One & Other: A.L.L.

Click to enlarge, please.

Artist Statement:

This work--entitled "One & Other: A.L.L."--intends to capture, create, and/or represent and inspire towards A & ~A (enunciated as "A and not A") as the integral metaphor pointing to the fundamental "thing" that is at once the generator, source, maintainer, and "benefactor" of (this last less about money--indeed, no reference to currency at all--but instead includes notions of "value" and as that which "helps" or "supports") manifestation; while also a symbolic engraving, as in "etching," our necessary relationship between necessary dualistic pairings (such as, but not limited to, (One, Other), (Internal, External), (Subject, Object), (True, False), & etc.), by which our understanding is necessarily incomplete, upon the psyche of the One who experiences.

In order to arrive at a necessarily incomplete possible understanding of the metaphor, it is possibly necessary for us to undertake an analysis and exploration of each of the images, which together form an animated triptych, whereby the individual panels are united in sequence over time; which is to say, the inherently singular representations of each panel occupy the same location in space, but, due to their inherent Otherness from One and Other, they must necessarily be separated and analyzed or interpreted as individual metaphors or pointing to that which by their unification over time symbolizes the whole that is greater than the sum of its parts.

Put differently, this work presents and represents a necessarily incomplete vision and enunciation of the Art and Science of Existential Engineering.

Analysis:

Image 1.

In this image we see the Milky Way galaxy as wrapped up inside a morphed representation of the horizon of our planet Earth. This panel of the triptych is entitled "OUTSIDE".

OUTSIDE

The Milky Way galaxy is home to our wonderful and mysterious solar system. While we have some ideas about the objects that occupy these structures--the Milky Way and the Solar system--we certainly lack anything that reassembles a complete knowledge of these "Heavenly" structures, but we have at least some knowledge of these. We understand, for instance, that the Milky Way is embedded within a larger galactic structure, that the Solar system is embedded within the Milky Way, that our Earth is embedded within the Solar system, and that we are embedded in the Earth's own systems.

We are, from our own individual perspectives, looking outwards from the source of our perceptions, and towards that which lies, perhaps in some sense "deceivingly" so, outside of ourselves. Now, "deceivingly so" insofar as all our observations of an apparently external world become the objects of our necessarily subjective experiences and interpretations whereby informative signals from a possibly external world are passed along our human nervous systems and then ultimately reconstructed as sensory data in the electrochemical processes of the brain and these in turn, or perhaps not really by "turn," but more as a mutual co-arising, reveal themselves to each of us privately as representations of what we can only logically assume, but not logically assert as fact, is a shared world. Since we are necessarily limited to direct experiencing of only our own interpretations of informative signals from a seemingly external world, we are unable to be certain that any Other's interpretations of their own informative signals are identical to that of our own. Indeed, given that each of us is a unique structure of biological matter, we can, it seems, almost be certain that no two internally self-referential reconstructions of an apparently external world are in fact identical. We can merely hope, which is to say "have faith," that there is much more overlap than less.

A ponderous type of individual might notice of this panel, "OUTSIDE," the necessary conjunction of land and sky--mutually exclusive to One and Other--which unite through our observations to inform us of the incidental differences between One and Other which thereby conjoin to create our perception of a horizon. That the image wraps up our unique and location specific vantage point from a singular view and enfolds this around what is the greater outside expanse of our universe, is, in fact, a delightful visual pun whereby the "as above" becomes necessarily engulfed within the "so below." We see in this a direct reversal, an irony of sorts, with regards to the previous recognition and discussion of the order of embedding: visually this image suggests that it is the Earth that is embedded in ourselves, and the Solar system that is embedded in the Earth, and the Milky Way which is embedded in that. It reflects upon the notion that everything seemingly "out there" is in fact embedded within each instance of any specific human being.

Image 2.

In this image we see the singularity, that is to say, the black hole, as depicted in the film Interstellar. In the context of the triptych, this panel is entitled "INSIDE".

INSIDE

Black holes as construed in theoretic physics are objects of intense interest and much theoretical work has been constructed around their analysis. Most of this is largely a sort of scientific mythology. We have never directly observed a black hole with our instruments and we have exactly zero satellites or space probes that have gotten anywhere near one. Moreover, we are strictly forbidden a look into the black hole beyond its event horizon and can not have access to the singularity that allegedly lies therein. Yet, we, some of us, anyway, still seem to like to talk about them a whole lot.

Every, or almost every, galaxy, it is speculated--because like we've ever really examined every galaxy in detail--has a massive black hole at its centre. We too, as human beings, we can also speculate, also have a "black hole" or "singularity" at our centre. This could be "cashed out" in terms of the Jungian archetype of the Self, but also "cashed out" not only in those terms.

Incoming informative signals from the things outside of ourselves cross the threshold of our own individual event horizons. These informative signals transit from something "out there" and become electrochemical impulses "in here." Once those signals cross the event horizon through our sensory apparatus and become these electrochemical signals, they are lost to the outside world in exactly the same way that things crossing the event horizon of a black hole are lost to the rest of the universe that the black hole is embedded within. We are, each of us, in this sense, the singular receiver and ultimate interpreter of our individually reconstructed version of whatever it is that might be "out there," and we are embedded within that which can only be knowable in itself as indirectly through our sensory apparatus.

As a singularity of Self, we are consuming or entrapping the incoming informative signals that are attracted to us by our own personal gravity. The individual mind is a singularity which bends the spacetime of collective consciousness in such a way as to generate a sense of individualized differentiation of One from Other. The mass of each of our necessarily differentiated and individualized minds warps the collective consciousness in such a way that the structure of this consciousness is stretched into a self and Other referencing loop that dances around and through the infinite. It is much like a Möbius Strip insofar as it is constructed from a seemingly two-sided surface which, when folded in a higher space, then becomes only a single sided structure. The length of the loop is itself infinite in the same way that a nonrotating singularity with no electric charge would also stretch the spacetime of the universe towards infinity as any object that passes its event horizon would then be able to observe. However, since the circles and cycles of our interpretive self-other referencing give our individual and singular minds what is an analogous occurrence of rotation and charge, the infinite recedes from our unique experiences of consciousness and instead grants us a comprehensible and seemingly finite interpretation of the received and processed sensory data.

To put all this a little bit differently, the "INSIDE" is where the "so below," that is, the incoming informative signals from the world as it is outside of us, becomes subsumed by "the above," by which we mean the individualized and uniquely personalized warping of collective consciousness that we each refer to as our own "mind."

Image 3.

In this image we see what is taken to be an "occult" or "alchemical" representation of reality. In the context of the work it is entitled "A.L.L. Together". It is itself composed of four unique symbols, perhaps in the same way that certain modes of "classic" thought suggested the universe was composed of four unique elements which occurred only together and could not be separated One from the Other to appear in their naked individuality or differentiated singularity. In the same way, this work, "One & Other: A.L.L." is actually four elements in one: there are the three individual images that form the triptych, and the animation, or movement, of the three images in time but not space then creates the fourth image, which is the whole of the work itself.

A.L.L. Together

We will, in order to arrive at a clearer understanding of not only this particular part of the work, but also, of the overall work itself, need to examine these four symbols and their relationships between themselves. So let's delineate the four apparent symbols: the Ouroboros, the Triangle, the Sun, and the Eye.

Let's start with the Triangle.

Triangles, especially equilateral ones such as the one that occurs in the image, mean many different things to different people. Triangles such as this are seen, for instance, as the strongest or most stable geometrical shape: due to their structure, they are the most stable and most efficient shapes in terms of handling applied forces. This is why triangles often feature in various load bearing engineering designs.

Triangles also represent, obviously, Trinities of all sorts and kinds. There's the Holy Trinity of Christianity (Father, Son, Holy Ghost) and there are also several Other instances of trinities in several other religions or mythologies: in Mesopotamia, there was Anu, Enlil, and Ea; in Egypt, there was Osiris, Isis, and Horus; in Babylon, there was Nimrod, Semiramas and Tammuz; in Plato's conception of the world, there's The Unknown Father, The World Soul, and the Logos. Indeed, there are occurrences of trinities to be found scattered throughout much of human conceptions of the world, ourselves, and the relation between the world and ourselves, which, clearly, is a trinity in itself: (world, ourselves, relation between).

