The Houses - A Guide for the Perplexed

Let’s talk about the houses in the sky — not their meanings, but what they are, and how they are determined.

I have taught a course on the basics of celestial mechanics for astrologers once. I’ll post the link at the end of this text (it’s cheap and people seemed to like it a lot). It’s easier to show these things than to explain it in writing.

But let me try, with as few technical terms and complications as I can.

First, let’s start with the obvious: astrology was always thought within a geocentrical view of the Universe: as if were living in a stactic Earth around which the entire Cosmos moves. This is not complicated, because that’s how each and everyone of us experiences it (or — as we would if we took our eyes off of bright screens for a while).

This ball that rotates around us does so according to an axis (let’s call it the North Pole-South Pole axis, we won’t be talking much about it), and it produces a great circle called the Equator, which cuts this sphere in two equal parts, one north of it, the other south of it.

The Equator (celestial — its projection onto us is the terrestrial Equator) shows us the direction of the motion of the sky: dragged by this movement, everything that is fixed, “resting”, as it were, on the sphere, goes along circles parallel to the Equator (or along it, of course).

But there are shiny thingies in this sphere, and some of them appear to move onto it. Think of a small bug walking on a rotating football — the ball does its thing and drags the bug, but when it completes a turn, the bug is not at the same point it was on it when the rotation started.

One of these is a very shiny golden bug called the Sun.

PLEASE READ THIS BEFORE WE PROCEED

By now, you might be thinking “Marcos thinks I’m stupid, he’s writing as if I was a child”.

That’s not the case. The thing is, it’s very easy to get tangled up in the technical terms and in the calculations, and people tend to follow two paths when facing them: find the subject too difficult/boring and give up, or understand the mathematics and geometry behind it and think they understood the houses.

What I want you to do is neither of those things; it’s to see them. That’s why the language is the most concrete possible.

Back to work.

So, this shiny golden junebug is really strict and methodic. It walks over the ball without changing its speed and without straying off its circular path: the Ecliptic.

Six other bugs walk, each in their own (varying) pace, mostly along a strip around this Eclpitic. These bugs are the other planets, this strip, this “street” in the middle of which the Sun goes and within which the others move (with the occasional slip into the road shoulder), is the Zodiac.

Now, this street goes in the counterflow of the direction of the ball’s rotation.

(I know the analogy changed in a very weird way, I’m sorry).

These two circles, the Equator and the Ecliptic, are “great” circles — which means that they have the greatest possible size for a circle on a sphere, and it also means that their center is coincident with the center of the sphere.

A property of such circles is that if they’re not the same, they must be inclined one in relation to the other, and must cut each other in opposed points.

(I strongly suggest you draw these two circles on a ball to understand it).

The angle between them is around 23o30’. The points where these circles cut each other are the equinoxes.

This is, in short, how the Sky appears to us: a giant sphere, rotating around us according to an axis that passes through the pole, with two important (invisible, of course) great circles around it, one in the same direction of the general motion, another inclined in relation to it along which seven shiny bodies move in their own paces, but generally in the opposite direction of the sphere.

Add some other shiny points that move so slowly they don’t concern us (the fixed stars), and that’s it.

But things get more interesting.

This is how it would be if we saw it from a point outside it. We can’t, because we live inside it — and on another sphere that, while tiny in comparison to the sky, is huge compared to us.

We live on its surface, with our vision of the sky limited by it. Moreover, we live in this surface in an oriented way. We all know where up and down are, and some of us even know where north, south, east, and west are.

This informs the way we look at the sky. We only see (almost) half of it at a time. We see it appearing on the East horizon, moving upwards until it reaches the point above our heads, then it goes down and disappears on the West horizon.

If you read that and thought “no, that’s what the Sun does”, please watch it at night. That’s the way all the stars go. This is how everything in the sky goes, being pushed by the general apparent celestial motion.

The motion of the Sun itself on the sky is not this one. As it’s very slow compared to it, it’s impossible to perceive it just by looking once in the sky for a few minutes. You can do that to the Moon if you watch it for a couple of hours, however.

But if you watch the position the Sun is at sunrise, noon, and sunset for a few months, you’ll surely notice that it changes. If you watch over a few years, you’ll notice it changes in an orderly manner — that’s the Sun moving on the sky.

OK. The Sky seems to move like I described for most of the planet (forget about the poles; if you’re not willing to do so, ask me about that again but only if you actually are at one of them).

