Nested Realities and the 'Fourth Dimension'
Introduction
In Part I of 'The Enneagram as Triple Mandala' we saw
how mandalas in general are often viewed as comprised of superimposed 'outer', 'inner', and 'innermost' layers, and how these correlate to three approaches to spiritual path - the 'Path of Renunciation', the 'Path of Transformation', and the 'Path of Realization'.
We discussed this tripartite structure and showed how
In Buddhist, Hindu, and Sufi path-of-realization teachings, these Spiritual Qualities
are likened to 'hidden jewels'. In Part II of 'The
Enneagram as Triple Mandala' we saw how, in the Path of Realization teachings
of the MAHAUTTARATANTRA SHASTRA this metaphor branches off into nine similar metaphors, related to nine Qualities, and also into parallel motifs that play a central role in the KALACAKRA texts - the idea of a 'hidden kingdom', profound 'buried' or 'hidden' teachings (terma), and a yet-to-be-born universal monarch.
The Literal Status of 'Spiritual' Truths
Curiously, just at the point at which we might have expected 'advanced' spiritual teachings to yield increasingly ethereal META-physical truths, (Maier, Atlanta Fugiens, 1618 from Edinger's Anatomy of the Psyche, page 92)
The stone hovers in the sky above a mountain and a church, a vision not unlike the one Birnbaum reports as common amongst lamas familiar with the Shambhala prophecy - the Chakravartin's iron wheel falling from the sky toward a house.
Jacob Boehme described Saturn as 'beginner of all corporeity and palpability'.
The METAPHORS themselves seem to insist on the literal and physical status of what they represent. The image of wheels falling from the sky, individuals waking from dreams with pages of physical texts in hand, or actual fruits - all seem to want to depict acts of embodiment, in which some THING comes literally out of nothing.
The seeming insistence, in 'path of realization' teachings, on the literal nature
of spiritual truth has a somewhat fundamentalist ring to it. Is it sufficient
(as we previously suggested) to argue that what is being represented is simply the RETURN of the seeker from the spiritual 'heights', to an embodied existence in the
ordinary, mundane world? Or is this too facile an explanation?
In this paper we shall introduce the idea that the truths that are being
expressed should not be construed as MERELY literal. They also function simultaneously at two other 'levels of meaning' that are sometimes called 'figurative', and 'transcendental'. As such, they might more aptly be considered 'super-literal' truths - and by this we mean to suggest statements that are literally true, but in a reality at a higher level of description.
For the OBJECTS that are symbolized by the 'path of realization' metaphors under discussion are ones that exist not exclusively in mundane (ego-based) reality, nor in
Realities can be likened to 'spaces' having a certain number of specifiable 'dimensions'. If the reality in which one exists has an n-dimensional space, then a reality that has n+1 or more dimensions can be said to constitute a 'hyperspace' with respect to it. Bodies in n-dimensional space will, of course, have n (or fewer) dimensions. So bodies that need n+1 dimensions to be adequately described can only fully 'exist' in the appropriate n+1 dimensional hyperspace - and we can refer to them as 'hyperbodies'. Accordingly, from a 3-dimensional perspective, a 4-dimensional cube is, by this definition, a 'hypercube'.
Self as Hyperbody, with 'Qualities'
What we want to suggest in this paper is that the 'Self' (in the Jungian sense of the word) is a HYPERBODY with respect to the typological space in which mundane personality resides. The words that Jung uses to refer to the Self - such as the 'philosopher's stone', for instance - all seem to suggest that this is the case. Furthermore, Jung's images are consistent with the 'Path of Realization' Buddhist metaphors that we have been considering in this series 1 - the 'precious jewel hidden in the lotus', and its variants. All fall under the rubric of metaphors pointing to the appearance of what we have called the 'superfluous ninth', metaphors dealing with the production of 'spiritual body'.
