Topocentric Houses

1
Mark wrote: However, I have noticed that a high proportion of mathematically inclined astrologers seem to have a strong objection to the Topocentric house system in a way you dont find being raised against other systems based on semi-arcs such as Placidus, Alcabitius or Koch. Why is this?

Here is an article by Michael Wackford challenging the mathematical soundness of Topocentric houses (which he contrasts unfavorably to Placidus semi-arcs)

http://skyscript.co.uk/pdf/TopocentricHouses.pdf

Wackford along with other astrologers like Cyril Fagan, Robert Hand, Neil Gillings, and Jose Lebron seem to feel the mathematical foundation of this house system is flawed.

I should say I am not taking sides in this debate. I lack the mathematical credentials to do so. However, I thought other members might find this interesting.
Just making a breakaway thread
http://juanestadella.com/Predictive-Ast ... adella.pdf
Chapter 2
The topocentric formulas do not belong to spherical trigonometry but
to the plane trigonometry applied to the cone.
Both of these pdfs mention a cone being used in the calculations. I don't understand that. It seems about a 1000 times easier than I've been led to believe so far. No cone, no funky math. Just a series of interpolated relocations.

The 1st - 7th house is the Horizon, obvious right,
the 4th- 10th house is the Horizon for a location 90degrees east or west but at the equator.
Interpolote the intermediate house cusps

There's no cone.

2nd - 8th, and 12th -6th are 30degrees east and west and 2/3 of the latitude expressed as the ratio of the rise over run of the sides of a triangle drawn on a cross section of the interior of the earth.
Image



After doing that, the following has an unfortunately misleading sense of complication. So complicated I can't follow it to conclusion.
http://skyscript.co.uk/pdf/TopocentricHouses.pdf
Using the Topo pole in this way is no more perverse than the process by which the pole itself is obtained. It merely reverses that process and, in so doing, reproduces conditions found on the cone, where semi-arcs aretrisected equally.

2
Hello Ariondys,

The Topocentric House system was mathematically derived to match empirical results.

ie. for this observed event, this intermediate house cusp should be here, so let's derive a house system that will put the cusp there

Better than trying to bend your mind around the math involved is to just analyze tightly timed charts and see how the intermediate cusps are appropriately contacted at times of the events that relate to those particular cusps.

Have fun,

James

3
Atlantean

Seeing as, for most of us, the cusps of the topocentric houses will be very close to those of Placidus, in what practical way is it not just as well to use Placidus?

You mention about empiricity, but in practice won't the differences be negligible for most of us? There is very little difference between the two for most people. As topocentric houses have come up several times recently perhaps we could post some significant event in some celebrity's life (with no chart rectification obviously) and compare that event in placidus and topocentric (with primary directions for example)?

I don't have a strong enough grasp of all the mathematics involved in the formulation of house cusps so if it's just a matter of empirical observation, at least everyone could join in.

4
The topo house cusps match perfectly to the arcsecond when I use what I described. It can be tested with any astrology software that lets you enter your own latitude and longitude. And a calculator that has a "tan" button and hopefully a "dms" button. Windows has such a calculator of course.

http://juanestadella.com/Predictive-Ast ... adella.pdf
At present, the calculation of Primary Directions is no problem, due to the availability of computer programs such as Polaris or Astro, which
automatically make the calculations. However, it is important that the
astrologer understands what this is based on and how these directions
are calculated manually.
It is important to understand how to do things manually. I certainly agree. Computers can easily spew a stream a garbage and we would have no way to double check. I could be using Solarfire to calculate primary directions if I was careless, right?

