Elemental Figure Symmetry
(This article was published in Studia Lulliana, Maioricensis Schola Lullistica,
Vol. XL #96, year 2000)
Introduction
Blessed Raymond Lull's instructions regarding the Elemental Figure are condensed, leaving many details to be worked out by the reader; at the end of Liber exponens figuram elementalem he writes:The statements we made in this book can be rationally demonstrated by following the discourse of Ars Demonstrativa: now if we went on to demonstrate everything said in this book, it would grow far too large and so we prefer to leave this as an exercise for artists. (MOG IV, 10)This article deals with one aspect of the Elemental Figure not explicitly demonstrated by the Doctor Illuminatus, namely the rationale for the placement of element names in its sixty-four compartments.I. First, there is a description of the Elemental Figure's basic layout, with a minimum of information needed to show the rationale for situating element names in the Figure, this includes:
1. an abridged table of element properties.
2. how the elements rule different parts of the Figure.
3. proper and appropriated qualities, degrees and colored rows.
II. Second, we deal with element name placement in the columns, rows and compartments of the Elemental Figure's four quadrangles. Here we deal with:
1. levity and gravity.
2. the first columns of the quadrangles.
3. the deployment of element names in the quadrangles.
4. a reference to Plato's Timaeus.
III.How
elements combine
through:
1. mixture.
2. digestion.
3. composition.IV. Three dimensions:
1. Visualizing Chaos.
2. Elemental Figure.V. Heuristics
1. Figure S.
2. Lightning.
3. Thunder.VI. Conclusion
VII. References
Main qualities of the four elements: Element levity/gravity spheres own quality appropriated quality active or passive color in Figure Fire lightest, top sphere heat dryness from Earth active red Air lighter, next to top moisture heat from Fire passive blue Water heavier, next to bottom cold moisture from Air active green Earth heaviest, bottom dryness cold from Water passive black I.2 Ruling elements. Element rulerships in the quadrangles
Above each quadrangle in the Elemental Figure appears a title: "Figure of Fire", "Figure of Air", "Figure of Water" and "Figure of Earth". This means that the title element rules the quadrangle and the elemented compounds signified in it. In each quadrangle, the ruling element's name occupies the top left to bottom right diagonal; the upper left compartment is the simple compartment which moves all the other "compound" compartments in its quadrangle. Each quadrangle as a whole represents one of the four elementary spheres and all four spheres are again represented within each quadrangle in the four horizontal rows.
Besides representing the four spheres, the four rows also stand for the four degrees of intensity of each element in its compounds: the top, or fourth row from the bottom stands for the fourth, or highest degree, the third row for the third degree, the second row for the second degree and the bottom row for the first degree of the ruling element.
Each quadrangle signifies compounds ruled only by the element of the quadrangle and not by the other elements.
A compound always contains all four elements, three of which are subservient to the ruling element in varying degrees.
When Fire forms a fourth degree fiery compound, one point of simple Fire divides itself into six compound points, three of which it gives to third degree Earth, two to second degree Air, and one to first degree Water.
In the red row at the top, Fire is in the fourth degree, Earth in the third, Air in the second and Water in the first degree.
Pepper, for instance, which is hot in the fourth degree, is situated in the red top row of the quadrangle of Fire.
Cinnamon, hot in the third degree, is in the black third row from the bottom, where third degree Fire rules over second degree Earth, first degree Air and 3/4 degree Water.
Fennel, hot in the second degree, is in the blue second row from the bottom, where second degree Fire rules over first degree Earth, 3/4 degree Air and 2/4 degree Water.
Anise, hot in the first degree is in the green bottom row of the fiery quadrangle, where first degree Fire rules over 3/4 degree Earth, 2/4 degree Air and 1/4 degree Water.
Wherever the name "Fire" is in a quadrangle not its own, Fire does not rule the other elements but is ruled by the element of that quadrangle: so the first degree Fire in green at the bottom right corner of the fiery quadrangle is not the same as the first degree Fire (also green) found in the Water quadrangle's top right corner in a compound cold to the fourth degree. First degree Fire in its own quadrangle is hotter than first degree Fire in the Water quadrangle because in the latter, the heat of Fire is mortified under the rule of strong fourth degree Water. In the former, Fire rules over very weak 1/4 degree Water.
The things said about Fire apply to the other elements and quadrangles.
The way that degrees work in medicinal mixtures and compounds is extensively covered in the Principles of Medicine and other medical works by Bl. Raymond. This brief overview of the Elemental Figure will not go any further into its pharmaceutical application as it is only one of many applications, each of which would deserve at least an entire book (theology, philosophy, law, grammar, logic, rhetoric, arithmetic, music, geometry, astronomy, etc.) .I.3 Colors - Element degrees, proper and appropriated qualities and colors
As previously shown in the abridged table, each element:
1. opposes an element,
2. gives its own quality to another element
3. receives an appropriated quality from yet another element and
4. has its own, or proper quality.
When an element rules a compound in the fourth degree, the element from which it receives its appropriated quality is in the third degree, the element to which it gives its own quality is in the second degree and the element that it opposes is in the first degree.
By this rule, in the fiery quadrangle, the top row is red. Fire receives dryness from Earth and Earth is in the third degree, whose row is black. Fire gives heat to Air and therefore the second degree row is blue. Fire and Water are opposed as hot and cold, Water is in the first degree and the bottom row is green.
This general pattern applies to each quadrangle in its own way: the ruling element's own color is in the top row of its quadrangle, the third degree row has the color of the ruler's appropriated quality the second degree row has the color of the element that appropriates the ruler's own quality and at the bottom stands the color of the element that opposes the ruling element.II. Order of element names
Now let us discuss levity, gravity and the spheres, so that we can then compare the first columns to the left in the quadrangles and explain the pattern of element names in the Elemental Figure.
