A fractal model of progressions - Introduction

[Jim Eshelman]

Jun 08, 2014

I propose to set out a model of progressions that unifies most of the accepted progression systems, namely Primaries, Secondary Q1 and Q2, Tertiary and Minor (or Quarternary), under one conceptual model.

Once this model is laid out in its basics, it becomes infinitely extendable in a fractal manner. It is likely that most of the results have minimal utility, however, to be determined by examination. It is likely that a “sweet spot” of some small but well-selected set of progressions provides the greatest utility without overtaxing the astrologer’s time and attention (and may already have been found).

[Jim Eshelman]

The basic units of the model consist of the day, the month and the year. Progressions are formed by mapping one unit of time to another unit of time of lesser duration, each in turn. This definition, we shall see, is not the whole story, but it will do for now.

The three equivalencies taken as basic and their names are as follows:

Secondary Progressions: 1 Year = 1 Day
Tertiary Progressions: 1 Month = 1 Day
Minor Progressions: 1 Year = 1 Month

In the next section, I will specify which year, month and day are meant. For starters, it is enough to grasp these concepts.

[Jim Eshelman]

At the outset, it's important to discuss the reasons why certain definitions of year, month and day will be considered and not others.

All cycles are based on recurring conjunctions of one point with another point. The conjunction of the local longitude with the Sun, the Sun with the Vernal Equinox, the Moon with its North Node, Mars with Jupiter, and so on into infinity, can be taken as cycles to be considered in astrology.

In this presentation, I take progressions to start with the most basic motions of the Earth system in relation to sidereal space. Thus a day is successive conjunctions of the meridian with a point in sidereal space, not with the Sun (or Moon!). A year is successive conjunctions of the Sun with a point in sidereal space, not the moving Vernal Equinox which has a different, strictly Earth-based set of rules for its existence. A month is successive conjunctions of the Moon with a point in sidereal space, not some other moving point, such as its perihelion, or its node, or Venus, or Ceres. This is not to say that such cycles can't be valuable somehow, but they cannot be considered fundamental.

[Jim Eshelman]

There are three kinds of days open to consideration:

1) The Civil Day (CD), which is the ordinary clock time we all use in the normal course of living. It is the average of the conjunction of the Sun with a fixed meridian.

2) The Sidereal Day (SD). This is defined by the Vernal Equinoctial Point crossing the Midheaven. Strictly speaking, this is a misnomer, since the equinox precesses and is not truly “sidereal.” Early Siderealist works by Cyril Fagan and Carl W. Stahl called Sidereal Time “Equinoctial Time.” While technically correct, it created peculiar terminology at odds with accepted and standard usage. One SD = 23h 56m 4.0905s CD.

3) The true “sidereal day” - that is, Sidereal Time expunged of precession – is called the Inertial Day (ID). It is 23h 56m 4.0989s CD.
(ref. http://www.kayelaby.npl.co.uk/general_p ... 2_7_2.html)

I will use 3) Inertial Day. Using the Sidereal Day instead, however, will cause negligible differences in some usages.

[Jim Eshelman]

Three sorts of years are available to consider:

1) The Tropical Year (TY) of 365d 5h 48m 45.5s. This is the average value, and it gradually changes by a small amount over time. It is based on the Sun's conjunction with the Vernal Equinox.

2) The Anomalistic Year of 365d 6h 13m 52.6s (on average, subject to change over time). The Sun's conjunction with the Earth's perihelion is its basis.

3) The Sidereal Year (SY) of 365d 6h 9m 9.5s. This, too, is an average and subject to long-term change.

I will adopt 3) Sidereal Year as the value to use.

[Jim Eshelman]

The Moon's motion is very complex. Astronomers have defined many “months” depending on what they intend to measure, and all values necessarily have “mean” or averaged lengths. There is the Synodic Month, the Moon in relation to the Sun; the Anomalistic Month, in relation to its perigee; and the Draconic Month, in relation to its nodes. I will not use them here.

This leaves:

1) The Tropical Month (TM) of 27d 7h 43m 4.7s (average).
2) The Sidereal Month (SM) of 27d 7h 43m 11.5s (average).

I adopt 2) Sidereal Month as the preferred choice in this model of progressions.

[Jim Eshelman]

While the Earth's rotation about its axis is very steady, the orbits of the Earth around the Sun, and the Moon around the Earth, are elliptical. Their rate of motion can change measurably. Whether one should use the mean or true motions of the Sun or Moon when calculating progressions still seems unresolved to everyone's satisfaction.