However, I am trying to do just that with Astro.
a snippet of data from the Speculum.
___RA________ De______MDO_____PHI______OA/OD
ME 220-44-24 -18-25-29 37-03-02 26-08-48 230-09-10
JU 305-07-35 -20-18-57 29-11-59 21-09-02 296-53-29

now PHI and MDO look like the information to create a house circle, PHI is the new latitude, and (90 - MDO) is the offset for the longitude. The circle passes near the planets, not near enough... still a puzzle in progress to me.
Image

that white dot is JU, it is 0-46 south of the ecliptic for scale reference, the yellow line is the ecliptic, and the red line is the great circle created using Astro speculum data.

it kind of looks like it missed. Then what happens is Astro calculates to the line instead of to JU (I think)
Last edited by Ariondys on Wed Apr 17, 2013 5:33 pm, edited 1 time in total.

5
Paul wrote:Atlantean

Seeing as, for most of us, the cusps of the topocentric houses will be very close to those of Placidus, in what practical way is it not just as well to use Placidus?
Somewhere in one of those pdfs they mention 1 degree difference between topo and placidus; let's delve a bit deeper.

There is a predicatable pattern. They have the least difference around the Aries-Libra axis. And the most around the Capricorn-Cancer axis

about 0-00-05 maxim difference at 10n
about 0-00-46 maxim difference at 20n
about 0-03 maximum difference at 30n
about 0-10 maximum difference at 40n
about 0-33 maximum difference at 50n
about 1-02 maximum difference at 55n
about 2-10 maximum difference at 600n
at around 64n59 it becomes possible to have out of order houses when the Ascendant is near 0 Capricorn or Cancer

If you pick a chart to consider, consider that we probably want a house cusp where the difference will be measureable. And intermediate cusp should be around 0 Capricorn or 0 Cancer, while they were born at something like 55n

Something from Denmark perhaps
http://www.worldatlas.com/webimage/coun ... famous.htm
http://www.astrotheme.com/astrology/Ale ... of_Denmark

6
Ariondys

That's right, I was thinking of someone with perhaps Capricorn-Cancer on the ascendant or MC axis. Someone with an accurate birth time, like perhaps Prince Harry (Capricorn Rising) or something like that.

That said, anyone with Capricorn/Cancer on any house cusp may be a suitable candidate if we choose something which is relevant to the symbolism of that house cusp.

I am curious about this though, the more I think of it, because Topocentric houses uses the same ascendant as Placidus so again perhaps it would be irrelevant, though presumably the primary directions may differ.

7
Hello Paul,

Re: "Seeing as, for most of us, the cusps of the topocentric houses will be very close to those of Placidus, in what practical way is it not just as well to use Placidus?"

Primary Directions and Secondary Progressions normally mature within 0? 11' of arc. When the difference between the two house systems is merely 0? 11' or arc (for example), then perfectly appropriate aspects that were there in Topocentric, will be outside the normal orbs when using Placidus. (In other words, you would have to introduce a larger standard "orb of maturity" for aspects just to compensate for the Placidian sloppiness...) The other issue, of course, is house rulerships. If the 8th Cusp is at 0? 5' Capricorn with Topocentric, you might select a different (and false) ruler for the 8th House if Placidus says 29? 50' Sagittarius.

Re: "You mention about empiricity, but in practice won't the differences be negligible for most of us?"

It will depend on each person's practical definition of "negligible." Additionally, the techniques that each person is using will likely play into it as well. For Transits, where maturation orbs extend to at least 1? 20' or arc, a few arc-minutes won't make that much difference in most cases. For Primary Directions and Secondary Progressions, it could make quite some difference, since the differences (occasionally) between Topocentric and Placidus would often be greater than the orb of maturation for the aspects!

Re: "There is very little difference between the two for most people."

I am hearing Kirk's (Placidus') "we are 4 light years from Alpha Centauri" as compared to Spock's (Topocentric's) "we are 4.36926 light years from Alpha Centauri." To most, it wouldn't make a bit of difference. If you're trying to get to Alpha Centauri, though, it just might be an important difference. If you want the correct house rulers or if you are using dynamic measurement systems such as Primary Directions, Secondary Progressions, Progressed Sidereal Solar Returns, and/or Age Harmonics; the difference between Placidus and Topocentric is like the difference between water at 2? Celsius vs. -2? Celsius.