As E.E. Rehmus frames it, there are, with respect to several instances of metaphysical trinities, the three following elements in the form of assertions:

1) There is one Immutable, Ineffable, Pre-manifestational Reality.

2) Everything is periodic or cyclic.

3) The cosmos is a hologram in which each part is a reflection of the whole.

The above three points are some things to consider about the elements of some trinities even if we choose not to believe in the elements of any specific trinity.

In terms of dualities, the triangle shows us how, exactly how, dualities exist in relation to One and Other. Indeed, One and Other is the primary mode of our experiencing: we exist as One in relation to an Other--many apparent Others, in fact. But there are two general categories of being in the world: self and Other. How is this a trinity we might ask? Because relations are objects. Indeed, on a deep analysis it seems as if relations are the only objects: the things we mark out as Other, the boundaries we define in our perceptions that determine our self, are merely a product of collecting as a whole, some set of relationships amongst apparent parts and bracketing these off in contrast to the rest of the relationships amongst the rest of the parts. So, to put it clearly, the Trinity of our actual being in the world is:

1. Self, as in myself, as in yourself, as in One.

2. Other, as in not myself, as in not yourself, as in Other.

3. &, as in the necessary relationship that must exist between the binary or dualistic pairing of (One, Other): One & Other is the trifold representation of the fundamental structure upon which any specific thing has its being in, and in contrast to, the world.

Further, we see that One is not Other when it comes to the relationship perceived between them. This is to say that, given the binary pairing of (One, Other), we can code this up in terms of symbolic logic as:

One := A, and since the negation of One, in terms of its dualistic pairing, is ~A, we see that:

Other := ~A, as the negation of A can only imply ~A in terms of a singular instance of a dualistic binary pairing.

Thus, the whole of our individualized and differentiated existences is entirely captured by the expression A & ~A. Each of these terms, (A, ~A, &) are "pointed to by" or "located at" the vertices of the equilateral triangle. The equilateral triangle itself demonstrates not only the necessary structure of our being, but also demonstrates that this is the strongest, most stable way to conceive of our existence: One in a necessarily conjunctive and ideally equitable relationship with the Other. QED.

Let's now turn our gaze towards the Eye, the Eye as it occurs in the triangle, which some people have some sort of fear or reservations towards, feeling that every occurrence of such a symbol is in fact evidence of some secret plot in which some secret and nebulous minority of people are, in fact, controlling everything. This is entirely not our concern here. What we see by the Eye as it occurs in the triangle is nothing more than the symbol that points to an Illuminated self, and not some Illuminati. Although, we might consider that any instance of an illuminated self would necessarily be part of an Illuminati ("Illumiated Ones") by definition.

But what is this self illuminating? Well, if we go back to our understanding of the triangle, then we see how the illumination is about the vertices of the triangle; that is, the eye exists in a single vertex of the triangle. This implies that we, as a singular conscious entity, are only able to illuminate one vertex in any given instance, or moment, of our being. We can, and most often habitually do, occupy the illuminated vertex as an instance of One, of self, of our own being. We can, however, through things like empathy, come to illuminate, as in see in our consciousness, as in give light to, the instances of Otherness, as in recognizing and identifying with the Others: we can, in this sense, see ourselves in or as the Other. And, finally, we can turn the triangle again, so that the vertex of & is where the light of our consciousness illuminates the relationship between any given thing and all the things it is not in order to understand exactly how One exists in contrast and conjunction to any Other.

This is the "Outside" description of the Eye as it occurs in the triangle. In other words, this is the Eye in the triangle as it represents the things outside our selves and their relationships to us. We can now turn inwards, and see the trinity that is illuminated by the Eye with respect to the "Inside."

The"Inside" trinity is:

1) Eye as object of seeing; that is, the mechanism by which informative external signals cross the event horizon of our being and are translated into internalized electrochemical informative signals.

2) Eye as in I, as in "Interpretation." We all have our modes of interpretation. Each of us has a decidedly unique and singular Interpretive structure that translates the internalized electrochemical informative signals into a picture, a representation, or manifestation of the world.

3) Eye as in I, as in the self, or ourselves, as Individuals with both eyes and Interpretive strategies for representing the world and the Others that occupy such a world to our unique, differentiated, and individualized instance of selfness.

This Inside trinity operates in conjunction with the Outside trinity. Put differently, there is a necessary conjunction between Inside & Outside; that is, we see in this conjunction yet another clear example of A & ~A: the Inside is not the Outside and vice versa--they are the negations of One and Other along a dualistic pairing of (Inside, Outside), whereby there is a necessary and, ideally, equitable relation of conjunction between Inside & Outside. We can literally and actually not have One without the Other in every possible sense of what that means.

So, the Inside Trinity operates in conjunction with the Outside trinity and we see how the Interpretive strategies of One must necessarily have at least some overlap with the Interpretive strategies of an Other if we are not only to be able to communicate and share in a reality, but also, have any ability to see ourselves in the Other. If the Other was entirely and utterly foreign to us, not only would we be unable to recognize our self in the Other, but we would not even be able to perceive the Other; which is to say, without mutually conjunctive and overlapping being in both an Internal and External sense, there would be no relation of One to an Other in any way at all. QED.

Let's now turn our increasingly dynamic and complex yet necessary gaze towards the Sun.

Ah, the Sun. Where would we be without the Sun? Well, we certainly would not be here at all. The Sun is central to our existence and it is what illuminates and powers our world: with regard to the Sun and its energies, which pour down upon us like so much Mana, it's not merely that without it life on earth would not exist, but the Earth itself would never have formed in the context or embedding in the gravitational wells allowed by the very mass of the Sun. So, is it any wonder that the Sun is the central figure in the triangle? No. Clearly it is the central object that allows for, and gives rise to, things like ourselves, Others, triangles, eyes, interpretations, and all the rest.

We could, if we wanted, examine the Sun in terms of Qabalistic or "occulted" meanings. In this sense, we can simply note that the Sun is central to the Tree of Life (the Sephiroth called "Tiphareth" aka "Beauty"), and it is associated with the heart, which is also central to our own Tree of Life; that is, the biological and metaphysical (aka "philosophical") necessity of the heart is clearly recognized as central to any instance of a human being, and that this Heart of things both real and ideal corresponds to what we call "Love." There is little question as to why we tend to draw hearts where we want to symbolize Love and we see through the lens of Qabalism that Love as Beauty is central to ourselves and Others. Put differently, Love is the beauty and the energy that is the force that acts within and without in regards to the equitable and strongest triangular manifestations of One and Other both Inside and Oustide. QED.

Finally, as in "last" but most certainly not the "least," we turn, as in circle, as in revolve--as in revolution--our thrice folded gaze, as in (Triangle, Eye, Sun), towards the Ouroboros.

Ah, the circle that consumes itself, that generates itself, that exists in its eternal perfection only in our ideals but is merely ever approximated in the world as a many sided object whose number of sides approach infinity, but since infinity is necessarily something that can not be represented adequately in a finite world, any actual instances of the circle are necessarily approximations--exactly like this entire evaluation, explanation, and interpretation of the images in the triptych: a necessarily incomplete representation of the whole.

The Ouroboros, then, is simply the cyclic oscillation between any instance of A in conjunction, &, with ~A. That is, it represents the necessary and complete union of all opposites whereby the seemingly apparent differences are collapsed into a singular circle of consuming and creating being. QED.

So, taken together as a whole, we see that the third image is nothing more and nothing less than a pictographic metaphor that intends to point the viewer, the experiencer, the I that Interprets through the Eye, towards that which, ultimately, can neither ever be fully understood nor wholly held in the mind in its entirety. It is a representation of the ineffable which intends to allow us inroads towards "effing" the ineffable. QED.

Image 4.

Is the whole of the work itself, the triptych as unified in space but necessarily differentiated in time. It is its own representation of the dynamics of "effing" the ineffable. As such, it is the Alchemical process of turning metaphorical lead into metaphorical gold, and this--no matter how it is analyzed or represented--is only something any individual can undertake alone. No One of us can understand for the Other, we can merely offer our own understandings with the hope that such understandings are well received by any Other, and it is the Other who must accomplish the Alchemical work in order to understand.