The arrangement of element names in the Elemental Figure signifies the lightness and heaviness of the elements and the way they are mixed in each other's spheres. Let us for the time being set aside other element qualities and colors to focus on their levity and gravity, or lightness and heaviness which are instruments that the elements use for ascending and descending. There are two heavy elements in the two lower spheres and two light elements in the two upper spheres. The element in the lowest of the two lower spheres, namely Earth, is the heaviest, and Water, the next element above it, is the heavier heavy element. Conversely, Fire is the lightest and Air is the lighter light element.
Fire, the lightest element has the topmost sphere and Earth as the heaviest element has the lowest sphere. Hence, Fire displaced to any other sphere can only move upward to regain its own sphere, and likewise Earth in any other sphere but its own can only move down to "go home" as it were.
Air is not as light as Fire because it does not have the topmost sphere and when it occupies the sphere of Fire, Air seeks its home sphere, just below that of Fire, by going down. As levity and gravity are instruments the elements use for moving up and down, Air exiled in the sphere of Fire has to move down to regain its own sphere and this detracts from the lightness of Air, and so Air is called the lighter element, not as light as Fire, which is the lightest element as we said.
Water, likewise, is not as heavy as Earth because it does not occupy the lowest sphere, and when Water is exiled in the sphere of Earth just below its own sphere, it has to rise to come back to its home: now as rising movement is associated with lightness, this detracts from the heaviness of Water and thus Water is called the heavier element, not as heavy as Earth.
To summarize the above, here is a list of the elements in the order of lightness and heaviness:
Fire: lightest (simplest, noblest, subtlest) has the topmost sphere, not encompassed by any other elemental sphere. Air: lighter (simpler, nobler, subtler) has the second sphere from the top, encompassed only by the fiery sphere.
Water: heavier (more compounded, base and gross) has the second sphere from the bottom, encompassed by the two spheres above it.
Earth: heaviest (most compounded, base and gross) has the lowest sphere, encompassed by the three other spheres. As the sphere of Earth encompasses no further sphere, it is a solid whereas the other spheres are hollow.
This pattern of "lighter and lightest, heavier and heaviest" seems to contradict what is said in Ars demonstrativa regarding the compartment of Fire and Air, namely that the light elements are equally light and the heavy elements equally heavy. The solution to this problem is that the elements depend on one another for their appropriated qualities: Fire must receive dryness from Earth in order to act in Air and Water, thus the lightest element is weighed down by the heaviest one and the heaviest element is by the same token lifted up by the lightest one. And Water must receive moisture from Air in order to act in Earth and Fire, so that the heavier element and the lighter element also diminish one another's ability to ascend and descend, although not as much as the lightest and heaviest elements do to each other. The result is that the light elements are made equally light and the heavy elements equally heavy by the interaction between the cycle of lightness and heaviness and the cycle of giving and receiving proper and appropriated qualities.
By the way, these two cycles determine two different ways of attributing the algebraic letters A B C D to the four elements found in Bl. Raymond's writings:Element alphabets in the Art:
In the Principles of Medicine, the four elements are assigned the following letters:
A = Fire
B = Earth
C = Air
D = Water
This order follows the pattern of elements combining in a fourth degree Fire compound, reflected in the colors of the rows in the quadrangle of Fire. Note that this is also the order of elements in the zodiac:The Zodiac
The order of Fire followed by Earth and then Air and Water is also observed in the element sequence of the zodiac: Aries, the first sign, is fiery, followed by earthy Taurus, airy Gemini and watery Cancer. The same sequence then repeats itself two more times in the remaining signs:
Order of Elements in the Zodiac Fire A 1. Aries 5. Leo 9. Sagittarius Earth B 2. Taurus 6. Virgo 10 Capricorn Air C 3. Gemini 7. Libra 11. Aquarius Water D 4. Cancer 8. Scorpio 12. Pisces Memory and Intelligence
Further, the acts of the rational soul's powers proceed in an order parallel to that of Fire receiving dryness from Earth, etc: the intellect first receives from memory, and from memory and intellect the will proceeds. Memory is associated with Earth, intellect with Fire and the will with Air. The combined act of the three powers is called belief, associated with Water.
Seasonal cycle
In other writings, like the Principles of Astronomy etc., the letters follow, in alphabetical order, the four seasons and times of day:
A = Air (spring, or morning)
B = Fire (summer, noon)
C = Earth (autumn, evening)
D = Water (winter, night)
If we follow this circular sequence beginning with C = Earth and consider the Spheres, the sequence C D A B is the sequence of spheres from the bottom to the top. Both sequences are simultaneously represented in the first column of the fiery quadrangle: the first sequence by the colors and the second sequence by the names. In both sequences Fire and Earth are contiguous.II.2 First columns
To show how the pattern of element names develops, let us compare the first columns of the quadrangles.
1. First columns in quadrangles of Fire and Earth: Fire (lightest) Earth (heaviest) Air (lighter) Water (heavier) Water (heavier) Air (lighter) Earth (heaviest) Fire (lightest) The order of elements written in the first column of the quadrangle of Fire is the same as the order of the spheres. Since Fire is the lightest element and Earth is the heaviest, the order of the elements in the first column of the Earth quadrangle is the reverse of that in the first column of the Fire quadrangle, to signify the opposition of the two extremes of lightest and heaviest in Fire and Earth. As greater simplicity implies greater nobility, and Fire is the noblest element, the element names in its column all stand in their own spheres. Earth, on the other hand, is the least noble of the elements and therefore in the first column of the Earth quadrangle the elements are mixed in the spheres in the most unnatural way that can exist within this arrangement. Therefore, the order of element names in the Earth quadrangle is exactly the opposite of the order of element names in the Fire quadrangle to signify the opposition between Fire's nobility and Earth's baseness.
