Thoughts on angularity strength percentages

[Mike V]

I'm putting this in Time Matters because, as the only software that can display these, I figure it only really matters for those of us who use it.

Jim’s models for angularity (and the non-cycloid models of preceding siderealists, from what I understand) follow a cosine wave structure that peaks at +1.0 and bottoms out at -1.0. This structure is then mapped to each quadrant in prime vertical longitude, so that a placement in the mundoscope is associated with a value of the cosine curve, which is the planet's angularity score, or expressiveness score. There are alterations to the pure cosine function depending on the model being used (and the curve may peak and trough at other values than +/- 1), but this is the core idea.

These values of the cosine curve are associated with a "strength" percentage, which goes from 100% strength at the angle down to 0% at some intermediate location - either the cadent cusp or some other point, depending on the model used. All of these models mark the foreground zone boundary at "75% strength," which corresponds to +0.5 of the basic cosine curve, and they mark the background boundary at 25%, or -0.5. So far, so good.

I find the cosine model very intriguing and want to use it more going forward. However, so far, I haven't found these particular strength percentages very useful in practice, even though I believe I understand their theoretical soundness and consistency within the model. Let me explain why, and what my proposed model for strength percentages (not for angularity per se) looks like. It's possible that I'm the only one who gets any use from this, but I'd like to open it up for discussion.

The existing strength percentages are based around the idea of how likely some planetary influence is to manifest, and that we really start to notice a planet's expressiveness at the "75% chance of showing up" boundary, which corresponds more or less to the 10° boundary we use for primary angles. Similarly, a planet's expression starts to seem really noticeably blocked around the 25% mark. These curves are smooth, without sharp boundaries, since most of nature does not have sharp boundaries.

This is not invariably the case, though, and I think that this is important. Events that are known in physics as symmetry breaking produce sharp boundaries in behavior - for example after the Big Bang, there seem to have been phase transitions in which the strong nuclear force, and then the weak nuclear force, abruptly split off from the electromagnetic force and started acting as separate forces. Similar phase transitions exist in the phase diagrams for various elements and compounds - even though water does not instantly and fully freeze at 0°C (at standard pressure), there is still a relatively sharp change in behavior that is centered at that point.

My difficulty with the way the current angularity strength models are displayed (not necessarily calculated) lies with all of the intermediate percentages. I think these add noise to a chart breakdown. I'm proposing this variant model because I think that it may be useful to treat the edge of the foreground zone as a phase transition of sorts, in which we transition from giving special attention and weight to planets' expressiveness, to not really differentiating between their expressiveness.

[Mike V]

Let's make up some angularity strengths for a hypothetical chart:

Moon 99%
Sun 98%
Mercury 96%
Venus 90%
Mars 70%
Jupiter 66%
Saturn 51%
Uranus 40%
Neptune 33%
Pluto 20%
Eris 8%

In this breakdown, the first 4 bodies are angular, and Pluto and Eris are background. Mars, Jupiter, Saturn, Uranus, and Neptune are middleground.

I think that the following would be a more useful display for a chart like this (though I'm not done):
Moon 99%
Sun 98%
Mercury 96%
Venus 90%
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto background
Eris background

This is actually the way that we, on this forum, often summarize charts, or sequences of factors: we totally ignore the middleground or unremarkable stuff. For example, I seem to recall seeing Jim post ingress charts that omit non-foreground planets (or at least ones that also don't aspect Moon) completely, and many of us refer to Lunar returns along the lines of "my next SLR is Mars Pluto Neptune."

So why display angularity strengths for planets that are, by definition, unremarkable?

[Mike V]

Here is another reason for my current thoughts on this topic: if we ignore middleground planets' angularity strengths, we then have more "room" percentage-wise to differentiate between foreground planets. Perhaps this leads to over-differentiation and making mountains out of molehills, but I'd like to explore the concept all the same.

Let's take these 4 foreground planets in this example. I'll add in the orbs now.
Moon 99% - 1°
Sun 98% - 3°
Mercury 96% - 4°
Venus 90% - 6°

Here is where I start to get discombobulated. A 1° orb and a 6° orb feel very distinct to me, much more distinct than the 9% difference in angularity strength indicates. My mind blurs percentages like these 4 together and I have trouble differentiating them when reading a chart breakdown. As a result, I have generally glanced over them and worked out the raw orbs manually when using Time Matters.

But what if, instead, we scale from 100% to 0% within the foreground zone? This then becomes an angular significance score rather than a pure angularity score. Or, said another way, it's a "how much do I need to care about this planet's angularity in this chart" score.

