This Isn't Quantum Physics. Wait. It Actually Is. OK, Maybe Not Really...

I don't know why I sometimes feel inclined to take decent, working, knowledgeable scientists to task, but there could be something Freudian there. Y'know: we don't really know ourselves, and we don't know what motivates us to do the things we do. Of course, that doesn't really explain much, does it? And perhaps claiming that "...really everything is quantum physics" doesn't explain much either or maybe it's simply a mistaken point of view to take.

I mean, it seems to me here's an example of mistaking the map for the territory. Sure, yeah, it seems that, when observed in a suiting manner, the universe and all the stuff in it is "... all happening by the interactions of tiny particles," which also happen to sometimes be waves (again, seemingly dependent upon the mode of observation)--a result which, in part, led to the development of Quantum Theory. Yet, "...the rules of quantum mechanics" are the (current) map by which we assess, experiment with, and otherwise observe the going-ons of the stuff in the universe in its seemingly "fundamental (by which we seem to actually mean "smallest scale")" expression. In other words, the interactions of the stuff of the universe--currently observed at very small scales as "tiny particles" and waves--is the territory and Quantum Mechanics is the map. And it's likely a "category error" to say that the interactions of the stuff of the universe are identical to Quantum Mechanics: they are not the same thing. One is a bunch of stuff, the other is a bunch of symbols: territory and map.

For a long time--maybe around two-thousand years--many of the people inclined to study such things thought that Aristotelian physics could explain most (or maybe some thought all) of the stuff of existence. Of course, a few people came along and ended up knocking all that down, and what ended up in its place was Newtonian physics. And maybe some people thought that Newtonian physics could or would explain most or all the stuff of existence. And of course they were mistaken since Quantum physics came along and supplanted the Newtonian version of physics. And no, they are not the same thing.

So, maybe once upon a time some people thought that everything was explainable by Aristotelian physics, and we know now that they were wrong. And then once upon a different time it's likely that some other people thought that everything was explainable by Newtonian physics. Well, we know now that they were wrong too. Now it so happens that currently there seems to be some people who feel like everything is explainable by Quantum physics (or some slight modification of it--gravity being the main trouble-maker here), and we know now that they are...?

History repeats itself, (ad infinitum) as some say, and I'm willing to wager everything I own (although myself and any takers on the bet may not be alive to collect the payoff) that some day something else--some other theory--will explain, well, some things anyway. Because, let's be realistic here, when we ask, "[w]hat is not quantum physics," well, there's a whole slew of things that aren't. And many of those things--at least seemingly so--can be collected under the general heading known as Qualia.

For instance, Quantum physics has nothing at all to say about my taste of, for example, chocolate--let alone whether or not my taste of chocolate is identical to yours. And what's Quantum physics got to say about my like or dislike of Tarantino films: it certainly won't predict if I like his next one or not. And y'know those days where you simply feel like pulling the covers back over your head and staying in bed (well, I know those days, anyway)? I don't think Quantum physics has much to say about that either.

Hossenfelder writes, "[i]f it wasn’t for Pauli’s exclusion principle, you’d fall right through the ground."

Y'know, I don't recall learning about anyone ever having a problem with falling through the ground before Pauli formulated the exclusion principle, but maybe that's a result of some sort of historical revisionism covering up some grand conspiracy or other? I mean, what if people used to fall right through a flat earth or something? But I digress...

Now I can't speak for Hossenfelder's point of view in general (not really knowing her personally or anything), but this particular article appears to reflect a kind of scientific reductionism that I find distasteful, and I suppose that neither Quantum physics nor Freudian psychology are going to explain that particular aversion. Perhaps this hostility towards scientific reductionism--at least in some self-reflective and (semi) self-conscious sort of manner--goes some way to informing my apparent compulsion to take decent, working, knowledgeable scientists to task.

Shrug. I dunno'.

