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)

Fallacies of Science

To the scientists in my circle: I’m more with you than you think. I don’t doubt for a minute the value of science. I find it absurd, e.g., that some people think religious texts can compete with science as a source of information about how the physical world works. But I like to amuse myself by playing watchdog for my scientific friends.

Even in my watchdog role, I can raise no objections to the scientific method, or to the analytical power that science has to unpack the facts and processes of the physical world. But as self-appointed guardian at the gates, I propose the following fallacies often committed by the scientifically-minded – all, again, fallacies of application or of scope, not intended to impeach the core value of the scientific method but to snap at the heels of scientists — and even our most admirable scientists like Neil DeGrasse Tyson and Stephen Hawking — when they make claims that go beyond the scope of their expertise.

The fallacy of metaphysical (external) scope

As I’ve argued elsewhere in this fine blog, science studies the “objective world” and has great analytical power within that scope. But science oversteps its scope when it claims that the “objective world” is the “real world period” and anything else is nonsense, thus implying that science is the one and only path to truth.

I propose that it’s misleading to call the “objective world” (which is the full scope of scientific inquiry) real or unreal; it is more accurately an abstraction from reality. There is no purely objective world just as there is no purely subjective world. Each is an abstraction from lived reality.

(Don’t the abstractions called “objects” in computer science suggest as much? A computer program at Tulane may, and probably does, have an “object” called Wayne xxx. This object is an abstraction that consists of a character string (name), numeric string (birthdate), etc. A different database—say that of the IRS—may also have an object called Wayne xxx but with different characteristics abstracted. The physical scientist, like the computer scientist, studies only those details relevant to his or her level of abstraction. But scientists sometimes forget this and make claims that go “beyond scope.”)

Just as the scientist elucidates valuable truths from her abstraction from reality (called the “objective world”), so might poets, philosophers, and Zen masters elucidate valuable truths from their abstractions from reality. It’s not at all clear to me that the subjective aspects of lived reality – art, justice, ethics, the felt joy of love and friendship, and the felt pain of loss and betrayal, are really reducible to (although they may be correlated to) scientific data about neurons. It’s not at all clear to me that the rich unconscious landscapes of Greek mythology or Blake’s visionary poetry, or the subjective-centered critique of empiricism in Kant’s philosophy, teach us less about lived reality than Darwin. To call the scientist’s abstraction of the world “the real world period” is to falsely assign it a metaphysical status, confusing one abstract way of looking at lived reality with the presumed metaphysical ground of lived reality itself.

The fallacy of substantive (internal) scope

Let’s look more narrowly at the role science plays within the scope of the objective world it studies. It mines and generates much knowledge about the physical world, and for that we are grateful. But how much of its substantive area does it really grasp? Even at its present power, it only nibbles the tip of the iceberg. Take the human body. Medical science knows much more about the body’s processes than it knew 350 years ago, when the Age of Science really started coming on line. We look back at the 17^th century as a kind of dark ages of leeches and blood-letters. Isn’t it obvious that science will expand its knowledge base just as rapidly, if not more rapidly, in the centuries to come? Won’t they look back at us with the same amusement, as a people nobly gathering knowledge but remarkably primitive in what we had gathered?

This telescopic view from the future should give us pause before we leap. Just a few decades ago, “science” was telling us that it could produce a baby formula more nutritious than mother’s milk. For every “well-tested” drug on the market, there’s a class action lawsuit addressing unintended consequences of that drug. One doesn’t have to be religious to believe that there is a vast (evolved) intelligence at work in the human body and in nature, and that science has only mapped a few percentage points of what is really going on in these systems. Don’t get me wrong – a few percentage points is better than no percentage points, and I’m all for science expanding its knowledge base. But when it comes to applying that knowledge, I take a humbler approach than some more eager proponents of science. The pro-implementation argument I most hear is that the things to be deployed have been tested exhaustively in study after study. Although this may be true, it is limited by context. If scientific understanding of its subject area (in this case the human body and the natural world) has leaped from 1% to 5% in the past few hundred years, it has still mapped just the tip of the iceberg, and still leaves enormous territory unexplored. So when you test exhaustively for results and side-effects, you are only really testing within the zone you understand. There are so many collateral aspects of human and natural ecological systems that are undiscovered that it is sheer arrogance to say that we’ve tested by 2015 standards and thus pronounce such-and-such safer and more effective than Mother Nature.