'The treasure', as Edward Edinger succinctly puts it, 'is the Self, the suprapersonal center of the psyche'. 2 And the 'Qualities' that characterize this hyperbody (which is sometimes called 'vajra body' in Tibetan Buddhism) - its attributes or facets, as it were - are more likely to appear in the lesser-dimensioned ego-based 'mundane' reality as 'contradictions' or 'conflicts', and sometimes 'mysteries' and 'paradoxes', than as simple 'traits'.
Indeed, the word 'vajra' (which does not actually mean 'diamond', although this is the English term that is often used in older translations of the word) refers to a pure, unobstructed space that is the quintessence of emptiness. This space is somehow also capable - however paradoxical this might at first seem - of presenting itself in solid form. Isn't it a similar quality, after all, which is the one that we
find perennially fascinating when we experience it in mundane jewelery - the fact that jewels are transparent and invisible - nearly nonexistent - but nonetheless adamantine, impenetrable.
And of the 'qualities' of the Self are likely to appear just as elusive as the light reflected from the FACETS of a jewel. They will manifest as contradictions, paradoxes, and mysteries in the lesser-dimensional Ego-space which is the home of our mundane 'personalities' simply because some of the attributes of objects in an n+1 dimensional space will remain inaccessible ('ineffable') in n-dimensional spaces. These contradictions indeed form the CORE of mundane pesonality. At the bottom of the 9 EnneaTypes are 9 characterological riddles that point to the hidden presence
of the 'Self'.
Take, as a very simple example of the level-specific nature of 'qualities', volume as an attribute of objects in 3-dimensional physical space. In 2-dimensional space the concept of volume has no meaning - although there is an equivalent concept ('area'). So a 2-dimensional being might, from the concept of 'area', the quality with which she is familiar, EXTRAPOLATE the existence of a similar quality ('volume') in 3-dimensional space. But she will not, however, be able to directly experience it in the (2-dimensional) objects to which she is privy. It will seem like a theoretical
'construct' to her, although it is a palpable 'quality' to those of us capable of experiencing in 3-dimensional space.
In Buddhism one sometimes hears terms like 'vajra pride' or 'vajra anger', which are used to describe something LIKE pride, or LIKE anger, in the enlightened individual who possesses the 'vajra body'. They are like pride and like anger, but also very DIFFERENT, insofar as they are not ego-based emotions.
At different points along the spiritual path, the individual will experience the Qualities associated with the Self differently. What may first look like tensions created by conflict and contradiction can later be appreciated as enantiodromic shifts associated with paradox. And still later, as spiritual 'mysteries' (ie, a "secret truth known only by 'divine' revelation").
Section One - Three Types of Meaning
In her book on Shambhala, LePage correlates what she calls the 'three planes of reality' (physical, psychic, and spiritual) with the three types of 'meaning' about which the nineteenth century French mystic Edouard Schure spoke. Schure reported that the ancient Egyptians had a language which expressed their thought at three levels simultaneously -
'In the same way', concludes LePage, 'the Tibetan Buddhist eight-petalled lotus-mandala depicting the hidden kingdom [of Shambhala] has a multilayered function and can be interpreted in three different ways, as having either a geographical meaning,
a psychosomatic meaning or a metaphysical meaning. Meditating on the diagram with the
aid of the Kalachakra texts [with which the prophecy of Shambhala is connected] and the various guidebooks compiled by lamas of the past, the yogi finds it is like a magic mirror reflecting the same truth on three different planes. These
three dimensions are united by [the mythical Mt.] Meru, the World Axis, which intersects them all at the center of the diagram and is the key to the whole mythology of Shambhala'. 3
LePage's views are consistent with what we have previously said on the topic of Shambhala, and with our understanding of why mandalas in general are often conceived as 'triple mandalas', as we've explained in Parts I, and II of 'The Enneagram as Triple-Mandala'. It is easy to see what she has in mind when she speaks of the 'physical', 'psychic', and 'spiritual' levels of existence, and how these might correlate to the 'outer', 'inner', and 'innermost' regions into which mandalas are often divided when they are conceived as 'triple mandalas'. As we shall see, Gregory Sparrow, in his attempt to devise a method that the lucid dreamer can use to shape her own in-dream behaviour, suggests that the dreamer map information about aspects of her 'physical', 'mental', and 'spiritual' experience respectively onto the outer, inner, and innermost regions of a mandala-like diagram.
