Good morning,

Reference is made to the related thread WHICH Ptolemaic confines?

Those particularly interested in solving mathematical riddles - astrological or others - are kindly requested to, like many illustrious persons before them, find a solution set of the 'Ptolemaic confines' that fulfils all of the conditions stated in the texts linked below. Mathematicians also without astrological leanings are cordially invited to view the problem in an abstract way. The underlying references are:

1. Klaudios Ptolomaios' Tetrabiblos, Book I, Sections 20 and 21;

2. the ancient Greek text prevails over the translations;

3. Dott. Giuseppe Bezza's analyses at Cielo e Terra;

4. Ms Deborah Houlding's paper HERE.

My hypothesis:

the set of solutions to the Ptolemaic confines problem has nil members.

One or more of the rules must be broken.

Consequence for astrological practice:

use the Chaldean confines,

even if they be for simpletons like yours truly. A good journeyman is expected to 'grasp' (comprehend) the tools of his trade. Alas, experts like Regulus Astrology have not yet tested the Chaldean confines but they seem to 'work' reasonably well in practice. Concerning the often used 'Egyptian' confines, to the best of my feeble knowledge no-one to date has published a coherent explanation of their underlying logic, if there be one.

Best regards,

lihin

lihin wrote: One or more of the rules must be broken.

What are the rules...?

Geoffrey

Good evening,

The rules are stated in the three linked references, Dott. Giuseppe Bezza's being in my humble opinion the clearest presentation.

One is, for example, the overall allotment of 360 degrees as follows:

Venus 82
Jupiter 79
Mercury 76
Mars 66
Saturn 57

Best regards,

lihin

Right... So you are not worried about the order of the planets in Ptolomy's terms, only the degrees allotted to each.

I take it that the order of planets is solved?

Geoffrey

Good evening,

Sorry, the aggregate number of degrees allotted to each planet is only ONE rule. There are several others related to dignities, who comes first, who gets the most degrees per sign, minimum number of degrees allotted to each planet in each sign (2), whom to subtract from and add to, etc.

Even to state the problem in clear, unambiguous mathematical language is, for my feeble mind, a Herculean task, but methinks it quite possible for a professional mathematician.

Best regards,

lihin

Hello Lithin.

By the time of Ptolemy there were several versions of the Terms. Why was this?

I suggest that reason is that the original logic by which the order of Terms had been set out was lost. And moreover, the logic was sufficiently obscure or complex that it was then not possible to reverse engineer the logic by which they had been created.

It may be that mistakes by scribes in copying out the Terms from primal source manuscripts had rendered the original logic incapable of being successfully reverse engineered from the copies. Or it may be that the original logic was so obscure that it was not possible to take a reasonable guess at what that logic may have been. Or it may be a combination of the two. And then later authors may have consequently felt free to 'correct' the table of Terms from the 'obvious' errors that may have crept in, according to a logic scheme of their own devising, which was so obviously what the original creator of the table of Terms had used that it was not worth reporting.

So, by the time we get to the era of Ptolemy, a number of variants of the table of Terms exist and there is no surviving record of how they came into being. Ptolemy has a stab at trying to reverse engineer one table of Terms, but he runs into the sand.

Given this state of affairs, it would obviously be useful to obtain the earliest possible table of Terms in the hope that there would a minimum degradation from the original creation of the Terms and there would be some hope of reverse engineering the logic by which they were created. With this logic secured, it would then be then possible to see how later versions varied from this seminal version. Then working forwards, it would be much easier to see the occurrence of mistakes and/or overlays of later rules.

As I have reported before, the remnant of a much earlier version of the table of Terms (circa 400 BC) has been sitting in the British Museum gathering dust for many decades, but was translated just a few years ago. See, A. Jones and J.M. Steele, "A New Discovery of a Component of Greek Astrology in Babylonian Tablets: The Terms", Institute for the Study of Ancient World (ISAW), 2011. About half the table of Terms is still readable and I have listed this partial table before.

I would suggest this table should the starting point for deriving the rules you seek.

Geoffrey

Good morning,

My question is not about the supposed 'true original' confines and their rules but simply if there is any solution for the Ptolemaic confines according to the rules that Klaudios Ptolomaios himself set out. As far as i know, neither Ptolemy himself nor anyone else has to date proposed a solution that fulfils all of the rules.