Now there is a further point to note regarding these two columns: comparing their compartments one by one, we see that the top compartments have the names "Fire" and "Earth" which are the lightest and heaviest element respectively. Next are "Air" and "Water", or the lighter and heavier elements, then "Water" and "Air" and finally "Earth" and "Fire". The element names in these columns compared in this way always yield pairs of opposites comprising either the lightest and heaviest, or the lighter and heavier elements. This pattern of opposition between lightest and heaviest and lighter and heavier will be applied below to construct the first column of the quadrangle of Water, after having done the first column of the quadrangle of Air.As the ruling element of a quadrangle is always in the top left corner of the quadrangle, Air is at the top in this column, the second compartment from the top is Fire. Water and Earth stand in their own spheres: there are only two exiled elements and they are not very far from their own spheres, the light elements are interchanged in the spheres of light elements and the heavy elements are both "at home". Air is a light, simple, noble element, although not to the same extent as Fire, so the element names are minimally displaced in this column. The light elements are both on top of the heavy elements.
2. First column - Air quadrangle Air (lighter) Fire (lightest) Water (heavier) Earth (heaviest) 3. The first column in the quadrangle of Water compared to that in the quadrangle of Air:
Water is naturally at the top of this column and the other element names are determined by the pattern of opposition of lightest to heaviest and lighter to heavier described above in the comparison between Fire and Earth. Therefore, we compare this column with the first column in Air to find the names: the top compartments match Water and Air, the next compartments down have Earth and Fire, then we have Air and Water and finally Fire and Earth. Further, following a pattern that is found everywhere in the Figure, the heavy elements and the light elements are clearly segregated in different halves of columns.
Water (heavier) Air (lighter) Earth (heaviest) Fire (lightest) Air (lighter) Water (heavier) Fire (lightest) Earth (heaviest) The overall symmetry of element names in the Elemental Figure:
Earth is the heaviest element, and Fire is the lightest. Further, if you superimpose the quadrangles of Earth and Fire, then the names of the elements in the corresponding compartments are always opposed as Fire to Earth and Air to Water, or the lightest to the heaviest and the lighter to the heavier. We observe the same opposition of names, compartment by compartment, when superimposing the quadrangles of Air and Water. This is not the case when comparing the quadrangle of Fire with that of Air or Water, or the quadrangle of Earth with Air or Water, as here we do not compare the lightest to the heaviest and the lighter to the heavier. Therefore, this symmetrical opposition occurs as a function of the greater and lesser lightness and heaviness of the elements.
Further, there is a greater opposition between heaviest and lightest than between heavier and lighter: this is shown in the Figure's mutual opposition of the quadrangles of Fire and Earth compared to that of the quadrangles of Air and Water: whereas the order of names in every corresponding row and column of the Fire and Earth quadrangles is exactly the opposite, this order of opposition in the Air and Water quadrangles is confined to the halves of the rows and columns, if you take the left half of the Air quadrangle divided vertically into columns and place it to the right of the right half, you obtain the name order in the Water quadrangle. Likewise, if you do the same with the Water quadrangle, you obtain the name order in the Air quadrangle. This also applies to the horizontal division of these two quadrangles. If we want to reverse the fiery quadrangle to make its name order like that of the Earth quadrangle, or vice-versa, we have to move all the columns and not only two halves. The opposition between the Figures of Air and Water is less complete than that between Fire and Earth, to signify the minor opposition of lighter and heavier as compared to the major opposition of lightest to heaviest.A brief summary of the above:
Fire (lightest) Earth (heaviest) Air (lighter) Water (heavier) Air (lighter) Water (heavier) Fire (lightest) Earth (heaviest) Water (heavier) Air (lighter) Water (heavier) Air (lighter) Earth (heaviest) Fire (lightest) Earth (heaviest) Fire (lightest) Comparing the first columns of all four quadrangles, Fire, the noblest, simplest, subtlest and lightest element has all element names in their spheres. Earth, the basest, most compounded, dense and heavy element has all element names exiled from their spheres. Air, the nobler element has only two names exiled and the light elements remain on top while the heavy ones stay at the bottom. Water, not quite as base as Earth, has the heavy elements in the top half and the light ones in the bottom half, but at least the heavier element is above the heaviest.
The same rationale of the element name order in the Elemental Figure:
To explain the same in other words and from a slightly different visual approach, we first observe that the light and heavy elements are segregated in the two halves of every column and row in the Figure.
In the first columns of the light element quadrangles, Fire and Air, the light elements are in the top half and the heavy elements in the bottom half. In the first columns of the heavy element quadrangles, Water and Earth, the heavy elements are in the top half and the light elements in the bottom half.
This signifies the principle of Fire's nobility: by this principle, Fire is the noblest and simplest of the elements because it is the lightest, and consequently Air, the other light element, is the nobler, simpler and lighter of the elements. Conversely, the heavy elements are base, more compounded and so Water is the baser, heavier and more compounded element and Earth is the heaviest, basest, most compounded one.
As the lightness and heaviness of the elements corresponds exactly to the high or low position of their spheres, and the four compartments of the first column signify the four spheres, the simple or compounded, light or heavy, noble or base character of each element is signified by how near or far the element's name stands from its sphere in the first column of its own quadrangle, where it always stands in the sphere of Fire at the top to signify its fourth degree.
In the first column of the Fire quadrangle, Fire has its name in its own sphere. In the first column of the Air quadrangle, Air has its name one sphere away from its own. Water has its name two spheres away from its own in the first column of the Water quadrangle. Earth has its name three spheres away from its own in the first column of the Earth quadrangle.
Further, the light or heavy qualities of the elements are signified in the first columns not only by the ruling element name's closeness or distance from its own sphere, but also by the extent to which the other element names in the column are near or far from their spheres.