But what about Shure's three types of meaning? Lets take a closer look at how they
relate to the three regions of the mandala and the three levels of existence.
We are all familiar with 'literal meaning' and 'figurative meaning'. What, however, is 'transcendent meaning'? Might Schure have had in mind a distinction somewhat like the one that was later propounded by Jung? Jung distinguished between two kinds of symbol - 1) PROFOUND symbols that 'point beyond' themselves to some ineffable order of existence that transcends ordinary reality, and 2) those lesser symbols that are mere 'signs' which 'stand for' something else within everyday life and do not presume to involve anything beyond that. In this series we have seen, for instance, how the mandala is a profound 'symbol' in the former sense. But there also exist metaphors (eg, 'He's as big as a house') that are statements with MERELY 'figurative' intent. They are not to be taken 'literally', but neither do they have 'transcendent' meaning.
In 'Path of Realization' teachings symbols are intended to carry all three types of meaning simultaneously. But why? So that the initiate can embrace all three worlds at once, as Schure would have it? Why is this so important?
Precisely because it is so much easier for us to think in terms of 'three worlds', separate and distinct, than to think in terms of one world with three levels. Putting this another way, we might say that the 'three worlds' psychologically require integration. Left alone, or considered individually, they pull us in different directions, and human experience as a result has a tendency to break down into distinctly realities that are not only separate, but can often also begin to
look as if they are in stark OPPOSITION to each other.
The reconciliation of incommensurable orders is, as we saw early on in this series, what mandalas seek to achieve - and they achieve this, in part, by relying on the device of 'outer', 'inner', and 'secret' layers. In this respect the mandala might even be considered the 'symbol par excellence'. It indeed provides us with a model for how other symbols, by possessing three types of meaning, can effect the reconciliation of the three levels of reality. 4
With this idea of a profound three-tier symbol in mind, lets look at the relationship between symbols (as objects), and the transcendent realities to which they 'point'. There is a sense in which the symbol-object, when it is a profound one that combines all three levels of meaning, can be said to EVOKE the reality to which it is linked. We saw, for instance, how the Shri Yantra does this by SIMULATING the kind of expansion and dilation of awareness that occurs in the special state which it 'symbolizes'. But there is also a sense in which, when the individual taps directly into the transcendental reality, the apropos symbol-object is spontaneously ELICITED - it precipitates, as it were, out of the individual's participation in that sur-reality. We can surmise that it is on the basis of this, perhaps, that Mookerjee believes that the Shri Yantra 'must have been created through revelation rather than by human ingenuity and craft'.
As an adjective, the word 'elicit' means 'evolved immediately from an active power or quality'. So by using it here, in this way, we mean to give the impression of the symbol itself as an object falling from, or precipitating out of, a particular reality-space. The symbol-object and the transcendent reality out of which it has precipitated are thus 'co-emergent'. Strictly speaking, neither can be
strictly considered the CAUSE of the other. Each arises in relationship to the other, simultaneously, as the bifurcation into 'container' (reality) and 'contained' (object) occurs in consciousness.
Section Two - The 'Superfluous' Nature of Hyperobjects
The notions of 'hyperspace' and 'hyperobject' are handy concepts when it comes to
trying to specify the relationship between 'transcendent' objects (eg, the Self),
their 'qualities' (eg, the 'Spiritual Qualities' of the individual), and
coming to understand how such qualities might manifest at the mundane level
of reality in which we normally abide (eg, as 'characterological defects', around which 'personalities' form).
The word 'hyperspace' is a relative term. In using it one is simply referring to a reality that has more dimensions than the base-line reality with which one is primarily concerned. A three-dimensional space, for instance, is a 'hyperspace' for the flatlander caught in a two-dimensional existence. The term 'hyperspace' is basically just a scientific substitute for the religious notion of a 'transcendent reality', although it is useful because it specifies that it is by virtue of additional DIMENSIONS that such a reality transcends ordinary reality. And it also treats transcendence as a relative term. No space is 'absolutely' transcendent, only relatively so with respect to some other particular space.