For the purposes of this presentation, I will use mean motions. This is to make the calculations simpler without getting bogged down in adjustments. It is not an endorsement of mean motion over true. Anyone interested enough to pursue this model further is encouraged to take the extra steps of making comparisons of one versus the other.

To state this another way: Does the Earth's rotation drive the progression, or does the Earth's revolution drive progressed rotation? In the case of Minor Progressions, what would determine the actual rate, the Sun or the Moon? I have no answers, but I hope this model will provide a better tool as the point of departure.

[Jim Eshelman]

I find this interesting. I worry that you are adopting definitions that will lead to theoretical conclusions that run contrary to what can be observed actually working, but I also realize we aren't yet at the end.

I do find it hard to follow, coming in a day later and reading something that depends on remembering all the definitions before it. Fortunately I know the material, so I can fill in the blanks. My saying this isn't a complaint, because there is also value in this patient pace. I'm probably just yammering, in fact <g>. I do find your process interesting.

[Jim Eshelman]

I worry that you are adopting definitions that will lead to theoretical conclusions that run contrary to what can be observed actually working, but I also realize we aren't yet at the end.

Thanks for for the kind words, Mr. E., even your reservations. Yes, there is more to come!

I want to emphasize that this is a model, not a claim of accuracy or a discovery that I have actually found "The Truth." At best, I hope to provide something that will introduce better computational rigor for astrologers; at worst, a foil for something better.

I do find it hard to follow, coming in a day later and reading something that depends on remembering all the definitions before it. ... there is also value in this patient pace.

I decided on this format because I figure it's better than dumping a long treatise all at once. Also, , I'm still writing it! I've been hinting at this over the years in various places on the Forum, and I decided it's past time for me to put it all out. By writing it in discrete pieces like this, it's psychologically easier for me to elaborate on each one coherently. And, for those who don't already know the material, I figured this piecemeal approach would be better for absorbing the material.

Your patience is appreciated.

-Derek

[Jim Eshelman]

Jun 15, 2014

We can now refine the series of equations in 1. THE BASIC MODEL to read this way:

Secondary Progressions: 1 Sidereal Year = 1 Inertial Day
Tertiary Progressions: 1 Sidereal Month = 1 Inertial Day
Minor Progressions: 1 Sidereal Year = 1 Sidereal Month

We can substitute values (changing their forms to decimals of the Civil Day):

Secondary Progressions: 365.256360 CD = 0.9972697 CD
Tertiary Progressions: 27.321661 CD = 0.9972697 CD
Minor Progressions: 365.256360 CD = 27.3216609 CD

If you want to use an astrological program to define custom progressions, the ratios to use are:

Secondary Progressions: 0.00273032809
Tertiary Progressions: 0.03650106428
Minor Progressions: 0.07480132826

[Jim Eshelman]

[In response to several brief back-and-forth posts.]

My theory starts with the idea that there are only progressions in astrology - that transits, for example, are progressions in the form of "1 day = 1 day." That gives us fewer variations to think about, and gets us away from the idea that transits are "more real" because something is "actually out there." (I don't think something "actually out there" is doing anything to us.)

So, the question then becomes more or less: Given that each individual moment interacts with us differently, when does the flow of moments (the progress of time) seem to flow simultaneously at variable rates.

The various flows are probably then related to some variety of "equivalency," in the nonphysical world where astrology operates, between different time periods, e.g., a sidereal year and a civil day being analogous or variations on a single time-cycle theme.

Or something like that.

(Stating the next part slightly obscurely. You'll get it, but it won't necessarily give away anyplace you were intending to go, even if it's in the same ballpark.) My theory of priority of type of time cycle is based on a layering, remembering that (1) the year is based on Earth's motion, not that of the Sun, and (2) our Moon isn't entirely a satellite, but much more of a twin-planet with satellite-like characteristics - both Earth and Moon rotate around a barycenter about a thousand miles below Earth's surface. A year is then Earth's revolution, sighting Sun against the next framework which is celestial; a month is primarily sidereal also because Moon's orbit is primarily the same as Earth's orbit but, secondarily, to the extent Moon is a satellite, it's "next up" layer is the Sun, giving the synodic a secondary ranking; and the day, being rotational, is measured against the "next up" reference layer, which is solar position. This gives weight to the sidereal year, the sidereal month (and secondarily the synodic month), and the civil day (mean solar day).

