Unlocking the Observatory: the Great Dial and Determining Times/Options

May 18, 2022 By polyphanes in occult Tags: age, divination, great dial, great mirror, planetary hours, prediction, telescope of zoroaster, time, unequal hours, unlocking the observatory, zoroaster's telescope 2 Comments

Where were we? We’re in the middle of discussing the obscure Telescope of Zoroaster (ZT), a manual of divination and spirituality originally published in French in 1796 (FZT) at the close of the French Revolution, which was later translated into German in 1797 (GZT) and then again in an abridged form as part of Johann Scheible’s 1846 Das Kloster (vol. 3, part II, chapter VII) (KZT), with Scheible’s work then translated into English in 2013 as released by Ouroboros Press (OZT). Although OZT is how most people nowadays tend to encounter this system, I put out my own English translation of FZT out a bit ago as part of my research, and while that translation was just part of the work I’ve been up to, there’s so much more to review, consider, and discover when it comes to this fascinating form of divination. Last time, we talked about the myriad ideal triangles in the Great Mirror and what sort of interpretive benefit they allow in divination. If you need a refresher on what we talked about last time, go read the last post!

※ For those following along with their own copy of ZT (get yours here!), the relevant chapters from ZT are the “Sixth Step”, “First Supplement”, and “Third Supplement”.

We’ve just finished up talking about the Great Mirror—or, at least, finished explaining and expanding slightly on what ZT has to say about it. As ZT itself says following its own talk of the Great Mirror:

We are rather far from having said all that it would be possible to say about the astronomical regime…We cannot repeat too often that this text can and should only be a key. Profound meditations, with compass and pen in hand, must have the double success for the Candidate of permanently inculcating in them a tearing-away and breaking of the avarice of indications from the very moment of our march. Now, the Great Cabala does not include a theory of this kind. By it, the road would be made more difficult than easy; by it, the Candidate would find themselves squeezed in some way between the two flanks of a relatively open angle, while they must move freely through all the content of an immense circle, which embarrassed nothing less than all that is for as long as it shall last.

In other words, while one can certainly expand on the various cosmological and interpretive significations of the Great Mirror more than what ZT has, ZT itself declines to say more than it has in the interest of brevity. (Or it may be that it has nothing more to say about it because it made it up and is masking that fact with claims of mysterious obfuscation, who knows.) All the same, it is true that the Great Mirror is just one of the two main ways to use the large hexangular figure of 37 tiles. While the Great Mirror is the so-called “astronomical regime” of the large hexagon, there is another: the “temporal regime”, which is a way to consider the large hexagon as indicating periods of time ranging from individual hours to a whole millennium. Rather than calling this sort of temporal view of the large hexagon the Great Mirror, the temporal regime calls it instead the Great Dial (as in the dial of a clock-face):

The above is a reproduction of ZT’s own Plate IV, with one minor correction (which I’ll touch on later):

Just as we might say that the Great Mirror (the large hexagram read in the astronomical regime) has both “essential interpretations” (reading the tiles according to their houses) and “accidental interpretations” (reading the tiles according to the ideal triangles they fall into with other tiles)—even if the use of such terms “essential” and “accidental” are my own imposition on ZT here based on astrological usage—the Great Dial has two ways to read it, as well, which ZT itself calls “movements”, where one starts with greater time periods and works its way down to smaller ones:

Eccentric movement (movement starting at the center and working towards the edge)
- Center house: 1000 years
- Inner belt: 100 years per house
- Middle belt: 7 years per house (as indicated by the number in these houses)
- Outer belt: 1 year per house
Concentric movement (movement starting at the edge and working towards the center)
- Outer belt: 5 years per house
- Middle belt: 1 month per house (as indicated by the sign in these houses)
- Inner belt + central house: 1 day per house (reckoned according to the weekday, as indicated by the planet in these houses)

Before we go on, let’s clarify a bit about how ZT breaks time into particular segments. Some segments you likely already know, dear reader: 1000 years makes a millennium, 100 years make a century, 12 months make a year, 7 days make a week, and so forth. Where does ZT’s use of 7-year segments and 5-year segments come from?

Climacteric period: a period of seven years, starting from the moment of one’s birth. This actually isn’t something that ZT makes up; climacteric periods are a thing that have been recognized since ancient times in medicine and astrology. ZT explains this as:

The transitions from the seventh year of life to the eighth, from the fourteenth to the fifteenth, and so on are the so-called “climacteric nodes” where, ordinarily, an individual is subject to revolutions either physical or moral. It is a commonplace in medicine and physiology, and is doubtlessly not unknown to anyone.

The word “climacteric” has its origins in Greek κλιμακτηρικὀς klimaktērikós “of a critical period”, where every seventh year of a person’s life was considered a time when they undergo particular (often critical or dangerous) changes to their body, life, and surroundings. Even today in modern medical contexts, “climacteric” is still used in some limited contexts to refer to natural changes in life accompanied by various health consequences. From an astrological standpoint, the origins of this are probably obvious: given that Saturn returns to its same position in the ecliptic every 27 to 29 years, this means that it crosses 90° of the ecliptic every seven years, causing a transiting Saturn to conjunct, square, or oppose one’s natal Saturn every seven years.
Lustral period: a period of five years, starting from the moment of one’s birth (each such period is also just called a “luster”). We haven’t covered how ZT considers the origin and process of a human life yet—it gets kinda weird involving two angels shedding sparks of divine fire which combust into a human soul at the time of conception—but ZT breaks up a human life into 18 “lusters”, each accounting for five years (or four, or seven, depending on whether a person is a man or woman and how old they are, which we’ll leave for a later discussion as well). To this end, ZT says that a human life only reaches its maximum of 90 years, because 5 × 18 = 90.

So, looking at the Great Dial, what do we make of the numbers and symbols there?

The numbers 1 through 18 in the outer belt indicate single years in eccentric movement, or the number of lusters (5-year periods) in concentric movement.
The numbers in the middle belt indicate climacteric years in eccentric movement, i.e. the year in which one moves from one climacteric period to the next. (There is a small error in these numbers: house 9, labeled “Taurus – 15”, should have the number 14, not 15. I’ve corrected this in my own redrawing of the Great Dial.)
The signs of the Zodiac in the middle belt indicate months in concentric movement (identifying March with Aries, April with Taurus, and so forth.)
The numbers and planetary symbols in the inner belt and center house indicate the days of the week in weekday order.

One note before moving on: although, in concentric movement, the middle zone is used primarily to determine months, it can also be used to refer to any smaller units of time that can be broken down into a twelvefold division: hours of the day or the night, minutes of an hour (with each house referring to periods of 5 minutes), and so forth. However, ZT says that the smallest reasonable unit of time to break down inquiries is to the level of the hour, and that while one could break inquiries down into smaller units of time to minutes or seconds:

…this mincing smacks too much of charlatanry to us, at least to seriously give ourselves over to accounting for the fussiest fractionation of time. It is a matter of divinatory nickel-and-diming which gives, at best, a knavish character to the accounts of people acting in bad faith. We indicate the possibility of extracting ever-smaller units of time only so we may establish that, if the Candidate were to find themselves deterred by some lack of teaching, then at least they should not attribute their embarrassment in this to some insufficiency of the means of the Great Cabala.

So, the obvious question arises: when do we use the Great Dial in eccentric movement vs. concentric movement? The way I like to think about it is that concentric movement deals with the events within a human timeframe, either within a human lifetime or otherwise something that happens in the near term. Eccentric movement, on the other hand, deals with events that occur over much grander periods of time—up to 1702 years down the line (or, I posit, in the past), beyond such a limit the Great Dial cannot be used. As a result, when ZT gives examples of determining matters of time, it generally uses examples of concentric movement on the Grand Dial, since it generally deals with events on a human timescale instead of a civilizational one. That said, at one point ZT does also present a fiery defense that some matters demand the inspection of not just the events of a single lifetime but even unto “the most distant future”, noting that sometimes events indicated in a Great Mirror might occur centuries from the time of the reading itself (e.g. when such a reading says that one’s descendants are destined for royalty or greatness, but such a thing only happens two or three centuries from the time of the reading).

Okay, so, we have the “what” and “why” of the Great Dial understood, so what about the “how”—how do we actually go about using the Great Dial? Well, uh, let’s back up a bit and reconsider first that the Great Dial is a way to use the large hexangular figure in order to answer matters specifically about time in the sense of when something will happen—assuming that it will, of course, which is a matter for the Great Mirror and other divinatory processes to conclude first. (This is much the same approach I’d take with geomantic divination: if someone wants to know when something will happen, I first confirm that it will or not, because if it won’t happen, then asking about when would yield a nonsense result.) As opposed to the use of the Great Mirror, which never earns a proper example or case study in ZT, ZT offers lots of smaller examples throughout the “First Supplement” about various ways to predict the time of an event.

The overall method that ZT mentions for determining details of time (and other such details) generally fall under what I call “option-whittling”:

For the topic under investigation, select a tile that accurately represents the thing being investigated (e.g. the 66 tile for marriage). This will be the “speaking tile” or, in modern terms, the significator of the questited.
Given a set of possible options, select a figure of the appropriate size that represents the number of those options. Take the speaking tile and however many other tiles you need to come up with that figure, mix them up without seeing, and arrange the figure in the usual order with all tiles face-down.
Starting from the last tile placed in the figure, announce what the last possible option available, and flip up that tile. If that tile is the speaking tile, then the announced option is the one indicated.
If, however, the announced option was not the speaking tile, proceed backwards through the rest of the tiles, proceeding through each option in turn in reverse, to find where the speaking tile is.

Say I know that a friend is planning a party in the coming week, but I don’t know what day of the week it’ll be on yet and, given that my friend is in the habit of giving little-to-no advance notice for such events, I want to plan ahead to see if I can make it in my otherwise busy schedule. For this, I’ll pick the 22 tile “happy associations, friendship” to represent the party, and given that I have seven options to pick from (seven days in the coming week), I’ll pick the figure that makes use of seven tiles: a small hexangular figure. So, to that end, I’ll take out the 22 tile and six other random tiles (it doesn’t matter what they are, even if they’re Intelligences or Principles or Spirits), put them all face down, mix them up, and arrange them in the usual small hexagon.

