Astrolog 7.00

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A new version of Astrolog has been released, and the new version 7.00 features improvements to "3D houses" and "chart spheres". Astrolog now supports multiple systems of 3D houses. The simplest model of 3D houses is what's been described so far. It's formed of 12 equal sized 3D wedges aligned with the local horizon, and is the the 3D model of Campanus. This can also be called "3D Equal houses". (It's only the 2D cross section as displayed in a classic wheel in which Campanus houses appear to be irregularly sized.)

The "3D houses" concept has been extended to generalized 3D versions of all standard house systems: They are defined by great circles drawn from the due South point to the due North point on the local horizon, passing through each 2D cusp where it intersects the ecliptic. 3D Regiomontanus houses can be seen above (which unlike Campanus are different sized wedges, although they're still fixed size over time at a given location). 3D Placidus houses can be seen below (which dynamically change sizes and wobble back and forth over time).
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Astrolog 7.60 freeware downloads: http://www.astrolog.org/astrolog.htm :)

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Fadi Mazboudi wrote:Can you please check out the house system in this book and give me some feedback: https://juanestadella.com/Predictive_As ... dition.pdf
Thank you for the pointer to this book. :' It nicely describes the essence of 3D houses, and the limitations of a 2D birthchart display, as seen in the following excerpt (p317-318):

"It is important to understand that despite the fact that we can see the birth chart drawn or printed on paper, it is not only two dimensional, but three dimensional. The elements of the birth chart are not found contained on a plane, but in a sphere. For this reason, there are many astronomical positions that we cannot see in an ordinary chart, and that are very important in the interpretation and prediction of a Radix. Therefore, beyond locating the planets in the Zodiac, due to its ecliptic longitude, we must also place them and consider them according to their declinations and latitudes, which could also mean that they are physically found in a different house than where they appear in a two dimensional birth chart. In addition, although placed in an ordinary two dimensional birth chart, the houses appear with different sizes, when in fact they are twelve identical parts of 30 degrees each."

The last sentence above describes "3D Campanus" houses (also known as "3D Equal houses") which are 12 equal sized wedges of 30 degrees each, but which appear different sizes in the 2D cross section of a 2D wheel chart.

Juan Estadella's book also describes Topocentric houses, and claims it's the best system. Note however that Topocentric is a quadrant system like many others (e.g. Placidus, Campanus, and Porphyry) and it only differs from the others in how the minor cusps are calculated. Standard Topocentric as most software computes is a classic 2D house system like all the others, in that only zodiac position longitude is used to determine house system.

Users of Topocentric houses may appreciate "3D Topocentric" in Astrolog (produced by turning on both Topocentric houses and 3D houses) and may find it to be an improvement or refinement of 2D Topocentric. As with other 3D house systems, Astrolog's 3D Topocentric has identical house placement as 2D Tropocentric for objects exactly on the ecliptic, and only differs for objects above or below it. 3D Topocentric will ensure objects above the horizon are never in houses 1-6, and that objects below the horizon are never in houses 7-12.
Astrolog 7.60 freeware downloads: http://www.astrolog.org/astrolog.htm :)

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Hi Walter

That stuff about 3D houses is really awesome... It's easy to imagine how excited Dane Rudhyar would have been about all this!

My only issue with it is that Astrology is not really based on a three-dimensional vista but essentially on a four-dimensional one... Which leaves us with Equal Houses as the most appropriate system of them all in my book. Which, BTW, I like to call the Hermetic House system, in line with some of the earlier German authors.

Nevertheless, I follow your demonstrations with interest - in order to really clarify what we are dealing with, if nothing else... :)
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Michael Sternbach wrote:That stuff about 3D houses is really awesome... It's easy to imagine how excited Dane Rudhyar would have been about all this!
Thank you! :D I understand Rudhyar preferred Campanus houses. However, even those preferring other systems may also appreciate the 3D version of that house system (such as "3D Topocentric" mentioned above).
Michael Sternbach wrote:My only issue with it is that Astrology is not really based on a three-dimensional vista but essentially on a four-dimensional one... Which leaves us with Equal Houses as the most appropriate system of them all in my book.
By "four-dimensional", do you mean 3D space combined with the 4th dimension of time? Indeed, astrology is very much about time and how energies change over time! That's why 3D houses are often presented in animated form, to see their changes over time. However, how does "four-dimensional vista" lead one to conclude that Equal houses is the most appropriate system?

Note there are various different Equal systems, as described in the thread: http://skyscript.co.uk/forums/viewtopic.php?t=10834. Which Equal system do you prefer? This might be a big discussion best had on the other thread! ;) Note that "3D houses" or the 3D model of Campanus is an Equal system too, when looked at in 3D. "3D Campanus" houses are 12 equal sized wedges of the celestial sphere of 30 degrees each, which only appear different sizes in the 2D cross section seen in a 2D wheel chart. That's why another name for 3D Campanus can be "3D Equal houses".

