49 by Ed F Martin Gansten wrote:Ed F wrote:...Ptolemy's method was used by generations of astrologers who simultaneously employed whole-sign houses, equal houses, Porphyry houses and/or Alcabitius houses as their 'domification model'. The idea that house system and method of directions should be somehow related was apparently alien to them... OK, I understand our different uses of the terms here. - Ed Quote Thu Mar 05, 2009 6:31 pm
50 by Martin Gansten Eddy wrote:If Ptolemy used the proportions of semi arcs for the primary directions and derived it from the seasonal hours which apparantly were common usage in Mediterranean (civil) life in his days then these (I reasoned) rather than the equinoctial hours should have been used in the directions. The formula should then have been 4 (seasonal time) minutes (based upon the position (declination) of the Sun in the first hours after birth, equals one year. But the basic idea isn't 'four minutes of time equal a year', but rather 'one degree in the turning of the celestial sphere equals a year'. And the celestial sphere turns (or, in the modern understanding, the earth turns on its axis) at a constant speed, completing 360? in 23h 56m of clock time. Quote Thu Mar 05, 2009 6:45 pm
51 by Olivia I think the ancients and medieval authors had a good grasp, too. The maths are mind-bending, and in that text Schoener just breezes through them as he gets to different techniques for all sorts of calculations and then gives you the fomulas so you can do them too (after you've read it about 20 times, tried pencil and paper, tried the calculator, and finally had a sort of 'a-ha' moment). Even then it's dicey, and I'm not bad at maths. If you read Ibn Ezra, you'll find that in certain places he gives you a formula, and then says if that's too difficult for you to work out, you can do it this other way, gives you a different formula, and that'll get you to the same results. And it does. Not stupid people. At all. Quote Fri Mar 06, 2009 3:50 am
52 by Eddy Martin Gansten wrote:But the basic idea isn't 'four minutes of time equal a year', but rather 'one degree in the turning of the celestial sphere equals a year'. And the celestial sphere turns (or, in the modern understanding, the earth turns on its axis) at a constant speed, completing 360? in 23h 56m of clock time.This is an interesting detail even though I personally would prefer as basis the true solar day. Note that the sidereal day isn't constant either but because of the effect of nutation it is slightly different. However this effect is so small that the difference in time couldn't be measured with the clocks until the 19th century. Bradley had discovered the nutation in declination in the 18th century. This difference between 'mean sidereal time' and 'apparent sidereal time' is of barely any significance in practice, about less than a second. Quote Fri Mar 06, 2009 11:23 am
53 by Martin Gansten Eddy wrote:This is an interesting detail even though I personally would prefer as basis the true solar day. Hardly a detail, surely? Note that the sidereal day isn't constant either My psychic powers must be up: I knew you'd say that! But (as you also say) this minute difference is not relevant for our purposes. Quote Fri Mar 06, 2009 1:52 pm
54 by Eddy Martin Gansten wrote:Eddy wrote:This is an interesting detail even though I personally would prefer as basis the true solar day. Hardly a detail, surely? Hmm... rather a cornerstone . Can you tell me if Ptolemy had the sidereal time in mind or rather the degree? If it is the time I wonder why the secondary progressions then never would have been used in his days. After all when the basis is considered 4 sidereal minutes (which in fact is the same as 1 equatorial degree) = 1 year, then I can imagine that they also would have thought about 4 sidereal minutes (or 1 equatorial degree) = 1 day. I always had these time proportions in mind and therefore it always has baffled me that the secondary progressions only were used from the 16th/17th century. On the other hand if it originally was intended a pure space basis 1 degree = 1 year then I can understand the criticism of Pico, Gassendi etc (according to Jim Tester's book) who considered this as rather arbitrary. "Why not 2? per year?": one could say. If this is the case then I have a sort of theory