So, somewhere in this small hexagon is the 22 tile, but I don’t know where. Let’s say that the current day is a Wednesday, and I know that my friend isn’t having the party today, so the party could be held as early as tomorrow (Thursday) or as late as one week away (next Wednesday). What I’ll do is I’ll lift up the seventh tile (being the last) and say/think “is the party being held this coming Wednesday”; if the tile is the 22 tile, then yes, but if not, I’ll proceed to the sixth tile and say/think “what about Tuesday”, and so forth, ending with the first tile laid down representing tomorrow/Thursay. Wherever the 22 tile is indicates the day of the week the party will be held on.

This “option-whittling” approach is described in many ways, and given the number of options one has to pick, different figures can be used:

Three options: small triangle
Four options: small diamond
Five options: small diamond + one tile held in reserve
Six options: hollow triangle
Seven options: small hexagon
Eight options: small hexagon + one tile held in reserve
Nine options: medium diamond
Ten options: full triangle
&c.

When I say “a tile held in reserve”, a good example of this is when ZT proposes how one might find out on which day of the month something might occur. Let’s say that that we know that our friend is planning another party later on in the year in October, but again, we don’t know when and they’re not in the habit of letting us know with much warning, so we want to find out what day to plan for. October has 31 days, but there’s no figure that comes anywhere close to that number; they’re either all too small (large triangle has only 15 tiles, large diamond only 16) or too big (large hexagon has 37), but what we can do is take the usual speaking tile and mix it together with 30 other tiles for a total of 31, then make two large triangles with one extra piece put near the second large triangle. What we’re doing here is essentially partitioning out October into two halves: the first large triangle is for days 1 through 15, the second large triangle is for days 16 through 30, and the tile in reserve is for the 31st day itself. We start with the first triangle and see if the speaking tile is found in that figure; if not, then the event won’t be held in the first half of the month, so we turn to the second triangle, but we start with the tile in reserve first—because it’s the actual “final” tile that represents the final option of the 31st day. If that tile in reserve is the speaking tile, then we have ourselves a Halloween party; if not, then we have some other day in October from days 16 through 30 that the party will be on.

In this way, we can go through any number of options, though ZT says that “rarely does a a particular question require larger figures” larger than ten-ish tiles, and even then, we can always use multiple figures to determine an answer in those cases when necessary. In this way, we can go down to three options using a small triangle, but what about a binary choice of just two options? ZT literally says to just take the speaking tile plus one other random tile, shake them around in the hand, and pick one. It’s that simple.

With all that understood, we now know how we can use the Great Dial in a similar way. Let’s say that we have someone who was told that one day their family give birth to someone who will become worldwide famous, and they want to know when such a birth will occur. For this, we’ll use the speaking tile of 1 (which indicates births), and compose a Great Dial with 36 other random pieces. Because of the nature of this query, we don’t know if the birth will happen anytime soon or not, so let’s first use eccentric motion to determine the general timeframe in which such a birth might happen. In eccentric motion, the outer belt is the yearly belt, the middle belt is climacteric, the inner belt is centurial, and the center house is millennial; to that end, we use the usual option-whittling approach to determine in what timeframe such a birth will occur: 18 years down the line, 17 years, 16 years, etc. down to just 1 year for tile 20. After that, 12 climacteric periods (84 years) following these 18 years away, then 11 (77 years), 10 (70 years), etc. down to one climacteric period (7) after the first 18 years. After that, 7 centuries (following 18 years and 12 climacteric periods), then 6, then 5, etc. After that, we have 1000 years, after seven centuries plus twelve climacteric periods plus eighteen years—or it could just be sometime further indefinitely off than that as some upper undefined limit.

What about something closer? Let’s say that a querent knows from a Great Mirror that they’ll be married sometime in the next few years of their life. For this, we’ll use the 66 tile (which indicates marriages) and compose a Great Dial with 36 other pieces. At first, we’ll read the outer belt in eccentric movement, interpreting each tile as being one year each, and so we’ll do the usual option-whittling starting with 18 years, then 17, etc. If we don’t find the 66 tile in the outer belt, though, then (in the context of this query) it’s not that the querent will marry sometime much later, but rather, sometime much sooner, so we’ll move to the middle belt now and switch to using concentric movement instead of eccentric, which means that we now read the middle belt as being one month each, starting with 12 months away from the reading, then 11, then 10, and so forth, ending with one month away. If we still don’t find the 66 tile, then that means that it must be in the inner belt or center, which is for weekdays; at this point, we can say that the marriage will occur sometime very soon in the present month, and the position of the 66 tile can indicate the week.

The point of this latter example is to show that a single Great Mirror can be read in either or both movements, depending on the nature of the query and what makes the most sense, but truth be told, most of the examples of ZT that indicate telling time don’t use the Great Dial at all, it’d seem. Of all the examples ZT gives, it determines:

Year: by either the outer band of the Great Dial in concentric movement (to determine lustral period of a human life) or any part of the Great Dial in eccentric movement (year, climacteric period, century, or millennium)
Month: by the middle belt of the Great Dial in concentric movement
Day of the month: by either:
- Two large triangles for a month of 30 days, or two large triangles plus one tile in reserve for a month of 31 days (for February, we could use one medium hexagon for the first 19 days plus either a medium diamond for the remaining 9 days or full triangle for the remaining 9 days in a leap year)
- One small hexagon to determine the day of the week, then to determine the week of the month, either a small diamond (for a month of four weeks containing that weekday) or a small diamond plus one tile in reserve (for a month of five weeks containing that weekday)
Climacteric period: by one small hexagon to determine the first seven climacteric periods, then another small hexagon to determine the next seven (or, more properly, a hollow triangle to determine the next six, since 6 + 7 = 13, and 13 × 7 = 91, which approximates the maximum lifespan of humans according to ZT)
Hour: …uh…well…

So, about determining hours: ZT offers two methods on this approach, which it spends a good amount of time clarifying on the first and offers the second as an alternative, and both seem slightly confused in minor ways that aren’t impossible to reconcile, but it’s still a little weird. It helps, however, that ZT just takes the usual system of planetary hours and planetary weekdays as a given, which we can use to our advantage here. My issue is, however, that neither of them seem particularly robust.

Hour determination, first method: For the purposes of this method, we only care about the tiles belonging to the solar or lunar intelligences, where all the tiles of Genhelia/matter-Sun and Psykelia/spirit-Sun indicate diurnality and all the tiles of Seleno/matter-Moon and Psykomena/spirit-Moon indicate nocturnality. We’ll give the Intelligence tiles to the midpoint of their respective periods, such that the Genhelia and Psykelia tiles represent the hour leading up to midday (thus the sixth hour of the day), and that the Seleno and Psykomena tiles represent the hour culminating in midnight (thus the sixth hour of the night). We rotate through the tiles in the given columns according to the Table of Numbers from Plate II accordingly to obtain the rest of the tiles for the hours of the day or night, starting from the middle-point of the column to indicate the twilight, working our way up to the Intelligence tile to represent the midpoint of the day/night, then rotating back from the bottom of the same column to represent the remaining hours of the day/night.

What we get is a table of solar/lunar tiles that represent the hours of the day and night accordingly:

Hour	Daytime		Nighttime
Hour	Genhelia	Psykelia	Seleno	Psykomena
1	37	45	38	44
2	28	36	29	35
3	19	27	20	26
4	10	18	11	17
5	1	9	2	8
6	☉	◎	☾	☽
7	91	99	92	98
8	82	90	83	89
9	73	81	74	80
10	64	72	65	71
11	55	63	56	62
12	46	54	47	53

So, to determine the hour in which something will happen, we use a large triangle of 15 tiles, with the outer rim of 12 tiles indicating the number of the hour, and the inner small triangle indicating whether it happens in the daytime (hours 1 through 12) or nighttime (hours 13 through 24). We inspect the inner (ideal) small triangle first: best 2 of 3 of solar or lunar tiles determines the period. Thus, if there’s any number of solar tile and no lunar tiles, or at least more solar tiles than lunar tiles, then the event will happen during the day; likewise, if there’s only lunar tiles and no solar tiles, or at least more lunar than solar tiles, then the event will happen at night. That done, we then proceed to look at the outer rim of 12 tiles on the large triangular figure we composed. We then proceed to find whatever solar or lunar tiles agree with the inner triangle, and use the outer rim tile(s) to indicate the hour itself of that given period. Thus, if the inner triangle indicates a nocturnal event, then if we find both a solar and a lunar tile in the outer rim, only the lunar tile matters to indicate the hour.

Of course, there are a number of questions about this method that ZT leaves unresolved:

All other tiles of any other planet are irrelevant and neutral for this approach, meaning they don’t indicate either diurnality or nocturnality. So what happens if there are neither solar nor lunar tiles in the inner ideal triangle?
Even if we can judge the diurnality/nocturnality of an event from the inner triangle, what if there are multiple tiles that agree in the outer rim? Does that mean the event could happen in any one of those hours, or in the range between them? Do we just pick which one using an option-whittling method afterward?
Even if we can judge the diurnality/nocturnality of an event from the inner triangle, what if there are no tiles that agree in the outer rim? Do we just say that it can’t be decided and that it’ll happen throughout the day or at any point which cannot yet be determined in that day?

There’s also one really weird bit about this method, however. ZT says that, regarding the hours:

Just as the solar and lunar pieces mark the exact points of noon and midnight, each hourly number marks the exact middle of the first, second, third, &c. hour, whether daytime or nighttime. Without being aware of this, one runs the risk of making a mistake of any time, sometimes by half an hour.

I can’t really make sense of this, honestly. If the solar and lunar Intelligence tiles themselves represent the exact points of midday and midnight, then that would indicate the border between two hours, not the middle of such hours. It also says earlier, however, that tiles 37, 47, 45, and 53 all “share the twilight hour of the morning”; usually we don’t say that an hour is split or that the twilight hour is split, but rather that a day starts at sunrise itself (which ZT agrees with). So does ZT mean by this note that our usual reckoning of dividing up the unequal hours is to be shifted forward by half an unequal hour? It’s unclear to me, and seems really confused or overly complicated.