The fourth image is A & ~A whereby A can be assigned to either INSIDE or OUTSIDE and that assignment determines which term becomes ~A and the two are both united in, and defined or differentiated by, &, which is the ineffable relationship pointed to in A.L.L. Together. The work is a rotational symmetry of evolving being. It is the blinking of the cosmic and all seeing (eye, I) by which Self comes to manifest as instances of Other as derivations from necessary and fundamental paradox.

QED.

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A Three by Ten Matrix Generating One Thousand
Possibly Intentional but Also Equally Unintentional Meanings of

A.L.L.

Presented in Terms of Alternating Sense and Nonsense

This Matrix Is Necessarily Incomplete.

Hi it's Eve bringing you a update from the year 2020. I read this over and when I got to here, I realized that it is not clear how the Matrix works, so here is how to play:

1) Use any method you Choose to pick a word from column 1,

2) Use any method you Choose to pick a word from column 2, and the method need not be the same as the last one you used if you do not Choose it to be,

3) As in (2) above, but for column 3.

4) The three words taken together generate a phrase: it will mean something to you--make sense--or not.

It occurs to me now, but didn't then, that we could also view each set of three words six different ways: there are 3! (three factorial) ways to order a set with 3 members. So we can repeat the above steps with each of the three words to determine a possibe set of up to six phrases from each set of 3 words.

Hunh. How about that?

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After the Fact

Discussion and development of the notion of consciousness expressed in the above work is at least partially unfolded here.

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Reference to E.E. Rehmus and his notions of the Trinity are from The Magician's Dictionary An Apocalyptic Cyclopaedia of Advanced Magic(k)al Arts and Alternative Meanings, by E.E. Rehmus, as published by Feral House, Los Angeles, CA, USA, 1990.

Original Images from:

"INSIDE" comes care of Miguel Claro with some some small alterations by myself of the edges to make for a more seamless representation in the overall work.

"OUTSIDE" comes from a Google search of images for the singularity as it has been advertised and disseminated far and wide with respect to the movie Interstellar. Find it yourself, it's easy to do. Also some minor alterations by myself in order to make its appearance in the animation more seamless.

"A.L.L. Together" comes care of The Royal Order of the Holy Mackerel and I have no idea where this Order co-opted this particular depiction of the Orouboros from, but I will say it was exactly the image needed for the work.

All images used entirely without any permission of their respected owners, and no ownership is claimed or implied on behalf of myself, b.e. hydomako, towards any specific image. Each image is used under the intention of "fair use" law insofar as such use by myself is intended as commentary, research, teaching, and scholarship, as specifically demonstrated in the above analysis of these images.

Terms and Conditions

The work itself--"One & Other: A.L.L."--is licensed as Attribution-NonCommercial-NoDerivatives 4.0 International, which, as I, b.e. hydomako, understand it means: any presentation of "One & Other: A.L.L." must also be accompanied by the complete text, or a clear and well defined link (embedded in the page of representation of this material) to the text as it occurs on this page, and no instance of the complete text shall be without accompaniment of the image "One & Other: A.L.L." or at least a clear and well defined link (embedded in the page of representation of this material) to this image as it occurs on this page. Any reproduction of the work in its entirety or in part must be accredited to b.e. hydomako either directly and include a link to this page on the page in which such reproduction occurs, or indirectly by including a clear and well defined link to this page on the page in which such reproduction occurs. Any hard copy version of this work in whole or in part must be accredited to b.e. hydomako and include somewhere in the hard copy a clear and well defined string of symbols which together define the URL of this page. Portions of the text may be used with respect to fair use law, but reference to the source (this page and its creator, b.e. hydomako) is always required. No other parties shall profit by any use of this page, in whole or in part, with regards to any of its contents--imagery or text--and any such profiting is open to liable action. Any monetary settlements from any such actions, after such settlements reimburse me, b.e. hydomako, for any and all and only the cost of such legal action and any expenses accrued in conjunction with such legal action, are to be donated in the entirety of their remainder to the charity of my choosing. Any commercial use of this work, whether for profit or nonprofit or not-for-profit, is strictly prohibited without the express written consent of its creator, b.e. hydomako. Any viewing of this page or pages in which material from this page occur which satisfy the aforementioned terms re: accreditation of source or any hard copy of this material in whole or in part which satisfy the aforementioned terms re: accreditation of source counts as recognition, acknowledgement, and agreement to the terms as presented herein. Any party or parties which do not give satisfactory accreditation of source, as defined in the above, in any reproduction of any of the materials on this page shall be solely responsible for all damages accrued from subsequent derivations and representations of the original unaccredited reproduction in any form. Any discrepancies between my understanding of the Attribution-NonCommercial-NoDerivatives 4.0 International license and the interpretation of this license as presented herein shall always defer to the terms presented herein. Any terms of licensing lacking as presented in the aforementioned interpretation of the Attribution-NonCommercial-NoDerivatives 4.0 International license shall always defer to the Attribution-NonCommercial-NoDerivatives 4.0 International license. Both the Terms and Conditions defined herein and the materials presented on this page are subject to change without notice and all such changes to the Terms and Conditions are binding to every specific instance of the presentation or the representation of the material on this page for all time and for every possible instance of change. Any profit from the use of this page or its contents and any future derivatives, reformulations, and representations of its contents in both their use and their possible or actual profits--excluding the use of the specific and individual images named herein as "OUTSIDE", "INSIDE", and "A.L.L. Together" as images separate and exclusive from the whole textual work of "One & Other: A.L.L." or as exclusive and individuated from the animated triptych; i.e., no ownership of any of the specific individual images as they are in themselves is ever intended or implied outside their use in terms of "fair use" with respect to their use in this presentation or any future possible derivatives--by their owner, b.e. hydomako, are and shall remain the sole property of said owner. Safe Muffins.

Horizons

Introduction: like "The Fractal Structure of a Dispositional Universe," this is another of my papers from my university days. I will be publishing several such works on this blog over time, so this is the latest entry into the online catalog of my previous work. Some minor stylistic and linguistic edits have been done for this representation.

This essay was written in the Fall of 2002 as part of a course on Hermeneutics which I attended with Dr. Morny Joy at the University of Calgary. It offers an interpretation and analysis of the word 'horizon' as it pertains to our experiences of such a thing both in the world and in our modes of interpretation. Perhaps by synchronicity, it also corresponds to a digital art project I am currently working on for release in the coming days.

Enjoy.

Horizons

  

Sometimes when we don't understand something we will remark that we are "in the dark" about this or that, or that the matter in question is "over our heads." In the former, we might say that we lack the "light" of comprehension--there is something in our interpretation of things that is obscured in shadow, that is unknown. In the latter, we may feel that the topic is too "airy" in the sense that it is unfixed and drifting, avoiding the grasp of our intellect or perhaps our interest. We might feel that our incomprehension is what keeps us chained, but perhaps also sure-footed, on the ground, while the interpretation that would promote some kind of understanding drifts aloft, soft, defined with fuzzy edges, and open to the fancies of imagination--a cloud in the sky. Off in the distance from where we stand, where the earth stops and the sky begins, we find a unique series of points which forms a line so special that it has its own name--the horizon. It is the horizon that traces the boundary between life amongst humans and life amongst the birds. We fly unaided only in our dreams.

An interesting thing occurs on the horizon, a trick of perspective: parallel lines intersect. We can imagine ourselves standing on a railroad track which stretches off into the distance, built with careful hands in a straight line over a vast and flat plain. Looking down (and assuming our basic understanding--our preunderstanding--of railways, trains, and tracks), we see that the two rails are side by side--never to meet--and we know that they will remain that way the whole length of the track. They are as two soulmates whose paths are entirely complementary, but are destined to remain forever unable to hold one and other in a loving embrace. Yet, when we look towards the horizon, we see that the rails come together--the hopelessly separated lovers merge into one line, they do get to embrace one and other after all! At, or perhaps in, the special location known as "the vanishing point" the two parallel lines become the same line. this unique point occurs on, or perhaps within, the horizon. It exists as a part of the edge of our world, the edge where the sky and the ground caress one and other.