As said above, in the first columns of Fire and Air, the light element names are in the top two spheres and the heavy ones in the bottom. This means less composition and more simplicity than signified by the element name orders of the heavy element columns where all the element names are outside of their own spheres, with the heavy ones on top of the light ones.
In Fire, all the element names in the first column are in their spheres.
In Air, only Fire and Air are displaced, yet they still remain in the light element spheres and the names of Earth and Water stand in their own spheres.
In Water, the heavy elements are on top and the light ones on the bottom, all element names are exiled from their spheres although Water, the heavier element, is above Earth, the heaviest element.
In Earth, the full extent of exile is found in the first column of Earth where the heaviest element is on top and the others below it in inverse order of heaviest, heavier, lighter, lightest.A note on the first column of the Water quadrangle:
In De Levitate et ponderositate elementorum, the human body is described as an inverted tree, the four main organs that are the seats of the four elements are, from top to bottom, as in the first column of the Water quadrangle:
the brain (Water)
the spleen (Earth)
the heart (Air)
the liver (Fire)II.3 Deployment
Once the names in the first column have been filled in as explained above, the remaining compartments in each quadrangle are completed as follows: write the names in the same order as in the first column
1. from left to right in the first line,
2. bottom to top in the last column
3. right to left in the bottom line,
4. and fill in the diagonals with the element names found in their extremes.
This process is identical for all quadrangles and yields the following results in every quadrangle:
1. In every quadrangle, the order of element names in the first column is the reverse of that in the last column, in other words, the orders of element names of the two outer columns are mutually reversed..
. The orders of element names in the second and third columns, or the two inner columns, are mutually reversed.
. The orders of element names in the top and bottom rows, or the two outer rows, are mutually reversed.
. The orders of element names in the second and third rows, or the two inner rows, are mutually reversed.
5. The element names in the first column and the top row are in the same order, and likewise in the second column from the left and the second row from the top, the same for the third and fourth rows and columns: the mutual reversal of name orders exists between inner and outer columns as well as between inner and outer rows. Since the top and bottom rows also signify the spheres of Fire and Earth, while the two inner rows signify the spheres of Water and Air, this opposition follows the pattern of lightest and heaviest, lighter and heavier that also exists between quadrangles, as previously shown.
6. In every row and column in the entire Figure, the light elements occupy one half of the row or column and the heavy elements the other half. A light and a heavy element are never found together in the same half of a row or column, just as there is an absolute opposition between virtue and vice: lightness symbolizes virtue, life and generation whereas heaviness symbolizes vice, death and corruption. This segregation of light and heavy elements in different halves of rows and columns gives rise to the phenomenon of "sub-squares" where every quadrangle is equally divided into four sub-squares always alternating the same two elements Fire/Air or Water/Earth, sub-squares that face each other diagonally.
. A sub-square always consists exclusively of either light or heavy elements, without ever mixing light and heavy elements in the same sub-square. Hence, we will refer to "light element sub-squares" and "heavy element sub-squares" in the following paragraph to show how their positions symbolize the ascent and descent of the elements.
8. Note that in the top left to bottom right diagonal of every quadrangle the four compartments bearing the name of the ruling element signify the ruling element in the fourth degree at the top and in successively lesser degrees ( third, second, and first) in the three following compartments on this diagonal as we move to the left and down. With this in mind, we see that the ascent and descent of the elements is portrayed in the positions of the sub-squares in the four quadrangles: first, in the two top quadrangles, ruled by the two light elements Air and Fire, the light element sub-squares are at the top left and bottom right whereas the heavy element sub-squares are at the bottom left and top right, to signify that while the light elements decrease in degree diagonally from left to right, they become exiled from their spheres into lower spheres while the heavy elements subjected to them move to the upper spheres.
Conversely, in the two lower quadrangles ruled by the heavy elements of Water and Earth, the heavy element sub-squares are at the top left and bottom right while the light element sub-squares are at the bottom left and top right, to signify that while the heavy elements decrease in degree diagonally from left to right, they move from the upper spheres to the lower spheres while the light elements subjected to them move from the lower spheres back to the upper ones.
Paradoxically, the heavy elements get farther from their own spheres as they increase in degree and nearer to their own spheres as they decrease in degree, which signifies that they are less noble, less simple and more compounded than the light elements which are nearer to their own spheres as they increase in degree and further from their spheres as they decrease in degree. The proper qualities of the heavy elements, namely cold and dryness, are indeed more intense at higher altitudes.II.4 Timaeus
The pattern of element names in the elemental figure was explained above by first considering the Fire and Earth quadrangles, then the quadrangle of Air, and finally Water. In Plato's Timaeus, the same order of elemental development is described:
Now that which is created is of necessity corporeal, and also visible and tangible. And nothing is visible where there is no Fire, or tangible which has no solidity, and nothing is solid without Earth. Wherefore also God in the beginning of creation made the body of the universe to consist of Fire and Earth. But two things cannot be rightly put together without a third; there must be some bond of union between them. And the fairest bond is that which makes the most complete fusion of itself and the things which it combines; and proportion is best adapted to effect such a union. For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean - then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one. If the universal frame had been created a surface only and having no depth, a single mean would have sufficed to bind together itself and the other terms; but now, as the world must be solid, and solid bodies are always compacted not by one mean but by two, God placed Water and Air in the mean between Fire and Earth, and made them to have the same proportion so far as was possible (as Fire is to Air so is Air to Water, and as Air is to Water so is Water to Earth); and thus he bound and put together a visible and tangible heaven. And for these reasons, and out of such elements which are in number four, the body of the world was created, and it was harmonized by proportion, and therefore has the spirit of friendship; and having been reconciled to itself, it was indissoluble by the hand of any other than the framer. (Timaeus, 31b3-32c6, trans. Benjamin Jowett)
III. Combination
Elemental motion and combination begin when Fire takes dryness from Earth. Motion is initiated by levity, not by gravity. Earth, the heaviest element, is lifted up by Fire receiving its dryness. Without this impulse of motion from the light elements, the heavy ones would only remain immobile in the two lower spheres. If the elements did not have to give and take proper and appropriated qualities to and from each other, they would not be moved to mix with one another by going to spheres not their own, nor could they go through digestion, composition and alteration, generation and decay.III.1 Mixture
Mixture is the child of Prime Matter, it grows through digestion, reaches maturity in composition whence it returns to Prime Matter through decay and alteration. There are four species of mixture:
First is the mixture of four essential parts: igneity, aereity, aqueity, terreity. In the first species of mixture, there is only continuous quantity.