that in the centuries before Ptolemy the astrologers worked with forerunners of Chronocrators and Ferdariae assigning years to the signs. For example many years to Capricorn Aquarius (because of Saturn) and few to Cancer (Moon), perhaps referring to the planet ages (Moon=4years, Mercury=10y....etc.). Then came a first 'scientification' based upon rising times per sign which finally were refined by Ptolemy. I could be totally wrong but perhaps the primary directions were derived from this and therefore the secondary directions came later. Quote: Note that the sidereal day isn't constant either My psychic powers must be up: I knew you'd say that! But (as you also say) this minute difference is not relevant for our purposes. I often can keep my mind busy for hours by thinking over these differences, building theories upon it etc. Quote Fri Mar 06, 2009 4:38 pm
55 by Martin Gansten Eddy wrote:Can you tell me if Ptolemy had the sidereal time in mind or rather the degree? Here is Robbins's translation (p. 289): [...] calculate after how many equinoctial periods* the place of the following body or aspect comes to the place of the one preceding at the actual time of birth, because the equinoctial periods pass evenly through both the horizon and the mid-heaven, to both of which are referred the proportions of spatial distances, and, as is reasonable, each one of the periods has the value of one solar year. The word translated as 'period' is ?????? chronos. Robbins adds in a footnote: 'An "equinoctial period" or "time" is the length of time which is takes one degree on the equator to pass a fixed point, i.e. 1/360 of 24 hours.' I can understand the criticism of Pico, Gassendi etc (according to Jim Tester's book) who considered this as rather arbitrary. Well, what part of astrology would be immune to that sort of criticism, if viewed with an unsympathetic mindset? If this is the case then I have a sort of theory [...] I could be totally wrong but perhaps the primary directions were derived from this and therefore the secondary directions came later. Simple directions by rising times (noting the motion of degrees and terms over the ascendant) seem to be one of the oldest techniques there are. And as I have mentioned before, I believe there is reason to suppose that Balbillus (and perhaps Thrasyllus before him) directed by a method quite similar to Ptolemy's (I plan to write something on this). So I don't think your theory is borne out by the evidence. And I can't see what is so compelling about secondary directions, or how they would follow naturally from Real Directions (if you will pardon the Frawleyism). Quote Fri Mar 06, 2009 9:33 pm
56 by Graham F Hello Martin You write: Robbins adds in a footnote: 'An "equinoctial period" or "time" is the length of time which is takes one degree on the equator to pass a fixed point, i.e. 1/360 of 24 hours.' This is the classic "1? = 1 year" key. Do you think Robbins had a solid justification for his assertion that this is what an "equinoctial period" was for Ptolemy, or for the tradition which Ptolemy drew on? It's hard of course to decide which key works best in practice, but in theory the 1/360th of a circle = 1yr seems rather arbitrary, whereas the Naibod or "Kepler/Brahe" keys (the distance represented by the mean or true apparent solar movement in a day = 1 year) seem more satisfying (especially, I'd have thought, the true rate, as it embodies an observable or measurable instance of the 1 day = 1 year axiom). What's your view about this? (I'm talking more in theory than in practice - I think you told me that empirically you tend to favour 1? = 1yr, or sometimes Naibod, but not the true solar rate). Graham Quote Sat Mar 07, 2009 12:44 am
57 by Eddy Martin Gansten wrote:The word translated as 'period' is ?????? chronos. Robbins adds in a footnote: 'An "equinoctial period" or "time" is the length of time which is takes one degree on the equator to pass a fixed point, i.e. 1/360 of 24 hours.'So it was 1?=1 year. Like Graham I would feel more comfortable with 1/365.25th of a day (either sidereal or (true) solar (which I would prefer)) as one year. And I can't see what is so compelling about secondary directions, or how they would follow naturally from Real Directions (if you will pardon the Frawleyism). I think I simply like to systematize. This wouldn't make me different from the Greeks, would it ? Quote Sat Mar 07, 2009 9:56 am