We notice it going around us in this manner; it appears east of us, goes over us, disappear west of us, and (even though we actually don’t see it) goes under us eastward to appear again.

It means there is a section of the sky which is “east and above us”, a section which is “west and above us”, one “west and below us”, and one “east and below us”. These are the quadrants.

Now, astrology must have decently precise measurements. We must locate planets, stars, and other points in order to know how they behave according to each other.

In theory, locating points on a sphere is easy. You get the spherical equivalent of a system of coordinates by measuring the distance the projection of a point has, along a great circle, to a given “zero point” on that circle; and the distance of the point we want to locate to the said circle.

I said we have two main great circles on the sphere, so we could have two different systems, and we do.

For the Equator we have something called “right ascension” (the distance along the equator from the vernal Equinox to the projection of the point) and “declination” (the distance between the point and the Equator).

For the Ecliptic, we have “longitude” (the distance along the Ecliptic from the vernal Equinox — remember, the Equinox is where the circles cross each other, so it is on both circles — to the projection of the point) and “latitude” (distance between the point and the Ecliptic).

Remember linear algebra at school? The x-axis is the circle, the y-axis is the distance from the point to the circle.

Now, there is a problem.

The Equator is way easier to measure — because it goes along the general motion of the sky — but the Sun and the other planets move along the Ecliptic, which is where we would like to put the “x-axis”. And we do that. The signs are 30-degree-chunks of the Ecliptic. To say a planet is at 15 of Leo is saying that it has 135 degrees of celestial longitude (four chunks of 30 degrees, plus the 15 degrees in Leo).

This problem has to do with the subject of this text because this sky motion I described is in the same direction of the Equator.

To determine in which of the four quadrants a thing is (and inside it, if it’s in the beginning, the middle, or the end of the quadrants — we’ll get to it soon enough) we must “translate” the quadrants (and those areas I just said within them, the actual houses) into “ecliptic measurements”, so you get those pretty images astrology software gives us.

Don’t worry, no animal will be killed, nor any calculation shown, in this text.

But I must present some simple concepts to tell you the different approaches to this problem.

First, let give definite names to some things I introduced before. We already know the Equator, the poles (technically, the points where the axis cuts the sphere. But just keep in mind your own idea of North Pole — minus Santa Claus — and South Pole and we’ll do fine), and the Ecliptic (which, of course, has poles of its own, distant 23o30’ to the poles of the Equator).

Now:

1) The point in the sky directly above our heads is called the zenith.

2) The point in the sky directly opposed the zenith is the nadir.

And

3) The circle which passes through both of them and the poles is called Meridian.

It divides the sky in a half that is “east of us” and a sky that is “west of us”. Of each one of us. Of each point on the earth except for the poles themselves (because, as the Zenith and the Nadir would be the poles themselves, it is not defined).

The Meridian is one of several circles called “hour circles”. By their name, “hour”, and its name, which means “[related to] midday”, you probably guessed their importance. But we won’t complicate things talking about hour circles here, I just mention them because they are usually brought up whenever houses are.

Another important concept is the Horizon, which is actually more than one concept, all them related.

In the first sense, the actual horizon is that outline that divides the sky from the earth or the sea.

In the most common sense, the “local horizon” is that same line if there was nothing obstructing it — a perfect circle.

The one used to calculate the houses is what this circle would be if we consider the radius of the Earth (its thickness) as negligible. Or a great circle (that is, a circle that cuts the center of the earth and divides it — and the sky — in two equal halves) parallel to the local horizon.

Now that four chunks of the sky are easy to determine. The Horizon and the Meridian (again, anywhere on earth except at the poles in theory, and not too close to the poles in practice) divide the sky in four quadrants; one above the horizon and east of us; one above the horizon and west of us; one below the horizon and west of us; one below the horizon and east of us.

Have you ever played with changing house system in your software chart? You’ll notice that most systems, while the other houses change quite a lot, have the same Ascendant, Descendant, Midheaven, and IC.

That’s because they’re “quadrant” house systems — they’re just ways of dividing what is inside each of these quadrants.

In fact, even the systems that are not quadrants show the same values (but in this case either the Ascendant/Descendant is not at the same places as the first/seven house cusps, or the MC/IC axis is not the same as the tenth/fourth cusps axis).

Why? For two reasons.

First, of course, they’re the most important. If you read this text with attention, you’ll have noticed that they correspond to the meaningful interactions of the circles mentioned before. There is an obvious importance in being above, or below, a person, or being east (coming towards us) or west (leaving us).