[Jim Eshelman]

Your "1 day = 1 day" equation is very compatible with the system I'm presenting.

For every astrologer reading this, please note this important fact: Mr. E is stating, essentially, that not all time is the same. There are many physical equations that ignore time. They are just as valid forward as backward. The general scientific thinking is that essentially all time is the same. Astrology challenges this idea. Astrology could not work if that were true. Time is meaningful, or maybe, has meaning in it.

I think this sort of dialogue is very constructive. Thank you, Mr. E.

-Derek

[Jim Eshelman]

Jun 16, 2014

We must note certain features of the results so far.

1) The version of Secondaries here is the Q1.

2) This version of Tertiaries has the angles making one full circuit in ≈27.3 days. In contrast, Donald Bradley's article about Tertiaries (American Astrology Magazine, Feb. 1970, “Give Tertiaries a Try!”) follows the original path laid down by E.H. Troinski, originator of Tertiaries, and Edward Lyndoe (Astrology for Everyone), where the Sidereal Time progresses about 13° per year and 360° in approximately 27 years.

In the next series of posts, I will derive 1) Primary Progressions, 2) the Q2 quotidian, and 3) the 13°+ motion of the “Tertiary” Midheaven.

[Jim Eshelman]

Jun 17, 2014

It is now necessary to become even more precise how we say things in the equations set forth in section 7. REFINED TERMINOLOGY.

Since we have mapped real time units onto progressed time units, it is correct to state the equivalencies this way:

1 Sidereal Year ~ 1 Progressed Inertial Day
1 Sidereal Month ~ 1 Progressed Inertial Day
1 Sidereal Year ~ 1 Progressed Sidereal Month

(I am using the “~” sign instead of “=” to signify “similarity” as is done in geometry.
Ref. http://www.rapidtables.com/math/symbols ... ymbols.htm
This is because, strictly speaking, the values are not “equal” but are considered similar in a proportionate manner.)

This change is necessary because it is, after all, correct terminology; also, I now introduce a new idea: A progression can itself be mapped onto yet another progression. So far, we have been dealing with First Order progressions (real time onto progressed time), and now we will venture into the area of Second Order progressions. In other words, I posit that there are progressions of progressions. Hence the use of fractal as a series of self-similar values at different scales.

[Jim Eshelman]

what does this have to do with Fractals.

With today's post (6/17/2014), I am proposing that progressions represent time as fractals. Mr. E., in our exchange earlier, did us all a favor by explicitly stating what I was content to leave assumed:

1 Real Day ~ 1 Real Day
1 Real Month ~ 1 Real Month
1 Real Year ~ 1 Real Year

While these time measures are all equal to each other as they stand, (let's call them "Zeroth-Order Progressions") it's when we start using the First-Order Progressions that things get interesting. Thus, the Q1, Tertiary, and the Minor Progressions are already fractalated (is that a word?) time. We might not think of it that way, until we reach Second-Order progressions where it becomes obvious.

I'm hoping this model can provoke insights into and development of progressions and astrology. Their utility remains to be seen.

-Derek

[Jim Eshelman]

Jun 18, 2014

THESIS

Primaries: 1 Secondary Sidereal Year ~ 1 Primary Inertial Day


ARGUMENT

It may be easier to understand the derivation of Primary Progressions by using a historical chart.

The Campion database in Solar Fire gives the beginning of the Holy Roman Empire as Dec. 25, 800 CE (Julian), 05:10:04 GMT, (06:00:07 LMT), Rome Italy. (I am not endorsing the date and time; it is simply useful.) The Sun's Sidereal longitude was Capricorn 0°10'19”. The Midheaven is Libra 0°18', ST 12:30:45.

The subsequent SSR took place Dec. 25, 801 CE Julian, 12:13:12 LMT. The difference between the two is 365.2591 Civil Days.

Let's pause here and think things through. Since:

1 Sidereal Year ~ 1 Progressed Inertial Day

we may say:

1 Secondary Progressed Sidereal Year ~ 1 Inertial Day in some new Progression.

Take, then, the natus of the Holy Roman Empire, and move forward in historical time. Each Real Sidereal Year is matched to one Secondary Progressed Inertial Day, so that we can expect that about 365 years and three months later (we'll use March 29, 1166 CE), the Empire would have its first Solar Return by Secondary Progression.