Hour determination, second method: This approach of assigning the tiles to the hours is similar to the previous method, but incorporates the given Zodiac sign of a known date. Recall in the Table of Numbers in Plate II how each of the rows of the table is assigned a sign of the Zodiac. The first hour of the day/night is the solar/lunar tiles of the row of that sign of the Zodiac, the second hour the one beneath that, the third one beneath the second, and so forth, looping around if we’ve reached the end of the column. Thus, while the Sun is in Gemini, tiles 10 and 18 are the first hour of the day and tiles 11 and 17 the first hour of the night, tiles 19 and 27 the second diurnal hour and tiles 20 and 26 the second nocturnal hour, and so on. Unfortunately, no example is specifically given with this second/alternative method, so if we use the same fundamental approach as before, then the same issues remain as before.

Of course, there is a sorta-secret third method to determine the hour that was hinted at earlier: use the Great Dial in concentric movement to determine the hour number, then use option-whittling to determine if it’ll happen in the day or night. No muss nor fuss with trying to allot tiles to unequal hours or worrying about what if you don’t get any (or if you get too many) solar or lunar tiles, whatever. Or, if we want to take a similar approach as what we did with the first method of determining the day of a month to innovate a fourth method, we could use four hollow triangles, because each hollow triangle has six tiles and 6 × 4 = 24, and use the usual option-whittling approach that way, splitting a whole day-night cycle into four separate chunks of morning (hours 1 through 6), afternoon (7 through 12), evening (13 through 18), and night (19 through 24). (Although we might conceivably break a set of 24 options into other figures like a large 15-tile triangle with a medium 9-tile diamond, having this broken out into equal segments pleases me more.)

I’ll be honest: while I get the underlying process that ZT shows for many of these forms of determining specific times, they feel kinda…I dunno, clunky? And especially for determining hours, that gets into levels of specificity that seem increasingly suspect to me (a concern magnified if we were to go any lower than hours, as ZT itself warns against), and the methods it explicitly suggest seem super rough and too ill-specified for my taste, at least without exploring other options. But then again, ZT also says this about the methods it shares:

The Candidate is warned that the means indicated in the First Supplement to find the climacteric, annual, monthly, hourly, and other periods are rather thus described as exercises rather than to assist them in quickly and surely finding a moment they might seek. Rather, they will be surprised indeed to find, at the proper time, other methods shorter, surer, and less childish than those we have offered earlier to their avid curiosity. Since there is much to learn and do before one begins to calculate months and hours, when the Candidate eventually gets to such a point, they will already know how to go about it and can dispense with the processes described as well as the Tables [of meanings of the tiles and the Great Mirror houses], by which we only wanted to offer some bait to the unreasonable impatience of most people who wish to read into the future.

It is unfortunately too true that, in a work that will someday be precious, what is less sound must serve for now as a recommendation for the rest.

Even by ZT’s own admission, it doesn’t think particularly highly of the methods it gives to determine times. I mean, it makes sense, doesn’t it? All that this “option-whittling” (as I’ve been calling it) is is just a variation on processes of elimination, which is about the most rudimentary form of sortilege you can do with little in the way of actual interpretation or intuition being called for. While there’s nothing saying that these methods can’t work, I admit my own skepticism of them to a degree, and can think of better methods involved. For instance, using the Great Dial in concentric movement with the middle belt indicating hours, it might be possible to conceive of a method that links up one of the 12 hourly houses in the middle belt with one of the seven daily houses of the inner belt + center house using ideal triangles to determine both the weekday, diurnality/nocturnality, and hour of the day/night. Alternatively, if we know the given weekday, then noting that the planetary day is ruled the planet of its first hour and planetary night of its first hour, we could use more tiles than just the solar/lunar ones to determine planetary days and hours, as well. Another option could be to give the other planets their own diurnal or nocturnal qualities in addition to the luminary ones to even things out.

As far as ZT is concerned, I think determining times along these lines is a tricky topic, in agreement with what ZT says. At the same time, I also think that either the author of ZT was intentionally holding back on intuitive/interpretive techniques to lead to such a result, or they just threw this in as an afterthought to let others fill in the gaps without ever thinking such methods through enough themselves. I’m sure that there are plenty of ways to determine time, and ZT has certainly given some ways, but even ZT itself doesn’t take them seriously; I don’t think we should, either.

Unlocking the Observatory: Ideal Triangles in the Great Mirror

May 15, 2022 By polyphanes in occult Tags: analysis, geometry, great mirror, list, telescope of zoroaster, triangle, unlocking the observatory, zoroaster's telescope 2 Comments

Where were we? We’re in the middle of discussing the obscure Telescope of Zoroaster (ZT), a manual of divination and spirituality originally published in French in 1796 (FZT) at the close of the French Revolution, which was later translated into German in 1797 (GZT) and then again in an abridged form as part of Johann Scheible’s 1846 Das Kloster (vol. 3, part II, chapter VII) (KZT), with Scheible’s work then translated into English in 2013 as released by Ouroboros Press (OZT). Although OZT is how most people nowadays tend to encounter this system, I put out my own English translation of FZT out a bit ago as part of my research, and while that translation was just part of the work I’ve been up to, there’s so much more to review, consider, and discover when it comes to this fascinating form of divination. Last time, we talked about the various figures and mirrors used for divination, especially the Great Mirror itself. If you need a refresher on what we talked about last time, go read the last post!

※ For those following along with their own copy of ZT (get yours here!), the relevant chapters from ZT are the “Fourth Step” and “Third Supplement”.

In the last post, we talked about the “spreads” of tiles that get used in the divinatory method of ZT, especially the Great Mirror. While all the triangular, quadrangular, and hexangular figures get used as mirrors at some point in ZT, it’s really the Great Mirror that takes center stage as being the primary divinatory “spread” of them all. We talked about how each of the 37 positions in the large hexagon, when used as the Great Mirror, have their own meanings and semantic fields, and how such meanings can be arrived at by considering the Great Mirror a sort of self-similar, self-replicating planetary arrangement. In this, one can already perform basic divination in ZT by simply asking a query, composing a Great Mirror, and inspecting each tile in its appropriate house.

Of course, that’d just be too simple, wouldn’t it? We’re not doing Tarot, after all.

In addition to inspecting each tile in the house it appears within, ZT also accounts for “triads” of tiles in the Great Mirror in what it calls “ideal triangles”. Recall from the last post the distinction of “real figures” versus “ideal figures”: a real figure is any complete figure that is composed from tiles and named according to its overall shape, while an “ideal figure” is a subset of tiles within a real figure that forms a subfigure of that larger figure. In the Great Mirror, particular kinds of “ideal triangles” are noted as being useful and important for interpreting a Great Mirror as a whole, not just looking at individual tiles where they fall but looking at groups of tiles and how they fall together. To borrow a bit of astrological terminology, by noting which tiles form a “triad” in the Great Mirror, we can interpret any given tile in two ways: an “essential interpretation” (the tile in its house) and an “accidental interpretation” (the tile in the triads it forms).

There’s one minor hiccup in this approach, however. The earlier description (from the “Second Step”) of “ideal figures” leads one to consider actual figures composed of many tiles together all at once, but later uses of “ideal triangles” (notably the “Fourth Step” and the “Third Supplement”) only refer to triangles—because equilateral triangles are “the only triangular figure to which the Great Cabala attaches any importance”—and further only to the corners of those triangles. We’ll see why in a bit.

First, let’s recall the numbering for the houses in the large hexagon, which is used for the Great Mirror:

This is based on the numbering system given in ZT’s Plate III, which describes the cosmological layout of the Great Mirror, the placement of Sisamoro and Senamira, and the number pattern of the individual houses thereof:

Do you see all those dashed lines across the plate? There are several kinds of dashed lines: circular dashed lines around each planetary house indicate that planet’s orbit, a wavy line that goes through all the houses of the Great Mirror indicating the order of the tiles from 1 to 37, and lots of straight lines that indicate particular ideal triangles in the Great Mirror. Consider the ideal triangle composed of houses 1, 9, and 11 (noted as 1–9–11): this is a “planetary triangle” formed from the houses of Sun, Mars, and Venus. Likewise, houses 1, 37, and 22 (or 1–37–22) form a slightly larger “zodiacal triangle” that incorporates the houses given to Aries and Taurus.

ZT has this to say about the ideal triangles:

…it is good to also become familiar with a more ideal yet highly essential division into triangles of different sizes. The main ones are indicated in Plate III: all these triangles indicated by dashed lines have their vertices at the center…and are distinguished and named according to their bases. In order to not throw ourselves here into details which would exceed the framework of a key, since it would be good for the Candidate to seek them until they come across them by analogy, we will not give an account here of triangles other than the planetary, zodiacal, and external triangles.

…

The observations to be made according to the triangles, either already described or arbitrarily noted in the Great Mirror, will be infinite; the care one takes in inspecting them will cost time and cause trouble, though ever less and less until none at all, as such calculations become ever more familiar. On the other hand, as such cares and costs decrease, the variety and richness increase, above all the infallibility of what such results will reveal.

The Candidate whose eye is not well-exercised in geometry would do well, when operating, to always have a compass in hand to find without error and without difficulty the third box which must complete a triangle for any two already chosen in the Great Mirror. For example, if a compass has one point in the center of box 18 and the other fixed in the center of box 31, lifting and moving the first half of the compass will only find a third center in box 12. This is the third point completing, together with boxes 18 and 31, an equilateral triangle, the only triangular figure to which the Great Cabala attaches any importance. So it is with all of the triangles which one will is able to imagine and whose formation is possible in the space of the Great Mirror.

Likewise, later on, it suggests several rules regarding how to make use of such ideal triangles, or at least which ones to pay special attention to:

Let us carefully observe whether and where there might be a triplicity of similar numbers, i.e. what quality a third number might have to form an equilateral triangle with two other numbers sharing the same or similar property.

Let us appreciate what such a triplicity might mean, whether for good or ill.

Let us clearly note the number which forms an equilateral triangle with two Intelligences, and that one profoundly contemplates what a triplicity of Intelligences or primitive numbers might mean.

Let the same attention be paid to a triplicity of numbers with zero or of doublets.