Second, they’re easier to measure.

See, you could call the “east part” of the Horizon as the Ascendant, the “above part” of the Meridian as the Midheaven, etc, and you’ll wouldn’t be very wrong.

But, specifically, the Ascendant is the point at which the Ecliptic cuts the eastern semi-horizon; the MC is the point where the Ecliptic cuts the above semi-meridian, and the Descendant and the IC are the opposite and correspondent points.

However, because astrologers are a nosy bunch who’ll love to babble about other people’s finances, kids, death, siblings, etc, and use the houses to do so, we must determine where, between the Ascendant and the IC, the second and third houses start. And here the problems start — they should be “equal” in some sense, because being equal is symbolically good; but in which sense?

The simplest answer would be “equal according to the degrees of the Ecliptic”. After all, that’s where we want to measure the positions of the planets anyway.

This is the answer given by the simplest systems of house division, the most famous of which are the Equal houses (just give each house 30 degrees of longitude from the Ascendant), and the Whole signs (just give the entire sign in which the Ascendant is for the first house, and proceed through the Zodiac).

There’s also the “M-House”, which is the “Equal houses”, but starting at the MC, not the Ascendant.

The advantages of these systems are obvious: they are dead easy to calculate, once you have the angles and an ephemeris table.

The disadvantages are also obvious: first, there is no way to do it and make the angles match the cusps of the houses, because the Ecliptic and the Equator are inclined to each other. Second (please don’t read the next two sentences if you use them, you’ll get mad and probably hate me. I have warned you) they are disconected from the actual experience of what’s actually happening on the sky. They don’t accurately translate the motion of the sky in relation to us.

The quadrant systems try to divide the quadrants according to themselves, respecting the distances between the angles… but in different ways.

Porphyry just does “equal houses” inside of each quadrant — it divides each of them in equal-sized longitude degrees.

Almost as simple (both to calculate and to understand) is Regiomontanus.

The reasoning is: since we want to divide the sky according to how the general motion of the sky appears to us, let’s do our division according to the circle that embodies the motion:

From the Ascendant, projected onto the Equator, we mark 30 degrees segments on the Equator, and then project them back onto the Ecliptic.

This means that the houses are “equal” measured along the Equator, as Porphyry houses are equally a third of a quadrant, and equal houses and whole signs are equal measured along the Ecliptic.

Campanus is one possible answer to the question: “OK, we divided along the Ecliptic; we divided along the Equator; why not do it along any other big circle?”

In this case, the circle is the Prime Vertical (not previously mentioned): it also passes through the Zenith and the Nadir, but cuts the East and West points (while the Meridian cuts the North and South), dividing the sky into “North” and “South” halves. It is at a right angle to the Meridian.

I know, it sounds a bit weird. But it has some computational advantages, which don’t concern us; and the Prime Vertical does run east-west, which has some relation to the general motion of the sky.

The divisions so far, more or less try to respect equality in a spacial way. They all measure, in some sense, “the same” according to some spacial measure.

But we’re dealing with a moving sky — what about trying to measure the houses in a way that reflects the speed in which it moves? That is, what about measuring them according to time?

The simplest of these is Alchabitius. It divides the Ecliptic according to the time it takes for a point to go from the Ascendant to the MC, and the time it takes from a point to go from the MC to the Descendant.

What is mechanically does: It takes the path a point on the Ascendant makes in the sky until it reaches the Descendant (we call it an arc, because motions on a sphere, being always circular, are segments of circle — that’s why we hear people talking about angles of distance on a circle, for example; it’s the angle of the arc) and divides it in six. Because the motion of the sky is uniform, these six chunks of the arc correspond to six equal divisions of the time it takes to go from one point to the other. Then, these points are projected onto the Ecliptic, and the other six houses are opposed to them.

Placidus does the same thing in principle (the actual calculation is not really the same), but with the time it takes from a point to go from the IC to the Ascendant and from there to the MC.

And that’s all.

There are many other systems, and you’re free to invent one just for you.

There are endless details and many calculations for those who like it, but this is sufficient, I think, for those who want to understand the principle behind them.

That is, in a very real sense, every system has “equal houses”; in another meaning, no one has.

*** HERE IS THE COURSE I MENTIONED:

BASIC CELESTIAL MECHANICS FOR ASTROLOGERS

I also have a course on the temperaments (the cheapest you’ll ever find, pay almost whatever you want)