At this point, it's important to understand what we expect to see. As of March 29, 1166, the Empire’s progressed MC (by the presumed new progression) returned to Libra 0°18' in the Sidereal Zodiac; in the meantime precession altered its Right Ascension since 800 CE. In 1166 this was 12:49:20, an increase of 00:18:35, or about 4°39'. We must take this into account.

While in 365.2591 years the MC returned to its original sidereal longitude, the increase in Right Ascension is really 360° + 4.6458°.

Dividing 364.6458° by 365.2591 years we get a yearly rate of 0°59'54” RAMC or 3m 59.6s. This is very close to the Ptolemaic progression rate of exactly 1° per year. The practice in Sidereal astrology is to expunge accrued precession. Having calculated the new MC, correct as usual with the SVP of date.

From case to case, this value will vary only slightly depending on the declination of the MC. A test using MC of Capricorn 0°18' for the same dates shows a total rotation in RAMC of 365.4542°, and a yearly progression rate of 1°0'2” or 4m 0.1s. Therefore, using exactly 4m/SY of ST (= 1°/SY of RA) is a quick and sufficiently accurate measurement in a normal human lifespan. The difference between actual and mean sidereal years is negligible in this circumstance.


CONCLUSIONS

1) It is demonstrated that Primary Progression is a Second Order system derived from, and intimately related to, Secondary Progressions, through the logic of the system of equivalencies set forth at the beginning of this essay.

2) This relationship may validate the practice of relating Primary Progressed angles to Secondary Progressed planets, as is commonly done through the mistaken method often used to calculate Secondaries. (The quotidian method is the only method that is consistent both conceptually and mathematically.)

3) It yields a result very close to the original Ptolemaic value (Tetrabiblos, III, 10), but it must be precessed. It is more than the Naibod value of 0°59'08” per year, and it is easy to see that this is because Naibod retains precessing values.

4) I conjecture that dissatisfaction with Primaries could be relieved using the method presented here, apart from any other difficulties or special procedures inherent to it.


ACKNOWLEDGEMENTS

First, I must thank Donald Bradley who first noted certain mathematical correspondences between Secondaries and Tertiaries. In “Give Tertiaries a Try!” he wrote, “There is also a beautiful synchronous meshing of the tertiaries with the secondaries. One could even propose, from this circumstance, that any system that that is not mathematically compatible in some basic way with known systems is probably too much of a maverick to have validity of its own; but this is just thinking out loud on the writer's part.” This gave me the germ of the idea that there could be an undiscovered interlocking system of progressions, and the impetus to find such.

Second, I am greatly indebted to astrologer Clay Reed who wrote lucidly on progressions in American Astrology Magazine, Sept., Oct., Nov., and Dec. 1991, in his series “Astrology for the '90s.” Most valuable was his explicit declaration “What we call 'primary progression' ... is based on 'one primary rotation equals one secondary revolution.'” (AAM, Oct. 1991) This simple statement cleared up years of confusion that often literally made my mind spin. To him belongs the concept of progressing progressions, and that the Secondary-Primary relationship is one of them. My treatment here is slightly different from Clay Reed's, but I suspect he would approve of the use of long-term precession effects.


HISTORICAL NOTE

The name “Primary Progression” comes from Latin “Primum Mobile.” There is often the mistaken notion that it means something like “First [Dominant] (progression).” Hence we get “Secondary Progression,” i.e., “the one that comes second [subordinate].” The original idea was evidently “The Highest Celestial Sphere Turns” or similar.

[Jim Eshelman]

Jun 19, 2014

THESIS

Quotidian-2: 1 Tertiary Sidereal Year ~ 1 Progressed Sidereal Month


ARGUMENT

We begin by posing the question: When, in real life, does the progressed SSR occur by Tertiaries?

We have seen:

1 Sidereal Month ~ 1 Progressed Inertial Day

and with their values:

Tertiary Progressions: 27.321661 CD ~ 0.9972697 Tertiary CD


We set up a simple equation, do some substitutions and solve:

27.321661 CD * 365.256360 ~ 0.9972697 Tertiary CD * 365.256360

9,979.41040 CD ~ 364.25910 Tertiary Progressed CD

The left-hand value is about 27.322 Real Sidereal Years.