Thus, while all possible ideal triangles within the Great Mirror should be considered, the most important ones are those that involve two or more tenfold compound Numbers, two or more doublet compound Numbers, two or more Intelligences, two or more primitive Numbers, or any triangle that contains “similar numbers…sharing the same or similar property” (i.e. those sharing a common digit or which reduce to the same digit). Presumably, we can also consider any triangle that also contains the two Spirits as also being significant.

That being said, when we say “all possible ideal triangles”…I mean, how many are we talking? Given ZT’s reference to using a compass to determine any kind of equilateral triangle formed between any of the houses in the Great Mirror, and given the example thereof where the triangle 18–12–31 has one vertical side compared to the planetary and zodiacal ideal triangles that have horizontal sides, in addition to the “external ideal triangles” formed between three of the corners of the outermost belt of the Great Mirror…well, it turns out that there are a lot of possible triads of figures we might consider. We can break all possible ideal triangles within the Great Mirror according to their orientation:

Horizontal: ideal triangles having one horizontal side (e.g. 1–9–11)
Vertical: ideal triangles having one vertical side (e.g. 18–12–31)
Skewed: ideal triangles having neither a horizontal nor vertical side (e.g. 32–26–30)

Likewise, within each group, we can classify the triangles further based on their size, although this is easier for some than others. We’ll cover all the triangles that I’ve been able to account for in the Great Mirror. I’m not too bad at those “how many squares are in this image?” puzzles you occasionally see online, so I hope to have accounted for all possible triangles. I apologize for the lack of standardization in how I might have accounted for the triangles in the lists below; this is, perhaps, something better for a spreadsheet than a series of HTML ordered lists.

Ideal Small Horizontal Triangles

Every small triangle has edges spanning two houses with one horizontal edge, and is the smallest possible ideal triangle (or ideal figure) that can be formed according to ZT. These are, by far, the most numerous kind of ideal triangle that can be formed in the Great Mirror. There are four kinds of small triangles: those that touch two signs of the Zodiac, those that have one sign of the Zodiac and one planet, those that have one planet, and those that touch only orbital houses.

Upwards (27 total)

34–35–17 (Aquarius, Moon)
33–17–16 (Capricorn, Moon)
32–16–15 (Sagittarius, Mercury)
31–15–30 (Scorpio, Mercury)
35–36–17 (Aquarius/Pisces)
17–18–6 (Moon)
16–6–5 (orbits of Moon/Mercury/Sun)
15–5–14 (Mercury)
30–14–29 (Libra/Scorpio)
36–37–19 (Pisces, Saturn)
18–19–7 (Saturn)
6–7–1 (Sun)
5–1–4 (Sun)
14–4–13 (Jupiter)
29–13–28 (Libra, Jupiter)
19–20–8 (Aries, Saturn)
7–8–2 (orbits of Saturn/Sun/Mars)
1–2–3 (Sun)
4–3–12 (orbits of Sun/Mars/Venus)
13–12–27 (Virgo, Jupiter)
8–21–9 (Taurus, Mars)
2–9–10 (Mars)
3–10–11 (Venus)
12–11–26 (Leo, Venus)
9–22–23 (Gemini, Mars)
10–23–24 (Gemini/Cancer)
11–24–25 (Cacner, Venus)

Downwards (27 total)

34–33–17 (Capricorn, Moon)
33–32–16 (Sagittarius/Capricorn)
32–31–15 (Sagittarius, Mercury)
35–17–18 (Aquarius, Moon)
17–16–6 (Moon)
16–15–5 (Mercury)
15–30–14 (Scorpio, Mercury)
36–18–19 (Pisces, Saturn)
18–6–7 (orbits of Moon/Saturn/Sun)
6–5–1 (Sun)
5–14–4 (orbits of Mercury/Sun/Jupiter)
14–29–13 (Libra, Jupiter)
37–19–20 (Aries, Saturn)
19–7–8 (Saturn)
7–1–2 (Sun)
1–4–3 (Sun)
4–13–12 (Jupiter)
13–28–27 (Virgo, Jupiter)
20–8–21 (Aries/Taurus)
8–2–9 (Mars)
2–3–10 (orbits of Sun/Mars/Venus)
3–12–11 (Venus)
12–27–26 (Leo/Virgo)
21–9–22 (Taurus, Mars)
9–10–23 (Gemini, Mars)
10–11–24 (Cancer, Venus)
11–26–25 (Leo, Venus)

Ideal Hollow Horizontal Triangles

Every hollow triangle has edges spanning three houses with one horizontal edge. A unique quality of all ideal medium triangles in the Great Mirror is that they must have one corner somewhere in the orbit of the Sun (houses 1–7), with the other two being the equivalent houses in the orbit of two other planets. For instance, given one corner in the house to the right of the Sun (house 4), then one can form two possible ideal medium triangles, both having one corner in the house to the right of Jupiter (house 28), and either an upwards triangle with the corner to the right of Mercury (house 30) or a downwards triangle with the corner to the right of Venus (house 26). This same quality is what allows such triangles to be highlighted in the “Fourth Step” as specifically being “planetary triangles”, because when an ideal medium triangle takes the Sun itself (house 1) as one corner, the other two must be two planetary houses themselves.

Given this property, it is easy to anticipate how many such ideal medium triangles there are. Given that any given house can form a triangle in one of six directions (two possible directions × three possible corners = six possible triangles) and that there are seven houses within the orbit of the Sun, there are thus 6 × 7 = 42 possible ideal medium triangles in the Great Mirror, six for each planet.

Planet-only, i.e. Sun-themed triangles (6 total)

1–19–9 (Sun, Saturn, Mars)
1–9–11 (Sun, Mars, Venus)
1–11–13 (Sun, Venus, Jupiter)
1–13–15 (Sun, Jupiter, Mercury)
1–15–17 (Sun, Mercury, Moon)
1–17–19 (Sun, Moon, Saturn)

Lower-left of the Sun, i.e. Mars-themed triangles (6 total)

2–20–22 (Sun-orbit, Saturn-orbit, Mars-orbit)
2–22–24 (Sun-orbit, Mars-orbit, Venus-orbit)
2–24–12 (Sun-orbit, Venus-orbit, Jupiter-orbit)
2–12–5 (Sun-orbit, Jupiter-orbit, Mercury-orbit)
2–5–18 (Sun-orbit, Mercury-orbit, Moon-orbit)
2–18–20 (Sun-orbit, Moon-orbit, Saturn-orbit)

Lower-right of the Sun, i.e. Venus-themed triangles (6 total)

3–8–23 (Sun-orbit, Saturn-orbit, Mars-orbit)
3–23–25 (Sun-orbit, Mars-orbit, Venus-orbit)
3–25–27 (Sun-orbit, Venus-orbit, Jupiter-orbit)
3–27–14 (Sun-orbit, Jupiter-orbit, Mercury-orbit)
3–14–6 (Sun-orbit, Mercury-orbit, Moon-orbit)
3–6–8 (Sun-orbit, Moon-orbit, Saturn-orbit)

Right of the Sun, i.e. Jupiter-themed triangles (6 total)

4–7–10 (Sun-orbit, Saturn-orbit, Mars-orbit)
4–10–26 (Sun-orbit, Mars-orbit, Venus-orbit)
4–26–28 (Sun-orbit, Venus-orbit, Jupiter-orbit)
4–28–30 (Sun-orbit, Jupiter-orbit, Mercury-orbit)
4–30–16 (Sun-orbit, Mercury-orbit, Moon-orbit)
4–16–7 (Sun-orbit, Moon-orbit, Saturn-orbit)

Upper-right of the Sun, i.e. Mercury-themed triangles (6 total)

5–18–2 (Sun-orbit, Saturn-orbit, Mars-orbit)
5–2–12 (Sun-orbit, Mars-orbit, Venus-orbit)
5–12–29 (Sun-orbit, Venus-orbit, Jupiter-orbit)
5–29–31 (Sun-orbit, Jupiter-orbit, Mercury-orbit)
5–31–33 (Sun-orbit, Mercury-orbit, Moon-orbit)
5–33–18 (Sun-orbit, Moon-orbit, Saturn-orbit)

Upper-left of the Sun, i.e. Moon-themed triangles (6 total)

6–36–8 (Sun-orbit, Saturn-orbit, Mars-orbit)
6–8–3 (Sun-orbit, Mars-orbit, Venus-orbit)
6–3–14 (Sun-orbit, Venus-orbit, Jupiter-orbit)
6–14–32 (Sun-orbit, Jupiter-orbit, Mercury-orbit)
6–32–34 (Sun-orbit, Mercury-orbit, Moon-orbit)
6–34–36 (Sun-orbit, Moon-orbit, Saturn-orbit)

Left of the Sun, i.e. Saturn-themed triangles (6 total)

7–37–21 (Sun-orbit, Saturn-orbit, Mars-orbit)
7–21–10 (Sun-orbit, Mars-orbit, Venus-orbit)
7–10–4 (Sun-orbit, Venus-orbit, Jupiter-orbit)
7–4–16 (Sun-orbit, Jupiter-orbit, Mercury-orbit)
7–16–35 (Sun-orbit, Mercury-orbit, Moon-orbit)
7–35–37 (Sun-orbit, Moon-orbit, Saturn-orbit)

However, of the above-listed triangles, there are a few duplicates, which reduces the number of distinct ideal hollow triangles. These duplicates are formed by triangles that contain opposing planets, e.g. 2–5–18 as the perspective of Mars from the Sun, but 5–18–2 as the perspective of Mercury from the Sun; each pair of opposing planets produces two duplicates, with the third corner of these ideal triangles placed on the cross-axis that forms between them between the other two planets on a given side. As a result, there are only 36 distinct ideal hollow triangles.

Ideal Full Horizontal Triangles

Every full triangle has edges spanning four houses with one horizontal edge, allowing for one house to form the center of such a triangle. The prototypical form of these triangles are the “zodiacal triangles” (as described in the “Fourth Step”), where the base of such a triangle can be formed along one whole edge of the Great Mirror from one corner to the next. Given the sixfold divisions of life in the “Fifth Step” (which we haven’t yet covered, but we will!), it may be that these triangles relate more to the various trials, tribulations, or experiences given in similar timeframes, especially as might impact particular lusters of life.

Of all the possible ideal large triangles, only two are contained completely within the Great Mirror without touching any of its edges or corners (internal), six involve two corners and an entire edge (fully external), and all the rest touch only one non-corner edge house (partially external).