In other words, Campanus is nice because it's both a quadrant system and an Equal system! :' It effectively bridges the differences between quadrant systems like Placidus, and Equal systems like Whole, taking the best of both worlds. Campanus always has 1st=Asc and 10th=MC like quadrant systems, however it's also an Equal system in which each house covers exactly 30 degrees (when you look at its 3D model).
Astrolog 7.60 freeware downloads: http://www.astrolog.org/astrolog.htm :)

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Cruiser1 wrote: however it's also an Equal system in which each house covers exactly 30 degrees (when you look at its 3D model).
Isn't that true of all house systems though? They all cover 30 degrees of something.
"The only true wisdom is in knowing you know nothing" - Socrates

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Cruiser1 wrote:
Michael Sternbach wrote:That stuff about 3D houses is really awesome... It's easy to imagine how excited Dane Rudhyar would have been about all this!
Thank you! :D I understand Rudhyar preferred Campanus houses. However, even those preferring other systems may also appreciate the 3D version of that house system (such as "3D Topocentric" mentioned above).
Michael Sternbach wrote:My only issue with it is that Astrology is not really based on a three-dimensional vista but essentially on a four-dimensional one... Which leaves us with Equal Houses as the most appropriate system of them all in my book.
By "four-dimensional", do you mean 3D space combined with the 4th dimension of time? Indeed, astrology is very much about time and how energies change over time! That's why 3D houses are often presented in animated form, to see their changes over time. However, how does "four-dimensional vista" lead one to conclude that Equal houses is the most appropriate system?
Walter,

By "four-dimensional", I was referring to an actual 4D space. BTW, that concept was introduced by Cambridge Platonist Henry Moore, even though you could say it was implied already in Plato's famous cave analogy, according to which the world we are seeing is the mere shadow of the archetypal "real" world. And the role that the (neo-)Platonic world view played for Astrology throughout the centuries - from Iamblichus to Robert Fludd - is out of the question.

Of course, today higher-dimensional space is a common concept in mainstream science, but in my view, it is important to understand the role it plays in Astrology and the other occult sciences as well. Without this concept, there would simply be no rational foundation available for them!

Thus, I am currently preparing a book for publication that explores this topic in depth, includings its mathematical side - from scratch, so any interested person should be able to follow. :)

Anyway, this is not the place to go into this topic.

For now, let me just emphasize that, as we use the ecliptic (aka the zodiac) as our frame of reference for the planets and pretty much everything else in our delineations, in geometric terms we are employing a circle and a two-dimensional plane, respectively. By analogy ("as above, so below"), the Wheel of Houses should then be a circle and a two-dimensional plane, respectively, as well, and sure enough, that's how we are treating it in practice, but when it comes to the question of how to calculate it, strangely intricate considerations tend to enter the picture...

In most systems, we first define the beginning of our Wheel as the degree of the Zodiac that rises on the horizon at any given moment, which is straightforward enough - however, the cusp of the 10th house (in all systems save for your basic Equal one) does not coincide with the degree of the Zodiac that has the highest altitude above the horizon (which would be the nonagesimal) - except of course for a brief moment twice a day.

And now we try to shoehorn our basic Zodiac-like conception of a wheel with twelve sectors into that quadrant scheme and end up with something that I had been taught to accept when I started out in Astrology some three decades ago, but that now looks rather distorted and ugly to me. Interestingly, lay people sometimes perceive it that way as well, like that client who, when I showed him his natal chart delineated with Koch houses, spontaneously assumed that there must be something wrong with my computer. :lol:

BTW, I elaborated on the reason why that kind of delineation is problematic not least from a perspective of celestial mechanics here:

http://skyscript.co.uk/forums/viewtopic ... ight=equal
Note there are various different Equal systems, as described in the thread: http://skyscript.co.uk/forums/viewtopic.php?t=10834. Which Equal system do you prefer? This might be a big discussion best had on the other thread! ;)
I exclusively use Equal with the ASC as the first house cusp, which I like to refer to as the Hermetic house system, as suggested by some of the earlier German researchers. And I treat the MC and IC as sensitive points whose house position yields useful further information this way.
Note that "3D houses" or the 3D model of Campanus is an Equal system too, when looked at in 3D. "3D Campanus" houses are 12 equal sized wedges of the celestial sphere of 30 degrees each, which only appear different sizes in the 2D cross section seen in a 2D wheel chart. That's why another name for 3D Campanus can be "3D Equal houses".