58 by Martin Gansten Graham Fox wrote:This is the classic "1? = 1 year" key. Do you think Robbins had a solid justification for his assertion that this is what an "equinoctial period" was for Ptolemy, or for the tradition which Ptolemy drew on? Yes, I do (though Robbins simplifies a bit with his '24 hours' statement). To the best of my knowledge, the so-called Naibod measure, though antedating Naibod, is absent from Hellenistic sources. Quote Sat Mar 07, 2009 11:38 am
59 by Graham F Martin You write "Yes I do". I presumed so, but I really wanted to know why you do. I know there's no hard evidence that 1/365.24th of a year (or the true daily equivalent ) was used until later, but does Ptolemy specify elsewhere that he really means 1/360th of the earth's daily rotation = 1 solar year? Or did someone else specify it before Prolemy? If not, how does Robbins know Ptolemy's thinking of the "ideal" figure of 360? This in effect means we're saying that the full circle = 360 years. Why 360? Using true or mean solar rate (Naibod, Kepler/Brahe or even Placidus keys) would mean "a day's worth apparent movement of the sun = a year's worth apparent movement of the sun", with no need to use ideal (arbitrary?) figures like 360. It's attractive, so I wondered how we can be sure enough to exclude that possibility. Also, maybe my thinking's fuzzy, but I don't like the sleight of hand involved in drawing a correpondence, as Robbins says Ptolemy did, between fraction of a sidereal day on the one hand and a tropical solar year on the other - it would seem to be mixing two systems without really acknowledging it. (I realise the difference between a sidereal solar and a tropical solar year is negligeable, about 20 minutes per year, but that between a sidereal day and and a solar day is not - average about 4 minutes per day, adding up to 366.24 sidereal days per solar year). Thanks for any clues as to why you're sure Robbins is right. Graham Quote Sat Mar 07, 2009 3:05 pm
60 by Eddy In this book on Google "Ptolemy's Geography" http://books.google.nl/books?id=65i-ETq ... aphy&hl=en I can't find any distinguishment made by Ptolemy between the sidereal day and the solar day. The "seasonal hours" are the most apparent when the Sun is involved. For example (from an example I calculated in another thread, more technical details in http://skyscript.co.uk/forums/viewtopic ... c&start=30) the semiarc of 0? Gemini at the latitude of Alexandria is 205.29 degrees or equinoctial times. If this is found in original tables of Ptolemy (Almagest) then this will mean that for these hours the motion of the Sun isn't taken into account. The true solar day would then be a bit more than half an equinoctial time longer i.e. 205.80 ? 205.90 eq.times approximately If this is done, then the two types of day seem to be mixed. ...but I don't like the sleight of hand involved in drawing a correpondence, as Robbins says Ptolemy did, between fraction of a sidereal day on the one hand and a tropical solar year on the other - it would seem to be mixing two systems without really acknowledging it. (I realise the difference between a sidereal solar and a tropical solar year is negligeable, about 20 minutes per year, but that between a sidereal day and and a solar day is not - average about 4 minutes per day, adding up to 366.24 sidereal days per solar year). I'm not sure if there's some confusion on this point but just to leave no doubt (to other readers) I'd like to illustrate that the astronomers' use of the term 'sidereal day' is somewhat misleading and in fact has nothing to do with the 'sidereal year' as opposed to the 'tropical year'. In astronomy the 'sidereal day' is the time it takes for 0?Aries to return to the meridian. The time it takes for a fixed star to return to the meridian is usually noted as the 'rotation period' of the Earth. Perhaps the astronomers should have called it the 'equinoctial day' instead of choosing the unfortunate term 'sidereal day'. The 'true solar day' is the time the Sun takes to return to the meridian (this is what we would see using a sundial). Nowadays for civil purposes the 'mean solar day' is used because the true solar day is irregular in respect to our mechanical clocks. Quote Sat Mar 07, 2009 4:10 pm