Internal (2 total)

8–12–16 (upwards)
18–14–10 (downwards)

Fully external (6 total)

1–37–22 (downwards, First Division, Aries/Taurus)
1–22–25 (upwards, Second Division, Gemini/Cancer)
1–25–28 (downwards, Third Division, Leo/Virgo)
1–28–31 (upwards, Fourth Division, Libra/Scorpio)
1–31–34 (downwards, Fifth Division, Sagittarius/Capricorn)
1–34–37 (upwards, Sixth Division, Aquarius/Pisces)

Partially external (12 total)

20–3–17 (upwards, Aries/Moon)
21–11–6 (upwards, Taurus/Venus)
23–4–19 (downwards, Gemini/Saturn)
24–13–7 (downwards, Cancer/Jupiter)
26–5–9 (upwards, Leo/Mars)
27–15–2 (upwards, Virgo/Mercury)
29–11–6 (downwards, Libra/Venus)
30–3–17 (downwards, Scorpio/Moon)
32–13–7 (upwards, Sagittarius/Jupiter)
33–4–19 (upwards, Capricorn/Saturn)
35–15–2 (downwards, Aquarius/Mercury)
36–5–9 (downwards, Pisces/Mars)

Some patterns can be noted regarding the above sets of triangles:

If an ideal full triangle touches one corner, it must touch another, with one of its corners in House 1 and one of its edges containing two signs of the Zodiac.
If an ideal full triangle touches only one non-corner edge house, then that edge house must be a sign of the Zodiac. One of the other corners must be a non-solar planet, and the last corner must be a non-planetary house in the shared solar orbit of the planet opposite the first, e.g. Moon of Venus and vice versa.
Every non-solar planet takes part in two ideal full triangles, one upward and one downward:
- Mars: Leo (upward) and Pisces (downward)
- Venus: Taurus (upward) and Libra (downward)
- Jupiter: Sagittarius (upward) and Cancer (downward)
- Mercury: Virgo (upward) and Aquarius (downward)
- Moon: Aries (upward) and Scorpio (downward)
- Saturn: Capricorn (upward) and Gemini (downward)
The internal ideal full triangles only have corners that are in the shared orbits of two non-solar planets, with each corner being adjacent to two signs of the Zodiac.

Ideal Large Horizontal Triangles

Every large horizontal triangle has edges spanning five houses with one horizontal edge, allowing for three houses to form the center of such a triangle. Unlike the other ideal triangles, large triangles are too large to have a base along the edges of the Great Mirror; instead, they can only have one of their corners on the Great Mirror’s edge. Each of these triangles involves two signs of the Zodiac, both of the same modality (cardinal, fixed, or mutable) but of incompatible elements (fire/earth or water/air). In each triangle, the third house is a non-planetary house between two planets in the planetary belt.

Upwards (3 total)

21–26–16 (Taurus/Leo)
20–12–33 (Aries/Capricorn)
8–27–32 (Virgo/Sagittarius)

Downwards (3 total)

35–30–10 (Scorpio/Aquarius)
36–14–23 (Gemini/Pisces)
18–29–24 (Cancer/Libra)

Ideal One-Skip Vertical Triangles

Now that we’re done with horizontal triangles, we have to consider vertical triangles. Due to the “grain” of houses in the Great Mirror, while it’s easy to state the base of a horizontal triangle in terms of how many houses it covers, vertical triangles are somewhat trickier. To resolve this, we’ll use the notion of “skips” it takes to go from one house along the vertical base of a vertical triangle to the next house directly above or below it. Thus, from house 34, it takes one skip to go to 34 to 18, two skips to go from 34 to 18, and three skips to go from 34 to 22.

One-skip vertical triangles fall into types: those touching one sign of the Zodiac and one planet in different orbits, those touching two signs of the Zodiac in the same orbit, those touching non-planetary and non-zodiacal houses within the same orbit, or those touching one planet and two non-planetary and non-zodiacal houses in other planets’ orbits.

Rightwards (19 total)

34–18–16 (all in orbit of the Moon, touching upper left corner)
8–22–10 (all in orbit of Mars, touching lower left corner)
14–12–28 (all in orbit of Jupiter, touching right corner)
35–19–6 (Aquarius and Saturn)
19–21–2 (Taurus and Saturn)
2–23–11 (Gemini and Venus)
4–11–27 (Virgo and Venus)
15–4–29 (Libra and Mercury)
33–6–15 (Capricorn and Mercury)
36–20–7 (Pisces/Aries in orbit of Saturn)
3–24–26 (Cancer/Leo in orbit of Venus)
32–5–30 (Sagittarius/Scorpio in orbit of Mercury)
17–7–5 (Moon)
7–9–3 (Mars)
5–3–15 (Jupiter)
18–8–1 (Sun)
1–10–12 (Sun)
16–1–14 (Sun)
6–2–4 (all in orbit of the Sun, surrounding the center)

Leftwards (19 total)

31–14–16 (all in orbit of Mercury, touching upper right corner)
18–8–37 (all in orbit of Saturn, touching left corner)
12–25–10 (all in orbit of Venus, touching lower right corner)
32–5–17 (Sagittarius and the Moon)
17–7–36 (Pisces and the Moon)
7–9–20 (Aries and Mars)
3–24–9 (Cancer and Mars)
13–26–3 (Leo and Jupiter)
30–13–5 (Scorpio and Jupiter)
33–6–35 (Capricorn/Aquarius in orbit of the Moon)
2–23–21 (Taurus/Gemini in orbit of Mars)
29–27–4 (Virgo/Libra in orbit of Jupiter)
15–4–6 (Mercury)
6–2–19 (Saturn)
4–11–2 (Venus)
16–1–18 (Sun)
1–10–8 (Sun)
14–12–1 (Sun)
5–3–7 (all in orbit of the Sun, surrounding the center)

Ideal Two-Skip Vertical Triangles

Two-skip vertical triangles fall into three types: those touching a single corner, those touching two signs of the Zodiac, and those touching three planets. As an interesting result of the astrological qualities of the signs, when a two-skip vertical triangle touches two signs of the Zodiac, the signs it touches are of opposing elements (fire/water, air/earth) but same modality (cardinal, fixed, mutable); all the rightward triangles of this sort touch only earth and air signs, while all the leftward triangles touch only fire and water signs.

Rightwards (7 total)

35–21–4 (Taurus/Aquarius)
23–27–6 (Gemini/Virgo)
33–29–2 (Libra/Capricorn)
34–8–14 (touching upper left corner)
22–12–18 (touching lower left corner)
10–28–16 (touching right corner)
17–13–9 (Moon/Jupiter/Mars)

Leftwards (7 total)

24–5–20 (Aries/Cancer)
30–26–7 (Leo/Scorpio)
32–3–36 (Sagittarius/Pisces)
31–12–18 (touching upper right corner)
25–14–8 (touching lower right corner)
10–16–37 (touching left corner)
15–11–19 (Mercury/Venus/Saturn)

Ideal Three-Skip Vertical Triangles

There are only two possible three-skip vertical triangles, one of which points to the right and one of which points to the left, and both of them involve the extreme corners of the Great Mirror. For this reason, ZT explicitly calls these two triangles “external triangles” in the “Fourth Step”, and notes that these are the “most ideal” of any triangles in the Great Mirror (possibly as a result of how they are the largest possible triangles that can be formed of any size or orientation).

22–28–34 (rightwards, extremes of Mercury/Venus/Saturn)
25–31–37 (leftwards, extremes of Moon/Mars/Jupiter)

Ideal Two-Move Skewed Triangles

Just as how we had to judge the size of vertical triangles differently from horizontal triangles, so too do we have to consider skewed triangles (which have neither horizontal nor vertical edges) differently. For this, we’ll use the notion of “moves”, how many houses one must cross to go from one corner of an ideal skewed triangle to the next. Thus, between houses 36 and 16 there are two moves, between 36 and 15 there are three moves, and between 36 and 30 there are four moves. Likewise, because there’s no horizontal or vertical base to such a triangle, it’s hard to say which direction these triangles are “pointing”. As a result, instead of going with upward/downward/rightward/leftward as we did with the other triangles, we’ll just group them into what they touch or make use of in the Great Mirror.

Single Planet + Planetary Zone + Solar Orbit (12 total)

17–14–2 (Moon)
17–8–4 (Moon)
19–16–3 (Saturn)
19–10–5 (Saturn)
9–18–4 (Mars)
9–12–6 (Mars)
11–8–5 (Venus)
11–14–7 (Venus)
13–10–6 (Jupiter)
13–16–2 (Jupiter)
15–12–7 (Mercury)
15–18–3 (Mercury)

Single Planet + Corner House + Solar Orbit (12 total)

17–31–4 (Moon)
17–37–2 (Moon)
19–34–5 (Saturn)
19–22–3 (Saturn)
9–37–6 (Mars)
9–25–4 (Mars)
11–22–7 (Venus)
11–28–5 (Venus)
13–25–2 (Jupiter)
13–31–6 (Jupiter)
15–28–3 (Mercury)
15–34–7 (Mercury)

Sun + Two Zodiac Signs (12 total)

1–20–23 (Sun, Aries/Gemini)
1–21–24 (Sun, Taurus/Cancer)
1–23–26 (Sun, Gemini/Leo)
1–24–27 (Sun, Cancer/Virgo)
1–26–29 (Sun, Leo/Libra)
1–27–30 (Sun, Virgo/Scorpio)
1–29–32 (Sun, Libra/Sagittarius)
1–30–33 (Sun, Scorpio/Capricorn)
1–32–35 (Sun, Sagittarius/Aquarius)
1–33–36 (Sun, Capricorn/Pisces)
1–35–20 (Sun, Aquarius/Aries)
1–36–21 (Sun, Pisces/Taurus)

Small Single Zodiac (12 total)

35–8–5 (Aquarius)
36–16–2 (Pisces)
20–20–6 (Aries)
21–18–3 (Taurus)
23–12–7 (Gemini)
24–8–4 (Cancer)
26–14–2 (Leo)
27–10–5 (Virgo)
29–16–3 (Libra)
30–12–6 (Scorpio)
32–18–4 (Sagittarius)
33–14–7 (Capricorn)

