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.

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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.