The notion of a 'hyperobject' is similarly useful, particularly in the context of a discussion
As beings in three-dimensional space, we humans cannot directly preceive a four-dimensional 'hypercube'. But such a thing 'exists', and can be described, and we can talk about its 'qualities', even if we are not in a position to directly experience them. Scientists do it all the time. According to mathematicians, the figure to the left is what a four-dimensional 'hypercube' looks like in three dimensional space. In the same way in which a three-dimensional cube has six square faces, the four-dimensional hypercube is comprised of eight three-dimensional cubes, one of which is completely hidden from view (because each of its six sides interfaces with another cube that obscures our vision, no matter what angle we might try to look at it from). 5
Double-crossed, Triple-Crossed
Leonard Shlain, in this book Art and Physics - Parallel Visions in Space, Time
Because the reproduction that we are using here is so small, you will not be able
to see the cross-like
So the four-dimensional cube is reflected in a 3-D representation (on which the Christ-figured is nailed), and this 3-D object is reflected in a 2-D figure on the floor.
One can't actually see the 4-D hypercube in this painting. It is therefore 'transcendent' and 'secret', part of the 'innermost mandala' of the painting, as it were. Yet it appears in the depicted 3-D reality as this strange cross-like figure comprised of eight cubes, its re-presentation in this reality of one less dimension. In Dali's picture the cross has tremendous FIGURATIVE meaning, as it represents the x-y-z co-ordinate system in three-dimensional geometry, which provides the 'framework' that is the constant backdrop for the 3-D spacial reality in which we live as human beings. The cross thus symbolizes or 'stands for' this more abstract notion of a FRAME, and just as frames provide limits for that which they enclose, the object in this reality (the Christ figure) is pictured as literally pinned to the frame.
As the frame is a less-than-adequate container for the hyperobject that is being represented (the 'son of God' - who is also, by the way, a 3-D re-presentation of the 4-D 'Supreme Being'), this 'containing' will LITERALLY entail suffering, represented by the body of Christ in its typical on-cross pose. This type of suffering can only be transcended when the confines of the lesser reality are transcended - that is, in the 'death' of the three-dimensional body. Or, alternatively,
it will be transcended insofar as the individual can somehow learn to straddle the interface between the 3-D reality and the 4-D reality, in a state that we might call 'enlightenment'. This alternative is represented, in the story of Christ, by the 'resurrection' - the return of the Christ to the 4-D reality, albeit
in full 'bodily' form. Dali's CRUCIFIXION, in addition to being about death, is
also, in other words, paradoxically a portrait of birth - the birth of the 4-D soul or spirit-body, as it were.
Anomaly, Stigmata, and Stigma
Taking the story of the crucifixion LITERALLY, the physical suffering that the Christ figure undergoes involves a penetration of the body by nails. When similar wounds (called 'stigmata') miraculously appear in the hands of Christian monks or nuns the Catholic Church takes these as SIGNS of the individual's sainthood (ie, the fact that they have achieved 'enlightenment'). It is as if, in identifying so strongly with Christ, the 3-D body of the monk or nun literally takes on the QUALITIES of Christ's 3-D body.
We could even say that these wounds are the ANOMALIES in the physical body of the saint which causes him/her to resemble Christ. They are literally the OPENINGS into the sur-reality in which the saint comes to abide.
But they are also, at a 'lower level' of description (ie, within the ordinary reality) perceived as injuries, defects. In this context, it is interesting that the words 'stigmata' and 'stigma' come from the same root, but stand for attributes that are almost polar opposites. Whereas stigmata are taken as a 'SIGN OF HOLINESS', a stigma is a 'TOKEN OF INFAMY, disgrace, or condemnation'. We point this out, of course, because the relationship between the two is not unsimilar to the relationship between the 'enlightened qualities' in the individual and his/her personality 'defects'.