Ideal Three-Move Skewed Triangles

Two Zodiac Signs (6 total)

20–24–5 (Aries/Cancer)
23–27–6 (Gemini/Virgo)
26–30–7 (Leo/Scorpio)
29–33–2 (Libra/Capricorn)
32–36–3 (Sagittarius/Pisces)
35–21–4 (Aquarius/Taurus)

Small Zodiac-Planet (12 total)

20–11–16 (Aries, Venus)
21–17–12 (Taurus, Moon)
23–13–18 (Gemini, Jupiter)
24–19–14 (Cancer, Saturn)
26–15–8 (Leo, Mercury)
27–9–16 (Virgo, Mars)
29–17–10 (Libra, Moon)
30–11–18 (Scorpio, Venus)
32–19–12 (Sagittarius, Saturn)
33–13–8 (Capricorn, Jupiter)
35–9–14 (Aquarius, Mars)
36–15–10 (Pisces, Mercury)

Large Single Zodiac (12 total)

35–31–3 (Aquarius)
36–22–4 (Pisces)
20–34–4 (Aries)
21–25–5 (Taurus)
23–37–5 (Gemini)
24–28–6 (Cancer)
26–22–6 (Leo)
27–31–7 (Virgo)
29–25–7 (Libra)
30–34–2 (Scorpio)
32–28–2 (Sagittarius)
33–37–3 (Capricorn)

Ideal Four-Move Skewed Triangles

Elemental Zodiac Groups (4 total)

32–26–20 (Aries/Leo/Sagittarius, i.e. fire signs)
33–27–21 (Taurus/Virgo/Capricorn, i.e. earth signs)
35–23–29 (Gemini/Libra/Aquarius, i.e. air signs)
36–24–30 (Cancer/Scorpio/Pisces, i.e. water signs)

Large Zodiac-Planet (12 total)

20–15–25 (Aries, Mercury)
21–13–34 (Taurus, Jupiter)
23–17–28 (Gemini, Moon)
24–15–37 (Cancer, Mercury)
26–19–31 (Leo, Saturn)
27–17–22 (Virgo, Moon)
29–9–34 (Libra, Mars)
30–19–25 (Scorpio, Saturn)
32–11–37 (Sagittarius, Venus)
33–9–28 (Capricorn, Mars)
35–13–22 (Aquarius, Jupiter)
36–11–31 (Pisces, Venus)

Ideal Principle Triangles

Although not explicitly called an ideal triangle as such, the placements of Sisamoro and Senamira around the Great Mirror is suggestive of one. ZT states that Sisamoro should be placed above the Great Mirror as the corner of an upwards equilateral triangle formed with houses 28 and 37, and Senamira likewise but downwards beneath the Great Mirror. Unlike some of the ideal triangles listed in the “Fourth Step” which are explicitly without dashed lines indicating them in Plate III, the triangles formed with the Principles do have those dashed lines, suggesting that these, too, form a kind of ideal triangle, albeit a nonstandard one that cannot be formed with any other houses in the Great Mirror. Technically, these seats form four ideal triangles each (one for each “layer” of the Great Mirror through its equator), but ZT suggests that it is only the largest possible triangle with the equator as its base that counts.

Given the importance of the leftmost and rightmost houses in the Great Mirror as being representative, respectively, of Saturn/Death and Jupiter/Life (akin to the bottom and top of the Wheel of Fortune in Tarot imagery), it might make sense that the Principles would find themselves in alignment with these points and no others. This may be a hint as to how the Principles, if drawn, are to be interpreted.

Whew. Assuming that I counted them right, didn’t miss any, and didn’t repeat any, all the above would yield a total of 264 possible ideal triangles (maybe 266 if we also allow for the Principles to form ideal triangles as well and if they are drawn in a Great Mirror). And, uh…yeah, this is a lot. Even just accounting for what the triangles are and a handful of patterns among them, this is a lot to note and remember—but that’s just the point, we don’t need to remember or memorize any of this stuff. Again, just like with learning the significations of the Numbers and the semantic fields of the houses, all we really need to do is account for the fundamental patterns that play themselves out in the Great Mirror. On top of that, while surely investigating all possible ideal triangles would be a noble thing to do, ZT gives us a handful of things to look out for which would highlight and whittle down the ideal triangles to what would be most important—note how many of those pieces of advice stated two Intelligences/primitive Numbers/doublets/nilleds, as opposed to just one. If you have just one tile like that, then it could form any number of triangles, but with two, it’s (almost) trivial to see what the third might be (to result in one or maybe two triangles depending on the spacing of those two given points).

Earlier I mentioned, borrowing astrological terminology, how we might consider these triad-based relationships of tiles that fall as giving a sort of “accidental” significance to any given tile (i.e. any tile relative to other tiles), as opposed to the “essential” significance given by the house a given tile falls into (i.e. any tile on its own where it is). I think that’s a useful way to consider this approach of using ideal triangles, but it raises the question of whether the houses themselves come into play when determining the meaning of a given ideal triangle, and personally, I’m inclined to think that there is. ZT doesn’t say as much, but then, ZT doesn’t say a whole lot, either. I think it would make sense for such a relationship to account for all of this together, which would indeed require a good amount of intuition as well as investigation on the part of the diviner. While the number of ideal triangles and the possible triads of tiles isn’t really infinite (though it is indeed likely a vast number), ZT is absolutely being honest with us when it says:

…the care one takes in inspecting them will cost time and cause trouble, though ever less and less until none at all, as such calculations become ever more familiar. On the other hand, as such cares and costs decrease, the variety and richness increase, above all the infallibility of what such results will reveal.

This is something to definitely take care with when trying out the divinatory method of ZT, and given the cosmological structure of the Great Mirror, I think there’s a good amount of stuff to contemplate and consider. If you think I’ve missed any triangles or overcounted any, or if there are any patterns or qualities you think are important that I didn’t get around in saying for particular kinds of ideal triangles, dear reader, please do say so in the comments!

Unlocking the Observatory: Figures, Mirrors, and the Great Mirror

May 11, 2022 By polyphanes in occult Tags: athanasius kircher, diamond, fractal geometry, geometry, great mirror, hexagon, hexangle, house, interpretation, lozenge, meaning, mirror, planetary hexagram, planets, quadrangle, rhombus, signification, telescope of zoroaster, tree of life, triangle, unlocking the observatory, zodiac, zoroaster's telescope 2 Comments

Where were we? We’re in the middle of discussing the obscure Telescope of Zoroaster (ZT), a manual of divination and spirituality originally published in French in 1796 (FZT) at the close of the French Revolution, which was later translated into German in 1797 (GZT) and then again in an abridged form as part of Johann Scheible’s 1846 Das Kloster (vol. 3, part II, chapter VII) (KZT), with Scheible’s work then translated into English in 2013 as released by Ouroboros Press (OZT). Although OZT is how most people nowadays tend to encounter this system, I put out my own English translation of FZT out a bit ago as part of my research, and while that translation was just part of the work I’ve been up to, there’s so much more to review, consider, and discover when it comes to this fascinating form of divination. Last time, we talked about the 112 (or 113) tiles used for divination, what each needs to have on it, and what each means in divination. If you need a refresher on what we talked about last time, go read the last post!

※ For those following along with their own copy of ZT (get yours here!), the relevant chapters from ZT are the “Second Step”, “Fourth Step”, “Seventh Step”, and “Third Supplement”.

Alright! As of the last post, we now have the toolset required for divination; in Tarot terms, we’ve taken a good look at all the cards (so to speak) and know what they are, what they represent, and the like. What comes next is how to make use of such tools, and just as Tarot cards get drawn and arranged into spreads, so too are the tiles of ZT drawn and arranged into…well, there’s a bit of terminology we have to go through and sort out first, I suppose, because ZT was trying to innovate its own terms in a time when such terms were still in the process of taking shape and becoming standardized.

Figure: A geometric shape composed of tiles, named after the shape that it forms.
Mirror: A whole figure that is used for divination.
Tablature: “The reasoned and just enunciation of what a Great Mirror gives to read”, i.e. the interpretation and reasoning of a divinatory session (especially, but not necessarily, making use of the “Great Mirror”—more on that term later).

In order to form a figure from tiles, one composes a figure by arranging successive tiles in an outward spiral, starting from one tile then proceeding counterclockwise, with the second tile always to the lower left of the first then proceeding outwards from there. Tiles within figures are always densely-packed, meaning that there is no space between them and tiles are pushed together against their own edges and corners. In this way, given the hexagonal geometry of the tiles, figures can be formed in shapes that are overall triangular, quadrangular, or hexangular.

There are four kinds of triangular figures that ZT allows:

The 3-tile triangular figure, also called the “small triangle”.
The 6-tile triangular figure, also called the “simple triangle” or “hollow triangle” (because its center is a meeting of three tiles at a vertex instead of a whole tile itself).
The 10-tile triangular figure, also called the “full triangle” (because its center is a whole tile).
The 15-tile triangular figure, also called the “large triangle” or “double triangle” (because its center is another whole triangular figure).

There are three kinds of quadrangular figures that ZT allows (which it calls “lozenges” or “diamonds”):

The 4-tile quadrangular figure, also called the “small diamond” or the “hollow diamond”.
The 9-tile quadrangular figure, also called the “medium diamond” or the “full diamond”.
The 16-tile quadrangular figure, also called the “large diamond” or the “double diamond”.

There are three kinds of hexangular figures that ZT allows (which it also just calls “hexagons”):

The 7-tile hexangular figure, also called the “small hexagon” or the “orbital hexagon” (because the outer six tiles form an orbit around the center tile).
The 19-tile hexangular figure, also called the “medium hexagon” or the “double hexagon”.
The 37-tile hexangular figure, also called the “large hexagon”, the “triple hexagon”, or “the totality” (because it includes all other possible figures that are permissible according to ZT).

ZT gives a lot of precedence and eminence to the large hexagon, because it forms the basis of many of the divinatory processes and cosmological models used in its “Great Cabala”. Although that is one of the reasons the large hexagon is called “the totality”, the other is more in the sense of a limitation. One might wonder why we might not make larger triangles or diamonds by adding in more tiles and continuing the spiral; ZT disallows this by saying that only the figures that can be contained within the large hexagon are permissible for use in divination. Thus, one cannot make a triangular figure out of 21 tiles or a quadrangular figure out of 25 tiles because they wouldn’t be able to “fit” inside the large hexagon.

