New quantification of angularity

[mikestar13]

This makes some changes in the width of grounds, the angular side of an angle has 10 degree of foreground and the cadent side has only nine degrees of foreground and the width of background is correspondingly narrowed, assuming the boundaries are now 80% and 20%. I could of course play with the numbers a bit but do we in essence want 1 degree shaved off each foreground and background?

[Jim Eshelman]

Yes, I know the boundaries aren't exactly what I've said I want or suggest. Nonetheless, by excitement is that a single equation generates a single curve that hits all the fundamental markers (exactly defines exactly angular, exactly cadent, exactly mid [twice] and is all but a coarse shave from the other points).

If nothing else, it gives me a pretty picture to use in the angularity chapter of the next book, which I'm writing at the moment

I suggest not spending energy on reworking the curve or grounds boundaries unless some of us actually work with this and give meaningful feedback on it. My current expectation is that, since the difference are only at the weak trails of the humps, one can't tell one way or the other in real life practice.

[mikestar13]

I've been working on other things besides the angularity curve, and it took me a month to get around to studying this. I think your equations do fit the cosine model well. Having the 80% mark at 10 and 81 is slightly awkward, but foreground planets that far from the angle aren't all influential anyway, just somewhat more expressive. I could easily implement it in TMSA 1.0, the minor angle curve (derived from the aspect curve) should probably stay as in. The seems reasonable as they are mathematically ecliptic squares to the major angles or in the case of Ea/Wa, right ascension squares to Mc, though different conceptually. If I do this, I can change the foreground specifications for the classes to % strength (and convert existing option files on first use in the program in the software, so users won't have to do anything). The mid-quadrant curve for mundane astrology can remain as is, since as far as I can see, there is no repressiveness curve in ingresses.

[mikestar13]

Also another thought, I could leave the foreground boundaries in degrees, and just accept the percentage number will be slightly different on opposite sides of an angle/cadent cusp. Also, though I've been using them, background marks just aren't as important in practice.

[Jim Eshelman]

My current thoughts: My excitement with this equation and approach is that it gives the whole pattern in a single equation. I'm not "sold" on it to the extent of all the percentages being precisely right - maybe yes, maybe no, but it's so subtle that I'm loathe to abandon something that has worked so well as the flat-number boundaries for angularity.

I'm also not inclined to ask you to do extra work while you already have so much you're trying to finish for just the next stage. The greater elegance of a single equation is intellectually satisfying but MAY not add anything practical to us.

There is also the fact that (our strength % be damned!) individual users will want different angularity orbs (and I want them in different contexts) and our thinking is still in terms of fixed bilateral orb boundaries (though perhaps it shouldn't be).

And, in most cases, it makes no great difference in practice.

My current thought, then, is that ONLY IF YOU ARE MOVED TO TAKE ON THIS CHANGE, use it for calculating precision % curve only, and continue to measure "grounds" based on the hard aspect divisions. The result: Both the % curve and the "grounds bounds" are evident side by side on the chart table - someone can see either of these at a glance and use whichever they want in close calls. Over the long run, this would give us input on which approach works better (even though there is almost no difference in practice).

[mikestar13]

I'll see what inspiration wills as I'm coding other features. The user selection for boundaries will be in degrees with bilateral symmetry as at present, only the percentages will differ slightly, should I decide the change is worth making. In any event, the basic scheme of 100% = exact foreground, 0% = exact background, 50% = exact middleground will be retained.