What ARE midpoints, anyway?

[Jim Eshelman]

I thought I'd start a brainstorming or thought exercise on this question: What ARE midpoints, anyway?

By "what are they," I mean structurally. I've written at length about what I term Astrological Structures here: https://solunars.com/viewtopic.php?f=10&t=1772

Potential answers to the question may come from the following list, or may be something I haven't considered.

1. Are midpoints the same type of thing as aspects? If so, what is the mechanism that distinguishes them?
2. Are midpoints more like planets? (By which I mean single items that have a point, position, and intrinsic nature of their own.)
3. Are they merely ratios of symmetry and, if so, exactly how does that mechanism work?

I understand structurally what planets, signs, aspects, and angularity are and how they work - how they are structurally formed and operate. In contrast, though I can use midpoints, I don't know what they really are. Are they akin to one of the other astrological structures such as planets or aspects, or something else altogether?

[Jim Eshelman]

NOTE MOSTLY TO MYSELF: I just figured out why midpoints to angles work ecliptically. It has to do with knowing exactly what midpoints are formatively: The contact is simultaneously ecliptical and mundane. (This does not yet solve the puzzle of why midpoints of an angle and a planet would behave ecliptically - still to be solved.)

I'm noting this on my commute as a reminder to write up the details sometime.

[Jim Eshelman]

BTW, the question, "What are midpoints?" reminds me of the question of whether light is a wave or particle. The answer seems to be that it is EITHER a wave or a particle for a given purpose depending on which it behaves like.

Similarly, I am approaching the question of the nature of a midpoint's structure in terms of behavior. Does it behave like a planet? Or like an aspect? Or like something else?

[mikestar13]

I haven't used most midpoints as extensively as Jim has (did I just beat whoever is in second place for understatement of the year?), but my thoughts are that midpoints are a species of aspect. In particular, a midpoint is only significant if a planet or angle contacts it. For example, I really don't give any significance to a sun moon midpoint which is unoccupied. It strikes me as similar to the question as what does the Sun not square the moon mean?

[Jim Eshelman]

I'm pulling together a theory today... if it fully matures, it will be a complex single model expressing aspects and midpoints as complementary components in the same matrix... and, because it is merely a mathematical model of the behavior we already know, I'm not sure that it will ever be provable. It's just a model.

Still, whether I stick to it or abandon it, I should get it down. I don't have the whole thing worked out yet, but I'm ready to talk about my current thoughts about the nature of midpoints. The model looks like this:

First, midpoints are normalized to a specific plane. They may operate in more than one plane (e.g., perhaps in the zodiac and prime vertical), but, in any case, their use is along one specific plane (at a time). For sake of the discussion that follows, let's only think about midpoints along the ecliptic.

Second, midpoints are like planets (or planet-like factors) in some ways and unlike them in other ways. Planets in astrology are actually more like particles - that is, they are points. In astrology, we don't use the whole of the physical planet, we only use its center. We treat it as a point. Midpoints are like planets in that they are individual units that have their own distinctive natures. (They don't dynamically bring together the planets that form the midpoint; they are their own thing, with an intrinsic nature that is a blend of the two planets' natures. But this singular quality belongs to the midpoint itself. For example, the Mercury/Uranus midpoint has the intrinsic nature of mental renewal, independent mind, discovery, and surprise but as its own thing, not simply dynamically link our mental and communication needs with our needs for freedom and renewal. -- However, midpoints are very much NOT like planets because (according to nearly all the people who use them heavily) they do not have meaningful sign positions or house positions, and, while they are regarded as forming aspects, they only form a limited number of aspects. (I will argue below that they don't form aspects at all.)

Third - and this is the single most important idea in this whole post - is the concept of circles of position. Some time back, I came to realize that aspects are not formed by single point-locations but by circles of position. What is a circle of position? I'm glad you asked...

Planet positions along the ecliptic are formed by a great circle passing through the planet and through the ecliptic poles. (Another way to say this is that the great circle is at right angles to the ecliptic.) But - something usually ignored - this is not a semi-circle but, rather, an entire great circle! It wraps clear around the celestial sphere in the same way that (on an Earth globe) the circle marking longitude 15° East is the same circle (continued around the other side of the globe) that marks 165° West longitude. Or, as another example, the circle that drops through my Moon and crosses the ecliptic at 27°24' Aquarius - since it's a full circle - wraps around the celestial sphere and also crosses the ecliptic at 27°24' Leo. These two longitudes are on the same circle.

In visualizing the celestial sphere, it eventually becomes clear that aspects are not formed between two individual points - say, a square of my Venus at 1°53' Scorpio and my Pluto at 2°06' Leo. Rather, the aspect (the angle of separation) is formed between two circles of position, one of which wraps around the sky at 1°53' Taurus-Scorpio and one that wraps around the sky at 2°06' Leo-Aquarius. These two great circles actually define planes passing through the celestial sphere. The planes are at a 90° angle to each other (within the small 0°13' orb of imprecision).

There are numerous implications for aspects arising out of this articulation. For example, it means that conjunctions and oppositions are essentially the same aspect - they are formed along the same circle of position. There isn't any need to detail the rest at this point. However, it IS necessary, for the current post, to explain how this impacts midpoints.

It is widely understood that the conjunction and opposition of two planets' half-sum are BOTH direct midpoints. That is, Venus at 1°53' Scorpio and Pluto at 2°06' Leo center on both 16°59' Virgo and 16°59' Pisces. (Most people who work with midpoints know this.) However, if we think of these planet positions as full circles of position (which, astronomically and mathematically, they are), then we aren't working just with 1°53' Scorpio and 2°06' Leo - we're working with 1°53' Taurus-Scorpio and 2°06' Leo-Aquarius. When you mark these FOUR POINTS on a circle, you instantly see that there are FOUR direct midpoints - falling at 16°59' of Gemini, Virgo, Sagittarius, and Pisces. - This matches the observation that the "squares to midpoints" aren't differentiatable in strength from what are usually considered "direct midpoints."

I didn't mention why a midpoint is significant in the first place. I haven't worked out the language for it fully. There are phenomena in nature where a point midway between two other points has a specific dynamic character as a result of its position. Every pair of planets ALWAYS has a set of midpoints. Similarly, every pair of planets ALWAYS has an aspect, in the astronomical sense where "aspect" means their elongation - how far apart they are. ALWAYS anchored in relationship by their midpoints, the two circles of position move closer to or farther from each other rhythmically and, as they reach specific separations, form what astrologers call an "aspect," i.e., a special relationship that vivifies their shared characteristics.

The midpoint structures are the complements of the aspects - part of the same master framework. I just haven't figured out how to explain the math of the larger picture yet.

Notice that midpoints may not form aspects at all!

For what are historically called the conjunction, opposition, and squares to a midpoint, these aren't aspects by the circles of position model. (Or, rather, they're all conjunctions.) What about the semi-squares and sesqui-squares (octiles), though? These are generally recognized as being significant or valid, but of a distinctly lesser strength. I am ready to suggest that saying the midpoints make these aspects is a stretch - probably not true. There is a simpler explanation consistent the overall structure we are seeing.

The simpler explanation arises out of taking midpoints of midpoints. If we have four Venus/Pluto midpoints at 16°59' Spoke, the midpoints between any two of them is the same as the semi-square; yet "midpoints of midpoints" is a simpler concept already in use in Uranian astrology and by some Cosmobiologists. The octiles to midpoints are really midpoints of midpoints. (What would the nature be of the midpoint of two Venus/Pluto midpoints? It would be the nature of Venus/Pluto - no different - just a difference in strength.)

I still have to work on the larger framework in which aspects are defined in the same conditions that give us the midpoints - as complementary information. I don't have this worked out but do have the root concept a bit of the semi-conscious feel of it.

Such is my thinking of the moment.

NOTE: Another approach to this post is detailed at https://solunars.com/viewtopic.php?f=16&t=5900. For now, I'm leaving the present post as it is, while sorting through whether to make the new thoughts a permanent theory.

[mikestar13]

I fully agree that squares to a midpoint are also direct midpoints. I understand that indirect midpoints are significant but weaker. Does this mean narrower orbs or reduced strength at exactness? It seems fairly well settled that with aspects, the former is the correct model. I do know that in my earlier days, the contrary model also yielded viable readings. For many years before ISR, I used Ptolemaic aspects to five degrees with a linear drop-off, and rated sextiles and trines at half the strength of conjuctions, squares, and oppositions of the same orb, fairly clearly not correct, but it worked.

[Jim Eshelman]

I understand that indirect midpoints are significant but weaker. Does this mean narrower orbs or reduced strength at exactness?

The practice I've fallen into is to read 0/90/180 within a degree and routinely ignore the 45/135 unless there aren't any (or nothing clear) in the stronger ones. Mostly I ignore them completely, but letting them shine through when nothing stronger is in their way seems practical.

[Jim Eshelman]

I want to summarize my current conclusions above (but without all the explanation and justification). However, this isn't over: This is a live thread open to everyone's engagement.

• Midpoints are like planets in some respects, but not like planets in most respects. For example, they do not have sign or house meanings and don't form aspects (though they do something that acts like forming aspects).
• Each midpoint appears to have its own distinctive, innate meaning (as a discrete point) and isn't simply a mechanism for a third planet to simultaneously relate to two other planets. (In practice, this distinction may be meaningless, though in the theory of what midpoints are, it is important.)
• Midpoints are not like aspects, though they may be part of a more complex geometry that also includes aspects. In this sense, midpoints and aspects are complements - points vs. spaces - in the same model.
• Midpoints operate in one or more explicit reference planes, e.g., on the ecliptic. (They may, and in fact probably do, also operate on other planes.)
• Planet positions are registered astrologically by circles of position. Midpoints are formed along the selected reference plane as points halfway between the circles of positions of two planets. Since the circles of position are great circles (circumscribing the entire sphere, touching opposite points of the reference circle, e.g., opposite points on the ecliptic), four midpoints (at 90° intervals) always exist for each planet pair. (Aspects also are formed as specific angular separations of two planets' circles of position.)
• As an example: Sun at 22°28' Virgo is marked by a circle of position intersecting the ecliptic at 22°28' Virgo and 22°28' Pisces. Saturn at 14°56' Libra is marked by a circle of position intersecting the ecliptic at 14°56' Libra and 14°56' Aries. These four points (22°28' Virgo, 14°56' Libra, 22°28' Pisces, and 14°56' Aries) have four simultaneous direct midpoints at 3°42' Cancer, Libra, Capricorn, and Aries, giving the mistaken impression that midpoints can form conjunctions, oppositions, and squares.
• Midpoints between midpoints are valid, though discernibly weaker. The midpoints between any two of the above Sun/Saturn midpoints will always be exactly 45° from them, giving the mistaken impression that midpoints can form semi-squares and sesqui-squares. The nature of a midpoint of one Sun/Saturn midpoint and another Sun/Saturn midpoint is of the nature of Sun/Saturn.
• Midpoints are intuitively meaningful. This intuition is confirmed in practice. Though we don't know the exact mechanism of their operation, the astrophysical universe and human neurology are both known to be highly responsive to bilateral or reflected symmetry.

This brings me to my discovery the other day of why midpoints - seemingly against all other astrological observation - seem to contact horoscopic angles ecliptically. It is this: Ecliptical midpoints are formed on the ecliptic itself, at a point halfway between the ecliptic's intersection with circles of position of two planets. Because ecliptical midpoints are always exactly on the ecliptic (celestial latitude 0°00'), they always cross the horizon and meridian mundanely and ecliptically at the same moment. That is, they probably actually cross the angles mundanely, but (since they are exactly on the ecliptic, like Sun) this always occurs at the exact instant that they cross it ecliptically.

Notice that this resolution requires that the midpoint is an actual point - existing as a thing itself, not merely a dynamic equilibrium between two planets. If a midpoint were more like an aspect, only existing by the separation of two planets, then the midpoint of their respective angle crossings would not be the moment the midpoint ecliptically crossed the angle. Defining midpoints as things unto themselves - always-existing point like "particles" - solves the puzzle.

I have not yet worked out one other case involving midpoints and angles, that in which a midpoint of an angle and a planet touches a third factor. I don't know if the above definitions and discussion justify that scenario. Perhaps they do, or perhaps another justification is still needed. - The places where the meridian or horizon intersects the ecliptic may not actually have any significance, which means that the circle of position of a planet is not in the same plane as the circles (meridian and horizon) that define the angles. - FWIW, in my own chart the dozen or so planetary pictures in this category are not my most persuasive pictures; the overall pattern of midpoints in my chart is much more persuasive / impressive if this category were ignored. Is it possible that, while midpoints can occupy angles, angles do not participate in forming midpoints?

[Jim Eshelman]

I have not yet worked out one other case involving midpoints and angles, that in which a midpoint of an angle and a planet touches a third factor. I don't know if the above definitions and discussion justify that. Perhaps they do, or perhaps another justification is still needed. - The places where the meridian or horizon intersects the ecliptic may not actually have any significance, which means that the circle of position of a planet is not in the same planet as the circles (meridian and horizon) that define the angles. - FWIW, in my own chart the dozen or so planetary pictures in this category are not my most persuasive pictures; the overall pattern of midpoints in my chart is much more persuasive / impressive if this category were ignored. Is it possible that, while midpoints can occupy angles, angles do not participate in forming midpoints?

If I were only to look at my own chart, it would be the easiest thing in the world for me to conclude that only planets form midpoints (though angles can occupy midpoints). However, it's premature to make that interesting leap.

I woke up this morning aware of a theory whereby angles can form midpoints; i.e., in A = B/C, a means by which angles could be B or C. It's an uneasy theory that, in consideration of the arguments above, is counterintuitive. Nonetheless, the intuition could be wrong and this phenomenon could exist. The ultimate test, of course, is whether actual charts show that it exists!

The block to thinking angles can be part of midpoints is this: The entire meridian circle is the MC/IC, not just points. The entire horizon is the Asc/Dsc, not just points. There are no "circle of position" that make sense for the ecliptic positions of these angles except that the meridian and horizon are themselves great circles. The problem is, they are not parallel the circles of positions of planets. Their shape on the celestial sphere is skewed. The "symmetry" is asymmetrical.

Nonetheless, it might be valid. We have to see from actual scrutiny.

A second theory is a bit strange: We do accept ecliptical positions of Eastpoint, Westpoint, Zenith, and Nadir. These are all formed by great circles perpendicular to the ecliptic passing through the actual points. If EP-WP and Z-N were taken as the actual involved points instead of MC-IC and Asc-Dsc, we get an interesting effect: The midpoints are shifted 45°, so that what have been though the direct midpoints involving an angle as B or C are in fact the indirect midpoints (and vice versa). It's an interesting artifact to consider, that would not have looked any different to Ebertin than he was seeing.

A third possibility is that we do have conditions where planets, meridian, and horizon all have circles of position that are parallel: It's when we are working in prime vertical longitude. It would be functionally strange, but responding to a valid, easy theory if all midpoints worked in longitude (including angles being at the midpoints of planet pairs) except that midpoints formed from a planet and an angle only work in PV longitude. (Remember, I'm following a thought exercise: I'm not saying this is so, only that it's mathematically possible.)

To move from theory to examples, here are my natal conjunction, opposition, or square ecliptical midpoints that have an angle as one of the factors forming the midpoint:

NE = Pl/MC = Ve/As
SA = Mo/MC
VE = Ne/MC = Ur/As
PL = Ne/MC = Ur/Asc = Ju/As

I submit that these don't fit - this, despite the fact that my other 0/180/90 midpoints fit quite well in most cases. By "don't fit" I'm talking about, first, taking Ebertin's interpretation text and, if it doesn't fit, being willing to override with basic knowledge of the planet pairs. I don't think any of them fit. - They do, in some cases, resemble other midpoints that do fit, usually straight from Ebertin's text or a minor adjustment (e.g., I have MC = Ne/Pl which, in theory, sounds like Ne = Pl/MC and Pl = Ne/MC but actually has very different outcomes). Sa = Mo/MC would be expected to produce quite distinct and recognizable patterns marking my life as a whole, and my relationships with my mother and, later in life, other women; but one has to stretch it a long way to fit. [OTOH, Marion also has Sa = Mo/MC = Pl/MC, which describes very well important events involving her mother's death.]

This could just be my chart, of course, or my view of it, so I don't hang a final conclusion on it.

We can test the "What if it's really EP and Zenith?" theory by looking for planet contacts to midpoints involving angles only at 45° and 135° degree aspects (which would be the 0/90/180 if the ecliptical aspect were really with EP or Z). I get these:

NE = Ve/MC = Pl/As
SA = Mo/As
VE = Ne/MC = Ur/MC = Ju/MC
PL = Ne/As = Ur/MC= Ju/MC
SU - Sa/MC

These look (at first glance) nearly identical, but the specific angle involved is different. Do they fit any better? (I'm using Ebertin's text as a basic.) To my surprise, about two-thirds of them have direct, solid hits. I cannot, therefore, rule out the possibility that angles 90° removed from MC and Asc (which are actually points) produce this effect, but A and M (which are planes or great circles) do not.

Finally, what if I calculate this group of possible midpoints along the prime vertical where circles of position are parallel? I only have these few (similar to but not always the same as the first group above):

PL = Ne/MC = Ma/As
VE = Ma/As = Ne/MC

About half of them fit. It's better than the first group (straight ecliptical calculation), not as good as the second group.

Again, this is a single case. By itself, it means nothing other than suggesting possibilities.

I'll do one more, checking whether Marion's ecliptical midpoints (with an angle as A or B) seem descriptive. She has these:

ME = Ve/As = Ne/As
SA = Pl/MC = Mo/MC
PL = MO = Ju/MC

About half of this fits, which is better than with mine. That is, they describe either character traits (such as Me = Ve/As and Mo = Ju/MC) or a defining life event (though it's not explicit in Ebertin, I take Sa = Pl/MC = Mo/MC to allude to her mother's death, which was a defining event of great significance.) The others are hard to justify, but this is at least better. - But, in contrast, her other (planet/planet) midpoints all fit quite well provided you set aside the fact that a lot of them mention violence. (It's not the only thing they mention, of course.)