(Thought this had better have a new thread)

Eddy writes (in thread "Fixed stars and ecliptic"):
"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)."

This is clear, except that, if the "equinoctial time/period" is a unit (generally accepted, as Martin points out to be 1/360th of the circle of 360?) defined at the moment when night and day are equal, why is it not 1/360th of 361? (the circle between passage of sun at zenith, i.e. the earth's rotational period with respect to the sun)? I know the difference is small (at least for the first few decades of life), but I don't understand why the primary keys are all based on the "sidereal day" of 23h56' and not on the true solar one of 24h (which is what we all think of as a day, and would seem to be more analogous to a solar year: noon = summer solstice, etc). (Placidus and Van Dam keys, as far as I can understand, are the only ones which don't use the sidereal day as the basis, their keys are based on the secondary progression on the sun in RA and longitude respectively).

Does anyone have any ideas about this, or can you briefly put me stright if I've misunderstood something incredibly obvious ?

Thanks
Graham

Hi Graham,

A few hours ago I saw this reply in the other thread and I was thinking about a new thread. You must have read my mind .

Graham Fox wrote: but I don't understand why the primary keys are all based on the "sidereal day" of 23h56' and not on the true solar one of 24h (which is what we all think of as a day, and would seem to be more analogous to a solar year: noon = summer solstice, etc).

I have the same feeling too. I don?t really feel comfortable with the sidereal day as a basis. Martin pointed out that Ptolemy and the Medieval astrologers used one degree of the equator as one year making it even more abstract. The original idea then may not have been based upon the formula of the tropical day, 1 : (365.242? * 365.242?) (and 1:265.242? in secondary progressions.) but I would feel more attracted to this. Nor the sidereal day would have been the basis which would have as formula 1: (366.24.. * 366.242?) formula (and 1:366.24? respectively).

To abstract this to a formula we can say that two main types are involved in the discussion. First the progressions are based upon a formula: cycle x = cycle y. In the ?usual? secondary progressions two formulae can be derived from the basis formula: A : C = B : C and A : B = B : C. In which A is MC/Meridian, B is the Sun and C is 0?Aries (or any other point on the zodiac but for ease I use this one and also stick to the tropical zodiac). The first one is based upon the 1 sidereal day = 1 year. The advantage is that there?s a big emphasis on the zodiac, one ?meeting? of Meridian with 0?Aries is again one meeting of the Sun with 0? Aries. The disadvantage in my view is that the sidereal day is not the obvious one. The solar day is visible and plays the most essential role in life. The other formula then takes one ?meeting?of the Meridian with the Sun as one meeting of the Sun with 0?. The symbolism that we find in the Tetrabiblos of the quadrants eastern for youth and western for older age (on marriage IV 5) resembles that of the ages in the zodiac (Tetr. I 10). The same could be done with the lunar phases. In Tetrabiblos I 8 , ?moisture? is attached to the first quarter of the Moon. Moisture was also attached to the spring signs. Another approach could be done taking the tropical lunar month of 27.32? rather referring to the A : C = B : C method. The synodical month of 29.53? is to me the more attractive one because it again is more obvious or natural, because of the visible waxing and waning, than the tropical month.

The second type is more symbolical the traditional directions use 1? Right Ascension = 1 year. Another method is that of the terms with different values. This is also done in Indian astrology where the nakshatras (13?20?) each don?t get 13.333 years but different values. However adding up the numbers gives 120 years for 9 nakshatras and 360 years for 27 nakshatras or the entire zodiac circle. This is a division along the ecliptic. Others use 1? = 1 year also on the ecliptic. I don?t know where this comes from, perhaps it?s a ?modern? usage. The question that rises in my mind is why this should be done, because the 360? circle symbolizes the ?ideal? year but still could be seen as arbitrary. However on the other side one can ask himself why we should be working with the method of proportions of cycle x = cycle y. Sometimes these doubts make me to use only the transits. However If I only use the traditional planets for transits some 'gaps' can be filled with these techniques.

However when I look at the progressions and directions I rather use the (in my eyes most natural) A : B = B : C of one true solar day is one tropical (solar) year. The primary directions then can be found with applying the same formula again. A sort of cycle x = cycle y?. Using this also gives some questions for a philosophical and technical debate but this post is already quite long.