Re: "As topocentric houses have come up several times recently perhaps we could post some significant event in some celebrity's life (with no chart rectification obviously) and compare that event in placidus and topocentric (with primary directions for example)?"

If you don't have a chart rectified to just seconds, you won't be using Primary Directions, so I can't find any reasonable way to implement the mentioned experiment without a very specific and precise rectification. Best would be to find someone with a documented time that actually is very, very close to the rectified time (Neil Armstrong was a good example, since his Mother documented his birth time to 12:31:30 pm! and the rectification is within 2 to 4 seconds of that time).

I'm all for a more detailed look...

Take care

James

8
Atlantean

If we're going to try to be impartial in comparing two systems, then I think we have to rule out rectification. After all when you rectify you're amending a time so that it better suits or conforms to topocentric house cusps. We should hardly be later surprised that the chart then corresponds better to topocentric cusps, when it was adjusted to do just that. Similarly we wouldn't want to rectify it so that it better suits placidean cusps and then hope to realistically compare to the two systems impartially.

In a practical sense if we're just rectifying every chart to better suit one house system then of course later we'll see better symbolism matching with that house system. The other way of looking at this is that if we need to rectify every chart in order for our house system to work, then might this not put a big question mark over how useful that house system is?

I think if we realistically stick to a Roden Rating of A or AA, then it's as much as we could hope to ask for in a real working situation.

The problem with rectification is that we might well use the very incident we would later examine to help rectify the chart - in other words we'll just amend the time until it fits with a given incident or set of incidents. But this could happen, presumably, with Placidus as well.

I'm not sure what you mean when you say that "Primary Directions and Secondary Progressions normally mature within 0? 11' of arc" - is this something common with the Topocentric system, or astrology generally? I've not heard of this 'maturation' orb before.

Obviously your point about the difference between 29d 50' and 0d 5' is a valid one but it's a problem with every house system. The converse of this is if the Placidus one is correct and you might select the false Topocentric one. Obviously the two are not the same, but in the majority of cases they will be very close. I'm curious in practice just how different the two would be if we don't rectify the chart (which arguably suits one system over another).

9
Paul wrote:I'm curious in practice just how different the two would be if we don't rectify the chart (which arguably suits one system over another).
This is an important point. No matter how you put it, rectification is the fine-tuning of a horoscope to a specific system, not only of houses and primary arcs of direction, but also of the way of converting arc into time, as well as of all other idiosyncratic elements of that particular system. The more choices are implied, the more any assertion about the accuracy of the system becomes circular, fallacious, and non-comparable.

For example: in addition to several possible "keys" to convert arc into time, directions can be in mundo or in zodiaco, they can be according to Regiomontanus, Campanus, Placidus, etc., the Moon can be geocentric or topocentric (parallax), it can be adjusted to its own motion during the time of the direction (dynamic or "primary progression").

Add to this the proliferation of factors such as the semi and sesqui-square and the quincunx, aspects to other house cusps, rapt parallels...

The more "rectified" a birth time is, the more it is entrenched and forced into the idiosyncracies of a particular technique and of a particular astrologer. It is therefore a fallacy to assume that rectification represents a "closing in" of the true or correct time of birth.

Juan

10
Hello Paul,

Re: "If we're going to try to be impartial in comparing two systems, then I think we have to rule out rectification."

If you're going to be using Primary Directions, you will have no choice but a very precise rectification, unless you're only using Primaries as some "time lord" type of silliness. Appropriate aspects occur to just minutes of arc, IF one is working with the correct birthtime. If these aspects are not there, quite simply, the birth time is WRONG.

Secondly, if Neil Armstrong's Mother (and as listed in his biography) remembers that Neil was born precisely at 12:31:30, is there really, I mean really a problem with using 12:31:26? Is that a major issue? We're talking four seconds, so I have a hard time seeing the hoopla, since 99% of charts we see AA-rated have much more than that level of error.

Re: "After all when you rectify you're amending a time so that it better suits or conforms to topocentric house cusps."

