TMSA Beats Solar Fire!

[mikestar13]

It is confirmed, TMSA does fine tuned timing (ingress times) better than Solar Fire. The chart discussed in this thread: viewtopic.php?f=55&p=42639#p42631 is an example. I knew in my gut I had it right, Jim had always suspected I did. I feel on top of the world. (Of course Terry regularly makes me feel that way too).

[Jim Eshelman]

Yay!

BTW once we have Quotidians and transits, I probably need to recalculate all 3,000 or so charts in SMA. I've started working where I can.

[Jim Eshelman]

PS - Congratulations on your good work!

[mikestar13]

One thing that has slowed us down in resolving this issue is my lack of access to Solar Fire. I had actually consider buying a copy in 2008 but couldn't quite fit it in the budget, and of course the $ situation went irretrievably south after my first stroke, so the only comparisons I have are provided by Solar Fire users who have tested TMSA. I do know that TMSA uses Swiss Ephemeris verion 2.12 which introduced the sun/moon crossing functions. Solar Fire 9 uses version 2.08, and Solar Fire 8 of necessity uses an earlier version (I don't know the number). I am also quite sure that the of necessity iterative calculation of the ingress times is bound to be more accurate when calculated by the SE internally than when the iteration is done via the program using SE. In the latter case, round off errors are magnified, not matter how logically perfect the algorithm is. An analogy: whats 2 +- 0.1 plus 2 +- 0.1? 4 +- 0.2!

[mikestar13]

Sorry about your new workload, Jim. Ironic that your Virgo lust for accuracy was satisfied by the flawless logic of a Pisces. Of course rising Mars sextile to Sun-Venus can give me more ability to cut through the crap than the average Pisces, reinforced by Pisces Mercury conjuct Aries Moon. Say as I said in my very first post to solunars, I'm a recovering Aries, but the recovery ain't complete.

[Jim Eshelman]

ROFL. The eventual re-do is critical for the full integrity of the SMA project. I actually could let it go EXCEPT there is one factor we know will be minutely changed with new calculations: At least a few minutes here and there on quotidian angles. This means I need to completely revalidate all quotidian crossings down to the minute to repeat the verification of the SVP!

Based on SF (and only half the data I currently have), the SVP appeared validated within 1"-2". Now that we know the data processing was slightly wrong, I have to reconfirm that, I feel. Imagine: Bradley did the original rectification of the zodiac (the "polish work" on an already close boundary) not only without TMSA, not only without the (known to be several minutes off) earlier versions of Solar Fire, but with a printed ephemeris and an adding machine (that was his tool of choice). He also wrote that he used only 27 events for this step!! This was quite doable because it was sufficient for him to know that the quotidian angles needed, on average, half a degree of correction - obviously a rounded figure that let him conclude that the Capsolars he'd been calculating were about two minutes of time off. The famous 5" final "polish" is simply how far Sun moves in two minutes of time in mid-January.

Using SF8, I replicated his approach but with 211 events - eight times the original number - and with automatic calculation of Capsolars and quotidians by Solar Fire. I found, on average, a need to shift shift angles 0°04', which meant a 1" shift in the SVP or, on average, a Capsolar 16 seconds later in time. Repeating with the Cansolars, the data suggested they should occur, on average, 40 time-seconds later.

Mike, you're probably ahead of me on this, but... look at those numbers... Capsolars averaging 16 seconds later, Cansolars averaging 40 seconds later... and (ahem) give me your opinion on whether TMSA calculations won't bring the discrepancies from Bradley's original 27-event determination of the zodiac boundaries to, oh, about... 0".

[Jim Eshelman]

A few examples to see a pattern listing UT only:

2018 Capsolar
SF 5:04:38
TM 5:04:50
Diff +12s

2018 Cansolar
SF 15:09:38
TM 15:09:51
Diff +13s

2019 Capsolar
SF 11:09:58
TM 11:10:06
Diff +8s

2019 Cansolar
SF 21:17:03
TM 21:17:20
Diff +17s

2020 Capsolar
SF 17:26:30
TM 17:26:50
Diff +20s

2020 Cansolar
SF 3:29:45
TM 3:29:57
Diff +2s

2021 Capsolar
SF 23:32:30
TM 23:31:01
Diff +31s

2021 Cansolar
SF 9:36:32
TM 9:36:49
Diff +17s

2022 Capsolar
SF 5:48:10
TM 5:48:12
Diff +2s

2022 Cansolar
SF 15:40:11
TM 15:40:44
Diff +33s

[Jim Eshelman]

For the five years selected centered on about now, there is variability - for example, three charts have almost no difference at all, most have more -- but, on average:

The five Capsolars were 12, 8, 20, 31, and 2 seconds later by TMSA calculation, averaging 14.6 seconds later. The most perfect fit for the SVP would be if the charts averaged 16 seconds later. That's almost a square hit!