The horizon is not merely responsible for invoking the paradox of intersecting parallel lines, it is also the prime and unique location of the rising and setting of celestial bodies. In particular, the sun brings its light each day, sweeping out an arc from east to west across the sky, but it begins its journey by rising out of the horizon and ends its travels by sinking into the horizon. The moon also traces its path from east to west. It too comes from and returns to the horizon each day. It is at this point, but only in passing, that we may note that occasionally the sun is associated with reason, and sometimes the moon is associated with our intuition. Of course, the two bleed into one and other--our intuition can sometimes be clearest in broad daylight, and our reason can keep us up late, working with precision and logic under the silvery light of the moon--and like our parallel lines, reason and intuition, in their distinctness, share a loving embrace.

Day breaks on the horizon, chasing away the twilight which was yielded by the dark (but later it is the dark which makes the twilight begot from the sun scurry off). The beauty of a sunrise is comparable only to that of a sunset, and the glory of both events is interwoven in the distant horizon. If there was no horizon, then there would be neither rising nor setting sun. There would not be a day separate from night, and there would be no subtle interim between the two that cloaks itself in greens and blues as stars fade from or into sight. The horizon is woven into the cycles of life, and appears to be a necessary aspect of our very being. If there were no earth as distinct from and complement to the sky, and if there were no sky as distinct from and complement to the earth, then there would be no life for humans: we would not be around to understand or misunderstand anything! Without a definition of the horizon, without a line between the earth and the sky, there would be no individuals who would utter, when they misunderstood something, "that's over my head."

Which returns us to our exclamation of misunderstanding that we began with before we embarked on a metaphorical, paradigmatic plane shifting journey provoked by thoughts on the horizon. But such a whimsical romp was not without purpose. In chapter two of his book Hermeneutics, Richard E. Palmer introduces us to the notion of a horizon.ⁱ He suggests that it is the meeting of horizons of understanding between an individual and, in the context of his discussion, a text, which gives rise to the "hermeneutical problem" (26). However, we could easily substitute 'other' for 'text,' ⁱⁱ and we would now have a better idea of the range of hermeneutical inquiry. Hermeneutics appears to be concerned with the "dynamic complexity of interpretation" (ibid.) that arises when the self encounters the other, and it seeks to study the ins and outs of understanding, which is generated out of this complexity. It is suggested here that our reading of Palmer's "horizon" would do well to include the shifting sense of our previous meanderings.

Our parallel lines might be framed as the self and other, polarized points of view, or perhaps any sharply defined dichotomies: appearing in the foreground as distinct and separate, but merging into a unity at a point on the horizon. Or perhaps the lines are like two differing interpretations. Our contrast between sky and earth could mark the distinction between our future--up in the air--and our past--roots firmly planted in the ground--with the horizon tracing out the meeting of these in the moment of the now. It is in the present moment that we live, and we live within our understanding of the world. The sky could also stand in for the unknown, the strange, the foreign which drifts beyond the reach of our understanding in vast expanses, while the earth could represent the known, the common place, the familiar things which make up our everyday comprehension of our world. Again, it is the horizon where these two contraries meet and mingle, blending together with subtlety, one embracing the other. Likewise, the cycles of day and night, the rise and setting of sun and moon, could be read as the alternating cycle of reason working in tandem with our intuition. It is these two aspects of our human lives that support and enhance one and other, and it is a relation of mutual respect and necessity for one and other which generates a broader understanding. We could also see these cycles as related to the hermeneutical circle, the interplay between part and whole within which understanding is generated "by a dialectical process [where] a partial understanding is used to understand further still..." (Palmer 25). The light of day being our understanding which must succumb to the night's darkness--our incomprehension--which will itself dissolve back into understanding when the sun returns from the horizon again during the dawn: the dawning of our comprehension. Again, it is the horizon which marks out distinctions, and without it there would be no separation of one from the other, but, at the same time, it is the horizon which blends and shades one into the other, and, as such, the horizon is a sort of paradox, but it is necessary for our lives. These possible readings of the elements of our journey are only part of an interpretation which might open up vast expanses of sense and meaning--the layers of the horizon are as intricate and bountiful as the complexities of human interaction.

It is my hope that these thoughts on the horizon point to a deeper and more meaningful understanding of Palmer's use of the word with respect to hermeneutics. Moreover, we can see that "the meeting of horizons" creates a further horizon: the boundary between our circles and cycles of understanding, and the circles and cycles of an other's understanding. This horizon is the turbulent edge where self and other are united, where experience is generated, where interaction and embrace gives rise to human interpretation and mutual understanding.

---

i) Palmer, Richard E., Hermeneutics; Northewest University Press, 1969.
ii) We do this in the spirit of David E. Klemm's opening remarks, on page one, in his Hermeneutical Inquiry Volume 1 The Interpretation of Texts; The American Academy of Religion, 1986.

Observations From A Fellow Traveler

I have been hard at work, again, lately--finally--at pushing, probing, and examining the limits of my conceptual models. I have, in other words, been testing the precepts of my reality. From a slightly different perspective, I have been reflecting self-referentially on my perceptions and looking for the doors with some intent to step through them.

In order to accomplish this with any sort of actuality, I need to engage in discourse that lies outside of any sort of private language in a Wittgensteinian sense. This is to say, I need to take the strings of my language that also have a sense and reference in the world, and compare and contrast them to the sense and references of other people. I am required to fit my concepts as best as possible to those of Others who also share in the use of these concepts. Again from a Wittgensteinian sense, I need to play within the boundaries of our language games in order to investigate these same boundaries. With reference to Alan Watts and in the context of my previous statement, I recognize I am playing a game that necessarily requires that I am not playing it alone. Thus, I am playing the game with not only myself, but with Others as well.

Some people believe, and I don't feel that they are wrong, that "work" on One's self is necessarily work on the world. Put differently, when we engage in playing the game in the milieu of self and Other referencing, we are necessarily also engaged with the conceptual models that Others use to play the game from their own perspective and experiencing. If we think closely about this, then we realize that when we are playing the game in such a way as to push at, question, and/or dismantle or otherwise alter our own conceptual models--our altars of being--then we are also necessarily, pushing at, questioning, and dismantling or altering the altars of Others. To put it more plainly, work at changing ourselves not only changes our world, but also changes the worlds of Others.

A problem we will sometimes encounter directly because of this necessary relationship between ourselves and Others is that while we are free to engage in the game from this sort of strategy, and they are also free to engage in the game from this sort of strategy, Others may not necessarily choose or desire to use such a strategy at this time. It is less that we, as investigators into our own concepts, are encroaching on the freedoms of Others, and much more that we are necessarily engaged with attempts to liberate them from the shackles of their concepts simply because we are also attempting to liberate ourselves from the shackles of our own conceptual limits. Put differently, work towards liberation of One's Self from the self, entails work towards liberating the Self from the self of Others. And to some not prepared or otherwise willing of their own free choice to join us in this process of liberation, in this potentially perilous journey, it can also sometimes make these same unwilling or unprepared Others become defensive in the protection of their self from the Self. People often tend towards deep emotional investment in the altars of their existences.

And this is where it can become somewhat tricky or otherwise problematic for us to proceed.

We are, as travelers wrapped up in notions of self necessarily dependent on our concepts and precepts of not only self but also Other, attempting to recognize and communicate with that greater archetype of Self. We seek to relate to the Other in a way that is explicated by Martin Buber as relating to our experiences and interpretations of our experiences not from a position of I and It, but from a position of I and Thou. Such a position seeks to recognize, acknowledge, and embrace the inherent divinity or absolute mystery wrapped up in the core of any particular thing and at the core of everything. Put differently, we are, in seeking to shed our current self images and instead reformulate them as informed by the Self, necessarily engaging with the Self as it manifests to us in instantiations of the Other. And, as noted previously, if the Other is not able to recognize this sense of Self within their self, well, our engaging with them from this perspective can create much friction.