The two ways I would prefer is a simple one using the ecliptic and a bit more complicated one using the equator. Ecliptic: Here the usual radix is used with the planets fixed on the tropical ecliptic. If the time it takes for the MC/Meridian to get its same distance in relation to the Sun (the solar day) is similar to 365.242? years then the distance that the MC/Meridian has travelled to get there is 360? + the distance of the Sun in that period. Throughout the year this varies but it is globally 360? : 365.242? = 0?59?8? (Naibod). 365.242?. : 360?59?8? = 1.01178 would be the key. If the variances according to the different speed of the Sun through the zodiac are taken into account, the key will be a bit different but this won?t be more than a couple of weeks for a 90 year old. I mentioned both the MC and the Meridian and there could also be some discussion on which to be used but the most used is the return of the similar position of Meridian to the Sun as a solar day. This is then equatorially measured In the other thread I theorized that the Placidus users should use the classical ?seasonal hours? based upon the proportions in the diurnal arcs, rather than the ?equinoctial hours?. Yet this would also count for the use of the ecliptic, my beloved plane. However I doubt about my own theory and stick to the equatorial movement. The ecliptic method only uses the movement of MC and Ascendant. It is very simple, just look in a house table for the moments when the angles conjunct and aspect a natal planet, look at the sidereal time that has passed convert this to degrees and finally multiply it by the key.

The other method would be fixing the natal planets to the ?earth? and look at the planets that pass (and aspect) the positions of the positions formerly occupied by the natal planets and the Meridian and Horizon which remain fixed. In my view the most logic system is that of using the Right Ascensions of the planets in relation to the Meridian i.e. the ?hour angle? and not their positions according to the (Ptolemean/Placidian) proportions of the diurnal arcs. The drawback though is that the Horizon plays a less significant role but I don?t mind. Anyway, the key I would apply in this case is taking the return of the Sun in the Meridian (or in the same angle to it) as 365.242? years. This return is 360? because the Meridian now is fixed and not moving through the ecliptic which now has gone out of sight. The key then would be 365.242? : 360 = 1.01456?.. The Moon and each planet have different motions. The Moon would need another ca. 12? to get to the Meridian and therefore the key of the Moon would be ca. 365.242?. : 348? = ca. 1.05. A slow planet?s key would be less than the Sun?s and a retrograde planet the slowest, For example a key of 1.009?. is possible.

.... or can you briefly put me stright if ...

I'm sorry but I don't manage to write things briefly , however I hope it's still readable.

Hi Graham and Eddy

Graham, I share your question marks regarding the siderial rotation period of 23 h 56 min 4,09 s. It makes more sense to me to take the time between two culminations of the sun and put it in relation to a revolution period as a basis of a primary direction key.
My favourite is the old Babylonian key of 4 min (clock time) = 1 year. This would actually be a ?Primary Progression? key including the motion of the moon and planets. It comes very close to Ptolemy?s key of 1? (RA) = 1 year, at least for the slow planets. The difference is only 1 year in 360 years or about 3 months in 100 years.

Eddy, I am not sure if accurate calculations are a real help. The rotation of the earth is not constant, it is slowing down. Since Babylonian times (700 BC) this slowdown has accumulated to about 5-6 hours. Going further, 4 billion years ago a day had about 14 hours and 300 million years ago it had about twenty hours (assuming a constant revolution).
So the time is not very far when a year will have exactly 360 days. Maybe this will be the ideal world or the end of it, if resonance makes things fly apart. My feeling is that nature is anticipating an ideal year with 360 days, so Ptolemy seemed to have a good intuition.

Ren?

3D wrote:My favourite is the old Babylonian key of 4 min (clock time) = 1 year.

Did the old Babylonians have clocks? Where does this come from?

This would actually be a ?Primary Progression? key including the motion of the moon and planets.

As this is the traditional forum, I just want to point out that this distiction between directions and progressions is wholly modern. Placidus, for instance, called his auxiliary technique 'secondary directions'. (He also had a third technique which he did call 'progressions', and which was similar to what Troinski, some 300 years later, called 'tertiary directions'.)

Hi Martin,

I am aware of the traditional term ?directions? used by Placidus. He never mentioned progressions(wrong; he never called secondary diretions 'progressions'; sorry for my english). I should have added that ?primary or secondary progression? is only used by our astrology circle here to distinguish between shifting time (progressions, 1 day= 1 year, 4 min = 1 year etc.) or shifting a whole sphere (primary directions) or an arc on the ecliptic (solar arc directions). I will add the traditional term next time to avoid misunderstandings.

Did the old Babylonians have clocks? Where does this come from?

They must have used hour glasses. As far as I know they measured minutes and even seconds. And 4 min are exactly 1/360th of a solar day.
This is from Rumen Kolev?s Babylonian Astrology Software ?SUMER?. I take it that it?s not his own invention? .(?)

Ren?

3D wrote:Eddy, I am not sure if accurate calculations are a real help. The rotation of the earth is not constant, it is slowing down. Since Babylonian times (700 BC) this slowdown has accumulated to about 5-6 hours. Going further, 4 billion years ago a day had about 14 hours and 300 million years ago it had about twenty hours (assuming a constant revolution).
So the time is not very far when a year will have exactly 360 days. Maybe this will be the ideal world or the end of it, if resonance makes things fly apart. My feeling is that nature is anticipating an ideal year with 360 days, so Ptolemy seemed to have a good intuition.

Ren?

It will at least take a 50 to 100 million years. I'm not that patient enough for the ideal world to come . The 'ideal year' of 360 days is obviously derived from the 12 lunar months and paved the path for the zodiac signs and the houses. Even though I prefer to base the key on 365.242.. perhaps this 360 key is of some worth. I must admit that sometimes I look at the 1?=1 year method measured along the ecliptic. It requires no lengthy calculations and can give some results at a quick glance. Often I torture my brain with thinking difficultly so perhaps that is why I sometimes feel attracted to this simplest method.

Martin Gansten wrote:As this is the traditional forum, I just want to point out that this distiction between directions and progressions is wholly modern.

There seems to be so much different terminology that I rather describe in a short way what I do and don't give it a name or perhaps in a formulized way as in my other post.

Quote:
Did the old Babylonians have clocks? Where does this come from?


They must have used hour glasses. As far as I know they measured minutes and even seconds. And 4 min are exactly 1/360th of a solar day.
This is from Rumen Kolev?s Babylonian Astrology Software ?SUMER?. I take it that it?s not his own invention? .(?)

As far as I know, the Babylonians used water clocks. I believe most of their measuring (either space or time) still was somewhat crude. The did have a very good estimation of the length of the lunar month and several other phemomenae but this was rather because of the large number of recorded observations rather than exact observation. Much was based upon counting days between repeating phenomenae. For example the number of months between lunar eclipses was counted and the number of days was devided by this number with as result quite exact length of the mean month. It is possible that the Bablyonians used the minutes as time measurement but I don't know if they used it for directions.

I wonder where Rumen Kolev got his sources from. I am a bit careful when people say that things come from Egyptian, Indian or Babylonian sources. Most what is called 'Egyptian' and 'Babylonian' (or rather 'Chaldean') is from several centuries from the period of Hellenization after Alexander the Great. The first mentioning of the ascendant as a mathematical point is from 4 BC. (I believe that this is mentioned in Michael Baigent's From the Omens of Babylon). For doing directions according to the classical methods I believe it would be necessary to be able to calculate this.

I don?t know what Kolev?s sources are but I think that astrologers have been far too easily persuaded that all the important developments were made by the Greeks and Hellenistic astrologers. We tend to forget that the main claim to fame of the Babylonian civilization was their brilliance in mathematics. Most of the major astronomical advances that needed to be made to facilitate astrological development were already in place by the time that Alexander conquered Babylon. The Greek conquest opened that knowledge to the west, and brought a synthesis with Egyptian techniques and that facilitated new developments, but in the main the ancient cultures seemed to be doing quite well by themselves . For example, Oppenheim, in his Ancient Mesopotamia, tells us that astronomical knowledge had already become quite reliable and detailed, with planetary ephemerides listing full and new Moons for up to two years, and eclipses for more than fifty years. They had already developed and integrated the zodiac and had tables listing lunar velocity, daily solar and lunar motions and planetary positions. (p.309) Rochberg also tells us that the information was already then being recorded by reference to mathematically derived calendar days rather than those of the lunar month.

Remember also, that many of the predictive techniques described by the likes of Ptolemy and Valens are ascribed to their ?ancients?. The Hellenistic texts themselves make frequent acknowledgement to the knowledge recorded by the Egyptians and Babylonians, so I don?t understand why their influence is so easily underestimated. It is true (at least as far as I?m aware without checking) that the first verified reference to the use of the ascendant is 4BC. But the suggestion that the ascendant was not used until 4BC is the wrong way to use the evidence ? all this proves is that the ascendant was definitely being recorded in that year or sometime before then. Personally, given the massive focus of attention that the Babylonians gave to astronomical events that occurred around the horizon, and the need that ancient cultures like the Mesopotamians and Egyptians had to monitor the stars as they rose and set over the horizon ? it was the basis of their timekeeping ? I simply cannot believe that the principle of the ascendant did not go hand-in-hand with the astronomical use of the ecliptic, and that there is much better evidence still awaiting our discovery.

3D wrote:I am aware of the traditional term ?directions? used by Placidus. He never mentioned progressions.

As I mentioned in my previous post, he did use the term progressions to refer to the supplementary technique of 'a synodic month for a year', which was used by followers of Placidus until the 19th century.

This is from Rumen Kolev?s Babylonian Astrology Software ?SUMER?. I take it that it?s not his own invention? .(?)

I couldn't say; I know too little of the Babylonian material. But just as there is quite a lot of Placidus in post-1600 'Ptolemaic astrology', and quite a lot of Schmidt in modern 'Hellenistic astrology', I find it very easy to imagine that there is a fair amount of Kolev in his 'Babylonian astrology'.