The parallel takes on even more profound significance when we realize that in the lives of saints disgrace and condemnation are often deliberately SOUGHT, not only as a means of 'purification' (according to 'path of transformation' explanations), but as if to emphasize that the lowest is LITERALLY the highest, indistinguishable
from it.
Dali's painting is nothing short of a personalized 'mandala'. We saw in the Shri Yantra that the anomaly at the center of the diagram was what created space for the emergence of the 'superfluous ninth triangle'. Similarly, in Dali's painting, the representation of the hypercube hovers anomalously in the sky. It is a metaphor that has magically materialized, like Trungpa's sky, into an object - a blue pancake that falls on one's head, or the iron wheel that falls from the sky into the Cakravartin's hand. But it also seems to miraculously defy physical law. The 'superluous ninth' that is created in the Enneagram, at Point Nine, where the interface between the (inner) 6-pointed figure and the (innermost) equilateral triangle occurs, is an object, like Dali's hypercube cross, that somehow straddles the two realities - the mundane and the eternal. This is the FUNCTION of profound Symbol, as we've come to understand it in this series.
If we were to search for a mandala that could be associated with the MBTI in the same
way that the figure of the Enneagram is connected to the 'Enneagram as Type' teachings, a figure that speaks to the profound psychological truths that Jung discovered in his mature period, AFTER formulating his personality theory, we might find no better a symbol than Dali's painting. For the painting AMPLIFIES the meaning of the two-dimensional cross, against the background of which Jung diagrammed his 'four functions'. The simple 2-D cross on the 'floor' makes its appearance in the context of a very meaningful relationship to the 3-D reality depicted in the painting, and the 4-D reality to which it alludes. The 2-D 'cross' is thus brought into relationship with a rich 'path of transformation' story-line (the transfiguration of Christ - which, at the psychological level, is equivalent to the death of Ego, and the resurrection of some 4-D equivalent of 'Ego', which can be called the 'Self'). It is also mapped ultimately into a four-dimensional (spiritual) hyper-space,
which lends meaning to the ('mythological') events occuring in 3-D space, and the ('literal') events occuring in 2-D space.
Dali's painting, as profound Symbol, thus EVOKES a hyperspace and ELICITS a hyperobject, even if such objects can only appear to us, who can become trapped in our three-dimensional human worlds, 'in imagination'. For us, imaginal space IS that hyperspace - which is why scientists called 'imaginary numbers' imaginary,
and why surrealists call themselves 'sur-realists'.
Hyperbody, Coagulatio, and the Birth of 'Inner' Children
For Edinger, who follows Jung in this regard, the Crucifixion is a 'coagulatio' symbol, representing the particular stage in the inner 'alchemical' process of individuation in which concretization takes place. Coagulatio is an embodiment or incarnation that is mythologically linked with desire, a 'fall from heaven', and with 'Saturnine' evil (that is associated with 'materiality'). Honey, Edinger tells us, is 'an agent of COAGULATIO'. Interestingly, honey, as we've seen, was one of the nine alternate metaphors for the 'hidden jewel' in the 'path of realization' text, the MAHAUTTARATANTRA SASTRA. Edinger quote's Jung's discussion of Dorn's use of honey -
Embodiment can be construed as a 'fall'.
When we translate what is being described here into the terms of personality theory - which is, after all, a major concern of the ENNEAGRAM - 'fixatio' translates into 'personality fixation'. But this imagery, as we've pointed out, is basically a 'Path of Renunciation' perspective on embodiment. From the point of view of a 'Path of Transformation' approach, the crucifixion is also, paradoxically, a release, and a transfiguration. And from the point of view of a 'Path of Realization' approach, it is REDEMPTION - which literally means 'to recover ownership of', or to restore!
At this level, embodiment can be heaven, and suffering bliss. If in the (Western) alchemical teachings, honey is the image juxtaposed with poison, in the 'path of realization' Dzogchen teachings poison is conceived not only as medicine, but also as a feast. As the reader may recall, in Tibetan mythology the peacock is believed to thrive on poison, which it transforms into its festive array of colorful feathers.