Second is the mixture of the four simple elements as discrete entities and integral parts. The first two species of mixture are invisible and inaccessible to the senses.
The third species of mixture is in the four elements commonly seen in our global environment: the land, bodies of water, the atmosphere, heat and light. The fourth species of mixture is in individual elemented supposites.
Mixture is signified by the presence of all four elements in every quadrangle, column and row of the Elemental Figure..III.2 Digestion
Digestion in elemental mixture proceeds as a part of fire diffused throughout all parts of the other elements digests the other parts according to its purpose and appetite, and according to site, habit, quantity, quality, relation, action, passion, time and place that this part receives from its superior principles, that is to say, from the first, second and third species of mixture into the fourth. (Liber Chaos, MOG III, 5, 15 (263)).
Whereas:
1. Fire needs to receive dryness from Earth in order to act in Air and Water,
2. Air must receive heat from Fire in order to act in Water and Earth,
3. Water must receive moisture from Air in order to act in Earth and Fire,
4. Earth must receive cold from Water in order to act in Fire and Air.
All the simple elements are homogeneously present in every part of the Chaos and this is because Fire receiving dryness from Earth also receives the cold that Earth receives from Water, and in this cold entering into Fire, Water carries along the moisture it receives from Air, and in this moisture there is heat that Fire gives to Air, so that the movement comes around full circle.
Digestion is the medium between mixture and composition and as such it participates in the nature of both extremes. Thus, digestion is shown in the Elemental Figure in the same way as mixture and composition are shown.III.3 Composition
"In elemented beings, there is both simple and compound fire. Now simple fire exists as the ignificative, the ignificable, the ignification and the ignificatum, all of one essence and in one essence of simple fire. But because the ignificative ignites the ignificable of other essences, namely the essence of air, etc., compound fire is subsequently produced. And this happens because the integral parts, namely the simple elements are mixed, and once they have been mixed, they are digested, and once digested, they are composed under the essential parts, namely the form and matter belonging to some compound. And whatever has been said about fire, likewise applies to the other elements". - Liber Chaos, MOG III, v, 8 (256).To form an elemented compound, for instance a peppercorn, the vegetal natural agent digests the discrete mixture arisen from undifferentiated prime matter into a typical pattern indicated in the first row of the quadrangle of Fire, a pattern that typically reflects the habitual preferences preserved in the form of simple Fire in Prime Chaos. If nothing impedes this digestion, the compound can be formed, that is to say, the peppercorn can be produced if there is no external interference causing indigestion. Each element brings compounds in four degrees out of Prime Chaos by digesting and compounding the mixture in Prime Chaos as moved by mineral, vegetal and animal natural agents and the motion of heaven.
Composition is shown in the Elemental Figure by the different orders of element names, colors and degrees in the quadrangles.IV. Three dimensions
This part deals with the three dimensional visualization of the Elemental Figure. Here we consider some excerpts from Bl. Raymond's works that deal with
1. three dimensional visualization of Prime Chaos.
2. three dimensional visualization of the Elemental Figure.IV.1 Visualizing Chaos
An excerpt from Bl. Raymond's Questions solved with Ars Demonstrativa, shows how he wanted to train the imagination to figure geometrically the unimaginable uniformity of mixture in Prime Chaos and make it more accessible to the intellect:Question: Since every part of a Mixture is in every other part, how are they situated within one another?
1. Solution: The way that the parts of elemented Mixture are situated is considered and understood according to the Situation of the Principles of which the said Mixture consists, in the following way: namely in the Circle, Square and Triangle and in the Lines in all directions.
They have a circular or round Situation following the Situation of the four spheres, three are circular and hollow and one is spherical and solid, this is Earth.
They are also situated in the Square, because there are four elements from which these parts arise, and they oppose one another square wise according to their substances and qualities: now Fire and Water are opposed through heat and cold, heaviness and lightness, density and subtlety, upward and downward motion, and the same with Air and Earth.
The parts of this Mixture are also situated in triangular fashion by way of concordance and contrariety, as follows: Fire is concordant with two opposites, namely Air and Earth, and this makes one Triangle. Likewise, Air is concordant with two opposites, namely Fire and Water, making another Triangle so that we have two triangles. Water, likewise, is concordant with two opposites, namely Air and Earth, making a third Triangle. Earth is concordant with two opposites, namely Water and Fire, making a fourth Triangle.