We are, as travelers in this manner, necessarily moving in a direction that is neither perceivable nor understandable from our common, everyday, "mundane" movements through time and space. Indeed, it can also be difficult for our own self to understand and perceive such movement and the direction along which this motion proceeds. It is precisely our need to represent such motion towards our Self to our self in a way that becomes comprehensible to our self that we must necessarily engage with the common language game and the existential game that we are all playing: we are all pieces embedded in an interpenetrating and binary cross self-referencing existential and linguistic milieu. So, when we seek to manifest the Self in instances of self, we are also manifesting the Self in the Others we are necessarily related to.

The Self, as entirely empty in itself, but full of all the Other possible archetypes as potentiae, is an awesome thing: it meets us in our own sense of awe. However, its very emptiness, its absolute Otherness in absence of any specific set of rules governing either our language games or our conceptual framings of our existential games, is also terrifying. As Rudolph Otto described it, it is the manifestation and experience of the mysterium tremendum et fascinans. It is, so much as we can describe it in language that must necessarily limit its unlimitedness--giving form to its empty formlessness--the meeting of the divine, the numinous, in our self and the Other; put differently, it is the meeting and recognition of the numinous from itself, to itself, and with itself.

Put differently still, it is a greeting and acknowledgement that we are, in fact, playing a game with our Self: it is breaking the fourth wall of reality where we as players come to see and communicate with our selves as the audience, and we as the audience come to see and communicate with ourselves as the players. Translation: we position the Self to acknowledge its Self as identical to both players and audience. And this is a threat, in some ways, to maintaining the illusion of the game. If the Self desired to maintain only a relationship to its Self, then it would not have ever bothered to begin the process of wrapping its Self in Self deception as manifest in the dual paring of One and Other.

Now, all the above simply to get to the notes of this particular traveler at this particular point in time at this particular point in space, so this particular traveler would like to thank you for coming along with me on this linguistic journey thus far: thanks, thanks to you.

To the notes, then.

As a human traveler we relate to the members of three general classes of Otherness in the world:

1) Members from the class of all things we commonly call "inanimate matter,"
2) Members from the class of all things we call "animate or biological matter" that excludes other humans, and
3) Members of the class of all things we call "other humans."

It is my opinion and experience that when we are pushing our own boundaries in order to move in an unnameable and incomprehensible direction that our relations to the instances of Others from class (1) and (2) relate to us from a position of joy. As Others that are not invested in, and shackled by, a human based sense of self, when we recognize our Self in them, then they can not help but be joyous in the manifestation of I and Thou. We, in relating to One and Other lift ourselves towards the direction of the divine, an embracing of the mystery that manifests the reality of One and Other. It is relating to the third class of Otherness that can be problematic.

There are, I think, I feel--I experience--three ways that relating to this class of Others tends to manifest in relation to our self:

1) Acceptance and mutual recognition.
2) Indifference.
3) Rejection of a mutual recognition.

Relating to those of type (1) is a positive experience of I and Thou. It can be as simple as an exchange of sincere smiles, including, perhaps, a warm and heartfelt greeting between strangers fully engaged in the fleeting moment of transitional recognition of Self. This will almost always be joined with at least a moment of direct and intimate eye contact, usually several such moments.

Relating to those of type (2) can also be a positive experience in terms of our own interpretation of that experience. Again, with reference to strangers, we offer a sincere smile and perhaps include a heartfelt greeting, and we receive in return something less than that. We might simply be ignored, we might get a forced or partial smile, we might get a mumbled greeting, we might get some formal "hello." This will sometimes involve fleeting eye contact, but not necessarily any eye contact at all.

Relating to those of type (3) is where the potential danger lies. We might simply get the very bottom of the barrel form of indifference, and this is the best we can hope for in such an encounter. We might also get a sense of possible negative outcomes, a sense of potential violence, a sense of a self acting out to openly defy the recognition of Self within itself. And, in the worst case scenario, we, in fact, get the manifestation of actual violence. It very much brings to mind a scene in the movie Inception:

It's obviously not as fantastical as all that. We aren't manipulating the very structures of existential experiences, but we are subtly imposing upon the Self, subtly beckoning to the Self, to acknowledge its Self, and the Self in some instances of self will do whatever it can to avoid acknowledging and recognizing its own entrapment within the game that it has created.

Sometimes, fleetingly, I get the sense of this last sort of interaction from strangers when I am out and about and engaged with the world. Rarely have instances of confrontation over acceptance ever spilled over into actual violence: perhaps never. However, sometimes, like recently, when I am really expending energy and training my focus intensely upon recognizing the Self in my self and Others, I get messages--brief, but clear--that from where I am and the motion I am attempting along that indescribable and incomprehensible direction that if only I take a few more steps, if only I am not very careful about the steps I take, then that Self that is inside the Others but also wrapped up so tightly as to deny its own existence, well, I feel like I am on a precipice where a simple transition or slight flutter leading to catastrophe is entirely possible and some kind of actual violence is a distinct outcome.

To conclude my notes on these matters, I will point out that the best way to banish such feelings--and it is best to banish such feelings swiftly and completely so as to not risk undesired and counterproductive consequences for our own mental and emotional well being--is invoking laughter. Laugh at One's self, laugh at One's Other, and laugh within the context of playing an incredibly complicated game of hide and seek. Because what we are encountering is not only, or merely, the resistance of Others to their recognition and embracing of Self in self within the context of I and Thou, but the remnants, the fragments, the slivers of our own resistance to acknowledging and embracing the Self in our self.

One day, perhaps, we will all be ready, each of us as manifestations within each of the three classes mentioned above, and we will call out with a sense of relief, a sense of sadness and mourning, and a sense of joy in our accomplishments and imaginations:

"Come out, come out wherever you are!"

And it is at that moment we will all cease our journeys and all return home: eternal in our undifferentiated Self, and yearning to once again become travelers in the next instance of the game.

Informal list of references (not necessarily referenced directly, but instead mentioned intuitively) for interested fellow travelers:

Wittgenstein and Language Games.

Alan Watts and the Game.

Carl Jung and The Self.

Martin Buber and I and Thou.

Rudolph Otto and mysterium tremendum et fascinans.

The Numinous. 

Catastrophe theory.

See also:

Warning.

Śūnyatā.

Pratītyasamutpāda.
The Holy Moment.

The Fractal Structure of a Dispositional Universe

Introduction: I wrote this essay many years ago--in 2001, as a matter of fact (gah, how the years go by!). I had made it available online, also many years ago, and it received what I'd consider to be some small degree of exposure. However, due to circumstances a few years ago I had to cancel the service where the paper was being hosted, so it has, until now, been unavailable online. As a result of some friendly exchange with a couple people--one in particular expressing interest in reading--I have decided to again make this essay available online. Thanks to those two people (you know who you are) for the motivation!

I'd also like to add that there was a bit of, er, "tom foolery," let's say, with regards to formatting the image placement that required digging into the HTML, which is not necessarily my specialty--more like not at all my specialty. It looks fine in the preview, but if the reader should find the images display in less than a tidy manner, well, blame that on my lack of coding skills. If there are problems in this regard, I hope it doesn't detract from the presentation too much.

So, without further explanations, I offer for your perusal:

The Fractal Structure of a Dispositional Universe

by

b.e. hydomako

There is no thing that exists which is not contained within the structure of the universe: a thing which exists must necessarily be extended in space-time. It does not make any sense to talk of a thing existing without it occupying a location of space during an interval of time¹. Thus, all things that are exist as part of the universe. However, we do not really know how space-time is structured; that is, we only know the order of the universe as it is received through our senses and then interpreted by our minds. This situation leads us to believe that reality is made up of various levels. We have the sub-atomic, the atomic, the chemical, the molecular, the biological, and the psychological-the order of the universe appears to us as if it is some sort of pyramid scheme! This way of dividing up the world leads directly to complication. We become puzzled as to how the levels interact, and as to how specific systems in one level work to influence systems of another level. "Where is the work done," we ask, "do the micro-systems supervene on the macro-systems, or vice-versa?" We are led to asking all sorts of questions like this, and they do not appear to have definite answers. This is simply because interpreting the world as divided up into levels is a dead-end, a dry well. However, there is a way of looking at the universe's structure that is a well spring-the view dissolves or resolves these sorts of questions (and others). A better way of seeing the world is not as divided up into levels, but as realizing that the whole of the universe manifests on one level-the base-and one level only. Such a notion is found in CB Martin's dispositional ontology. We will use his theory in this examination in order to understand that all of the apparently discrete things in the universe are actually a complex whole which has its manifestation within the boundaries of a base level: we will come to see that a fractal model best describes the structure of the dispositional universe, and this will allow us to clearly see that the work of the universe takes place within the only existing level of reality.