Since we have the equivalence:

Minor Progressions: 1 Sidereal Year ~ 1 Progressed Sidereal Month

we can state:

1 Tert. Prog. Yr. ~ 1 Sideral Month of some new progression

or, substituting values:

9,979.41040 Real CD ~ 364.25910 Tert. Prog. CD ~ 27.321661 CD new progression

Notice that Inertial Days are no longer involved here. We can also drop the Tertiary values as they are of no interest to us. We only want to find the rate of Real time to new Progressed time.

Divide all values by 27.321661 in order to find how many Real Days equate to one day of this new progression. The result is:

365.256360 Civil Days ~ 1 Civil Day new progression

As it turns out, this is not so new after all! It is, in fact, the familiar ratio of the Quotidian-2.


CONCLUSIONS

1) The Quotidian-2 is a valid progression by this model.

2) It is a Second Order progression, whose true origin lies in the equivalence of the Tertiary year to the Sidereal month.

3) By assuming the fundamental units as being sidereal, it's natural to derive the Q2, which is the equivalence of the Year to the Civil Day on the surface only. However, by taking 1 Year ~ 1 Civil Day as fundamental, it is probably not possible to derive the Q1.

The next post will continue by comparing this derivation with the example used in Primer of Sidereal Astrology.

[Jim Eshelman]

Jun 20, 2014

EXAMPLE

My derivation of Q2 is so remarkable, so seemingly from left-field, I feel that it is necessary to have a publicly available comparison to make it credible. I have selected the case used in Primer of Sidereal Astrology by Fagan and Firebrace, which is still in print and ought to be in the library of every Siderealist.

Firebrace's granddaughter, Susan Walker, was born October 8, 1949 02:33 GMT, Kensington London, W 0°09'44”, N 51°29'33”. She fell off a horse, suffering injury, March 27, 1960, about 12:00 noon GMT, Blewbury, Berkshire, England, W 1°17', N 51°35' (page 25).

Chapter VII covers the instructions for calculating the Q1 progressed horoscope. On page 33, pay attention to the line:

Uncorrected age of native in days, etc. 10 11 13 29

The Primer doesn't do more with this other than being the starting point of the bija correction, which ultimately leads to the Q1. However, had the authors of the Primer seen fit to cover the Q2, the chart would have been cast for birthday + uncorrected age = October 18, 1949 13:46:29 GMT.

Using a spreadsheet (I recommend Open Office), it is possible to enter the dates and times of the birth and the accident to find the age, which is 3,823 days 09:27:00, or if you prefer 3,823.39375 days. The length of a Tertiary year in real time is 9,979.41040 days, so the accident occurred 38.313% through her first Tert year. Since one Tert year maps onto one progressed Month (27.321661 days), that is also the percentage of the progression through that month.

38.313% of 27.321661 days is 10.46775 progressed days, or an age of 10 days 11:13:29, exactly as calculated in the Primer by using the Mean Sun.

The identity of the Q2 with the progression 1 Sidereal Tertiary year ~ 1 Sidereal Month is confirmed.

[Jim Eshelman]

Jun 21, 2014

Earlier (Sections 7 and 8), we saw that the equivalence:

Tertiary Progressions: 1 Sidereal Month ~ 1 Inertial Day

gives a result that differs from the traditional calculation: one day - including the rotation of the angles - is replicated during one month. In this, it is similar to the Q1: 1 Year ~ 1 Day, so the angles change accordingly.

Yet, the system advocated by Troinski, Lyndoe and Bradley give something else: in the space of a Real Year, the angles move some 13°. The fact that the progressed Sun moves the same amount should remind one of how the Secondary Sun behaves in relation to Primary angles. This is enough to make one suspect that there is still another Second Order progression lurking around. Indeed there is.

The clue is in the timing.

27.32 Real Years ~ 1 Day by new progression

We have already seen this value, 27.32 Years, in Section 11 as the time it takes to undergo a Solar Return by Tertiary Progression. There, it was equivalent to one month. Here we see it equivalent to one day. We can say:

1 Tertiary progressed Year ~ 1 Inertial Day new progression

and with their numbers:

9,979.41040 CD Real ~ 0.9972697 CD new progression

Let's use an approximation to show what's going on:

27.3216609 Years ~ 24 hours Sidereal Time

Divide both sides by 27.3216609 time find how much progressed Sidereal Time passes in one year.