Calculating this is simple. We just take the original scale from +1 to -1 of the cosine curve and apply this percentage to only the +0.5 and up range, which would be 75% in existing models.
The formula is:
significance = (cosine_value - 0.5) x 200, which is only displayed if it's a positive score.

Converting from an existing angular strength score is also simple:
significance = (score - 75) x 4

Separately, if it’s -0.5 or lower, just call it background and don’t give it any percentage.

Nature doesn’t typically have sharp cutoffs like this, which the existing models respect - but the analytical faculty of my brain does use this sharp cutoff as a tool for analyzing.

This differentiates more starkly between smaller differences in orb. Here are the same 4 angular planets with "angular significance scores":

Moon 96% - 1°
Sun 92% - 3°
Mercury 84% - 4°
Venus 60% - 6°

I'm wondering if this is more useful - especially as a breakdown given to non-astrologers - than seeing 4 planets at 99%, 98%, 96% and 90%, then all of the other ones at sub-75% scores. This is also much closer to how I actually read and interpret angular planets.

I'm interested in what you think. I'll calculate some more examples as I have time.

[Jim Eshelman]

A few answers to "why."

1. In pure research - say, in the study of a large collection of one kind of natal, or of one kind of return chart - one approach (and one that Bradley and Duncan kept working on all their lives as an important statistical tool) is the ability to give just exactly this sort of score.

2. They give us the best way to compare the different models of angularity. (As you point out, crude-grouping of planets has no granularity.) Switching between different curve models and paying attention to these granular differences (either anecdotally or in larger statistical projects) is the most direct path to understanding the right model.

4. It has one concrete use right now that I use in almost every chart I touch: the Hierarchy of Needs relies primarily (but not exclusively) on these.

6. It does no harm.

I have fallen away from paying as much attention as I used to because the calculations are broken (and have been for a year or more). Still, they're important enough that I created a spreadsheet to calculate the correct minor angle scores. I'm particularly eager to start using them again when the third scoring model is added (it handles middleground better and has different finesses for the boundaries of the Grounds: I expect to learn a lot).

I do pay attention to them - in natals. They don't mean much to me in returns or ingresses because, for returns and ingresses, the main tactic is to rule out the planets you aren't reading (those that aren't foreground) and read the rest. But in natals they're nearly always important to me. (Even in returns I'll often glance to see just how background a background planet is.)

For returns and ingresses, I always list by orb because I know how those feel quite granularly. But the main reason is that I'm not convinced we have the scoring exactly right. (Or, rather, I know part of it is broken and don't have the certainty I'd like to have on the other.) If I ever feel we have a nailed-down-this-is-it-and-I-know-I'm-right scoring formula, I'll probably start training myself to read that directly. - Meantime, I'm playing it safe using what I know.

Those are my thoughts...

[Mike V]

You make strong arguments. Thank you for taking the time to talk it out. This is stirring a semi-related idea which I'll make a new thread for.

I'm particularly eager to start using them again when the third scoring model is added (it handles middleground better and has different finesses for the boundaries of the Grounds: I expect to learn a lot).

Hopefully within the next few days

Actually, for that matter... I'm not done with tweaks, and biwheel info table stuff might be broken in certain circumstances (I'm still testing), but I can put the alpha up for download in a little bit if that would be useful for you. It includes a setting that allows you to use the Eureka curve model, since I was doing all the mathy stuff at once and I think it's all set now.

[Jim Eshelman]

BTW, though I would not want to lose that angularity strength column, if one DID do that - follow the idea of "just strength if foreground" - the simplest way (and most connected to historic astrology) is just treat foreground as (mundane) conjunctions with the angles. In a sense, that's what they are and it would put angularity and aspects on the same gradients. Default major and minor angle class bounds are essentially the same as conjunction and minor aspect bounds.

This would abandon the idea of and rising and falling angularity curve throughout each quadrant and replace it with a return to "conjunct an angle" modelling.

I'm not suggesting this, of course I'm just mentioning the most internally consistent way to do it.

If I were nudged really hard I might endorse the idea of allowing users to turn on aspects to angles (conjunctions and mundane only) which would let someone ignore the upper data tables altogether and simply find angularity as one more kind of aspect in the aspectarian. I wouldn't use it myself other than as a weird thing to try... but it would probably be the simplest. (I'd have some curiosity about whether angularity scaled into an aspectarian automatically showed correctly their relative importance, e.g., would it turn out that a 2° planet-planet conjunction stands out more importantly than a 4° angularity?) I'd consider this a "when we are settled the program is done and we're looking for other features to add" sort of thing.