In other words, Campanus is nice because it's both a quadrant system and an Equal system! :' It effectively bridges the differences between quadrant systems like Placidus, and Equal systems like Whole, taking the best of both worlds. Campanus always has 1st=Asc and 10th=MC like quadrant systems, however it's also an Equal system in which each house covers exactly 30 degrees (when you look at its 3D model).
Well, I think basically the same could be said of Regiomontanus and other space oriented systems, which divide some circle into twelve equal sectors, but then the question arises, what the astrological significance of that would be, i.e., why that particular circle should be preferred over another.
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Paul wrote:Isn't that true of all house systems though? They all cover 30 degrees of something.
No, many house systems are unequal. That means their houses are different sizes, and a particular house in that system may cover less than or more than 30 degrees. These smaller or larger houses sometimes result in intercepted signs and houses, in which a 30 degree sign is completely covered by a large house, or a small house is completely within a 30 degree sign. Equal house systems (in which all 12 houses are exactly 30 degrees) never have interceptions (which one might consider to be a good thing or a bad thing).
Michael Sternbach wrote:For now, let me just emphasize that, as we use the ecliptic (aka the zodiac) as our frame of reference for the planets and pretty much everything else in our delineations...
"3D houses" departs from this model! :P The ecliptic only defines the signs of the zodiac, which are the 12 equally sized wedges whose "equator" is the ecliptic and whose poles are the celestial poles. 3D houses are also 12 equal sized wedges, however they're aligned with a different "axis", in which their "equator" is the prime vertical, and their poles are the North and South points on the local horizon.
Michael Sternbach wrote:In most systems, we first define the beginning of our Wheel as the degree of the Zodiac that rises on the horizon at any given moment, which is straightforward enough...
"3D houses" departs from this model too! ;) The horizon (and therefore the boundary of the 1st 3D house) isn't a single degree on the ecliptic, but instead is the entire eastern half of the horizon, which spans multiple zodiac degrees. With 3D houses, there's no "1st house cusp", or at least no longer house boundaries that can be expressed as a single zodiac degree.
Michael Sternbach wrote:Well, I think basically the same could be said of Regiomontanus and other space oriented systems, which divide some circle into twelve equal sectors
Regiomontanus is indeed a space-based system, however it is not an equal space-based system like Campanus is. Regiomontanus produces different sized houses covering different sized areas of space. In the diagram below, notice how the Regiomontanus 12th and 7th houses are smaller, and how its 10th and 9th houses are larger. In contrast, compare to Campanus below in which all 12 houses are always equal sized wedges. 3D Campanus is the one and only equal 3D model in which all houses cover the same area of space, and which also stays a quadrant system in which the 1st house boundary is the horizon, and the 10th house boundary is the meridian. That's why 3D Campanus is the only equal quadrant system. 8)

Campanus houses 3D model:
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Regiomontanus houses 3D model:
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Cruiser1 wrote:
Paul wrote:Isn't that true of all house systems though? They all cover 30 degrees of something.
No, many house systems are unequal. That means their houses are different sizes, and a particular house in that system may cover less than or more than 30 degrees. These smaller or larger houses sometimes result in intercepted signs and houses, in which a 30 degree sign is completely covered by a large house, or a small house is completely within a 30 degree sign. Equal house systems (in which all 12 houses are exactly 30 degrees) never have interceptions (which one might consider to be a good thing or a bad thing).
Well to be specific, with more intent, don't all houses cover 30º of something?

For example, Regiomontanus covers 30º of the equator. Campanus covers 30º of the Prime Vertical. Ok not all cover 30 degrees, but a lot do, but they all cover 1/3rd of something.
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Paul wrote:Well to be specific, with more intent, don't all houses cover 30º of something? For example, Regiomontanus covers 30º of the equator. Campanus covers 30º of the Prime Vertical. Ok not all cover 30 degrees, but a lot do, but they all cover 1/3rd of something.
Indeed, Porphyry houses don't cover 30 degrees of anything, because Porphyry houses simply trisect or take 1/3 of each quadrant seprately. But I agree that every house system in an abstract sense has houses cover 1/12 or 1/3 of something. However, regardless of the internal math used to calculate house positions, only a few house systems end up with equal 30 degree size houses in the end (or 12 equal sized 30 degree wedges when looked at in 3D). Those are the true "equal" house systems, such as Equal (Asc), Equal (MC), Vedic, Whole (and Campanus when looked at in 3D).
Paul wrote:For example, Regiomontanus covers 30º of the equator.
Indeed, and this raises an interesting point! :' Regiomontanus is an unequal system, because although it divides the celestial equator into 12 equal 30 degree sections, it then composes wedges which meet at the North and South points on the local horizon, which makes those wedges different sizes. However, if Regiomontanus instead composed its wedges to meet at the celestial poles, then it would be a 3D equal system! It would be like 3D Campanus, just tilted to a different alignment on the celestial sphere. However, this alternate 3D Regiomontanus would not be aligned with the local horizon, and would still (like 2D house systems) sometimes have planets below the horizon be in houses 7-12, or planets West of the meridian be in houses 4-9.
Michael Sternbach wrote:Well, I think I understand what Walter is getting at: The Prime Vertical (the circle that connects East and West) is the only great circle whose division will result in getting regular sectors of the observer's space. If that's what houses are supposed to be all about. Anyway, that's why Campanus was Rudhyar's method of choice.
Yes, the above is the essence of "3D Equal houses". Also, dividing the prime vertical into unequal sections is how we get 3D versions of other house systems, like 3D Placidus, which produce the same house positions for planets exactly on the ecliptic. Anyway, whether 3D houses produces more accurate astrology than the various simple 2D house systems would be difficult to prove, but it at least seems more precise, and is a useful model to be able to visualize and display.