Section Three - Speculations on Four Dimensional Space and Liminocentric Structure
Mathematicians frequently deal with spaces that have dimensions much larger than three - sometimes hundreds of dimensions. But there appears to be something mathematically unique about four-dimensional space -
This may be because the fourth dimension 'wraps back around' on zero-dimensionalilty
(represented by the mathematical 'point'). We normally picture dimensions in a way
that mislead us when we think of them as separate objects that are independent of each other, like limbs growing from a tree trunk. But scientist Arthur Young conceives of their relationship in a rather different way. He models the relationship
between 'dimensions' on the relationship between the 'time derivatives' in calculus.
The relationship between the 'dimensions', in other words, is similar to the relationship between 'distance' (the first dimension), 'velocity' (the second
dimension), and 'acceleration' (the third dimension) - where change in distance with respect to time is velocity, and change in velocity with respect to time is acceleration.
The 'fourth dimension' (which would be equivalent to 'change in acceleration
with respect to time'), argues Young, brings us full-circle back to the
When 'zero-dimensionality' (which is ignored by Young) is taken into consideration - the fourth dimension might be thought of as wrapping back not on the FIRST dimension, but on the starting place for the entire sequence, 'emptiness' (the mathematical 'point', as opposed to the 'line' which we use to represent distance). Using the vocabulary that we have introduced in this series, we would say that the dimensions of human reality are heirarchically nested, but in a non-linear (or 'circular') fashion, with the top-most level of the heirarchy wrapping back around on the bottom-most.
Young's hypothesis might explain why the fourth dimension is literally 'missing' in our world, as this dimension would simply appear to us as zero-dimensionality, nothingness. The description also seems to parallel Jung's notion of the 'missing fourth', which it enriches by linking it to scientific speculations about the fundamental structure of reality and related philosophical and psychological speculations about the fundamental structure of consciousness.
If the fourth dimension does indeed 'wrap around' onto the zero-dimension, the joining would seem to occur somewhere BETWEEN the 3rd and 4th dimension. In 'fractal geometry' (which we might call the 'geometry of liminocentric structures') one is permitted 'fractional' dimensions. You can have objects that are 2-dimensional, and 3-dimensional; but you can also objects that are 1.5-dimensional, or 2.73-dimensional. Is it possible that the turning point, the place where the dimensional wrapping occurs, is at the fractional dimension equal to 'pi'? Pi was at one time approximated as 22/7ths (or 3 1/7, which equals 3.142857).
If dimensions have this kind of chinese-box relationship with each other, then 3 1/7 turnings of the 'wheel' (or 'circumabulations' of the 'mandala') might take us not only into the center, but also shoot us full-circle back out to our starting point at the periphery.
And what can we say of objects IN realites that have this kind of involuted structure, or the 'qualities' that they possess? This is the subject of the following papers
in this series. Perhaps, at the moment, we might acknowledge that the best that we can do through the use of ordinary language is to think of such objects as having 'levels', in a way that is consistent with the 'Path of Realization' triple-mandala teachings.
1. Jung, in his description, in the Secret of the Golden Flower
(Harvest/HBJ Books, 1931/1962, translated and edited by Richard Wilhelm),
speaks in the following way of the birth of the 'spiritual body' - what we are here calling 'hyperbody' -
One of the 'Nine Metaphors' for the 'hidden jewel' in the MAHUTTARATANTRA SASTRA, as the
The figure to the left is a detail from an illustration in The Secret of the Golden Flower (page 37), a Taoist text on inner alchemical processes. Wilhelm labeled it, 'Meditation, Stage 2 - Origin of a New Being in the Place of Power'.
Jung has the following to say about the 'spiritual body' -
In the Pauline Christ symbol the deepest religious experiences of the West and
of the East confront each other. Christ the sorrow-laden hero, and the Golden
Flower that blooms in the purple hall of the city of jade - what a contrast, what an infinity of difference, what an abysss of history! A problem fit for the
crowning work of a future psychologist! (The Secret of the Golden Flower,
page 133)
3. Victoria LePage, Shambhala, the Fascinating Truth Behind the Myth of Shambhala, 1996, The Theosophical Publishing House, page 23.