This leads to a distinction that ZT makes between what it calls “real figures” versus “ideal figures”:

Any isolated figure is called “real”; it therefore forms a picture, a mirror. Any included or contained figure is called “ideal”.

In other words, a whole figure that is composed from tiles and seen as a whole is considered “real”, while any subset of tiles within such a figure that could also be composed as a separate figure on its own is called “ideal”. Let’s say that we draw three tiles and form a small triangle; this would be a real figure. If we draw another 16 tiles and, with all the tiles put together, make a medium hexagon, then this is another real figure. However, if we look at the bottom “pie slice” of that medium hexagon (tiles 1, 2, 3, 9, 10, and 11), and note how those tiles form a sort of sub-figure in the shape of a hollow triangle, then this sub-figure is an ideal figure, because it is not a figure on its own but is part of a larger figure that it is found within. In that light, a real large hexagon contains all other possible figures as ideal figures within it; thus, although one might consider the large hexagon to be the goal of being built-up from smaller figures, ZT takes the opposite approach and says that the large hexagon is what “came first” in a sense, from which the smaller figures could be broken out. Although this seems like an odd distinction to make, it forms the basis of a powerful interpretive technique later on, so it’s good to start paying attention to the possible ideal figures that might occur within a larger real figure.

When it comes to the structure of the large hexagon, it helps to consider it in terms of its general structure as having one center and three “belts” or “zones:

Center: house 1 (also called the “focus”)
Inner belt: houses 2 through 7
Middle belt: houses 8 through 19
Outer belt: houses 20 through 37 (also called the “frontier”)

With all that out of the way, we’re finally able to talk about ZT’s main approach to divination: the Great Mirror. This is a large hexagon formed in the usual way, but each tile-position (what I’ll call “house”) in the Great Mirror has particular cosmological signification. As a result, ZT also talks about the large hexagon as using the “astronomical aspect” or “sidereal aspect” (in contrast to the “temporal aspect” or “chronic aspect” which is another use of the large hexagon we’ll get to later). In many ways, the Great Mirror is the ZT equivalent of the Celtic Cross spread in Tarot or the Grand Tableau in Lenormand.

The above diagram is a reproduction of ZT’s own Plate III, which includes a bit more information than what’s shown above but which we’ll get to in a bit:

The Great Mirror is generated the same way as with any large mirror: counting in an outwards counterclockwise spiral starting from the center and proceeding to the lower left. The Great Mirror is broken down into four regions based on its overall structure:

The center, which is the single house 1 in the middle of the Great Mirror.
The solar belt, which consists of houses 2 through 7 (i.e. the Great Mirror use of the inner belt), immediately around the center. This belt is also called the “central belt”.
The planetary belt, which consists of houses 8 through 19 (i.e. the Great Mirror use of the middle belt), immediately around the solar belt. This belt is also called the “sidereal belt”.
The zodiacal belt, which consists of houses 20 through 37 (i.e. the Great Mirror use of the outer belt), immediately around the planetary belt.

Of special significance in the Great Mirror are houses 1, 9, 11, 13, 15, 17, and 19, because these are the houses given (respectively) to the Sun, Mars, Venus, Jupiter, Mercury, the Moon, and Saturn. All the other houses are said to be “in the orbit” of one or two planets; thus, when we look at Mars (the “inner corner” of the Great Mirror on the lower left), then we can say that house 9 is Mars itself; houses 21, 22, and 23 are houses exclusively in the orbit of Mars; house 10 is in the shared orbit of Mars and Venus, house 2 is in the shared orbit of Mars and the Sun, and house 8 is in the shared orbit of Mars and Saturn. Note how, while all the non-solar planets have three houses that are in their own orbit exclusively, every house in the Sun’s orbit is shared with another planet. Thus, if we consider a planet together with that planet’s orbit, then what we’re doing is effectively considering an “ideal small hexagon” within the larger Great Mirror. This is why the other term for a “small hexagon” is “orbital hexagon”, because it represents a single planet in one of the focal points of the Great Mirror and the six houses that surround it.

And yes, we’re being bumped back down to seven planets here, not to nine planetary intelligences. As opposed to a 9-fold system of numerology, we’re using a 7-fold system of geometry here, which necessitates that we talk about seven places of interest and not nine. To that end, it would be inaccurate to say “house of Adamasto” or “orbit of Seleno” (rather “house of Mars” or “orbit of Moon” respectively), because the Great Mirror focuses on planets and not planetary intelligences, even if the intelligences have their seats in their own planets. Thus, both Genhelia and Psykelia share the same orbit of the Sun, just as Seleno and Psykomena share the same orbit of the Moon. (It gets a little more complicated later, but that’s later, not now.)

So, as you might have predicted, each house in the Great Mirror has its own set of meanings, its own contextual or semantic field, just as the twelve houses do in an astrological horoscope or each of the card positions in a Tarot spread. When a tile is placed in one of these houses, the meaning of that tile is to be interpreted in the scope of the house it’s found in. Thus, there are 37 such houses, each with their own meaning—but again, there’s a system behind this. Recall how when we were talking about the Intelligences and Numbers how, although each Number has its own signification, the significations didn’t have to be memorized but rather “generated” based on their smaller digits? A similar approach is used for the meanings of the individual houses of the Great Mirror.

Take a look at the layout of planets on the Great Mirror: we have the Sun in the Middle, Mars to the lower left, Venus to the lower right, Jupiter to the right, Mercury to the upper right, the Moon to the upper left, and Saturn to the left. Each planet has its own orbit of six houses, but if you consider things at a grander scale, the large hexagram is a collection of seven orbital hexagrams in the same geometric arrangement as an orbital hexagram has seven houses, kinda like a fractal. If we consider a smaller “fractal” of the Great Mirror…

…then we can overlay this on each orbit of the Great Mirror as a whole to get a sort of “main planet vs. sub-planet” arrangement.

Consider house 24. This is a house in the orbit of Venus, but it’s to the lower-left of this planet, which is the “fractal direction” of Mars. In this light, we might say that house 24 is the house of “Mars of Venus”, so even though this house fundamentally has something to do with Venus, it’s about the Martian aspects of Venus’ domain. Thus, this house has the meaning of “intense or violent passions and senses”. By taking the overall planetary layout of the Great Mirror and applying it on a smaller scale to an individual planet’s orbit, we can arrive at a specific context through pairwise planetary interactions—not unlike the how we paired together the tens-digit vs. ones-digit of the compound Numbers to arrive at a specific indication through pairwise interactions of the primitive Numbers.

What about the planetary houses themselves? Well, they have the “fractal direction” of being in the center, which is the house of the Sun: thus, the “Sun of whatever-planet” house is just that planet itself; just as the font of all power in the solar system is the Sun, the font of all power within a given planet’s own orbit is that planet itself. Thus, house 9 (the house of Mars itself) is given to “military status, valor or bravery”, and house 13 (the house of Jupiter) is given to “high wisdom, science”. The system checks out pretty well in this case.

What about houses that are in two orbits at once? Consider house 7: this is a house in the orbit of the Sun, but it’s to the left of the Sun, the “fractal direction” of Saturn. Thus, house 7 is the house of “Saturn of the Sun”, so this house is about the Saturnine aspects of the Sun’s domain. Thus, this house has the meanings of “advanced age, health”. At the same time, house 2 is also in the orbit of Saturn, to the right of the planet and thus the “fractal direction” of Jupiter. The indications of “advanced age and health” can be thought of as much as the Saturnine aspects of Saturn’s domain as it is the Jovian aspects of Saturn’s domain, in this regard. Likewise, if we consider house 10, the house between the positions of Mars and Venus, this house has the meaning of “romantic adventures” (again, “romantic” in the sense of being chivalrous and novel-worthy events). From the perspective of Mars, house 10 is to Mars’ right in the “fractal direction” of Jupiter (so “Jupiter of Mars”), but at the same time, it’s also to Venus’ left in the “fractal direction” of Saturn (so “Saturn of Venus”). Sure, it might be about “romantic adventures”, but the different perspectives here can shine a different light on that same topic.

So, in that light, here’s what ZT gives as meanings for the 37 houses of the Great Mirror, along with what the planetary considerations are of each house.

Grandeur, power. (Sun of Sun)
Strength, triumph, glory. (Mars of Sun, Mercury of Mars)
Beauty, happy love. (Venus of Sun, Moon of Venus)
Genius, great reputation. (Jupiter of Sun, Saturn of Jupiter)
Treasures, gains of all kinds. (Mercury of Sun, Mars of Mercury)
Domestic prosperity, inheritance. (Moon of Sun, Venus of Moon)
Advanced age, health. (Saturn of Sun, Jupiter of Saturn)
Severe bodily injury. (Moon of Mars, Venus of Saturn)
Military status, valor or bravery. (Sun of Mars)
Romantic adventures. (Jupiter of Mars, Saturn of Venus)
Good fortune. (Sun of Venus)
Marriage, pure feelings. (Mercury of Venus, Mars of Jupiter)
High wisdom, science. (Sun of Jupiter)
Magistracies or judiciaries, equity and fairness. (Moon of Jupiter, Venus of Mercury)
Finance, trading or business. (Sun of Mercury)
Maladministration or bad management. (Saturn of Mercury, Jupiter of Moon)
Family, sedentary or domestic life. (Sun of Moon)
Melancholy, weak health. (Mars of Moon, Mercury of Saturn)
Envy, sorrows, setbacks or reversals of fortune. (Sun of Saturn)
Birth, candor, inaction. (Mars of Saturn)
Infancy, playfulness or mischief. (Saturn of Mars)
Puberty, turbulence, quarrels or squabbles. (Mars of Mars)
Adolescence, sympathy. (Venus of Mars)
Intense or violent passions and senses. (Mars of Venus)
Debauchery, infidelity. (Venus of Venus)
Tenacious passions, constancy. (Jupiter of Venus)
Celibacy, marital fidelity. (Venus of Jupiter)
Moral perfection, maturity. (Jupiter of Jupiter)
Prudence or caution, good philosophy. (Mercury of Jupiter)
Bad faith, decline. (Jupiter of Mercury)
Illicit and perilous fortunes. (Mercury of Mercury)
Travel, hectic life. (Moon of Mercury)
Inconstancy, wasted or lost time. (Mercury of Moon)
Ancestors, old age. (Moon of Moon)
Apathy, waning of fortune. (Saturn of Moon)
Infirmity, indigence. (Moon of Saturn)
Ruin, death. (Saturn of Saturn)

The list of meanings above makes sense, given the structure of the Great Mirror and these “fractal directions” that allow for different planets to overlap their meanings. According to ZT’s own admission, however, the table given above is intentionally limited and limiting:

Be extremely careful to not take the Table that follows for a fixed indication of the significations of each of the 37 boxes from which the Great Mirror is composed. This Table is only a vehicle by which the Candidate should orient themselves, especially in the approaches which have as their goal only the ordinary career of human life.* However, if the Candidate has retained well all that we have established as precepts up until this point, then they will soon regard this Table as of little use, since there is not a single piece of the Great Mirror which does not modify, either for weal or for woe, the box assigned to it—and here we say “modify”, not “distort”.

