A brief history of space

If Stephen Hawking could write A Brief History of Time, I can surely write a brief history of space. Indeed, I’ll one-up Hawking and make my monograph actually, and not just putatively, brief.

At first glance in our little history of space, we can follow a trajectory from Democritus and Plato’s view of space as a container, to a view of space as a relation between things rather than a container (Leibniz), and finally to a view of space as a purely subjective construct – a way of organizing the world rather than a thing in the world (Kant – and I’ll welcome comments from expert readers like the ever-helpful STEVE MORRIS on the extent to which this continues into Einstein and modern physics).

Democritus and Plato both saw space as a receptacle but in quite different ways. Democritus (5^th century BC) famously said, “Nothing exists except atoms and empty space.” This sense of space as a universal void is perhaps still the most common sense of the term. In Timaeus, Plato specifically calls space “a receptacle,” but he seems to mean it in a more local sense, as that which houses a series of shapes. In a weird way, space is matter to Plato, per his example of gold. You see now a pyramid of gold, then a cube of gold, then a sphere of gold. The gold is the receptacle space inhabited by the succession of different shapes. Idiosyncratic maybe, but more of that later.

As we move toward what I perhaps simplistically call the Leibniz position, space is not a receptacle at all – not the local matter that houses shapes nor the void. It is rather a relation between things, and it has no existence other than as a relation between things. Then onto Kant, and space as purely a subjective way of organizing the world. It seems at this point that we’ve come a long way from Plato, but the canny Greek has a way of coming back (nb. Alfred North Whitehead’s comment that all of Western philosophy is “a series of footnotes to Plato”).

I’ll step back to Plato by way of a convenient half-way point – Boethius (late 5^th/early 6^th century, on the cusp between classical and post-classical culture, roughly 1000 years after Plato and 1500 before us). To quote my fine former post on Boethius, who wrote The Consolation of Philosophy while in prison pondering his forthcoming execution, “The relationship between the ever-changing course of Fate and the stable simplicity of Providence is like that between reasoning and understanding … or between the moving circle and the still point in the middle.”

That image of the circle, of seeing reality from two points of view – the still point in the middle and the moving point along the perimeter – can be applied to both time and space. Here, it more directly applies to time. From the point of view of eternity (the still point in the middle), all things are simultaneous. From the temporal point of view (moving along the perimeter), we see reality in its aspect of “always becoming,” as philosophers have called it.

To extrapolate, from the eternal point of view, time does not exist; similarly, from the infinite point of view, space does not exist. Rather, space only exists where that dynamical relation between things exists – distance and extension only make sense within the scope of finite reality.

So is Boethius the great Hegelian synthesizer who can push the dialectic between Plato and Kant forward (thesis – antithesis – synthesis)? Or is the double vision of Boethius merely an indicator of his historical moment, one foot dancing with the wine-bibbing Greek and the other tiptoeing toward the finicky Prussian? Is he just a midway point toward our more accurate modern view?

No, the midpoint reading won’t do. On some level, Plato anticipated the whole circus. Or, to further twist the metaphor, we have circled back to Plato. In the Timaeus, Plato, like Boethius, has a double view, though it plays out a little differently. In Plato, there are two primary levels of reality (which can be further subdivided, as in the myth of the cave): “that which always is and has no becoming” and “that which is always becoming and never is.” The realm of eternal, unchanging ideals (being) is the subject of rational knowledge, whereas the visible world of the senses (reality in its aspect of “always becoming”) is the subject of empirical knowledge. Plato notably privileges the rational side, but he at least here grants the empirical its purview. And this turns out to be crucial to our present argument.

If we focus the history of ideas on the world of becoming – the physical world, we might call it – we can, to recap, follow a movement from space as a container to space as a relation between things  and finally to Kant’s purely subjective construct.

But if we look at the other realm in Plato, the realm of being, the intellectual realm of the unchanging ideals, rather than the realm of becoming, we see that he had already recognized space as an imaginary construct.

He quite explicitly says that the concept of “space” does not apply in the intellectual realm, but is only needed to accommodate the dynamics in the realm of becoming.

Indeed, some time after introducing those two realms (the realm of being and the realm of becoming), he refers back to the two natures corresponding to the two realms: “one … was a pattern intelligible and always the same; and the second was only the imitation of the pattern, generated and visible.” Then he adds: “Now a third must be revealed … the receptacle, and in a manner the nurse, of all generation,” insofar it enables all the processes of generation or becoming to happen.

The “receptacle,” whether you call it space or matter, is only introduced as a way of explaining processes in the realm of becoming.  But the realm of becoming for Plato is the realm of more-or-less degraded knock-offs from the realm of being. When reality is seen in it most true and stable aspect, the ontologically prior realm of being, space (or matter) does not exist.