To begin we will look at our current notions regarding the various levels of reality. The goal is to arrive at an understanding of how the various levels we see are actually all part of the same level. It is important that we recognize that the purpose here will not be confined to illustrating only that the parts we see are of a whole (indeed, some of us who agree with the current division of the world into levels would also assent to the fact that the levels work together to produce a whole). The task here will be to understand that, as there is only one level to reality's manifestation, the work that appears as divided (e.g. that the interactions which occur on a chemical level work to produce actions on a biological level) is not divided at all; that is, there is no division of labour into these artificially constructed levels: there are only partnerings of dispositions which are identical to manifestings, and all of this occurs within the same level-the level within which reality finds its various expressions.

As humans we have developed tools and skills which allow us to delve into reality in a manner which goes deeper than the macro-systems which commonly and readily manifest in conjunction with us. Examining what is generally thought to be the smallest level of reality we have the discipline of physics. This way of assessing the "deep structure" of the world around us leads to two of the initial levels in the pyramid scheme model: the sub-atomic and the atomic. These two levels of reality are often asserted to be the foundation upon which further more complex structures are built. We can suppose that the pictures of these levels of reality look like the illustrations A and B respectively². Notice that in A and B the picture appears as unique: there is nothing in A to suggest that it is the same as B; that is, in both A and B we see that each picture seems to imply that the two levels of reality are somehow separate from each other in that their constituents appear as different from each other. It is important to recognize that while A and B are not meant to adequately capture the real picture of the atomic and sub-atomic domains the differences in the illustrations do reflect the fact that we perceive the levels as qualitatively distinct-we experience the qualia of one domain as different from the qualia of the other.

Illustration A.

Illustration C.

Illustration B.

To carry this further we will now refer to illustration C which will stand in for the next level which is the domain of chemistry. In this level we commonly think that interactions in the previous two levels of A and B have worked to produce complex systems which are in turn differentiated from the systems found in the levels which A and B represent. Again, we see that the picture of reality on this level is somehow unique and separate from the two previous pictures. We feel that the chemical level then follows rules which are distinct to this domain, and thus, interact in ways which produce more complex systems of molecules (pictured in D). These molecules then go on to work to provide picture E-standing in for the biological level, and then we get, through interactions within E, the level which the psychologists study. This level of our cognitive capacities is represented by F.

Illustration D.

Illustration F.

Illustration E.

Each of these pictures represents a unique level of our world with respect to this analysis of the current popular conception regarding the workings of our universe. There is cross-level action; that is, the interactions on one level are seen to spur events on another level-in this pyramid scheme of a picture we have work being done all over the place! This does not appear as a sensible way to view the world's workings. It offers an interpretation where there is wasted energy through redundant actions betwixt the levels. Martin says of this, "if you have levels of being which really be, [and they] do the work over again, then [we must] provide an account of how there is work to be done!" (beh 1). This is where our nagging unanswerable questions come from. We look at this sort of structure and can not help but asking, "how do the interactions within A work to produce a different order of interactions within D?" As well, this is what leads us to the inclination to reduce, say, the cognitive capacities of human beings down to the mere chemical interactions within our brains. Then there is the further inclination to reduce the work of the chemicals to mere atoms swerving in the void. It is clear that once we are on this path we remove any notion of what it is to be human from our account: atoms swerving in a void possess no emotions or anything else remotely human! As Martin is fond of saying (quoting physicist Richard Feynman), "We have to have a way of putting it all back together again!" (ibid.). In other words, the reductionist tale we tell must account for how things like emotions and colour (a mere two examples of the many kinds of qualia) end up occurring in the world when the world itself seems to be composed of bits of things which do not partake of these qualities at all. There are many other problems which come out of our misconceived notions regarding the structure of our universe, but we are not here to list them all. We are here to see that this pyramid scheme of work on multiple levels is a mistaken way to represent the actual structure and workings of the universe.

In the above we saw that we have the notion that there are various levels to reality, and we noted (through the illustrations) that each apparent level looks different, acts different, and produces separate conceptions of the systems found within the universe. We will now show that even though these separate pictures of the world appear to be radically different from each other they are all in fact part and parcel of the same system; that is, there are not different and unique levels which stack-up in some fashion in order to produce the world. All of our perceptions regarding the variety of systems found on different levels are in fact sub-systems of a singular over-arching system occurring within one level of being. To understand this in a visual way we will now look at illustration G.

Illustration G.

Illustration G (above) is a picture of a mathematical structure called a fractal. In particular it is a picture of the Mandelbrot set which has been called, "...a universal object." It has received this title because, "[s]ets remarkably similar to the Mandelbrot set occur in many other [fractals]" (Devaney and Keen 77). Due to the fact that the Mandelbrot fractal seems to be the only set which has this ubiquitous nature we will use it as the paradigmatic example of the fractal model which is being asserted as the best conception of the structure of our universe (this is not to say that the Mandelbrot set is the structure of the universe, but that the fractal structure of the universe would also have this same ubiquitous nature-its occurrence would be found in all the sub-systems within the manifested world).

G illustrates that what has been previously seen as separate and unique pictures are in fact all parts of the same picture. We can see that illustrations A, B, C, D, E, and F are all contained within the larger structure of the Mandelbrot set. Recall though, it is not merely our goal to see the parts as a complex whole, but to account for why there is not a division of labour amongst the ill-conceived levels of reality. In order to understand this we will first take a detour into why the fractal model fits like a glove to the hand of CB Martin's dispositional ontology, and we will also come to understand specific qualities of a fractal structure. It is through the latter that we will arrive at an account of how the work that occurs within the universe can only occur within a base level.

Composition

In Martin's theory of dispositions he claims that reality is, "a composition or constitution of simple/simpler parts..." (Martin 196). The simplest parts are known as base dispositions, and they are the smallest dispositions that exist-they are atomic. Martin asserts that the manifestation of reality occurs as a product of the partnerings of these base dispositions. This is summed up on page 202, "[c]apacities are capacities for (dispositions for) their exercises or fulfillments (manifestations) under certain conditions (reciprocal disposition partners)." This is saying that the base dispositions have the ability to undergo composition with other dispositions, and it is in this composition that manifestation occurs. It is important to note here that regardless of whether or not a given disposition has a partner for a manifestation, it is the dispositions which are real in the sense that the dispositions are actual.

The fractal model is also a composition. A typical equation for generating the Mandelbrot set relies on what is known as limit cases. Dr. Clifton Cunningham has described limits as, "...a game that requires two players" (beh 2). In the mathematics of fractals, a given number (the input) is then compared with another number. If the numbers "agree" then a limit does exist, and the result of this process gets mapped within the fractal. If the numbers do not "agree" then there is no existing limit, and then the point gets mapped outside the boundary of the fractal³. In other words, for any number, the number only gets mapped into the fractal if it is able to undergo composition with another number.

We see that this is an analogous process to the dispositional account: the solitary number (like the lone disposition) does not get mapped within the fractal (has no manifestation) without first partnering with some other number. In this account we see that the whole of the fractal picture is manifest through both those things which have partners and those things which do not. The fractal itself is the structure of the manifestation occurring through partnerings, and the edge of the fractal is defined by those things (numbers qua dispositions) which do not have partnerings. Both the partnered dispositions and the unpartnered dispositions must be present in order to define the whole: it is impossible to create the picture without having both the manifest and the unmanifest.