This is true, but do you want to know what is amazing? When we find the birth time using EXCLUSIVELY Primary Directions, we still have the appropriate aspects in Secondary Progressions to those very same house cusps that were determined strictly with Primaries. Remember, please, that one of these (Primaries) are based on the ROTATION of the Earth while the other (Secondaries) are based on the REVOLUTION of the Earth around the Sun....YET, both systems underline the same exact intermediate house cusps. Isn't that special?! :p

Re: "We should hardly be later surprised that the chart then corresponds better to topocentric cusps, when it was adjusted to do just that. Similarly we wouldn't want to rectify it so that it better suits placidean cusps and then hope to realistically compare to the two systems impartially."

See above point. Rectifying with Primaries to find exact house cusps, shouldn't bias the Secondaries in any way whatsoever.

Re: "The other way of looking at this is that if we need to rectify every chart in order for our house system to work, then might this not put a big question mark over how useful that house system is?"

No, we're not rectifying in order to get the house system to "work", we are rectifying to make for the smallest cumulative error in orb. Once this time is found to work in Primary Directions, then it will also work perfectly in Secondary Progressions, Progressed Sidereal Solar Returns, and Age Harmonics as well, even though the first system is based on the Earth's rotation, while the others are based on the revolution.

Re: "I think if we realistically stick to a Roden Rating of A or AA, then it's as much as we could hope to ask for in a real working situation."

Many Rodden-AA charts are still more than 5 minutes off in time, which means we don't even have the right degree on the Angles. Again, you won't be using any of these and looking at the right Primary Directions at events.

Re: "The problem with rectification is that we might well use the very incident we would later examine to help rectify the chart - in other words we'll just amend the time until it fits with a given incident or set of incidents. But this could happen, presumably, with Placidus as well."

Use out-of-sample events. That appears to solve both problems. If I rectify a chart so that events 1 through 20 give a specific time, and you are arguing that the rectification is arbitrarily playing to those events, then out-of-sample events 21 through 25 should be MORE error-prone if the rectification was, in fact, arbitrary and incorrect. If the rectification was fundamentally sound, then events 21 through 25 will be EQUALLY astrologically correct as 1 through 20.

Re: "I'm not sure what you mean when you say that "Primary Directions and Secondary Progressions normally mature within 0? 11' of arc" - is this something common with the Topocentric system, or astrology generally? I've not heard of this 'maturation' orb before."

Observational in THOUSANDS of analyzed events.

Re: "Obviously your point about the difference between 29d 50' and 0d 5' is a valid one but it's a problem with every house system. The converse of this is if the Placidus one is correct and you might select the false Topocentric one."

But in some ways, that's my point. Using the Topocentric always (with the right birth time) IS where those cusps are... you won't be able to change the time and get better Primaries, Secondaries, etc.

Re: "I'm curious in practice just how different the two would be if we don't rectify the chart (which arguably suits one system over another)."

Without rectification, we wouldn't know how right either was...we would only see the difference. In other words, using bogus time #1 could give us +x error for a particular cusp in Placidus and -x error in Topocentric.

I still think the very best solution is to take a tightly-timed birth (such as Neil Armstrong) and to use the rectification which is only 4 seconds and therefore doesn't make any large-scale difference whichever is used.

What's wrong with the Neil Armstrong chart? We have an eye-witness that recorded the birth time to the second.


Take care

James

11
Hi Atlantean

I don't mind about Neil Armstrong either way, my points are more general than any specific example at the moment.