The manuscript Mr Geoffrey has mentioned is a variant of the 'Egyptian' confines. Since no-one to my knowledge has to date explained the underpinnings of these, it will probably be even more difficult to decide whether the newly discovered variant is more or less 'correct', if at all, due to lack of criteria. Ptolemy criticised the 'Egyptian' confines because they appear incoherent, although they seem to 'work' fairly well.

Best regards,

lihin

Hello Lihin
You say

Consequence for astrological practice: use the Chaldean confines, even if they be for simpletons like yours truly. A good journeyman is expected to 'grasp' (comprehend) the tools of his trade. Alas, experts like Regulus Astrology have not yet tested the Chaldean confines but they seem to 'work' reasonably well in practice.

I must say I agree in principle, except that the number of degrees of each confine (and hence the "years", if one gets that far) seem rather too neat and unconvincing in their totals. Does this bother you? Do you find that they "seem to work" with these degree values? Or do you thnk more research needs to be done as to whether there may be another earlier/better distribution of the degrees/years?
Ptolemy's Chaldean totals are : Venus 75 ; Jupiter 72; Mars 69 ; diurnal Saturn or nocturnal Mercury 78 ; nocturnal Saturn or diurnal Mercury 66; Mars 69
If, for example, instead of varying Saturn and Mercury according to sect of chart, we postulate "Saturn 1st in positive signs, Mercury in negative", then Jupiter, Mercury and Saturn all get 72. Venus in any case is the most generous, as in the "Egyptian" system.
Also, the Indian trimsamsa (D30) chart, which probably derives from Greek sources, though suspiciously regular and too far from any logic of the triplicities in its sequence, is worth examining. If, for example, we reverse the sequence of Chaldean rulerships in the negative signs (as the Indian trimsamsa does for its rulerships) and assign the Indian degree values to each segment, (55875 in positive signs, 57855 in the reversed negative ones, i.e. the same but counted backwards), then we get the interesting degree values of : Ju 66 ? Ve 69 ? Me 72 ? Ma 75 ? Sa 78 (counting Saturn always first, i.e. first when counting forwards in positive signs and second when counting backwards in negative ones). The greater benefics thus give the lowest count (years?) and the the greater malefics the highest (in Indian astrology, death as such is often considered a benefic event, though this may be irrelevant here).
Please excuse my musings if this doesn't interest you, but I would like to know if you yourself are happy with Ptolemy's degree/year totals for his Chaldean scheme.
Many thanks
Graham

Good morning,

Thank you, Mr Fox, the the pertinent questions. Aside from Klaudios Ptolomaios Tetrabiblos, Book I, Section 21 quoted below and a broken clay tablet with an incomplete list of 'Babylonian' confines, as far as i know we have little documentary evidence for the Chaldaean confines. The clay tablet apparently gives no values of degrees per confine. Might this perhaps mean that they were 5 subdivisions of equal length, 6 degrees each, like other numerical subdivisions of the signs of equal length?

21. According to the Chaldaeans.

The Chaldaean method 109 involves a sequence, simple, to be sure, and more plausible, though not so self-sufficient with respect to the government of the triangles and the disposition of quantity, so that, nevertheless, one could easily understand them even without a diagram. 110 For in the first triplicity, Aries, Leo, and Sagittarius, which has with them the same division by signs as with the Egyptians, the lord of the triplicity, Jupiter, 111 is the first to receive terms, then the lord of the next triangle, Venus, next the lord of the triangle of Gemini, Saturn, and Mercury, and finally the lord of the remaining triplicity, Mars. In the second triplicity, Taurus, Virgo, and Capricorn, which again has the same division by signs, Venus is first, then Saturn, and again Mercury, after these Mars, and finally Jupiter. this arrangement in general is observed also in the remaining two triplicities.112 Of the two lords of the same triplicity, however, Saturn and Mercury, by day 113 Saturn takes the first place in the order of ownership, by night Mercury. The number assigned to each is also a simple matter. For in order that the number of terms of each planet may be less by one degree than the preceding, to correspond with the descending order in which first place is assigned, they always assign 8? to the first, 7? to the second, 6? to the third, 5? to the fourth, and 4? to the last; thus the 30? of a sign is made up. The sum of the number of degrees thus assigned to Saturn is 78 by day and 66 by night, to Jupiter 72, to Mars 69, to Venus 75, to Mercury 66 by day and 78 by night; the total is 360 degrees.