Hence, there are four Triangles in the said Square of Fire, Air, Water and Earth; and this Square is further deployed into the Circle while the four said Triangles have equal and equidistant Lines.2. In the said Square, we consider Lines and Triangles as follows: place A, B, C, D, at the four corners of a Square. E stands in the middle between A and B, and F between B and C, and G between C and D, and H between D and A. Draw a Line from A to C, another Line from B to D, which results in four Triangles:
from A to B
from B to C
from C to D
from D to A
There is a further Line from E to G and another from F to H making another Square. Consequently, each of the said four Triangles is divided into two Triangles, making eight Triangles from the center to the periphery of the Circle, as shown in this Figure:
which we consider as entirely spherical, like an apple. And the entire Sphere is filled with Squares as follows: namely, Line AB has contiguous and continuous Lines across the entire surface of the Square from AB to CD and back, and the same with line BC to DA and back; likewise, across the entire Surface:
from AB to E and
from CD to G and
from BC to F and
from DA to H;
and the same with the entire surface of Square EFGH, so that the entire elemented body in all its dimensions is full of Lines situated in triangular and square fashion, as well as in a circular way by contiguous and continuous circular Lines deployed through the entire Surface of the Circle all the way to its Center, as the figure shows. The spherical body is entirely full, and the parts of this elemented substance are within one another, each Line in the other Lines in a triangular, square and circular way; and these parts constitute both straight and oblique lines as well as fractional ones. And the Lines of the Triangle and Square all together make up the elemented Body in such a way that each and every one of its parts is partly linear, partly triangular, partly square and partly circular in every dimension. Now this situation of parts is impossible to visualize, but we can best imagine it as filling the bodies and the entire space within the lunar sphere. And although the above Figure cannot suffice for all this, it nonetheless gives some direction to the imagination when considered in all its dimensions and slopes.3. According to the above statements, all the parts of elemented things are situated within one another through Lines, Triangles, Squares and Circles. And this is to say that every part of every Line is itself linear in nature, and every part of every Triangle is naturally triangular and every part of every Square naturally square, and every part of every circle is naturally circular; and this applies everywhere, from the Center to the outer Surface, for otherwise the Line, the Triangle, the Square and the Circle could not possibly arise from these parts; and consequently they could not possibly fill the entire space occupied by elemented things. And this is to say that all the parts of Triangles and Squares reach, in a triangular and square fashion, into every part of the Circle, and conversely, every part of the Circle reaches into all parts of all Triangles and Squares, and also, all the parts of the Triangles reach into all parts of the Squares in a triangular way, and conversely, all parts of Squares reach into all parts of Triangles in a square way. This is how space is entirely filled, and all parts are within one another, and this is how all parts move virtually within one another following their linear, triangular, square and circular nature.
4. From what was said about the Situation of parts in Lines, Triangles, Squares and Circles we understand how the entire Chaos is situated in fullness and how every part of Chaos is situated in every other part, and how each part is deployed in itself and in all others in a circular, square and triangular way, and how each part reaches into other parts both like and unlike itself, straight or oblique, direct or transversal, slanted or circular; and just as these parts thus mixed and connected are situated in the Chaos, so likewise are they situated in elemented things like plants, animals and metals; and thus we see that their Figures have round shapes, like eggs, apples, fingers, tibia, the neck, the human head; and there are also parts of elemented things with square Figures, like the shape of a man's face or shoulders, and triangular like the nose and tongue, and so forth, so that each and every elemented thing is entirely full of the said Sites where parts exist within one another; and as elemented things are of the essence of their Superior Principles, we therefore conclude that all individuals of species are situated in the essence of these Principles in a circular, square, triangular and linear way. But these Sites considered in this way cannot be sensed by the senses although they figuratively appear wherever elemented things exist in Air with the circular, square and triangular Figure as we said above. - Quaestiones per Artem demonstrativem solubiles. MOG vol 3 p 161 (177).
IV.2 Elemental Figure - Spatial symbolism
The light elements, Fire and Water, have the two top quadrangles whereas the heavy elements, Water and Earth, have the two bottom quadrangles. The active elements, Fire and Water have the two quadrangles on the left and the passive elements, Air and Earth have the two quadrangles on the right. This shows the general pattern of priority given to the three axes or dimensions of physical space: wherever the three dimensions or six directions are mentioned in Blessed Raymond's writings, the order is almost invariably: 1. up, 2. down; 3. front, 4. back; 5. right, 6. left.. The vertical axis is first, since elemental motion is mainly determined by the rising light elements that initiate motion in the heavy elements. Also, the vertical axis signifies the division between heaven and hell, which is of the first importance as regards our ultimate destination. The two upper spheres and their two light elements agree more with generation, life, virtue and heaven, whereas the two bottom spheres and their two heavy elements agree more with corruption, death, vice, and hell. This clear division between light and heavy elements is reflected throughout the Elemental Figure, not only in the disposition of quadrangles but also in the position of element names in rows and columns: in every row and every column, the light and heavy elements are segregated in two halves.
. The forward - backward axis is second in priority: given that the Elemental Figure is to be imagined in three dimensions where the columns stand for the vertical axis, the rows for the front to back axis and the transverse and diagonal lines for the right to left axis. Thus, the rows we see going from left to right in the two dimensional Elemental Figure are to be visualized as going from back to front, and not from left to right. For instance, in the quadrangle of Fire, in the blue row: Water is in front and Air behind; Air in front, Fire behind; Fire in front, Earth behind; in the green row Air is in front, Water behind; Water in front, Earth behind; Earth in front, Fire behind: the opposite order to that of the green row is found in the red row and the black row has an order opposite to that of the blue row. And this shows that in the entirety of the said mixture, as this figure indicates, Fire is more in front and less behind than Earth, and Earth than Air, and Air than Water; and the more Fire descends from the top to the bottom row, the more it falls behind while Water comes forward and the opposite happens as Fire ascends from the bottom row to the top; and likewise as Earth recedes from the first vertical column to the last, it falls more and more behind while Air comes forward, and the opposite happens when Earth recedes from the last column to the first.
The left to right axis is represented by the transverse lines and diagonals.
In human activity, movement along the front to back axis, and especially forward movement is more current than vertical or lateral movement. For this reason, the horizontal rows portraying forward movement are emphasized by the colors and also because the colors signify degrees and degrees are considered as high and low in the way the rows are stacked on top of one another.