I'm going to start with something you said toward the end of your reply:
[quote]Using the Topocentric always (with the right birth time) IS where those cusps are... you won't be able to change the time and get better Primaries, Secondaries, etc. [/quote]

This is, for me, making the conclusion before doing the investigation. I appreciate that what you have said is true for you, and may well be true for everyone, but the whole point I was trying to make when I suggested this was in comparing Placidus and Topocentric cusps to determine whether their relatively minor differences are actually negligible or not. Now, for you, it's a foregone conclusion that the "right" (to use your word) birth time will be found by studying primary directions against House Cusp X (where X is Topocentric) and rectifying, but why not let X be Regiomontanus, Placidus, whatever else. We need to first examine if the claim that rectifying by Topocentric does indeed produce the 'right' birth time. With no objective way of discovering the right birth time all we're left with is to deduce a time which corresponds best to a set of events. The time we get from this may not be the correct birth time. If we use Placidus cusps perhaps we'll get the right birth time when we do it with events against those cusps - especially bearing in mind my point that in a lot of cases (not all obviously there are fringe cases to any examination) they will be very similar.

We cannot realistically compare Placidus and Topocentric whilst favouring Topocentric by rectifying a chart using it. You say that the Secondary Progressions will then also better respond, and that is indeed an interesting point. I doubt, however, that realistically speaking there will be any major difference in a given secondary progression will be noticeable based on a timing difference of a couple of minutes - do you progress to house cusps?

Regarding Armstrong, and by extension all charts, I do not believe for one moment that anyone can accurately record the time of a baby's birth - for one thing people time it differently. Is it when the head emerges? When the child first takes a breath? When the cord is cut? Actually people do not always agree on these things. Secondly I am not familiar with any mother or midwife who keeps a perfectly accurate watch or clock such that it is accurate to within seconds. It just doesn't happen. I could get everyone in the room to tell me the time and they'd provide slightly different answers.

Remember though, we're not examining rectification here, but cusps generally.I still maintain that if we rectify using one house then we cannot realistically compare that new chart with another house cusp. We might want to rectify the chart using both systems - and then what? Would the real time please stand up? We do not know which it is. We can then further look at what you say about secondary progressions also corresponding, but again we'd have to do it on the topocentric rectified chart and also on the placidus rectified chart. Otherwise we are not making an intellectually honest comparison.

If we start with a foregone conclusion that topocentric is the best rectification then we have already made our conclusions before we even start to investigate.

The whole point (at least for me) isn't to necessarily demonstrate one house as superior to the other, but just to examine how truly different the house cusps are for one another, in a basic chart (ignoring potential problems in extreme latitudes etc). Will there really be that much difference? Or is it just that the apparent success is due to reformatting the entire chart to suit one particular house system due to rectifying via that house system.

The point about secondary progressions is interesting but as I say I'm skeptical to what level accuracy we might expect from the secondary progressions and again the only true comparison is with a placidus rectified chart versus a topocentric rectified chart, because if the comparison is negligible the a likely conclusion we could make is that rectifying a chart using your preferred house system is responsible for apparent success with that chart, and NOT that topocentric or placidus or any specific one is superior. We might want to do further investigation once that has been established to discover anything more.

12
Atlantean wrote:Appropriate aspects occur to just minutes of arc, IF one is working with the correct birthtime. If these aspects are not there, quite simply, the birth time is WRONG.
Actually, all you can say is: "the time for which the chart is made does not fit this system of primary directions (or of domification) used with this key to convert arc into time", so you shift the time until it fits. The conclusions about the accuracy or not of the time of birth are only speculation, assumption, or belief.
we're not rectifying in order to get the house system to "work", we are rectifying to make for the smallest cumulative error in orb. Once this time is found to work in Primary Directions, then it will also work perfectly in Secondary Progressions, Progressed Sidereal Solar Returns, and Age Harmonics as well
That is "the smallest cumulative error according to the topocentric system and to naibod's arc", and presumably after comparing it with all other systems of directing and of converting arc into time and after proving statistically that other times during the day cannot yield similar or even better results. If we take only 4 systems and 4 keys (which is a simplification), we have at least 16 different possibilities of timing for each direction. If we add the zodiacl directions it becomes 32, and if the Moon is involved it becomes 64 (parallax) and 128 (lunar progression in the course of a few hours).

That is 128 possibilities for one single arc of direction involving the Moon, and this is excluding other non-standard keys and domification systems.

Juan