1 Year ~ 0h 52m 42.33s

which is virtually identical to the value given by Bradley in his Tertiary article:

Motion of Mean Sun = Tertiary Equivalent
One Year = 0h 52m 42.3259s


CONCLUSIONS

There is another progression system hidden in the standard Tertiary calculations. The Midheaven progresses by about 24 hours Sidereal Time in about 27.32 years; the planets also must be progressed at this rate.

It was consensus of Lyndoe and Bradley (and maybe Troinski) that these angles were sensitive to Tertiary planets. If this can be confirmed, it may because of their fractal connection.

In a 90-year lifespan, this progression advances about 3.3 days.

POSTSCRIPT

While this progression is logically valid from the assumptions of this posting, it has yet to be investigated. Primary progressions has historically been used via their mundane (that is, semi-arc) aspects. It remains to be seen whether this progression works the same way, or through zodiacal aspects (the progressed Moon, for example, moves about 44° in 90 years), or whether it works at all.

Progression systems are starting to stack up. To me, this is worrisome. It begins to resemble the weed-like growth of predictive systems in Sidereal astrology's earlier years (the 1960s and 1970s). I have to draw a distinction between the interests of the practicing astrologer, and those of the researching astrologer. For the former, there is danger of getting bogged down in too many charts of questionable worth, with little to be gained in interpretive clarity. These newer progressions need to be left to systematic study and comparison by examination of test cases.

Unfortunately, I have not reached the end of the implications of this model, this proliferation of progressions. On the bright, side, I hope that some insight into astrology on a grand scale will come about by this effort.

[Jim Eshelman]

Progression systems are starting to stack up. To me, this is worrisome. It begins to resemble the weed-like growth of predictive systems in Sidereal astrology's earlier years (the 1960s and 1970s). I have to draw a distinction between the interests of the practicing astrologer, and those of the researching astrologer. For the former, there is danger of getting bogged down in too many charts of questionable worth, with little to be gained in interpretive clarity. These newer progressions need to be left to systematic study and comparison by examination of test cases.

Nicely said.

[Jim Eshelman]

Jun 29, 2014

BACKGROUND
In the October 1991 issues of American Astrology Magazine, Clay Reed introduced a new progression that equates 750.56627 days real-time to one day in what he dubbed the "Reed Progression." To me, the explanation was a bit confusing, but that does not negate the validity of the progression itself. I will now derive this progression anew.

THESIS
1 Tertiary Month ~ 1 Inertial Day

ARGUMENT
How long is one Tertiary Month? Since one sidereal month is 27.321661 Civil days, one month of them is that number squared = 746.4732 days. We set this value equivalent to one Inertial Day:

746.4732 CD real time ~ 0.9972697 CD progressed time

and then divide both sides by 0.9972697:

748.5218 CD real time ~ 1.00 CD progressed time

DISCUSSION
My result differs from Reed's value, which is 750.56627 days. This is because my value is (Month^2)/Day, whereas Reed's is (Month/Day)^2. I think I know the reasoning process behind that number, but that is a whole other discussion. For now, I will politely disagree with Mr. Reed, while keeping an open mind that his perceptions into progressions were far clearer than mine.

[Jim Eshelman]

Jun 30, 2014

In an exchange on this Forum between Mr. E and myself, it became apparent (and logically consistent) to describe transits as a species of progression; let's call them Zeroth-Order Progressions.

I defined as First-Order Progressions: the Quotidian-1, one variety of Tertiaries, and Minor Progressions.

Then, I described several Second-Order Progressions, or progressions of progressions, in a manner intended to introduce the concept, and to cover known and published progressions, both explicit and implied. Among them was the "Reed Progression," which made little impact after its publication. Perhaps by re-presenting it as part of a coherent system, interest can be ignited and its usefulness (or otherwise) can be determined.
The exposition of Second-Order Progressions was haphazard as far as logical order goes, and this will now be remedied.

[Jim Eshelman]

Jul 02, 2014

0. 0TH-ORDER PROGRESSIONS
0.1. 1 Sidereal Day ~ 1 Sidereal Day
0.2. 1 Sidereal Month ~ 1 Sidereal Month
0.3. 1 Sidereal Year ~ 1 Sidereal Year

Note: These are transits. They appear trivially the same, but they form the building blocks of fractal time.


