematical basis of this relationship that we don?t understand. The Sun is used as the starting point because (as he tells us in book IX.8 ) ?the sun?s position always indicates the length of day and night, depending on which sign it is in?.
Rochberg also talks about how the dodekatemoria were used to establish the rising signs of the climes by the Babylonians (p.159), and she assumes this to be the use of the 2?? divisions of the ecliptic because the text says ?the first portion of Scorpius, Scorpius of Scorpius?. But this is exactly how the text she has earlier described (which multiplies by 12 and adds to the position of the planet) makes reference, and Rochberg does not seem to realise that there is a difference between this, which shows a ?travelled distance?, and the 2?? divisions of the micro-zodiac she describes on p.157.
So if I seem a little obstinate in not simply settling for assumptions that might reasonably be drawn, it is not because I am trying to reject something that might be very plausible, it is because this issue has a conflict running right down the middle of it, with the older sources not reporting what we expect them to. I think we have to allow the possibility of two separate techniques that appeared to become unified at a certain point through a different calculation for the multiplied position, which is why I'm hesitant to accept references to divisions by 2?? as being necessarily implicit of the method described by Firmicus, though not wanting to deny that (of course) they could be.