Bear with me a moment.
Go to the diagram of the double loop, Book of Thoth. Copy out the diagram accuratly (or be reckless and draw in your book like I did)
Write the number 1 next to IV (the lowest in the series of Roman Numerals shown) and go around the diagram attributing the next number (2) to the next highest Roman Numeral (V) and so on. Dont loop, go around the diagram in a circular path. Now do the same with the astrological signs in their order; 1 to Aries, 2 to Taurus, etc.. Now look at how the two sets of numbers you have written at each position compare with each other (starting from IV / Aries and going anti-clockwise); 1-1,12-12, 11-11, (left hand side) 2-2, 3-3, 4-4, 5-7, 6-6, 7-5 (right hand side) 8-8, 9-9, 10-10. The loop is only on one the right hand side where Adjustment / Lust trump number swap is. There is no left hand loop or double loop!....
Crowley tweaked the loop on the left hand side himself, just by , mearly, drawing it that way. There is no astrological / numerical order switch in the Tarot to justify it on the left hand side.
Now look at the tables in The Book of Thoth, p. 278. (the 'wrong' ones) with the strange attribution of Aries / Star, Aquarius / Emperor. Go down the attribution column but start at Aries; Aries, Pisces, [go up to the top] Aquarius, Taurus (the left hand loop in the diagram), Cancer, Libra, Virgo, Leo, (right hand loop), Scorpio, Sag. Capricorn. The double loop only works (in the tables) if you swap the previous astrological attribution to the Emperor and Star. That is why the attributions are out of wack in the table.
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In any case the loop diagram attributes IV to Emperor and XVII to Star (as do the cards themselves), again, no need to loop the diagram on the left. Even if we use Crowleys table and put Aries to the Star and Aquarius to the Emperor on the double loop diagram, the loop disappears as the astrological progression is back in order.
This does, however, loop the Roman numeral progression on the left hand side, but why do we need to loop the numbers when the astro progression works out?The only way to justify that is to say that the signs loop on the right and the numbers loop on the left but non of that is valid anyway as it is trying to justify a Hebrew letter swapped attribution.
The double loop in the zodiac diagram is a 'fudge' as far as I can see....
In the Book of Thoth A.C. glosses over it (p.4) "Tzaddi is the Emperor; and therefore the positions of XVII and IV must be counterchanged " (yes, but on the Tree of Life not the Zodiac). And unfortunatly Crowley refers to this balanced double loop as, "The most convincing evidence possible that the Book of the Law is a genuine message from the Secret Chiefs".
Some pertinent excerpts from this interersting close look at the loop. But I don't think this is all a "fudge" of forcing correspondences. Yes, we don't need to make the loop, since the astrological progression already works. But the loop itself creates a different scheme of meaning that breaks away from prior fixed schemes. It's a new, dynamic change of picturing. But not the only picture, anymore than Chinese or Hindu astrology or astrosophy (heliocentric) carries the only whole picture. The only whole picture is the fully awake unity with the whole. All metaphysical schemes are maps and fingers pointing.