1. 1ST-ORDER PROGRESSIONS
1.1. 1 Sidereal Month ~ 1 Sidereal Day
Note: A variety of Tertiaries; the RAMC rotates once per month.
Custom Progressed Ratio: 0.03650106428

1.2. 1 Sidereal Year ~ 1 Sidereal Day
Note: This is the Quotidian-1.
Custom Progressed Ratio: 0.00273032809

1.3. 1 Sidereal Year ~ 1 Month Sidereal
Note: This is Minor Progressions, based on sidereal periods not tropical.
Custom Progressed Ratio: 0.07480132826


2. 2ND-ORDER PROGRESSIONS
2.1. TERTIARY-BASED PROGRESSIONS

2.1.1. 1 Tertiary Month ~ 1 Progressed Day
Note: A variety of the “Reed Progression.”
Custom Progressed Ratio: 0.00133597531

2.1.2. 1 Tertiary Year ~ 1 Progressed Day
Note: This gives (approximately) the Sidereal Time of Tertiaries as traditionally taught.
Custom Progressed Ratio: 0.00009993273

2.1.3. 1 Tertiary Year ~ 1 Progressed Month
Note: This is the Quotidian-2.
Custom Progressed Ratio: 0.00273780311


2.2. SECONDARY-BASED PROGRESSIONS
2.2.1. 1 Secondary Month ~ 1 Progressed Day
Note: This is identical to 2.1.2. above; the traditional Tertiary Sidereal Time.
Custom Progressed Ratio: 0.00009993273

2.2.2. 1 Secondary Year ~ 1 Progressed Day
Note: Primary Progressions; nearly identical to the Ptolemaic rate in Sidereal Time.
Custom Progressed Ratio: 0.00000747510

2.2.3. 1 Secondary Year ~ 1 Progressed Month
Note: A hitherto unknown progression. Similar to 2.3.2. below. To be discussed.
Custom Progressed Ratio: 0.00020479131


2.3. MINOR-BASED PROGRESSIONS
2.3.1. 1 Minor Month ~ 1 Progressed Day
Note: This works out to be the same as the Quotidian-1.
Custom Progressed Ratio: 0.00273032809

2.3.2. 1 Minor Year ~ 1 Progressed Day
Note: A hitherto unknown progression. Similar to 2.2.3. above. To be discussed.
Custom Progressed Ratio: 0.00020423217

2.3.3. 1 Minor Year ~ 1 Progressed Month
Note: A hitherto unrecognized progression.
Custom Progressed Ratio: 0.00559523871


SUMMARY
The number of First- and Second-Order progressions at first glance looks to be twelve, but close inspection shows that two are identical. (I will leave the proof to the reader.) Most are already known. One has been glimpsed at but conflated with true Tertiaries.

Only three seem to be genuine discoveries. We'll review these next.

[Jim Eshelman]

We get two pairs of progressions in which one represents an Inertial Day and the other a Civil Day. One pair is the Q-1/Q-2 set. We have another pair in the newly derived (“discovery” is too bold a word) progressions. There is one where one Secondary Year maps onto a progressed Month. In the other, one Minor Year maps onto one progressed Civil Day day. When the ratios are worked out, the difference between the two is another Inertial/Civil Day pairing in the vicinity of 13 years and 4.5 months of life. The Midheaven takes about two weeks to move 1 degree. In 90 years of life, the difference between the two is merely 00:26:30.

One final Second-Order progression comes from making an equivalence between one Minor Year to one progressed Month. At 90 years of life, the progressed horoscope is about 1.5 years after birth.

These progressions run the gamut from being a bit faster than Primaries to a little faster than the Quotidians. On the basis of length alone, they're comparable to established systems.

How to use them? Cautiously. One may take a set of favored charts that have worked well already, but they may not be the best choice. In order to establish whether a new progression is valid, perhaps one should take cases that have a middling or poor showing by established systems, in order to see whether these newer, speculative methods fill in the gaps.

Ultimately we are looking for a judicious use of progressions. We do not want to become bogged down in a swamp of charts, not knowing which deserve consideration. We also run the risk of introducing so many charts that some of them are always bound to show something that looks “appropriate.” In the Introduction, I spoke of “well-selected” sets that an astrologer should use. What does this mean? Perhaps it means 1) at least 80% of external events and internal states can be accounted for, 2) no major event should be unaccountable, and 3) there are very few patently false predictions (excluding lack of the astrologer's understanding). Any sub-set of methods chosen from this set of ten progressions, along with transits and transitive techniques, that meet this test would be “appropriate.”

