The whole world in His hands

"In some sense man is a microcosm of the universe;
therefore what man is, is a clue to the universe." ~ David Bohm

 

 

 

 

So yesterday we talked, not especially transparently, about how one goes about deconstructing oneself in order to mirror the world around one. We didn't really get into the why of it - curiosity about the transcendental seems both an incongruously casual aim for such an all-encompassing task, and to some extent a mismatch of concepts (how can one be curious about a subject one cannot intellectually grasp?) - and we aren't going to today, either. Why is a very important question; in fact, it may be the only question, but it's off-topic (is it?).

 

We're going to dodge 'why' for the moment because the transcendent doesn't truck with why. The question denotes purpose - which can have meaning only in the context of an outcome state different from the present state (that's actually too simple; conservatism is a legitimate purpose if its viewed as opposing an organic trend in the current metastate towards transformation, although the subtle difference between the two may only be apparent to a sufficiently Zenoic examination). The transcendental, which is always everywhere equally immanent upon the subjective, has no purpose - all possibilities are equally within and beyond the transcendental.

 

We're instead going to look at what, which is to say we're going to consider identity again. Specifically, we're going to consider identity from the perspective of the transcendental, which means we're going to indulge again in vague analogies. We'd mentioned the Aleph, the point that contains the whole universe; that represents one extreme of the possibility space (if we suspend for a moment our bourgeois notions about particles sharing space and time coordinates - think of it as a Paulian conversion). But for a probability space to exist, it has to contain all the possibilities. The mirrors we talked about yesterday clearly lie some way along a continuum from the universally accessible max-local Aleph to the locally accessible universal mirror (the parasimplex). There should, indeed, be a far limit to that continuum: the point which doesn't partake of the universe at all, the transcendent immanent upon the void. We call this singularity, and it's another terrifically useful and important concept that we'll hit up in another metanow.

 

We could advance the hypothesis that every entity in the apparently objective universe around us lies somewhere upon this continuum - but then the transcendental would be immanent upon the objective as well as the subjective, which would mean that objective and subjective map perfectly across the transcendental (it has to be across the transcendental, because objective and subjective are necessarily estranged). It is certainly possible that such a perfect mapping exists, but there is no reason why it must; accordingly, the transcendental may indeed be immanent upon such perfectly-mapped objectives and subjectives, but should also be immanent upon the conceivable subjective which maps to nothing objectively real - to rephrase, the transcendent immanesces upon impression and idea alike.

 

And this means that there can conceivably exist in the world objects which are merely objective; objects which are merely subjective; and objects which partake of the character of the Aleph, and in some fashion bridge the divide between the two. And that means that what we talked about before, about making ourselves a mirror, might really be overcomplicating things. It might be simpler to find a thing, or a system of things, that offer us a different sort of mirror. And the reason it might be simpler is that the transcendental is right there in all of us, in the process by which we interrogate the world.

 

But we'll get to that, in the next cycle. 23, skidoo!

 



Zenophilia

"Never confuse motion with action."

~ Benjamin Franklin

 

 

 

 

Zeno of Elea anticipated many of the points I've touched upon over the preceding few posts in formulating what Bertrand Russell described as "immeasurably subtle and profound" paradoxes. Zeno was a Parmenidean philosopher, who shared Parmenides' belief that "All is One;" his paradoxes challenge the notions of Time and Space and the existence of entitites within them.

 

His 'Paradox of Place,' for example, is both a Platonic Form of the self-reference paradox and, paradoxically enough, a refutation of the Platonic Theory of Forms:

 

"If everything has a place, then place itself has a place, and so on ad infinitum."

 

He similarly challenges Time in the Fletcher's Paradox:

 

"If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless."

 

In fact, elsewhere in his writings, Zeno demonstrates that not only is it impossible to move, it is impossible to start a journey or to reach a destination. Yet it is even more clearly demonstrable that motion occurs and that physical entities undergo motion travelling from place to place.

 

Intriguingly, advances in quantum physics suggest that apparent motion - and even more importantly, apparent lack of motion - are both not as straightforward as they seem. A famous experimental result, Young's Double-Slit Experiment, proves that light operates as a wave; Einstein's Nobel-Prizewinning verification of the photoelectric effect proves that it operates as a particle. The fundamentally paradoxical notion of wave-particle duality, which follows from these two results and leads to a bizarre conception of matter as a measure of quantum interference patterns and mass as a byproduct of collisions with Higgs bosons - all of this is just another paradigmatic way of representing the Parasimplicity Principle.

Wheels within wheels

“Clouds are not spheres, mountains are not cones, coastlines are not circles,
and bark is not smooth, nor does lightning travel in a straight line.”
~ Benoit Mandelbrot

 

Of course, there’s more to mathematics than numbers. Mathematics is a way of modeling reality, and there are a range of approaches to that modeling. One of these is to simply interrogate some aspect of reality, and attempt to devise a representation that models the result.

The French mathematician Benoit Mandelbrot took on the formidable challenge of modeling the physical contours of things in the objective realm. He pursued a method of modelling the shapes of clouds and mountains and coastlines, which were not immediately apparent as obeying any coherent mathematical principle. In 1967, he published a paper that asked the innocuous question “How Long is the Coast of Britain?” – it was to prove revolutionary, and would give rise to the concept of fractals. This concept is very important to my own parasimplistic worldview, but of course it has far more important implications than that.

Coastlines, it turns out, are tricky things to measure. If one attempted to measure the coastline in units of, say, 10-meter lengths – approximating the actual contours of the coastline – one would find a shorter result than if one used 1-meter lengths. The 1-meter lengths would give a better approximation, and would be longer as a result. In fact, as Mandelbrot’s paper illustrated, the shorter the unit of measurement becomes, the longer the overall measurement becomes. In the limit of an infinitesimally small unit of measure, the coastline of Britain becomes infinite.

This might seem at first blush to be absurd, but Mandelbrot expanded on this result to show its consistency with a whole family of known mathematical relationships that exhibit the property of self-similarity – that is, the curve viewed at a large scale resembles the same curve at successively smaller scales. With a self-similar curve modeling variable x against variable y, the appearance of the curve between, say, 1 and 2 will be the same as the appearance of the curve between 1.0 and 1.1, or between 1.00 and 1.01, or at any smaller scale of measure. Such curves are said to have a Hausdorff dimension between 1 and 2 – the upper bound, curves of Hausdorff dimension 2, are known as Peano curves and have the property on successive iteration of completely filling the space over which they are measured, after the fashion of a ‘Greek key’ motif. Moreover, Mandelbrot listed several examples of naturally occuring self-similar relations – famously including the leaf fronds of ferns.

Mandelbrot was, like most mathematicians, building on the work of predecessors (including in this case Lewis Fry Richardson, who had tackled the coastline paradox himself and posited a mathematical law governing coastlines that foreshadowed Mandelbrot’s result that coastlines were self-similar). The focus of his 1967 paper, which was to form the basis of his work until his death of pancreatic cancer in 2010, was actually a modern application of a very ancient paradox proposed by the Greek philosopher Zeno of Elea – the dichotomy paradox, famously elaborated in his paradigm of a race between Achilles and the tortoise. Zeno’s paradoxes give us a useful structure for considering parasimplicity and being-in-time (what Heidegger refers to as Sein-in-der-Welt), and we will be returning to them.