The priorities of the three axes in spatial symbolism are also explained by the development of a line from a forward moving point followed by the development of a surface by a laterally moving line. The dimension of volume or depth is prior to length and width because of the point's round shape. In the Hundred Forms of Ars Generalis Ultima, the example of spherical buds that develop into straight branches is given to clarify the concept of points developing into lines. Volume, or depth is already present in the point because of its spherical shape, even before it begins to move in any determined direction.
There is spatial symbolism of inside and outside in the Elemental Figure: the 12 compartments around the edges of the quadrangles are external as compared to the four compartments in the middle. Likewise, there are inner and outer rows and columns. Circles, squares and triangles are represented in the rows of the Elemental Figure in the following way:Circles: we just saw that the compartments in the rows are considered as "in front of" and "behind" each other. This means that the sequence of compartment s in each row can be repeated indefinitely, in a circular way.
Squares: each row has four compartments containing all four element names, one per compartment. Thus, each row contains the entire square of the four elements.
. Triangles: each row is subdivided into two triangles: the first, second and third compartments from left to right form the first triangle and the second, third and fourth compartments form the second triangle (the second and third compartments are common to both triangles). And each of the two triangles is considered in two ways:
1. by emphasizing concordance because in each triangle there is one element that is concordant with the two others,
2. by emphasizing contrariety, because in each triangle there is a pair of opposite elements.
Thus there are four triangular configurations to be considered in each row, and as there are four rows per quadrangle, this gives sixteen triangles per quadrangle, and sixty-four in the entire Figure of four quadrangles.
Visualized in three dimensions, the Elemental Figure is like a memory palace.
There is more about three dimensional visualization in the Breviculum.V. Heuristics
The Elemental Figure as a heuristic tool provides symmetrical loci that mirror the natural process of digestion and composition, which can help to sort out complex issues, all the more so as there is a symmetry between the Elemental Figure and Figure S, or the Figure of the Rational Soul.Figure S, signifying the acts of the rational soul's powers.
What the letters stand for in Figure S
in blue:
B. Memory remembering
C. The intellect understanding
D. The will willing
E. The compound act of B.C.D.in black:
F. Memory remembering
G. The intellect understanding
H. The will not willing
I. The compound act of F.G.H.in red:
K. Memory forgetting
L. The intellect ignoring
M. The will wiling or not willing
N. The compound act of K.L.M.in green:
O. The compound act of B.F.K.
P. The compound act of C.G.L.
Q. The compound act of D.H.M.
R. The compound act of O.P.Q.There is a parallel between Figure S and the Elemental Figure, because the three powers of the soul produce their acts through elemented physical organs: memory remembering corresponds to Earth, the intellect understanding to Fire, the will willing to Air and the compound act of all three to Water. Further, the four colors of the squares in Figure S mean that those squares correspond to elemental complexions of the same colors, the blue square to Air, the black square to Earth, the red square to Fire and the green square to Water.
B is operative by means of dryness and cold, like a receptacle that is empty on the side facing earth and closed on the side facing water, which is due to the fact that earth is evacuable and water is restrictable. Similarly, C is operative by means of heat and dryness, for just as fire is divisive and evacuative, so C is similarly evacuative and divisive as it goes from species to species; as a result, C is more subtle in a hot and dry body than in one of any other complexion, which is why excessive application to study makes the body dry up. In a similar way, D is operative by means of moisture and heat, since heat makes it ardently desire repletion through moisture, because it is characteristic of air to fill things up. - Lectura super figuras Artis demonstrativae (MOG III, iv, 40 (236).
The genesis of S is comparable to the genesis of Chaos, each has three degrees: the first degree of Chaos is the primordial homogeneous mixture of the elements. The second degree of Chaos consists in the first ancestral individuals of every mineral, plant and animal species and the third degree of Chaos consists in all the successive descendants of the first ancestors up to the present. The first degree of S is in the eternal Ideas of God, the second degree is in the created individual souls and the third degree is in the acts of the soul's powers (memory, intellect and will), which are to the soul what the act of reproduction is to the body. As plants and animals multiply their likenesses through procreation, so do souls multiply their likenesses through the acts remembering, understanding and willing. (This does not mean that a soul can procreate another soul, as souls are created directly by God.)
The instrument of pairwise comparison and contrast, namely the square of [being privation / perfection imperfection] is implicit in Figure S and the Elemental Figure:
The Compartment of [RR]
1. A has ordained that, in R, S should be a creature similar in operation to the Elemental Figure, for just as some elements enter others by means of the green, yellow and red triangles, and form elemented bodies, similarly when these three triangles enter into the memorative, intellective and volitional faculties, they form R in which the following compartments are found: [being privation / perfection imperfection] - Ars demonstrativa, II, 8/10.
The interface between Figure S and the Elemental Figure is discussed at length in Ars Demonstrativa (ibid. pp. 415 ff), in other books related to Ars Demonstrativa (in MOG III), and in Salzinger's Revelatio Secretorum Artis (in MOG I). The information given in the present article is just enough to give the reader a general idea of the system, and to follow the patterns in the following passages on Lightning and Thunder where the Elemental Figure is visualized in conjunction with S and other Figures.
Let us note that in the Elemental Figure, four terms of Figure X, namely "Being - Privation / Perfection - Defect", are used as prototypes for pairwise comparisons. In the Principles of Medicine, where these 4 terms are set out on the corners of a square, Being is associated with the red color, Privation with black, Perfection with blue and Defect with green. These pairwise oppositions of colors, translated into the elements they signify in the above table of elemental attributes, oppose Fire to Earth as Being to Privation, and Air to Water as Perfection to Defect. We may ask, if Fire is the most noble element, why does it only have "Being" whereas Air has "Perfection", since Perfection is better than mere being? The answer is that these colors refer to Figure S, where blue E is more perfect than the red N, in terms of the acts of the powers of the soul. In E, as shown above in Figure S, memory remembers, the intellect understands and the will loves whereas in N, memory forgets, the intellect ignores and the will either loves or hates.V.2 Lightning
The following excerpts from Ars compendiosa inveniendi veritatem show how the Art combines the power of hieroglyph with the power of the alphabet.Question 56: What is lightning?