Hello all
Thanks for Deb's reminder about the importance of the Babylonian heritage and the risk of over-emphasising or exaggerating the Greek one which has tended to eclipse its roots.

Eddy: I agree with your reasoning about the solar day, and the various a:b=b:c etc ratios you give, but I don't follow when you say

Anyway, the key I would apply in this case is taking the return of the Sun in the Meridian (or in the same angle to it) as 365.242? years. This return is 360? because the Meridian now is fixed and not moving through the ecliptic which now has gone out of sight. The key then would be 365.242? : 360 = 1.01456?

That key is simply Naibod, based on the sidereal ("rotation with respect to VP") year. To make it inot a key WRT the solar year, we have to multiply it by 360/361 = a key of 1.01175122 yrs =1?. The difference in results is of course small, about 1 month per 25 yrs of life.

I'm surprised that Martin is rather scathing about the idea of a key of 4 minutes = 1 year. It's just a simpler way of saying 1/360th of 1 solar day= 1 solar year, and the return of sun to the meridian would have been relatively easy for the "ancients" to measure. It's simpler than saying 1/360 x 361 sidereal degrees = 1yr, but it's the same thing, unless I'm getting muddled again. To use this 4'=1yr key with e.g; Kolev's program, I calculate that you have to create a custom key of "1?=0.99723 yrs". (Difference to results: about 1 month per 25 yrs).

In any case, it's important to remember that when we talk about "rotation", it has to be rotation with respect to something else considered as (relatively) fixed. Some examples of references for rotational periods used in used in astronomy and astrology, in descending order of relative fixity, are:
- the galactic equator (very fixed indeed, but doubtless not completely so)
- the "fixed" stars (some more fixed than others, but none completely so)
- the vernal point and derived degree points on ecliptic
- the sun
- the moon

I shouldn't argue with Robbins, but I don't see how we can be so sure Ptolemy's equinoctial "period" (or "time" : these are the usual translations) don't refer to 4 minutes (1/360th of earth's rotation WRT the sun) rather than to 1 sidereal degree (1/360th of earth's rotation WRT the vernal point).

The usual keys based on "1?" (e.g. in Kolev's program) refer to 1/360th of a circle based on the vernal point - but that's not the only option. We could try out a key based, for example, on 1/360th of a mean tidal lunar day (return of the moon the meridian) = 360 MTLD, which would be a key of 1? (of sidereal circle) =0.98306 (solar) yrs.

It's really interesting playing around with the different "years" and multiples of 360. For example, I've noticed that the mean value of 360 mean tidal lunar days and 360 sidereal days is 365.8 solar days. So a solar year is a sort of compromise between a "year" of 360 sidereal days and one of 360 MTL days. I think this is what mathematicians mean by reciprocals, which apprently were very important in Babylonian base-60 mathematics.

Graham

Graham Fox wrote:I'm surprised that Martin is rather scathing about the idea of a key of 4 minutes = 1 year.

I apologize if I came across as scathing. I was just mildly amused by the 'clock time' comment, as well as curious about the source of that Babylonian key.

(Difference to results: about 1 month per 25 yrs).

I think we should note that this difference would have seemed wholly immaterial to astrologers from the beginnings of primary directions up to the 19th century. Despite occasional enthusiastic claims to the contrary, primary directions were never meant to time single events to the day or even to the month. From Ptolemy to Lilly and beyond, astrologers have always used supplementary techniques (profections, transits, revolutions, etc) for more precise timing. I have seen profections in particular perform very impressively when combined with directions.

Oh, I forgot the picture??..

Martin
I absolutely agree that absolute accuracy is not going to be achieved. I was suggesting more that, since we're always going to be a bit approximate anyway, lets not compound it. Also, good to keep things simple: if you're using a program like Kolev's, 1? = 1yr is the easiest. If you're looking at when something sets or culminates in real life or with an astronomy animation (with secondary motion built in, to boot), 4 minutes = 1yr is easier than 3.9891 minutes.

I was told by my teacher Denis Labour? that the early astrologers used primaries to define the beginning of a period (rather than a point in time) which lasted until the next major direction of the same type (I didn't study them in detail with him, so not sure what is considered as "same type": maybe he was talking just about conjucntions to the angles). Do you agree with this? If so, we should in fact notice if our periods start systematically a couple of months early in later life.

Anyway, for the time being I still find Naibod (1? sidereal=1.01456 yrs, or 4.0582' of time =1yr)) seems to work best, though I'm now uncertain of its rationale. Perhaps one way of thinking of it is as working from a base of 1/360th of a solar year (1.01456 days = "A"). So 1/360th of A is taken to represent 360 x A. I previously thought Naibod was a way of getting away of from the arbitrary/ideal 360, but not at all.

Graham