For his proposal of his own system of confines Ptolemy wrote that he based himself on an old, worn book. He expressed himself with less certainty than wonted. To the best of my rudimentary knowledge the 'greater years of the planets' reflected in the totals of the Egyptian confines per planet lack an astronomical foundation in contrast to the 'lesser years of the planets' that reflect synodic cycles. (We might recall than Monsieur Jean-Baptiste Morin de Villefranche rejected confines altogether for this reason.) Attempts to integrate the confines, based above all on elemental correspondences of the planets, with the 'greater years' have produced until proof of the contrary a solution set with nil members.

The Chaldaean confines listed by Ptolemy reflect his attributes of elemental triangle rulers, excluding the Lights: Fire - Jupiter, Earth - Venus, Air - Saturn (Day), Mercury (Night), Water - Mars.

With reference to Messrs. Geoffrey's and Fox's suggestions, a much simpler (and therefore even more soothing for my feeble mind) version of the Chaldaean confines than that related by Ptolemy might be as follows, consisting of 5 confines per sign, 6 degrees each, same by Day and Night:

Fire signs: Jupiter, Venus, Saturn, Mercury, Mars
Earth signs: Venus, Mercury, Saturn, Mars, Jupiter
Air signs: Saturn, Mercury, Mars, Jupiter, Venus
Water signs: Mars, Jupiter, Venus, Mercury, Saturn

Each planet rules 72 degrees, 1/5 of 360. Thus there is no skewing in favour of the Benefics in contrast to the Egyptian and Ptolemaic systems.

As 'the proof of the pudding is in the eating', one of course would have to rigorously test such a proposal in astrological tools like 'circumambulation of the Ascendant through the confines'. Janus software and perhaps others allow one to define a custom set of confines.

Best regards,

lihin

lihin wrote: As 'the proof of the pudding is in the eating', one of course would have to rigorously test such a proposal in astrological tools like 'circumambulation of the Ascendant through the confines'. Janus software and perhaps others allow one to define a custom set of confines.

I would be grateful if you would expand on the logic of this test in more detail

Thanks

Geoffrey

P.S. On the Babylonian clay tablets, my reading of the paper is that the tablets do allot degrees to each term, but that the state of the tablets are such that the degrees allotted are unreadable. This would infer that there was not an equal division of degrees per term on the tablets.

lihin wrote:
The manuscript Mr Geoffrey has mentioned is a variant of the 'Egyptian' confines.

This statement implies that in your opinion, the terms set out on the Babylonian tablets (dating circa. 400 BCE) are based on an earlier set of terms whose origin is Egypt. Or, that the 'Egyption' table of Terms given by Ptolemy pre-date the Babylonian table of Terms given on the Babylonian tablets. Do you have proof of either?

I quote from the abstract of the ISAW paper I cited earlier: "The system of Terms is shown to be so far the most technically complex component of Greek astrology to originate in Babylonia. Over the course of the Hellenistic period an Egyptian origin was ascribed to the system of Terms as it was combined with components of Greek horoscopic astrology. By Ptolemy's day, this spurious history had largely replaced the true."

Geoffrey

Thank you
I agree that "directing the ascendant through the bounds" (more precisely, treating the ascendant as significator, the bound-limits as promissors, and directing the latter by direct movement to the former) would probably be the best way to test the bound limits. According to Martin Gansten in his excellent book on primary directions, this was the first use made of primary directing. The very good freeware "Morin" offers the possibility of defining custom bounds. Of course, you have to have decided which primary key you trust, and bear in mind that, should you be working sidereally (as Martin prefers), the result will be sensitive to choice of ayanamsa (unlike most work with primaries). "Morin" offers a choice of ayanamsa, but unfortunately does not allow a custom one (or a custom offset from a standard one). This problem can be overcome (for this purpose ONLY) by choosing the nearest pre-defined ayanamsa to what you would like, and slightly "doctoring" the birth time to get the ?'"of ascendant that you would with your desired offset, then generating a table of directions of the terms to that ascendant. For tropicalists, of course, no problems of ayanamsa!
Graham