* It will be seen, for example, that this table would furnish nothing to whoever would occupy themselves with the future destinies of empires, nations, &c.

What ZT is saying is that, even though it gives this table of contextual and semantic meanings for each of the 37 houses, it’s meant for illustrative purposes only as regards an individual human’s life, and as such, the indications above aren’t really valid for whole groups of people, the governments of nations and state, companies or industries, and the like—because the indications of table above were generated using that “sub-planet of main-planet” approach only for the scope of an individual human. ZT, given that it is “only a key and not a treatise”, does not give tables for other scopes, but it gives us the means to come up with such tables using the same underlying method as this one.

For instance, say we’re in a battle with some army, and I want to know something about the tactics and strategy I should engage with in order to emerge victorious. Understanding the difference of “strategy” (overall battle plan) and “tactics” (individual steps + logistics), I would want to turn to houses 2 and 5. If we consider the table above, these two houses have the respective meanings of “strength/triumph/glory” and “treasures/gains of all kinds”, which…yeah, kinda work, I guess? But if we look at the planetary considerations, house 2 is both “Mars of the Sun” as well as “Mercury of Mars” (the planning and direction of battle, i.e. strategy), and house 5 is both “Mercury of the Sun” as well as “Mars of Mercury” (the attacks and drives of planning and plotting, i.e. tactics). By doing this, we can expand the indications of each house in the Great Mirror from the scant description given in ZT by understanding the overall method and then extrapolating from it as necessary and as befits a given situation we might be faced with.

Personally? I think this is a really ingenious and elegant system of dividing up a situation into its many different aspects based on particular considerations. Just like with the compound Numbers, a few basic principles are used on general ideas to produce a wide variety of specific ones. Of course, just like with the compound Numbers, this is a lot to take in all at once, or so it’d seem—but the trick behind it is that we don’t need to take it in all at once, but rather just need to understand the method behind the madness. While the table as given above is great for readings at the level of the individual human being, we yet have a method to expand on that to any level or field or context. That said, we’re not done talking about the Great Mirror yet, because there are a few more considerations we have to work through, first.

First, when it comes to drawing tiles to compose the Great Mirror, the process works much as we would expect with Tarot cards or runes: individual tiles are drawn from the Urn without replacement (i.e. a tile can only be drawn a maximum of once), and it is placed in the first available house in the Great Mirror, not skipping to any later house nor replacing the tile in any earlier house. While this makes obvious sense to us modern folk (you don’t take the first Tarot card you draw for a Celtic Cross spread and put it anywhere else but the first position, nor do you take any later card and swap it out with a card in an earlier position), I assume that ZT makes this point explicit because of how new the idea might have been and to reduce any chances of people “making their own fate” by fiddling with the order tiles come out of the Urn and thus how the Great Mirror ought to be composed.

As one reads through ZT, it establishes the rule that, even though there are 112 (or 113) tiles in the whole set used for divination, no more than 37 tiles are to be used in any given reading, because the large hexagram (i.e. the Great Mirror) has only 37 houses. However, that is not technically entirely true, because ZT also has the rule that the two Principles are never used in a Great Mirror. It’s not that they’re separated out from the Urn and can’t be drawn, but if one or both are drawn in the course of composing a Great Mirror, then they’re placed outside it entirely:

Sisamoro (the Good Principle) is placed at the zenith of the Great Mirror, at the top vertex of an equilateral triangle with the leftmost and rightmost corners of the Great Mirror. Senamira, likewise, is placed at the nadir of the Great Mirror, below it in the same sort of arrangement. ZT is, perhaps unsurprisingly, unclear on the exact signification of the Principles if they should appear in a Great Mirror, just that it makes such a divination super notable:

The presence of a Principle, whether one or both, imparts to the Great Mirror superlative properties, the development of which is not the responsibility of a Key. The Pure Spirit then must speak, or the student remains more embarrassed than enlightened by the intervention of these extreme influences; it is even worse when there is conflict [i.e. when both Principles appear]. On the contrary, the true Cabalist is never better served than by those effective extractions where Fate majestically reveals its most admirable decrees.

The only concrete advice that ZT gives us is this, along with what to note when considering when an Intelligence is drawn and put into the Great Mirror as well:

Let us observe at which junction in the laying out of pieces for a Great Mirror where a Principle or Spirit appears.

Let us pay great attention to the quality of two numbers by which an Intelligence, drawn from the Urn, follows and precedes, and also how, in the Great Mirror, such an Intelligence is surrounded, and whether it forms a full orbit in its placement or a truncated one.

That latter point is especially interesting when it comes to the Intellligences. If an Intelligence is drawn, then it has a meaning just like any Number tile, but it also forms a sort of incidental planetary house of its own, and thus the houses that surround it form a sort of accidental orbit—but if such an Intelligence appears in the outer belt of the Great Mirror, such an orbit will necessarily be “truncated” and, thus, incomplete. If such an accidental orbit is a full/complete one, then that might give an extra planetary consideration to each of the houses according to its “fractal directions”; if such an orbit is a truncated/incomplete one, then not all planets would get to be represented in such a way. It’s a really neat idea to play with.

Astute readers will note that I’ve avoided talking about the inclusion of the signs of the Zodiac in the Great Mirror. For the most part, the signs of the Zodiac don’t matter all that much for the overall indications of the houses. However—and we’ll get to this more in a later post—the signs of the Zodiac are used by ZT to relate to the various stages of life that one undergoes, starting with Aries as birth and ending with Pisces as death. Each of the sides of the zodiacal belt relate to one of the “six divisions of life” according to ZT (childhood, youth, adulthood, middle age, old age, senility), and so the signs of the Zodiac within them correspond to particular aspects of that growth (which is why house 20, given to Aries, also has “birth” in its indications, 21 “infancy”, 22 “puberty”, and so forth). Beyond that, however, ZT doesn’t really do a whole lot with the Zodiac here, although that doesn’t say that one couldn’t feasibly find some way to work it into the system (even if ZT might discourage doing so, given its anti-astrology bias).

One last topic to round out this discussion on the Great Mirror. Although ZT says that the planets are all equal and aren’t ranked among themselves in the planetary belt of the Great Mirror (the only planet with primacy being the Sun in the center), ZT also notes that it doesn’t have an account for why the planets are positioned on the Great Mirror the way they are: it notes that it does not appear to have anything necessarily astronomical about it nor anything that is particular astrological, either, just that it’s something that (it claims) is “of such antiquity sunk deepest into the darkness of the past; sub judice lis est [the case is still before the judge]”. Admittedly, I’m not sure where ZT might have gotten this planetary arrangement from, either. When it comes to hexagonal arrangements of the planets, one might be more inclined to recall the planetary hexagram…

…which is, of course, a development from the qabbalistic Tree of Life, like that of Athanasius Kircher in his Œdipus Ægyptiacus from 1652, and later used for any number of Hermetic or Western occultists who make use of the so-called “Kircher Tree”:

Of course, given how distant ZT’s own “Great Cabala” is from anything properly seen in kabbala of any sort, to say nothing of how much it would caustically say about established traditions anyway, I somehow doubt that this would have been an influence here along these lines. However, if we compare the qabbalistic planetary hexagram with the hexagram formed by the Great Mirror, we see the same planetary triangles (Saturn-Mercury-Venus, Mars-Jupiter-Moon), just with a different rotation/reflection applied.

That being said, wherever the pattern of planets here came from, there is a logic and order in it. If we proceed through pairs of the planets counterclockwise around the Great Mirror, we see two kinds of patterns arising of similar pairs and dissimilar pairs:

Similar pairs arise between Venus-Jupiter (the benefics), Mercury-Moon (the neutrals), and Saturn-Mars (the malefics). This has the result of making the horizontal rows of the Great Mirror form pairs as well: the middle row (Saturn-Jupiter) represents the greater planets (the greater malefic and benefic), the lower row (Mars-Venus) the lesser planets (the lesser malefic and benefic), and the upper row (Moon-Mercury) the neutral small planets.
Dissimilar pairs arise between Mars-Venus (male/female), Jupiter-Mercury (king/servant or philosopher/sophist), and Moon-Saturn (creator/destroyer or youth/elder). This suggests an awareness of the opposition of particular zodiac signs and extending that to the planets, e.g. how Mars rules Aries and Scorpio, which are in opposition to Venus-ruled Libra and Taurus.

As of this writing, I’m not familiar with any source that arranges the planets in the way ZT does; while ZT definitely has a logic that suggests a good awareness of basic astrological principles and zodiacal correspondences, I’m not sure if that’s enough to trace it to any particular origin, especially when such arrangements have usually been more magical than astrological. This is another of those unanswered questions I have, and it may be that this arrangement is unique to ZT. If you have any notion of where such an arrangement might have an antecedent or any similar leads for further research, dear reader, or if you spy any other insights or patterns in this arrangement, do let me know in the comments!

The Digital Ambler

Always Forward Between Heaven and Earth

Tag Archives: great mirror

Unlocking the Observatory: the Great Dial and Determining Times/Options

Unlocking the Observatory: Figures, Mirrors, and the Great Mirror