The five Cansolars were 13, 17, 2, 17, and 33 seconds later by TMSA calculation, averaging 16.4 seconds later. The most perfect fit for the SVP would be if the charts averaged 40 seconds later. While this is a larger gap, the CanQ is a weaker tool than the CapQ.

If we presume TMSA to be exactly accurate (in the worst case, it's the best we have at the moment) and take my 211-event study as controlling (and, for the moment, overlook rounding errors along the way), it seems that Capsolars only (on average) 1.4 seconds later in time with Sun's daily motion of 61', it suggests the SVP needs adjusting 0.0" of arc!

Making the same assumptions but with the Cansolar data, it seems that Cansolars only (on average) 23.6 seconds later in time with Sun's daily motion of 57', it suggests the SVP needs adjusting 0.9" of arc.

Of the two, I lean toward valuing the Capsolar results over the Cansolar results; but even their average is under 0.5", i.e., rounds to 0".

It may be that TMSA affirms the SVP value as accurate to the second of arc with no need for modification at all. - This makes Bradley's hand-calculated, ephemeris-based, 27-event rectification of the zodiac all the more stunning.

[mikestar13]

I suspect Bradley was psychically guided as well as mathematically able, whether he was aware of it or not. I'm rather sure Fagan was when he resolved the hypsomata and rectified the Hindu Spica = 0Li0'0' zodiac to Spica = 29Vi0'0". Impressive indeed those feats were. Rectifying the true zodiac from an approximation of it.

[Jim Eshelman]

Little known fact: Bradley, based on the Profession & Birth Date project, first reported to Fagan (by trans-Atlantic letter) that it looked like the zodiac should be one degree sooner than the Lahiri standard with which Fagan had started. And look (Bradley continued), that not only puts Spica in Virgo, it put Aldebaran-Antares at 15° Taurus-Scorpio. "Bull's eye" and all.

Fagan's return letter (probably not par avion in those days, but possibly on that post-war tissue paper that Firebrace kept in vogue the rest of his life) said something like yes, thanks, he agreed, and, oh, by the way, he just solved the problem of the exaltations and it required the same 1° shift.

This is the start of my allegation that the coolest thing about the identification of the exact boundaries of the zodiac is that it was independently discovered by archaeological and statistical means: One person was finding and confirming what the ancients did, while the other person was starting from scratch and seeing if there was a zodiac at all and, if so, where it fell. Garty Duncan was rightly insistent that if Fagan never had the archaeological data to back him, the correct zodiac would have been uncovered in the mid-20th century simply by work that was already in motion. (But it's so much cooler that we do have Fagan's work on the history.)

I tend to think of Bradley's work as the more valuable, but Fagan's initial impulse and committed monthly writings as the core of what brought this further. Fagan's archaeology doesn't persuade me of the Sidereal zodiac: It confirms what a bunch of inter-connected places did once upon a time. It's neither stronger nor weaker than observing that for most of the last two thousand years a bunch of inter-connected places has used the Tropical zodiac. But Bradley's work - that's mind-boggling. It shows first that there actually is a zodiac (something that behaves as 12 30° sections with distinctive characteristics) and that those boundaries fall at about 24° off the equinoxes in most of the 20th century and 23° off the equinoxes in the 19th century. It then went on narrow this probably to within about 0°00'00" of precision. The fact that Fagan's work shows that, gosh, do you know this happens to be exactly what the ancient Egyptians did? and other researchers have shown that, gosh, you know the Babylonian zodiac is, more or less to the minute, in the same place - that just makes it all the sweeter.

OTOH, Fagan's basic points are easier to explain to people. Bradley's work requires an understanding of statistical methodology and the kind of mathematical organization most people have never thought about. Almost like studying economics (in which most people think "inflation is expansion, things cost more," and economics say, "no, no, it's constriction, because money is worth less").

[Jim Eshelman]

Anyway... yeah, TMSA beats Solar Fire!