Iteration

We will now turn our attention to the process by which the universe becomes manifest under Martin's ontology. In Martin's theory the partnerings of dispositions are the manifestation⁴. This is summed up in his equation "D + P = M (where D is a disposition, P is the disposition's reciprocal partner, and M is the manifestation)" (beh I). The important aspect of this is that for any M the manifestation itself becomes a disposition for further manifestations. Martin says of this on page 207, "...it could be tempting to treat manifestations as themselves disposition-free, or at least not to raise the question of their dispositionality. This would be a gross error." What we have then, on Martin's account, is an iterative process. The output of the initial partnerings become the input for the next occurrence of partnering in a further mutual manifestation. There is nothing that is novel above and beyond the dispositional constituents; that is, the dispositions, even in their partnerings, never become anything other then more complex dispositional systems: there is never a manifestation that is not "...ready to go" (beh 1) for further partnerings.

It should come as no surprise that this is exactly how the generation of a fractal occurs. When composing a fractal we rely on an iterative process where, "the result of one cycle... becom[es] the starting point of the next" (Marshall and Zohar 211). The result that is generated by plugging in a specific number into the equation of the fractal becomes the input of the next step in determining the constituents of the given fractal.

We recognize that what is occurring in the generation of the fractal is exactly what is going on in Martin's dispositional theory. The output of the partnerings is a manifestation which is itself the input for the next potential partnering. The fractal, as noted above, is created by exactly the same process. We now see that an iterative process of composition creates both the dispositional universe and the fractal model.

Deterministic Yet Unpredictable

On Martin's account of the ontology of the universe he asserts that, ultimately, the universe's construction is completely determined; that is, the entire universe, when taken as whole and complete-from start to finish-is completely mapped out and could not have been any other way then how it is. However, he does not think, at any one time or over some length of time, that we can exactly predict which partnerings will occur for the next manifestation. Martin says, "we can't begin to keep up with the mutual manifestations-my God!" (beh 1). By this he means that the interactions of all the dispositions and their partners for the mutual manifestation of the world are so complex that we don't even have a chance to consider all the partnerings which occur at any given moment. This is the epistemic realization that we can't know it all (ibid.). We are only able to have some useful (but incomplete) generalizations about what we expect to occur; however, we can never know with absolute certainty what will manifest next. This is due to the fact that, "we cannot examine an entity without including all its interconnections and interrelations with other entities" (ibid.); in other words, to properly predict the course of the manifestations we would already have to know everything about every manifestation that currently is-this seems well nigh impossible!

The fractal model is, of course, exactly like this as well. The fractal, in its whole and complete form is entirely deterministic. There is not one point that occurs inside or outside the fractal which can not be accounted for by its predecessors. In other words, the entire fractal can be deconstructed to find with certitude what went where and why. However, this is not possible from within the system itself; that is, during the process of the fractal's construction we can not tell, for a given input, if the result is going to have a limit which exists or not until the input has been run through the equation of the fractal's generation. This means that we are unable to predict a priori whether any given unit undergoes composition or not.

Again, we see a startling and obvious connection between Martin's dispositional theory and the fractal model: the entire structure in finished form is absolutely deterministic, but while the structure is being formed there is no way to exactly predict what will happen next. As Benoit Mandelbrot puts it, "The notion of [a] deterministic yet unpredictable [system] is a surprise to most people" (Hall 122).

Self-Similarity⁵ 

A key feature of a fractal is the quality of self-similarity. This concept is best illustrated by Benoit Mandelbrot's example of a cauliflower. In the video, "Fractals: an Animated Discussion," Mandelbrot holds up a sizable cauliflower and asks us to examine its shape and structure. He then proceeds to break off a chunk of the cauliflower and then asks us to examine this piece of the whole. He notes that it looks very much like the original, but only smaller. He then breaks off another bit from the smaller part of the whole. Again, we are asked to observe that this even smaller bit looks like the piece it came from, and that it mirrors the structure of the whole: the point being that this same sort of self-similarity is an essential aspect of any fractal.

The Mandelbrot set displays this self-similarity, but as Bodil Branner informs us, "M [the Mandelbrot set] contains small copies of itself which in turn contain smaller copies...ad infinitum...every mini-Mandelbrot set has its very own pattern of external decorations, every one different from every other" (Devaney and Keen 76). So it is not an identical self-similarity, but only a rough self-similarity; however, there is no doubt that the Mandelbrot is a fractal!

Now in a similar sense, we see that our world has this feature: things in the world are self-similar, but not strictly identical. We see that one person exists as a similar system to another, but that does not make them the same person. The same can be said of birds, houses, trees, whatever. There seems to be in our universe this same sort of self-similarity among its constituents where each complex dispositional system, "...has its very own pattern of external decorations, every one different from every other."

Now since the universe on Martin's account is composed out of dispositions, it is reasonable that we can look to the manifestations around us and recognize that these complex dispositional systems share this sort of self-similarity with our paradigmatic example of the Mandelbrot set. Everything that exists appears to have its unique pattern in the world, but there is also much that is similar amongst the differing kinds of expressions.

The Base Level (The Only Level)

It is in this section that we will come to understand why there is not work being done across levels, but only interactions and interrelations all happening on one level.

On Martin's account the only work that is being done occurs at the only level of reality. "What it comes down to," Martin says, "is the interactions and interrelations amongst the quarks of the base level"⁶ (beh 1). From what we have seen of the theory this far we understand that there can be no other level above and beyond the level in which the dispositions interact and interrelate. To think otherwise is to think incorrectly about what is occurring in Martin's dispositional ontology. We have seen that dispositions partner for mutual manifestation. The manifestations can become very complex sub-systems of the overall whole, but simply because they are complex does not somehow bump them up into another level of being⁷. On Martin's account there is the substratum of space-time, and this is where the manifestations take place. Space-time provides the canvas upon which the manifestations are the paint. Granted, we may perceive layers of paint, but this is a product of our interpretation of the manifestations in space-time: the paint of the dispositions is whole and complete and only ever occurs upon the surface of one canvas! There are not several canvasses layered one on top the other (and this would be a peculiar way to try and paint a picture-with canvasses obscuring the work done on previous canvasses)-it is but a single substratum on which all manifestations occur.

On the fractal model we have an analogous situation occurring. In the case of the Mandelbrot, the fractal occurs on the complex plane. This is a two-dimensional surface. In extending the model to account for the universe we understand that the fractal which models our world would be composed in a three dimensional space. The surface (or space) is the substratum upon which the creation of the fractal occurs. While it might seem to some that we could designate the dimensions (i.e., length, width, and height) as different levels this is merely a semantic mistake: the dimensions themselves are not levels, but instead they exist together to form the singular space in which the fractal finds its expression over time. In other words, the fractal is contained and constructed on only one level. All the mathematics that goes into generating the fractal results in points being mapped into one space and one space only.

Now from this we find Martin's explanation of the base level not only plausible, but also mandatory under the fractal model interpretation. From what we have developed over the course of justifying that the fractal model fits like a second skin to Martin's description of the universe-that is, through showing that the generation and perpetuation of both the fractal and the dispositional universe is identical-we find that it no longer makes any sense to think of a division of labour occurring within a hierarchy of levels. The fractal model illustrates clearly that there is only one level in which manifestation occurs, and thus, there is only the base level within which the dispositional universe finds its expression.

One Model and One Object

We have come to understand that a fractal model best captures the notions contained within CB Martin's dispositional ontology. A result of this analysis was discovering that Martin is correct in the assertion that reality plays out within a singular base level. It also appears that the fractal model can account for much more with respect to the workings of the dispositional universe⁸. Between the fractal and the non-existing limits, for instance, is a "crumpled boundary." It is called this because the defining edge of the fractal is in a constant state of turbulence. Under the dispositional theory this is likely where we will find true emergence taking place: the boundary of the fractal is in a perpetual state of novel manifestation, and this reflects the idea found in Martin's ontology that new properties can emerge from the composition of existing dispositions-none of which posses the property before the partnering. As well, when asked how many things there are in the universe, Martin responded, "It is a one object universe" (beh 1). We see this due to the fact that we can not examine any dispositional system without considering its ties to other dispositional systems. This creates a vision of reality where there are really only complex dispositional sub-systems. These sub-systems all interact together to produce a singular complex dispositional system which is the whole of the manifested universe. When we compare this to the fractal we see more strong evidence to tie the two models together: the fractal is a complex whole that contains within it an infinite number of sub-fractals. Under both descriptions we find that we can not help but take the idea of "the oneness of everything" to heart.