[Jim Eshelman]

Jul 04, 2014

This Fractal Model of Progressions doesn't end here. These are fractals, after all, and it's conceivable to take yet another step and form Third-Order Progressions. Eventually, it is bound to reach pointlessness. I have not taken this step, but it looks likely that among the ever-smaller values, the faster-moving progressions might yield something marginally useful.

We are so accustomed to thinking that a thirty year old adult is being influenced by the transits in force at 30 days of age. But what of the reverse? Is the month-old baby in the crib being influenced by the “hyper-progression” of 30 years hence? (I am indebted to siderealist John Kahila for the idea and the term.) If so, then is the 30 year-old adult being influenced by the transits some 4 million days in the future?

Were this true what could be done with it? Could a trained psychic or remote viewer use a hyper-progressed chart as a target and gain a glimpse into the future through some future incarnation?

Mystics have said that there is no time, that time is an illusion. Maybe this means that our linear habits of thinking about time is the illusion. It may be that all particles are quantumly entangled from their common origin at the Big Bang – that is why space is an “illusion”: it's all connected. Could this be said of Time as well? Past, Present and Future are illusions because Time is recursive; Time has structure; Time connects with itself; Time is self-similar at different scales. Astrology measures those scales – at least for us humans on Earth. What of other Solar Systems and their alien astrologies?

Long have I resisted using Regressions. Mostly because in my early days, getting the appropriate ephemerides was problematic and the additional paperwork was too tedious and prone to error. After the advent of the personal computer, I resisted them because I couldn't accept that transits before my birth had anything to do with me, except through their living embodiments, my elders. But if the transits a month after my birth should still affect me at different points in my life, isn't that already saying that my concept of Time is flawed? The fractal points of time not only recurve forward, but maybe also backward. This could explain prophecy, presentiments, foreshadowings. Progressions and Regressions in all their fractal representations maybe have something to contribute to our understanding of astrology as a whole and the nature of Time or Mind or both.

These are dizzying concepts; the mind boggles, spins everywhen. Yet, all we really have is living and deciding and acting in this illusory Present. “Live in the moment,” goes the phrase. “Be-right-here-now!” said Cheech Wizard. “Zitina,” I say when I'm practicing Loglan. Maybe how one lives at this fractal point of time influences one's life, both past and future - even history, past and future! - via those other, fractal-connected points in time. If so, let them be good decisions; let them be good actions.

THE END

[RingsOfSaturn22]

Jun 18, 2014

THESIS

Primaries: 1 Secondary Sidereal Year ~ 1 Primary Inertial Day


ARGUMENT

It may be easier to understand the derivation of Primary Progressions by using a historical chart.

The Campion database in Solar Fire gives the beginning of the Holy Roman Empire as Dec. 25, 800 CE (Julian), 05:10:04 GMT, (06:00:07 LMT), Rome Italy. (I am not endorsing the date and time; it is simply useful.) The Sun's Sidereal longitude was Capricorn 0°10'19”. The Midheaven is Libra 0°18', ST 12:30:45.

The subsequent SSR took place Dec. 25, 801 CE Julian, 12:13:12 LMT. The difference between the two is 365.2591 Civil Days.

I don't think Derek posts here anymore, and I'm not sure if this thread is the best place to post this, but I have a question regarding the calculation here.

For a one year period, he came up with 365.2591 civil days. Using the same information he did, I too came up with 365.2591, so there doesn't seem to be a calculation error.

But if this is supposed to be a SIDEREAL YEAR of 365.256 civil days, why are we coming up with a number closer to the anomalistic year of 365.2596? Further, why does he use that number in his calculation instead of a number that would be closer to the average sidereal year length?

[Jim Eshelman]

I'm not going back to reconstruct a decade-old thread. I think, though, the simple answer you want is that the length of the sidereal year isn't stable. It varies by at least plus-or-minus 10 minutes (I've seen it larger), which 0.007 days. I think it might vary by as much as 0.01 days.

We need this number for a specific year for accurate PSSR calculations, so it's been watched a lot over the last 60-70 years. The time between my current SSR and next SSR is 365.25494 days, which is much closer to the average than one usually sees.

[RingsOfSaturn22]

I figured the sidereal year length varies from year to year. I just don't understand why he would use a number that is not close to the average to be representative of a calculation for 365 years, which was then forming the basis for the rest of the theory.

Aside from that, I think the thread is great and well done. Thank you for reposting it and thanks for your reply!