As the page http://www.quadibloc.com/other/as01.htm says, "To keep things simple for astrologers, however, tables of houses, instead of recording the entire path of the line between houses, give the boundary of each house as a single angular position. That is the location where the line bounding a house crosses the Ecliptic, since the planets always move close to the Ecliptic." That's the essence of 3D houses in general: We no longer need to "keep things simple" as we did in previous centuries, and modern computers can properly see and work with the entire path of the line between houses. 8)
Astrolog 7.60 freeware downloads: http://www.astrolog.org/astrolog.htm :)

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A new version of Astrolog has been released, and the new version 7.30 features enhancements to "3D houses" and "chart spheres". :D Astrolog now supports multiple models of 3D houses. Everything described up until now is a 3D model in which houses are arranged along the prime vertical, and have their poles at the North and South points on the local horizon. However, there are other orientations one can use for houses too. Here's a summary of the four models Astrolog supports:
  1. Ecliptic: Houses are arranged along the ecliptic, and have their poles (where the 12 houses meet) at the North and South ecliptic poles. This is classic 2D houses, because signs are also arranged along the ecliptic and use the ecliptic poles, which means only zodiac position longitude is used to determine house placement (and latitude is ignored).
  2. Prime Vertical: Houses are arranged along the prime vertical, and have their poles at the North and South points on the local horizon. Campanus houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Campanus and all quadrant systems, the Ascendant will always be on the 1st house boundary line, and the MC on the 10th house boundary line. This can be considered the preferred model for 3D houses (and was the only model available before Astrolog 7.30) since for quadrant systems it ensures that all parts of houses 1-6 are below the horizon, and all parts of houses 7-12 are above the horizon.
  3. Local horizon: Houses are arranged along the azimuth of the local horizon, and have their poles at the Zenith and Nadir points straight up and down on the local horizon. Horizon houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Horizon houses, the Ascendant won’t necessarily be on 1st house boundary line, but the Vertex will always be on the 7th house boundary line. As with Horizon houses themselves, stepping across Earth's equator will flip all houses 180 degrees.
  4. Celestial Equator: Houses are arranged along the celestial equator, and have their poles at the celestial poles or the points directly above Earth's North and South poles. Meridian houses combined with this 3D model is a "3D Equal system", in which all houses are equal sized 30 degree wedges of the celestial sphere. As with 2D Meridian houses, the Ascendant won't necessarily be on the 1st house boundary line, but the East Point (i.e. equatorial Ascendant) will always be on this boundary.
The animation above is an example of Porphyry houses displayed in a chart sphere in all four models, in which the 12 signs are in purple, and the 12 houses are in green. The four chart spheres are identical, and it's only the green colored house wedges that differ in orientation. Note how in all four spheres, all house boundaries intersect the ecliptic at the point of the 2D Porphyry house cusps.

In summary, there are four "3D Equal systems", in which all houses are equal sized 30 degree wedges of the celestial sphere. They are: (1) Any classic Equal system with 2D Ecliptic model. (2) Campanus combined with 3D Prime Vertical model. (3) Horizon houses combined with 3D Local Horizon model. (4) Meridian houses combined with 3D Celestial Equator model. Equal, Campanus, Horizon, and Meridian are therefore special house systems which could be considered "better" than others, since they are the only systems that can be "3D Equal". I like Campanus in 3D Prime Vertical the best, since it's the only system and model that's 3D Equal but can also ensure all parts of houses 1-6 are below the horizon, and all parts of houses 7-12 are above it.

(Note Regiomontanus houses mentioned in the previous post isn't a "3D Equal" system like the others. Campanus is entirely based on the local horizon, in which houses are simply equal sized 30 degree wedges along the prime vertical. Meridian is entirely based on the celestial equator, in which houses are equal sized 30 degree wedges along the celestial equator. Regiomontanus mixes the two: It divides the celestial equator into 12 equal arc segments like Meridian, however it then draws lines from the North and South points on the local horizon like Campanus, and where those lines intersect the ecliptic forms Regiomontanus house cusps. Mixing the models in this way results in irregular sized Regiomontanus houses in both 2D and 3D.)
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