Solution: [F.G.T.][E.A.V.Y.][I.V.Z.][E.I.N.R.]
To find out about lightning, F.G. should move through the Elemental Figure following the mode signified in the second and third compartment s; now as E. moves to seek greater status in the second compartment , so do Fire and heat move to seek greater status in simple conjunction; and as I. seeks its greater status in the third compartment , so do Fire and heat seek their greater status by destroying the other elements: when Fire, on account of a great abundance of appetite moves so suddenly that the other compartments are not ready to bear its heat, lightning is formed, moving from the uppermost compartment to the lowest, retrieving its parts from the other elements just like E.I.N. issuing from R. reduce its figure to privation and dissolve its matter when every species retrieves its compartment s from R. (MOG I, ii, 39-40 (471-2))
The Figure of Fire highlighted to indicate the lightning path.
F: (Figure S.) memory remembering
G: (Figure S.) the intellect understanding
T: Figure T with its triangles
E: the blue square of Figure S
A : Figure A, or God with the divine Dignities: Goodness, Greatness, Eternity, etc.
VY: the virtues and truth
I: the black square in Figure S
VZ: vices and falsehood
E. I. N. R. : the four squares of Figure SUsed algebraically in this way, alphabet letters resume the function of signifying gestalts. The letter B, for instance, in the Liber propositionum secundum artem demonstrativam (MOG III, viii. 503ff.) signifies:
1. Creature in Figure T
2. Goodness in Figure A
3. Memory remembering in Figure S
4. Faith in Figure V
5. Predestination in Figure X
6. Essence in Theology
7. First Cause in Philosophy
8. Form in Law
9. Igneity in the Elements
Committed to memory, each algebraic letter is similar to a stone: while holding a stone we simultaneously feel its heaviness, dryness, coldness, roughness or smoothness. Likewise, the different meanings of a letter combine to form a whole. Different letters combine in the figures that are geometrical hieroglyphs connected through their common alphabet.
"Tearfully the lover sang songs of his beloved. He sang that love was quicker in the lover's heart than the brilliance of lightning to the eye, or thunder to the ear; that water had more vitality in tears than in the sea's waves, and that sighs were closer to love than whiteness to snow." - Book of the Lover and the Beloved, v. 38.Question 57: What is thunder?
Solution: [E.E.][I.I.][N.N.][R.R.][E.I.][E.N.][E.R.][I.N.][I.R.][N.R.]
To show what thunder is, F.G. should move through this figure and through the green, red and saffron triangles to perceive, in the figure, the motion that the three said triangles have in the Elemental Figure, as this motion generates thunder; and this is on account of the motion and violent impulse of winds and the sixteen compartments of the Figure of Air: and this kind of motion and impulse occurs in forty-two ways in the Elemental Figure: twelve are horizontal and another twelve are vertical and eighteen in the angles: three of the eighteen belong to Air, two to Fire, two to Water, three to Earth, four to Air and Water and four to Fire and Earth. Hence, when this kind of movement reaches its maximum, the compartments move so strongly and for such a long time against one another as they seek out their loci and intentions, so much so that Air produces the tumultuous noise of thunder, and on account of this maximal impulse, moisture is consumed and heat and dryness are generated from which comes lightning impelled to move to its own place as it flees this driving impulse: hence, this figure is most necessary for Theologians and Physicists." (MOG I, vii, 40 (472))
The quadrangle of Air, showing the abovementioned divisions in order with first priority to the top, then to the left
twelve are horizontal: 1 to 12
and another twelve are vertical: 13 to 24
and eighteen in the angles:
three of the eighteen belong to Air: 25, 26 and 27
two to Fire: 28 and 29
two to Water: 30 and 31
three to Earth: 32, 33 and 34
four to Air and Water: 35, 36, 37, 38
and four to Fire and Earth. 39, 40, 41, 42.VI. Conclusion
We have tried to give an overview of the visual interface of the Elemental Figure with its verbal meanings. Much more was said about this Figure by the Doctor Illuminatus than in these few excerpts gleaned from his numerous works that deal with the elements. The Art is indeed immense, like a lofty mountain it can be viewed from different angles. I beg the indulgence of readers who may prefer a different angle, and hope this article will be of help in clarifying general issues related to the Elemental Figure.Yanis Dambergs
Hull, Quebec,
CanadaVII. References
Llull, R. (1985) Selected Works of Ramon Llull. A. Bonner, editor, 2 vols. Princeton University Press, Princeton, N.J.
Llull, R. (1993) Doctor Illuminatus. A Ramon Llull Reader. A. Bonner and E. Bonner, editors, Princeton University Press, Princeton, N.J.
Llull, R. De Ponderositate et Levitate Elementorum
Lavinheta, Bernard de , O.F.M. Explanatio compendiosaque applicatio Artis Raymundi Lulli. edited by Platzeck, Hildesheim, Gerstenberg Verlag, 1977.
Pereira, M. Le opere mediche di Lullo in rapporto con la sua filosofia naturale e con la medicina del XIII secolo. EL, Tom.XXIII, fasc. 1 Palma de Mallorca.
Plato Timaeus, Jowett's translation
Bonner, Anthony What Was Llull Up To? http://www.geocities.com/Athens/Forum/5284/compbon.html
Abbreviations
MOG = Raymundi Lulli Opera Omnia, Ivo Salzinger editor, 8 vols., Mainz, 1721-1742 (reprint Stegmüller Frankfurt, 1965)
ROL = Raimundi Lulli Opera Latina, F. Stegmüller et al., editors, 21 vols. published so far, Palma de Mallorca/Turnholt, Belgium,
EL = Estudios Lullianos