How does this translate to policy? If you have a serious illness, by all means draw upon that scientific knowledge base and try a scientific cure. If you have a less serious illness, you may be better off trusting to the body’s natural healing mechanisms, insofar science has only scratched the surface on how these mechanisms work, and tampering with biochemical processes may do more harm than good. I and everyone will have to judge this case by case, but by no means am I willing to conclude that science understands every aspect of how the body works and has therefore tested and measured every collateral effect for a particular drug or procedure.

On a tricky subject such as GMO foods, I am not as rabidly anti- as some of my hippie-ish brethren, but not as naively optimistic as some of my scientist friends. I like the idea of scientists building a knowledge base on this topic. But when it comes to implementation, I tend to keep one foot on the brakes, especially since radical changes can now be implemented globally and with much greater speed than in centuries past. I’m not at all convinced that science in its current state understands all the collateral processes of nature well enough to make the “exhaustively tested” claim. Or, to go back to our telescope of time, isn’t it possible that scientists 200 years from now will look back and shake their heads in amusement at our “exhaustively tested” claims?

And I haven’t even gotten to the corruptive influence of money and big corporations when it comes to what substantive areas of scientific inquiry will be funded and how results will be implemented. There may be something like a “fallacy of scientific purity” embedded here.

The fallacy of epistemological scope

Here, I use epistemology broadly as the quest for knowledge – almost, one could say, the quest for self-actualization that drives human reality, if not every aspect of reality. British Romantic poets will be my outside reference point here. The Romantics saw the development of self-knowledge, or self-actualization, in three stages. In Blake, these correspond to an Age of Innocence, Age of Experience, and an Age of Redeemed Imagination. In the Age of Innocence, we access knowledge through the fantastic mechanism of imagination, which keeps us in a state of wonder but leaves us naïve about the world and easily exploited. In the Age of Experience, we begin to access knowledge through reason and science, gaining factual knowledge that makes us less naïve and more worldly, but with that worldliness comes a cynicism, a sense of world-weariness, a sense of loss, of fallenness. Indeed, the Romantic world view at times seems to equate the world of Experience, the world of objective facts, with the world in its deadened aspect. The trick in Blake is to find the turn into a third stage, wherein the power of imagination re-engages at a mature level, re-animates the dry world of abstract facts, and saves us from the cynicism of Experience. In a word, we can put the scientific-type knowledge of Experience into perspective. We can still see its value but without being constrained by it in our quest for self-actualization. In Wordsworth’s “Tintern Abbey,” this plays out as the innocence of “boyish days” (73), experience “‘mid the din / Of towns and cities” (25-26), and the “tranquil restoration” of the mature poet (30). In the third stage, the sensory raptures of youth and the worldly knowledge of experience have both lost their traction. Specifically, the poet has lost the pleasure of immediacy but has gained the power of inward reflection. The “sense sublime / Of something far more deeply interfused” (95-96) is reserved for the third stage, and indeed is specifically used as a counterpoint to the sensory appreciation and worldly knowledge of earlier phases.

These 3 stages can easily be projected beyond the individual onto the cultural or even the cosmic screen. Blake, with his Jungian vision of the archetypal sources of consciousness, readily applies it to the cosmic level. I’ll apply it to the level of cultural history by saying that the Age of Science fits the second stage very well. Science emerged as the dominant epistemology around the late 17^th century, putting to bed some childish theories and introducing us to a more worldly-wise engagement with the physical world. Who knows when this Age of Science will end, but when it does, perhaps then we will enter the Age of Aquarius I’ve promoted only half tongue-in-cheek. And perhaps then we will look back at the Age of Science as Blake or Wordsworth look back at their middle stage – as an epistemological period that starts out liberating but eventually binds our imaginations, makes us a little cynical about the possibilities of self-actualization, chains us to what Plato calls “the prison-house” of materialism. So the fallacy of epistemological scope is the fallacy of myopically seeing only that force of knowledge that is present in the middle period, whereas true wisdom may be broader than that. It may be that the innocent child and the mature poet can grasp things about reality that are inaccessible to the purely scientific mind.

The watchdog sleeps

So those are my fallacy sketches for my scientific friends. Now pause and ponder.

 And if in your pondering, you find yourself viewing me with the gaze of the character above (provided by the talented Rachael Gautier), remember: When my watchdog shift ends, I’m more on your side than you think. At least you can take comfort that in the next U.S. election I will be voting for the party that takes science seriously and not the party that seems perpetually at war with science. Meanwhile, I’m happy to revise, especially if a particular Ukrainian physicist I know will home-brew another batch of Russian Imperial Stout to facilitate the review process.