There is a view, often repeated, that Hellenistic astrologers viewed degrees of longitude as discrete units, so that, for instance, a planet conjunct the Sun within 10 or 20 seconds of arc but in a different degree (say, with the Sun at 7?50' and the planet at 8?10') would not be considered to be conjunct it within one degree (the condition later called cazimi). I have often wondered what textual support there is for this view, and would be grateful for any quotations from Hellenistic (or even later) authors.

What prompted my question at this time was a post by Larxene in this thread, where he makes the position very clear (I've underlined some parts):

Note that the closeness of aspects and conjunction were mostly determined using degrees. Smaller units like minutes or seconds were not present in most the literature I've read (Dorotheus, Valens, Maternus, and a bit of Ptolemy, Hephaistio and Paulus). [...]

Therefore, for all intents and purposes, a planet within one degree from the Sun is considered to be 'in its heart', as every minute within that degree belongs to the same space.

In light of the idea of "discrete spaces", however, this sentence construction is potentially misleading, because it leads the modern mind to translate it like this: "a planet within SIXTY MINUTES from the Sun is 'in the heart' of the Sun."

This is NOT what is meant. A better sentence construction would be this. "A planet within the SAME DEGREE as the Sun is 'in the heart' of the Sun."

Actually, however, Paul[us] does say explicitly in chapter 14 that a distance of under sixty minutes is exactly what is meant. Here is Holden's translation (p. 22 f):

They become conjunct whenever they happen to be in the same degree as the Sun in the same sign, not being distant from it by more than approximately 59 minutes.

And here is Greenbaum's translation (p. 21):

And they become conjunct whenever they happen to be in the same degree as the Sun in the same z?idia, not being away from it by more or less than 59 minutes.

Holden's version seems more reasonable to me, but in either case, we are definitely dealing with a degree in the sense of 60 consecutive minutes of arc, not a discrete unit. So -- are there any counter-examples in the classical texts?

Martin,

I would read those translations as supporting discrete units. What does the Greek say?

If Paul had had discrete degrees in mind, the latter part of the sentence would be completely superfluous (as a planet in the same discrete degree as the Sun is necessarily 0-59 minutes of arc away). The Greek says, in simplified transliteration: sunodikoi de ginontai, hotan kata to auto z?idion isomoiroi t?i H?li?i tuch?si m? apechontes ap' autou pleion ? elatton lept?n 59.

I'll revise my earlier opinion slightly and say that Greenbaum's 'not ... by more or less' is truer to the original, now that I've looked it up. But that only strengthens my case: Paul is saying that a planet becomes 'synodic' or conjunct the Sun exactly when the distance between them becomes 59 minutes (he doesn't mention seconds, but obviously the idea is as soon as the distance goes under a degree or 60 minutes). Only very rarely will this happen while the planet and the Sun are in the same discrete degree.

I really don't think this can be plausibly read any other way.

Thanks for looking that up.

I don't really have anything helpful to add. I looked up the Arabic authors, but, as can be expected from their astrology, they spoke of minutes. As you know, a lot of them counted a planet being in Cazimi as being 17 minutes from the Sun's own degree and minute.

Like Larxene, I don't recall seeing much of a mention of minutes of arc from the Hellensitic authors I have read.

I'd be interested in any evidence at all that degrees were conceived as discrete units by at least some Greek astrological authors, not just in relation to cazimi. I mean unambiguous statements or examples, not just expressions like 'in the same degree', because, as we have seen, such phrases can be interpreted in different ways.

My sneaking suspicion is that the doctrine of discrete degrees began as a hypothesis put forward by the two Roberts in the 1990s and was subsequently turned into a supposed fact by parts of the astrological community. But I could be wrong.

Hello Martin,

Thanks for starting this thread. Indeed, most of what I have read about this degree/portion/moira concept was written by Schmidt and/or Hand. I do not have evidence that this was explicitly mentioned in the texts I have (mostly Maternus, Valens and Dorotheus). Also note that I've only read 3 or 4 sections in Paulus, so I did not see that quote.

For me, what convinced me of their interpretation partly has to do with the various quotes spread in different places. But before that, a caveat: my memory for specifics isn't that good, and I have a habit of seeing patterns when there may be none. An example would be like, I see a silhouette of a dragon among the clouds in the sky. This is perhaps a condition called Apophenia. So maybe it's just me.

Anyway, there were many quotes spread in various places along the lines of "if A is in one degree with B...". The delineation seemed to indicate that the effects become more intense. But this alone doesn't support discrete units. The issue is that "A in one degree with B" can also be interpreted as "A in the SAME degree as B". Of course, it may simply mean 60 minutes, as Paulus explicitly stated.

Another reason I find that interpretation appropriate has to do with Greek arithmetics. When calculating the Lots, they seem to count in degrees, disregarding the minutes. With the Lots of Acquisition and Exaltation, they seem to count by signs, seemingly disregarding the smaller units. Then of course, we have the whole signs houses, where house=sign. These things hint at a Platonic perfection underlying their works.

Of course, maybe they simply didn't want to obscure their students with specific and tedious calculation of degrees and minutes. Perhaps they simply wanted their students to focus on the concepts rather than the math.

What we have is an incomplete corpus of occult works, where some things are simply undefinitive.



Larxene Xenohart

Note: When I listed the authors I've gone through, I actually meant that I have read:

- Dorotheus, Valens and Maternus
- A little bit of Ptolemy, a little bit of Hephaistio and a little bit of Paulus.

I knew there was an ambiguity there, but I didn't think I needed to clarify. Looks like I was wrong. :3

So it isn't that I ignored the quote from Paulus, or that I didn't notice it, but rather because I have only read a small portion of The Introduction, so I have not seen that quote.



Larxene Xenohart

Martin Gansten wrote:I'd be interested in any evidence at all that degrees were conceived as discrete units by at least some Greek astrological authors, not just in relation to cazimi. I mean unambiguous statements or examples, not just expressions like 'in the same degree', because, as we have seen, such phrases can be interpreted in different ways.

My sneaking suspicion is that the doctrine of discrete degrees began as a hypothesis put forward by the two Roberts in the 1990s and was subsequently turned into a supposed fact by parts of the astrological community. But I could be wrong.

I had a brain wave !!

This will be the thin end of the wedge - if the discrete degree boundary doesn't hold then there would be no boundaries that can not be broken .The VOC sign boundary is already broken and we are dealing with a circle - so we will just go round and round

I would be reading Alan Leo again.

Pankaj,

Well, we still have boundaries. The question is whether the boundaries are fixed (as with discrete degrees) or moving (as with continuous degrees).



Larxene Xenohart

Martin, I may have to eat my words with evidence to the contrary, but it is hard to see how Hellenistic astrologers would have finely divided degrees or distinguished much between them because their time-keeping was so inaccurate. Many birth times had to be guesstimated.

When I cast some of Valens's charts based on corrected dates from Neugebauer and Van Hoesen (Greek Horoscopes,) for this thread http://skyscript.co.uk/forums/viewtopic.php?t=8120 I found that Valens didn't actually calculate the part of fortune by degree, but simply by counting houses (aka signs, since he also seemed to be using whole signs houses.)

Larxene wrote:Pankaj,

Well, we still have boundaries. The question is whether the boundaries are fixed (as with discrete degrees) or moving (as with continuous degrees).



Larxene Xenohart

In that case the fixity will have to come from houses, whereas, signs and degrees will all be fluid.The only dignity will be accidental because in degrees things will just flow.
The next fixed thing will be an aspect.
Houses and aspect combined will be neo modern traditional astrology of Alan Leo.

waybread wrote:Martin, I may have to eat my words with evidence to the contrary, but it is hard to see how Hellenistic astrologers would have finely divided degrees or distinguished much between them because their time-keeping was so inaccurate. Many birth times had to be guesstimated.

You're right about the problems of time-keeping, of course, and we may add inexact formulae for calculating planetary positions. But I think you're conflating theory and practice. Hellenistic authors certainly did have sophisticated theories based on minute divisions of the zodiac (just look at the doctrine of myriogenesis mentioned by Firmicus!), even if from a modern perspective their calculations were often off, and even if practising astrologers fudged or eye-balled things a lot of the time.

In any case, whether you look at degrees as discrete units or as units of 60 consecutive minutes of arc, you need the same level of precision, so for the purposes of the present discussion, inexact practices aren't that relevant.