End Notes

1. We realize that this is controversial to some people when it comes to so-called "mental" phenomena; however, we recognize, if nothing else, that thoughts, ideas, and feelings must also have extension in space and time even if we are unwilling to call such extension "physical."

2. All illustrations in this paper appear on page 318 of Michael Barnsley's "Fractals Everywhere"; Acadmeic Press, Inc.; San Diego, CA, USA; 1988.

3. In G the fractal is the black structure. All that is outside this structure are the limits which do not exist.

4. Here we will note that this is the key feature of Martin's theory which deals with the problems of causality; however such problems are not the focus of this analysis, and so, we will not delve into this aspect of Martin's theory here.

5. While self-similarity is key feature of fractals, it is not a key feature in Martin's dispositional ontology; however, Martin is not obligated to discuss self-similarity, but in the case being developed here we have to account for this feature in the universe. That is to say, if we desire to see the fractal model as the best model of a dispositional universe, then we have to illustrate that self-similarity exists in the universe. To provide a strong and convincing argument for this would be a paper of its own; thus, the argument here is only a brief sketch of this notion.

6. At this point (since it has not yet been mentioned) we note that Martin uses the word "quarks" to designate the atomic dispositions; thus, "quarks" is being used here to refer to the most basic dispositions.

7. We can see here an analogy with the archaic notion of the shell model of the atom. It was at one time supposed that the electrons of a given atom circled the nucleus in tidy orbits with levels which expanded ever outward from the nucleus. We now know that this was an overly simplistic way to represent the workings of the atom. Modern physics declares that the electrons could be anywhere, and that there are not these neat shells which the electron gets "bumped into" due to its becoming more or less energetic. In a similar sense, we find that there are not tidy well-defined levels of reality that more "energetic" (i.e., complex) dispositional systems get knocked into. We find that there is only an increasing complexity contained in one level with respect to both the orbits of electrons and dispositional systems.

8. It was thought upon initial conception that this paper would deal in more detail with at least the idea of how our "readiness lines" (as Martin calls them) work to create a "dispositional tunnel" through which we interact with the rest of the fractal system. This would provide an explanation of why we see the world as divided up when really it is not. Due to spatial limitations the concept of the dispositional tunnel will have to be reserved for a later exposition.

Works Cited

beh 1. Notes from "The Physical and the Mental". Collected during CB Martin's Philosophy 589.45 class at the University of Calgary, Winter semester 2001.

beh 2. Conversations with a Mathematician. Interviews conducted with Dr. Clifton Cunningham over the course of the Winter Semester of 2001 at the University of Calgary.

Devaney, Robert L. & Keen, Linda, eds. Chaos and Fractals The Mathematics Behind the Computer Graphics.American Mathematical Society, USA; 1980.

Fractals: an Animated Discussion. Peitgen, H. O., H. Jürgens, D. Saupe, & C. Zahlten. Videocassette. New York: Freeman, 1990.

Hall, Nina, ed. Exploring Chaos A Guide to the New Science of Disorder. W.W. Norton & Company, New York, USA; 1993

Marshall, Ian & Zohar, Dana. Who's Affraid of Schrodinger's Cat?. Quill, William Morrow, New York, USA; 1997.

Martin, CB. On the Need for Properties The Road to Pythagorianism and Back. Handout for Martin's 589.45 class, reprinted from the original, but source unknown. Pages numbers correspond to original source.

Threat Level

A little while ago I was watching the news with my mother. Of course, as there has so often been lately, there was some piece on the IS or ISIS. You know, those fanatics running around in Iraq and Syria taking over cities, killing, looting, maiming, and being generally all around unpleasant people. And, perhaps like many people over on this side of the world, and, I suppose, in other parts of the world as well, my mother has some degree of concern about this group of so-called "terrorists" and the level of the immanent threat to our lives.

This, of course, has spawned a few interesting conversations between my mother and I.

Now, I'm not going to say that these people aren't terrorists, but I am going to say that the word "terrorist" frequently seems to be levelled by those on one side of some conflict or other against those on the other side of this same conflict. The enemies are the terrorists and the good guys are the freedom fighters. That seems to pretty much be the overall generic formula to the story--whichever story.

Of course, it gets a bit more complicated to sort out who is really the enemy and the good guy when it comes to the Middle East and its seemingly ongoing plethora of conflicts. There's a whole socio-political-economic stew going on with the nations and groups involved and it has been cooking so long now that it all merely tastes brown to me. So, none of that is really what I wanted to discuss here.

Oh yes, the conversation between my mother and I about the level of threat that the IS, or, really, terrorists in general, realistically have on our lives here on Vancouver Island, or, for that matter, on the rest of Canada or even the United States. I was hoping to assuage her fears a bit, so I simply asked her:

"Mom, since that terrible 9-11 event, how many people have been killed by terrorists (because it is, in some ways, the idea that terrorists are going to kill her--like they beheaded those other people, say--that scares her) here in Canada or even the US?"

And I didn't even go into (and won't here either) anything about 9-11 and the whole "official story". Was it official? Yes, it was official. Was it a story, well, there's very little room for doubt about that! But I wouldn't claim to know the actual story. Wait, I said I wasn't going to go into that...

OK, so, anyway, I don't know what the official numbers are of people who have been killed by bona fide terrorists here in Canada or the United States. I'm not even sure if such information is publicly available. I am fairly confident about one thing, though, that it's a pretty low number. Like less than a hundred type of low. Maybe less than ten type of low. *shrugs*

So, I asked my Mom how many people she figured were killed by automobiles here in Canada and/or the US since 9-11. She said she didn't know. Hell, I didn't know either--and still don't (related: 12, 516 people have died in automobile related incidents in Canada from 2006 to 2010--thanks internet!)--but the point really is that, obviously, the number of deaths caused by vehicles is much, much higher than the number of deaths caused by terrorists, I mean, as far as we are talking domestically here, you know, the "homeland".

Nobody calls automobiles "terrorists" or, really, thinks there's any sort of significant threat level associated with them. You don't see nightly news stories about the threat levels of daily driving. Sure, there is the occasional report on the local news about a local fatal car crash, yes, and perhaps every now and then a particularly bothersome multi-vehicular incident somewhere else might make a less than local news story, but automobiles in their hazards to the population do not enjoy the same amount of coverage as the terrorists du jour; yet, the act of daily driving poses a much more significant threat to any particular citizen's life, here in Canada, than does some thirty-odd thousand people behaving badly thousands and thousands of kilometres away (over ten thousand of them, apparently).

Further, I asked her, how many people are killed each year, again, here in Canada or in the US, by the police? Again, I didn't have a number and neither did she, but she could easily realize that the number of people killed by the police since 9-11 is likely larger than number of people killed by terrorists, Again, we are talking domestically.

(A quick Google search revealed little in the way of quality info, and I can't be bothered to find actual numbers. Some sources throw around that over 5, 000 people have been killed in the US by their police since 9-11. Google at your own leisure and make your own assessment!)

Now, as to whether or not the police can be considered "terrorists," well, that might go back to the formula of which side of a conflict is doing the defining. Regardless, most people would not label the police as "terrorists" and many people are under the impression that the police are here to "protect and serve" (who they are actually protecting and serving seems to become a less distinct and more controversial issue, but I digress…) and are, in general, not a threat to the population.

However, if we take the numbers and look at them statistically, it becomes quite clear that if you live in the US or Canada (and I'm sure some other countries too, but those two countries are the ongoing examples of this piece) you are much more likely to be killed by an automobile or a police officer as compared to being killed by a terrorist.

Now, this is not to say that terrorists--whoever we might define them to be--pose no threat to people or to dismiss the need to figure out a way to squelch terrorism in whatever form it takes. Hardly. No, this is about the perceived level of threat, or perhaps even the encouraged perceived level of threat, versus the actual level of threat.

I'm sorry, Mom, but you're much more likely to die in a myriad of other ways than you are at the hands of any terrorist. Quit letting the news scare you. Don't believe the hype.