4. Here is an example of how one simple, seemingly mundane, statement can simultaneously have all three levels of meaning. Imagine, for instance, that we,
the authors of this paper, live in a city called 'Troy'. For us, the statement 'We live in Troy' would then express a literal truth. But the same sentence, 'We live in Troy', can also take on a figurative quality in certain contexts. For instance, if someone were to point out to us that some would-be friend means us harm and has snuck into our good graces with flattery and praise we could shrug off our naivety with the comment, 'We live in Troy', which is now an allusion to the Trojan Horse incident. Or, aware of the fact that LePage described ancient Troy as a 'wisdom city' constructed in accord with mandalic principles that divide it into 'outer', 'inner', and 'secret' levels, one of us could use the same sentence to remind the other of the
sacred nature of the city in which we live. In this case the words 'elicit', or 'draw forth' a realization of that 'secret' (ie, sacred) level of 'place', but also the words themselves are 'elicited', ie, 'evolved immediately from an active power or quality'. In the mind of one who uses them this way they come forth, like a joke, out of nothing, but also point back TO that nothing.
One can even imagine a situation in which the same sentence, 'We live in Troy',
can have all three meanings at once. For instance - imagine that we have been considering making a move. And one day, while we are in the midst of talking about LePage's interesting comments about the three-fold structure of Troy, the doorbell rings. It is our friend and he has come to reveal to us that there is a traitor in our midst, a local man named 'Jack'. Seeing our friend's concern, one of us shrugs and says, 'We live in Troy'. The visitor takes it as a humorous allusion to the Trojan horse incident, and is relieved, thinking that it meant 'After all, in Troy, such things can be expected to happen'. But given our recent conversation, the other knows that 'We live in Troy' is also an expression of the decision that has just been made (to stay in Troy) - based partly on the realization that what the situation here needs is people who can see the politics in the current situation as an expression of deeper needs that are basically positive.
The comment happens in a split-second. Both of us spontaneously laugh,
seeing humor in the fact that we have been writing about the motif of jewels hidden in less desirable objects, and are now presented with a real-life example of the converse situation - a wolf in sheep's clothing. And both images - diametrically opposed to each other - come together, in this synchronistic real-life event that invokes the image of 'Troy'. One might ask, Is it really a coincidence that the motifs of the Trojan Horse and the hidden kingdom should find a home in the mythology
surrounding the same city?
5. This eighth 'hidden' cube resembles the 'eigth piece', in our
analysis of the Ostyak ritual described
by Eliade. It is out of the 'sacrifice' of the 'eighth' that the 'superfluous ninth'
emerges. The 'superfluous ninth', in the case of Dali's picture, is the Christ figure, who appears sur-realistically pinned to the hovering 3-dimensional representation of the 4-dimensional cube.
6. See page 19 in Mathematics, Physics, and Reality (1990, Robert Briggs
Associates, Portland, Oregon), by Arthur Young.
Interestingly, some of statements about the 'fourth dimension' that appear
in the work of Tharthang Tulku, a Buddhist, are similar to Young's -
7. Arthur Young, Mathematics, Physics, and Reality, 1990, Robert Briggs
Associates, Portland, Oregon, page 45.
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The Stone of Saturn
arrangement of checkerboard tiles in the two-dimensional floor below the Christ-figure. It looks like the illustration to the left, when seen head on. As Shlain points out, the cross made of tiles is the shadow that would be cast by Dali's 3-D cross if a light source were to shine directly down on it from above. It is, in other words, literally the shadow of the three-dimensional representation of the hypercube in two-dimensional space. As if to emphasize this fact, Dali tiled the floor in such a way that the COMPOSITION of that two-dimensional shadow-cross also mirrors the ARRANGEMENT of the eight cubes. The 2-D cross is comprised of five black tile-squares, with the one in the middle sharing all four of its sides with another square, just like the eighth cube in Dali's cross shares each of its six sides with one other cube and has no side that is not covered by another cube.