Science is cool, science is fascinating, science is a worthwhile human endeavour and has clearly aided the human race (yet also helped our seemingly insatiable appetite for self/other destruction as well...yet that's not science's fault--or is it? Perhaps if we hold that everything is quantum physics, then, yes, maybe science can be held morally accountable for all the atrocities it's helped to create...oh, sorry, again, my tendency to sometimes digress). But, at least currently, science isn't everything--can't explain everything, at any rate. And when it comes down to the fine grained details none of the stuff of existence is science. Science seems to be a method which produces a body of knowledge: together these inform investigations over a specific and limited range of human-based experiences.

Maybe one day science can and will explain everything there is to human experiences, but I guarantee that from our current position in the timeline we would not understand whatever that will be as science: its theories would likely seem to us as gibberish and its results as some form of sorcery. As it currently stands with or without Quantum--or any other formulation of physics--there are still milkshakes, weight loss, basketball, and Noam Chomsky. Sorry, Sabine.

On the Holographic Principle and the Fractal Model of the Universe

This is a response prompted by +rare avis asking if I had seen this article and was asked in this post. I am posting my response to Drifting Labyrinths for the sake of posterity.

No, I haven't seen this particular article yet, but it seems to misrepresent the "holographic principle," which is common in popular articles on the matter. The Holographic Principle does not say that we "live in a hologram." And every time someone says this it makes baby Jesus cry and I throw up--just a little--in my mouth.

The "holographic principle" is defined as: ...a mathematical principle that the total information contained in a volume of space corresponds to an equal amount of information contained on the boundary of that space (source).

Here's a thing: we seem to live in at least a four dimensional universe: the three spatial dimensions that define things with volume + the time dimension = spacetime (of Relativity) = 4 dimensions.

So, there is a sense in which our experiences are occurring in a "fractal dimension" where a "fractal dimension" is defined as: a measure of how "complicated" a self-similar figure is. In a rough sense, it measures "how many points" lie in a given set. A plane is "larger" than a line, while S sits somewhere in between these two sets (source).

Put differently, a "fractal dimension" is not a whole number but some number between two whole numbers. The plane in the above definition has 2 dimensions, and the line is described in a single dimension, and the fractal dimension of the set of points that define the fractal S in that plane is greater than 1 but less than 2.

So, similarly, our experience of time can be seen as occurring on the boundary of a fractal that exists in a four dimensional space. So, the fractal dimension, then, is greater than 3 but less than 4, and that is kind of like our experience of the possibly four dimensions of spacetime: we readily experience the 3 dimensions of volume in their completeness (as whole numbers, say) but not so with the fourth dimension of time, which we only experience in increments--as some fraction of the whole--and, really, only one "point" at a time.

So, what the "holographic principle" implies in such a model, is that the information in the four dimensional volume of spacetime can be encoded on the surface of that volume, and this surface is the 3 dimensions of volume we readily experience + the "partial" experience of the fourth dimension of time because existence, as is my conjecture, happens on the fractal boundary of a n-dimensional volume (in this case we are discussing, n = 4).

As I put forward months ago (but stated somewhat improperly at the time with respect to the current experiment to test for such a property) and now restated here with more precision and clarity:

The fractal model of the universe is a possible explanation of the structure of the universe if and only if the holographic principle is a property of our universe.

That is a prediction of the model, in other words, and one that can be verified scientifically by experiment.

Put differently, by my understanding of the fractal model that I am endorsing as a possible model of the structure of the universe this model necessarily requires that the holographic principle be true of our universe, or so it seems to me.

And this is precisely because the experiences that we have seem to be of a fractal dimension that is greater than 3 but less than 4 (if we posit the universe is a 4d structure). In other words, we exist on or within the lesser space that describes the surface or boundary of a larger volume, and in order to have experiences that are derived from that larger volume the information contained in that volume must be available on its surface, which is what the holographic principle says.

Put differently still, in a "block universe" conception of our universe (to use a current model that "fits" the following description), the whole universe already exists as whole and complete--from beginning to end--and is a four dimensional object, which is to say a volume inscribed in four dimensional spacetime. But we don't experience that object and its volume directly. We experience parts of the total information that the 4d volume contains, and we do so exactly because such information is available in total on the greater than 3 but less than 4 fractal "surface" of this 4d volume. That is our experience of the total information as divided in time and is part of the turbulent boundary of the fractal.