Now, one could argue that the spaceless, timeless, immaterial zone of true reality (prior to all the knock-offs in the realm of becoming) in Plato is not truly subjective as in Kant, that Plato imagines this reality as objective reality. To which I say, maybe. I’m not sure how truly significant that distinction is. I don’t think Plato would call it objective in the modern sense of objective (which implies physical, spatial reality). All Plato postulates is that the spaceless, timeless realm of pure being, pure forms, is the true base of reality. That he treats it as an intellectual realm as opposed to the sensible is clear – so does that imply that it IS subjective, as in Kant? I’m not sure but, back to Alfred North Whitehead: we are quibbling about footnotes here. Face it, everyone (especially angst-ridden academics seeking tenure) wants to find the next ground-breaking idea, but it’s still hard to beat the old Greeks. See my other fine post on Aristotle, Wittgenstein, and Identity Politics if you don’t believe me.

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Particles and Swarms

Does anyone know about particle swarm theory? It seems close to a unified theory of everything. Or at least like a pebble whose waves ripple through everything – biology and computer science, quantum physics and relativity, metaphysics and religion.

Basically, it says that independent particles form swarms, wherein each particle spontaneously takes advantage of the experience of the entire swarm. Examples in the natural world include fish schooling, bird flocking, and ant colonies. Swarm intelligence (SI) has apparently (I’m no expert) become increasingly important in artificial intelligence and robotics.

Can this bridge the persistent gap between the predictions of relativity and those of quantum physics? The problem as I see it is that relativity assumes a universe with physical matter of determinate location and mass. Quantum theory says that when you get down to the building block elements in the atom, units of matter no longer have such determinate values, but can only be described in terms of clouds of probability.

The relativity/quantum theory discrepancy has been scrutinized lately by “oil drop experiments” and “pilot waves.” It seems that you can drop oil on a liquid surface and as it bounces along, it interacts with its own ripple waves, creating a pilot wave that resembles the blur that quantum physicists see when they look at an electron or elemental particle – this would mean (I think) that underneath quantum physics is a stable physical reality after all.

So what if you looked at all the fundamental particles (or waves or whatever units you prefer) of the universe together as a swarm, all those pilot waves interacting, the every move of each affected by the every move of all the others, all one singular pattern of vibration? Do you get a 21^st-century physics that recapitulates Leibniz’s 17^th-century metaphysics of the indivisible unit, the monad? To wit, Leibniz:

“Each monad … adapts itself to all the others outside itself … This connection of all created things … the connection and adaptation of every single thing to all others, has the result that every single substance [every monad] stands in relations which express all the others. Whence every single substance is a perpetual living mirror of the universe … They are but perspectives of a single universe, varied according to the points of view which differ in each monad.”

From Leibniz, it is an easy step to the world view of the Eastern religions. This connectedness of all things, objective or subjective, expressed as material or expressed as Soul – is particle swarm theory the underpinning here also? And in that swarm lies an immanent intelligence, transcendent and mysterious to the individual, but not requiring any external or anthropomorphic god.

To shift from this synchronic view (how the swarm functions across the space of the many particles) to a diachronic view (how the swarm functions across time), the swarm is the intelligence that drives the trajectories of evolution, terrestrial and cosmic, or, more viscerally, all a singular shudder in some vast cosmic orgasm. A fifteen billion year–old orgasm, you say? Why not? From what I know of Einstein and Hawking, the universe may be one minute old from some other reference point, but only seem fifteen billion years old to us because we are near the event horizon of some black hole, where time becomes stretched toward infinity.

I am no expert in these fields, but I hope that my lateral thinking about them can stimulate a few thoughts. Even if I do nothing but stimulate streams of imagination, I hope that that in itself is no mean accomplishment.

“Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” (Albert Einstein)

The meme and the monad

Steve Morris recently posted a curious piece on the “meme.”   Evolutionary biologist, Richard Dawkins, coined the term in The Selfish Gene (1976). Predating the Internet, Dawkins’s interest was in how memes – units of cultural transmission – emulate evolution, with successful ones proliferating and duds dying out. Steve points out the irony that in today’s social media, it’s the most “unfit” memes – those that promote ignorance and bigotry – that seem to survive and proliferate. To enhance the scope of the entertainment, I’d like to weave in an additional discourse – Leibniz’s philosophy of the monad.

h/t: Dank an meine leibe Freundin, Claudia, für den Bild von Leibniz’s Hanover

 

As a 17^th-century German philosopher, Leibniz predated evolutionary biology as well as the Internet, but his speculative philosophy (the metaphysics of the monad) was grounded in his street cred as a mathematician and physicist, and perhaps for that reason it can sound eerily prescient of the holographic models of the universe about which today’s physicists speculate.