A little differently still, the fractal itself is "timeless" and it is defined exactly because it is all possible manifestation of or in the total 4D universe in contrast to all the other possible manifestations that did not occur, and the boundary between these two sets of points define the reality of our experiences: it is the turbulent boundary of a fractal or can be adequately modeled that way, anyway. All the information of the universe is found in that 4D volume and the fractal boundary that is the surface of that volume mirrors this information as the boundary goes towards infinity--which is to say takes on a sort of volume itself that is greater than 3 and less than 4, but is always approaching 4.

---

It is interesting, in a synchronicity sort of way, for the following reason:

I believe this model--or one very much like it--will become part of a future scientific understanding of our universe. This is also a prediction, but not a scientific one--it is an intuitive prediction--although this prediction will be shown true or false in time, so it is a "testable" prediction. I am not aware of anyone who has constructed a similar model as this one, but I am sure it is coming. It only makes sense.

Now, earlier tonight I was on the telephone with an old friend, +Lisa Mizeri, and we hadn't talked for awhile, so we were catching up on all sorts of things, and I mentioned that since I did not get accepted into the Masters of Philosophy program here at the University of Victoria that I was seriously considering starting a BSc in physics.

Part of our earlier conversation was about how, at least in theory, if we live in some odd folding 4D "hyperwhatever" type shape, then we ought to be able to do things, as was her suggestion, like "hiding rows in Excel." We were talking specifically about making travel easier, and in particular travel across Canada. She was saying we should just be able to "click" and hide Alberta, Saskatchewan, Manitoba, and Ontario, and then it would be easier to get from BC, where I live, to Quebec where she and her family currently live. And then we'd simply "click" again, and those provinces would all be revealed once again.

Later, in the conversation, when I mentioned, among other things, that I might go do this BSc in physics, then I joked that perhaps I would figure out how to fold space in such a way that I could open my apartment door, step through it, and step into her and her family's apartment in Montreal and close the door behind me. I have not made it out their way for a real live visit and Montreal would be a pretty cool place to visit in addition to seeing my old friend.

Anyway, I think that an understanding of the universe in terms of a fractal model is going to be at least a step in that direction. And we were joking earlier about my having written a voluminous tome that would somehow survive into the future--as an actual bound book of paper pages--about my various "conjectures" about reality (some of which we discussed peppered throughout the conversation) that would turn out to be true, and folks, some of them anyway, would wear buttons or t-shirts (or whatever the future equivalent of such things would be) that read "Hydomako Was Right."

And of course we laughed about this. And I joked "What the fuck is a 'Hydomako'?" as I am sure most, if they were bothered to, would be prone to ask, heh.

Now, I think it is much more likely that some ingenious person already in the field of physics with a PhD will publish something that is very much like this model, and is more rigorous in terms of its formalization, that is, it will have equations that show such and such and the math will be present to justify the ideas. So people in the future will, if they do at all, wear buttons and t-shirts that say "[Ingenious Physicist with PhD's Name Here] Was Right."

So, I'd be lying if I said I didn't want my name attached to a revolutionary scientific idea. That would be awesome. I think this or a similar fractal model is that revolutionary scientific idea or at least part of it, but I am not sure if I will end up being the one to publish that more rigorous and mathematically sound paper that sparks or is part of such a revolution. I think by the time I earn a PhD in physics (at least five to seven years and maybe more, if my plan to earn a PhD in Philosophy is any indicator of success (going on seventeen years now and still sitting pretty with a BA), yup)--if indeed I ever accomplish such an endeavor--well, someone is likely going to write that paper before I do.

On the other hand, it is more about the idea--this idea, I feel, needs to get out there--and if I have this idea, others do too because that is how ideas and the "collective consciousness" works. So, if you have this idea too, dear reader, and are in a position to make it more rigorous and have also been prompted by some of my "rough work," then, hey, give me a footnote or something, ok?

See also this thread for further work on the fractal model or at least further explication of it in terms of the A & ~A "theory" about the world. With thanks to +sreejith s, of course.

For a whole lot more on A & ~A see my philosophy website.

And if you really want the hardcore stuff, then read this.

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.

"Holographic" Universe?

There's a recent article that I've seen circulating around Google+, namely:

Simulations back up the theory that Universe is a hologram, Published on Nature.com, Dec. 10, 2013.

This is a bit of a synchronicity for me in some ways as I've been revisiting some ideas regarding notions of a "holographic" universe and, indeed, have been planning on doing some review/analysis here on Drifting Labyrinths of a few YouTube videos on the subject, which I have watched this past week. But this is an aside--now let's get to the matter at hand.

I've seen some comments regarding this article, and I think that some people misunderstand what the article is actually saying. It does not say that we are living in a hologram and it certainly does not say we are living in something that is similar to The Matrix. What it does say is that certain interpretations of string theory--ones which use nine spatial dimensions with one dimension of time (for a total of ten dimensions)--can be seen as a projection, or "hologram," of a specific sort of one dimensional model of quantum mechanics. From the article:

The mathematically intricate world of strings...would be merely a hologram: the real action would play out in a simpler, flatter cosmos where there is no gravity.

and the article later says of this "simpler flatter universe":

The lower-dimensional, gravity-free [universe] has but a single dimension and its menagerie of quantum particles resembles a group of idealized springs, or harmonic oscillators, attached to one another.

What some people seem to miss in the article is where theoretical physicist Juan Maldacena is paraphrased as saying:

Neither of these model universes...resembles our own.

What the article is actually reporting on is the fact that there are problems/solutions which are translatable from the more complicated and thus, mathematically more difficult, ten dimensional model of superstrings to this simpler one dimensional model. In the article, these problems and solutions concern properties of certain kinds of black holes.

Now, the fact that a specific one dimensional model has some sort of equivalency with a ten dimensional model does not seem particularly surprising in this instance: in string theory the strings themselves are seen to be one dimensional objects and these one dimensional objects are "vibrating" in the ten dimensions. It seems at least intuitively possible that a simplified model of the ten dimensions of certain formulations of string theory would be able to be expressed in a single dimension--perhaps not much differently from how we can think of and express four dimensional "light cones" in two dimensions, how we can explore four dimensional geometry by the projection of four dimensional objects onto a two dimensional surface, or how we create a three dimensional visual experience from the two dimensional representation of images on our retinas. What I am getting at here is that it seems there are several instances of translating phenomena from such and such a dimensional configuration to another, and so, it's not like such translations are something new.

Moreover, it's not like the discoveries reported in this article are conclusive that certain ten dimensional string theories are entirely translatable into this specific one dimensional model. As the article itself says the research being reported upon is not a proof but provides "...compelling evidence that Maldacena's conjecture is true."

What was this conjecture? It's not that we are living in a hologram or The Matrix that's for sure; rather, the conjecture is that there exists a model of the universe such that a "...model of the Universe in which gravity arises from infinitesimally thin vibrating strings [i.e., in the context of the content of the research reported on in the article, specific models of ten dimensional string theory] could be reinterpreted in terms of well-established physics [and this would be, apparently, the physics of the one dimensional model reported on in the article]". In other words, the "compelling" evidence is in regards to the fact that there is a simplified model of a more complex model.

And that's the so-called "rub" here: we are talking about models of the universe and not the universe itself. Pretty much by definition all models are going to be simplified versions of whatever it is the model is modeling. Further, since all these models in current physics are essentially mathematical in nature, I can't help but think that any model is going to run up against some problematic manifestation similar to Gödel's Incompleteness Theorem, by which I mean that, for any given model of the universe, it will be impossible for it to be both complete and consistent. Put differently, it seems likely that there will always be truths of the universe that are unable to be fully represented within a physical model of the universe.

There are more things in heaven and earth, Horatio,
Than are dreamt of in your philosophy.