As in his mathematical theory of “infinitesimal analysis,”* which in the minds of many gave Leibniz a claim equal to Newton’s as the inventor of calculus, Leibniz sought to base his metaphysics on the idea of indivisible units. These indivisible units, “monads,” were “the elements of all things.” Because they are indivisible, they are in themselves inscrutable. “The monads have no windows through which anything can enter or leave.” After all, only a “composite” can add or subtract something, and the whole point of the monad is that it is a theoretical projection of the simplest, indivisible unit. (Mathematically, as far as I can understand Leibniz’s math, it is the unit that, having no increments, is by definition too small to ever be measured.)

Furthermore, each monad must be unique. For this, we need to get into the physics of space, according to Leibniz, of which I can only scratch the surface. For Leibniz, there is no such thing as empty space. There is only motion, rest, and change. And the fundamental unit of motion, rest, and change we call the “monad.” So there is no “space” per se, but there is a force field consisting of infinitesimal monads, each defined by inherent force, the qualities and laws of which are utterly inaccessible to the outside (no windows, remember). And the physics of the force field requires that “each monad while following its own inherent nature and laws adapts itself to all the others outside itself.” Each monad must by necessity fill a unique orientation point in the force field. And this is how Leibniz teases us to his logical (holographic) conclusion about the universe: “This connection of all created things … the connection and adaptation of every single thing to all others, has the result that every single substance [every monad] stands in relations which express all the others. Whence every single substance is a perpetual living mirror of the universe … They are but perspectives of a single universe, varied according to the points of view which differ in each monad.”

Leibniz’s holographic conclusion applies not only to the objective world but to the subjective one as well: “Consequently, everybody experiences everything that goes on in the universe, so much so that he who sees everything might read in any body what is happening anywhere, and even what has happened or will happen. He would be able to observe in the present what is remote in both time and space.”

The limiting phrase here is “he who sees everything.” This suggests that although each monad contains all the information to reconstruct the entire universe of which it is a part, it is no simple matter for us to decode that information. Only “one who sees everything” would be able to see the entire universe within the single monad. Each soul is limited in its self-discovery by its own orientation. Each soul “can read in itself only what is distinctly represented in it; it is unable to unfold all at once all its folds; for these go on to infinity.”

So back to the meme. Whether or not it expresses the evolutionary model of adaptation, does it express the mathematical/metaphysical model of the monad? Take as an example this meme that I sent around on the Internet.

The meme is not completely indivisible. There are letters and pixels and so forth within. But one could argue that the meme as a whole expresses one cultural orientation point, and that none of those simpler units is a cultural expression in the same way – they are not units in the cultural force field of the meme. It might lack the mathematical tightness that Leibniz would wish for, but perhaps that was Leibniz’s limitation. Math aside, it might be very useful to view the meme as a more-or-less simple expression of one cultural orientation point. To what extent is it in a holographic force field? With studious effort, one could certainly infer how the meme defines itself as a unit of force relative to the various positions staked out on gay rights. Perhaps from there, one could broaden the scope and see how the gay rights field of discourses illuminated by our monad-meme in turn illuminates all the discourses of sexuality implied thereby, not to mention various religions and philosophies and political formations at the perimeter, etc. Like ripples from a pebble dropped.

I think Steve is right about the meme’s relations to evolutionary biology. I have serious doubts about whether the Internet is predisposed to favor the “fittest” memes, unless we define “fittest” in an extremely idiosyncratic (and humorous no doubt) way. But the meme might express in its way Leibniz’s metaphysics of the monad. The holographic universe of the cultural dimension. And for those physicists who balk at the holographic universe, we give you the black hole. No, I am not inventing a new insult (“giving you the black hole”), although that in itself might be a tangent meme worth following. What I mean is this: Black holes are universally accepted in today’s physics, and what are black holes after all? Monads, universes unto themselves, with “no windows,” units of force that are utterly inscrutable and yet “perpetual living mirror[s] of the universe” around them. They might be like the mysterious “signs” in the modernist linguistics of Saussure and Wittgenstein, where words/signs have no “windows” to any referent in the world “out there” – there is no peephole into the system of signification – but each sign achieves a unique meaning relative to all the other signs within the system. Like signs in the linguistic universe, so black holes in the physical — monads, my friends, cosmic scale reflections of the sorry memes of which Steve Morris laments.

I once heard of an art historian who said, “Show me one artifact, one button, from a long-lost civilization, and given time I will reconstruct all the values of that civilization.” Academic bravado aside, this art historian was a monadologist par excellence, a believer in the holographic universe. Perhaps, when we are long gone and re-discovered by some future civilization, some wily future art historian might do me the honor of an infinitesimal analysis of my gay alpaca meme.

*The way I understand it, Leibniz’s infinitesimal analysis offered a solution to the age-old problem of rectifying curvilinear figures – squaring the circle – and thus rendering them accessible to precise geometric analysis. By casting the circle as a series of infinitesimally distant next points, Leibniz could in theory decompose any curvilinear figure into partial triangles.

Postscript: See this National Geographic article suggesting that our universe may exist inside a black hole, with many other inaccessible universes in their own black holes: