Zeno’s paradox revisited

Sitting in Tokyo over an innocent bowl of sake, my philosopher friend from London brought up Zeno’s paradox. Damn philosophers. Always something. He knows more about ancient Greek philosophy than I do, but let me have a go at it from the poet’s side of the field.

Space

I guess Zeno’s paradox (5^th century BC) comes in various forms, but I think of it in terms of space. Paradoxically, mathematically, motion is impossible. To move from point A to point B, we have to cross midpoint C. But to move from point A to midpoint C, we have to cross midpoint D. Etc. But since simple geometry tells us that there are an infinite number of points between any two points, we can never get to the nearest midpoint.

Or forget about midpoints. In order to move we must cross an adjacent point. But there are an infinite number of points between us and any adjacent point. In today’s computer programming lingo, we’d have to execute an infinite number of tasks before reaching the adjacent point, which is impossible.

There are only two conclusions I can draw from the paradox. Either it shows us that motion is truly impossible or it shows us the limits of logic – that logic can solve a lot of local problems but there are points at which it fails as a conduit of knowledge and results in an absurdity.

Time

My tipsy interlocutor pointed out that the paradox works along a time axis as well. The idea of a linear flow of time is equally impossible, as we’d have to move past the adjacent moment, which is impossible. However, conceptualizing it along a time axis opened a different tangent of thought for me.

My more devoted readers will note that I’ve looked at the following William Faulkner quote HERE as a way of theorizing time:

“The past is never dead. It’s not even past” (Requiem for a Nun, 1951).

Pondering the Faulkner quote led me to consider that our conventional way of looking at time – with the past as a thread disappearing into some distant place that no longer exists – is actually counterintuitive. Doesn’t it make more sense to see the past as something very much still with us, but at a depth, providing the real-time substructure of the present, just as the rings of a tree do not disappear as years go by but rather continue to provide the real-time substructure of the tree? In the same way, the “past” is not gone, but is right here, at a depth, providing in real time all the folds and substructure without which the present would collapse.

So if Zeno’s paradox suggests that we cannot move along a linear path of time, does the tree ring model of time show us a way out of the paradox? On the one hand, it seems to do so, as it shows we can conceptualize the manifold of time without requiring a linear flow. On the other hand, we still need some kind of wiggle room, as time, though not extending backward into some now-absent past, does recede to the center (of the tree) or the depth (on which the present stands). Would Zeno be able to grant us so much without giving up his precious paradox? To untie this further knot in the fabric, we need a to add a third category to space and time. And here it comes …

Imagination

Kant, in the Critique of Judgment (1790), speaks of the dynamical and mathematical sublime, and makes a rigorous case for the power of human reason as the sublime human faculty. In the mathematical sublime, for example, we might look up on a starry night and imagine how many stars are up there. The imagination, however, can only stretch so far and is overwhelmed by the sheer numbers in the scenario at hand. Reason, however, can step in and calculate numbers beyond what the imagination can fathom (estimating that there are something like 10²⁴ stars in the universe). It is reason that inspires the highest awe in Kant.

Now let’s use Zeno to turn Kant on his head. Reason leads you down the rabbit hole of Zeno’s paradox, and there you get stuck. No motion. But where reason folds into absurdity, imagination steps in and liberates us. We imagine ourselves in motion. We imagine ourselves moving through time. And if reason can’t back that up, that’s reason’s problem. And if the flow of our experience into the future is an imagined flow, so much the better. Without imagination, perhaps Zeno’s paradox would hold. Reason is trapped in what is; and what is, is fixed. The world as a static object of knowledge. But imagination is the one faculty that allows us to project and manifest all manner of possible futures. Imagination creates destiny, and imagination is what moves us toward that destiny.

So philosophers and scientists, keep up the good work but go to the back of the bus. Poets, artists, and mythmakers, move forward.

“In art and dream may you proceed with abandon” (Patti Smith)

“Imagination is more important than knowledge. For knowledge is limited, whereas imagination encircles the world” (Albert Einstein)

“Artists are here to disturb the peace” (James Baldwin)

Now for my real poetry, click the book cover below.

mountain lantern light
breaking through bamboo and ice
a thousand angels

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Necessity and Becoming

Paul Adkin’s blog entry on logical necessity in the universe got the amateur philosopher in me thinking. Maybe it’s true that the processes of the universe work by logical necessity – generally – but maybe there’s always a small gap in the field of necessity. If the logical necessity were absolute, everything would be absolutely fixed – no possibility of transformation, of evolution*. But that little gap in the system, the space of anxiety, of longing, is the source of all becoming. And where the power of logical necessity fails within that gap, the power of imagination steps in to fill the void. After all, if logical necessity allows us to explain what is, imagination allows us to envision what could be. It’s my name for what Paul calls “the power to transform” reality. Or, to use Paul’s other term, “embellishment,” let’s say the universe is characterized by 99% necessity and 1% embellishment, but that 1% embellishment – that’s where all the action is – all the longing, anxiety, subjective and intersubjective joys and pains of becoming – i.e., all of what gives our lives value. Maybe I could substitute “consciousness” here for “imagination.” But where the intellect might prefer “consciousness,” the child in me prefers “imagination.” The child in me always wins 😊.

*Maybe, in a way, evolution is an ongoing negotiation between those processes that operate by logical necessity and the processes that rupture the necessity and push laterally, allowing for freeplay and divergence.

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Break the left-right paradigm

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(Click covers for links)

              

Purposiveness and Imagination

Blogmate Paul Adkin has been posting on becoming and purposiveness lately, so I thought I’d chime in.

Stasis and change. This duality has puzzled brains since the ancient Greeks, if not the primeval mind itself. The laws of physics give you the “how,” but what about the “why”? Why all this movement from one state to another? In our own lives, we can call it “purposiveness.” We might not have a definite destination (or a definite purpose) in mind, but movement is always movement toward a destination, however unspecified.

If “purposiveness” characterizes our movements, or changes in state, “imagination” is the best term we have for the force that drives the changes. Imagination is our capacity to project beyond the immediate real, the here and now of our existence. We can anticipate possible futures, reflect on things remote in time and space or visualize things that seem impossible in real time and space. All the possibilities and impossibilities that are not in our immediate sensory arena. That is the scope of imagination. In this sense, it is the source not only of the arts but of scientific investigation in its theorizing mode. Indeed, the quest for knowledge generally is driven by imagination, a reaching out in the mind to grasp what cannot be presently grasped. The scientific method is nothing but imagination systematized.

One might propose a cognate force in the physical universe (or in that aspect of lived reality that we, imaginatively, call the physical universe). As the seed becomes the tree, as mountains rise and fall, as the solar systems steady into their fixed movements, as black holes expand their mass and devour matter, always this drive to change from one state to another. Why? An intelligent God or anthropomorphic consciousness might be too much to swallow, but the laws of physics express a kind of purposiveness, a method to the continual striving from one state to another. And if imagination is the force behind the striving in our little lives, is it too far of a stretch to assume that the same force is behind the striving enacted by natural processes?

I’ll take Occam’s Razor on this one. If there are two ways to explain a phenomenon, start with the simpler, the one that requires the fewest assumptions. Assuming that the same force that drives the trajectory of our lived reality drives the movements of the (purportedly) physical universe is simpler than assuming that there are two separate but remarkably similar forces driving changes in the two (artificially) separate spheres.

Of course, everything could be entirely random. But my imagination tells me otherwise. The capacity to project and orient toward possible futures and possible outcomes, toward fantastic visions and goals at a distance from present reality – that capacity seems to throw a monkey wrench into the randomness. And once you throw in the monkey wrench, where does it stop?

x x x

Urge and urge and urge,
Always the procreant urge of the world.

Out of the dimness opposite equals advance, always substance and increase, always sex,
Always a knit of identity, always distinction, always a breed of life.

To elaborate is no avail, learn’d and unlearn’d feel that it is so.

Sure as the most certain sure, plumb in the uprights, well entretied, braced in the beams,
Stout as a horse, affectionate, haughty, electrical,
I and this mystery here we stand.

(Walt Whitman, Song of Myself)

(Click images below for links)

                     

The Life of the Bee

Naturalists just don’t write with the same style and imaginative power as they did 100 years ago, as in this excerpt from “The Life of the Bee” (Maurice Maeterlinck, 1901).

x x x

“The queen started laying again in the first days of February. The workers have flocked to the willows and nut-trees, gorse and violets, anemones and lungworts. Then spring invades the earth, and cellar and stream with honey and pollen, while each day beholds the birth of thousands of bees. The overgrown males now all sally forth from their cells, and disport themselves on the combs; and so crowded does the too prosperous city become that hundreds of belated workers, coming back from the flowers towards evening, will vainly seek shelter within, and will be forced to spend the night on the threshold, where they will be decimated by the cold. Restlessness seizes the people, and the old queen begins to stir. She feels that a new destiny is being prepared. She has religiously fulfilled her duty as a good creatress; and from this duty done there result only tribulation and sorrow; she will soon be forced to quit this city of hers, where she has reigned. But this city is her work, it is she, herself . . . . She has peopled it with her own substance; and all who move within its walls – workers, males, larvae, nymphs, and the young princesses whose approaching birth will hasten her own departure …

“What is this ‘spirit of the hive’ . . . that after the queen’s impregnation, when flowers begin to close sooner … will coldly decree the simultaneous and general massacre of every male? It allots their task to the nurses who tend the nymphs and the larvae, the ladies of honour who wait on the queen and never allow her out of their sight; the house-bees who air, refresh, or heat the hive by fanning their wings, and hasten the evaporation of the honey that may be too highly charged with water, the architects, masons, wax-workers, and sculptors who form the chain and construct the combs, the foragers who sally forth to the flowers in search of the nectar that turns into honey, of the pollen that feeds the nymphs and the larvae, the propolis that welds and strengthens the buildings of the city, or the water and salt required by the youth of the nation. Its orders have gone to the chemists who ensure the preservation of the honey by letting a drop of formic acid fall in from the end of their sting; to the capsule-makers who seal down the cells when the treasure is ripe, to the sweepers who maintain public places and streets most irreproachably clean, to the bearers whose duty it is to remove the corpses, and to the amazons of the guard who keep watch on the threshold by night and by day . . . .

“Finally, it is the spirit of the hive that fixes the hour of the great annual sacrifice to the genius of the race: the hour, that is, of the swarm; when we find a whole people, who have attained the topmost pinnacle of prosperity and power, suddenly abandoning to the generation to come their wealth and their palaces, their homes and the fruits of their labour; themselves content to encounter the hardships and perils of a new and distant country.”

x x x

x x x

                     

 (Click images for links)

Artificial intelligence and human experience

1. Anticipation and Fulfillment in Visual Perception

Reading an interview with philosopher Michael Madary, I was thinking as so many do about how far artificial intelligence (AI) can go in mimicking the human experience. Madary’s bailiwick is philosophy of mind and the ethics of emerging technologies, especially virtual reality. The interview focuses mainly on Madary’s anticipation and fulfillment model of visual perception. The basic model, it seems to me, is equally applicable to human or AI behavior; i.e., visual perception as proliferating perspectives across time. You first see the object from one limited point of view. To truly grasp it, though, you need to anticipate what it looks like from additional perspectives. You move around, double-check, and your anticipation is more or less “fulfilled” or verified. Then the point of fulfillment becomes a starting point for next stage of anticipation, etc. Visual perception is this process of constantly accumulating perspectives, ever absorbing regions of indeterminacy into determinacy, ever approximating an unreachable objectivity of perspective.

It seems AI should be very good at all of this. So what, if anything, about human reality does AI miss? Is it that there is no psychological reality corresponding to the process as AI executes it? Can the distinction of the human’s psychological reality be evidenced? Is it manifest in the idea of motivation? AI can execute the same process but has a different (or absent) motivation vis-à-vis the human counterpart? The human viewing a modern sculpture from different perspectives may be seeking aesthetic beauty or pleasure, which would seem beyond the scope of AI. Although local human actions may mimic AI processes, it may be that the ultimate motivation behind human action in general falls outside the scope of AI – let’s call that ultimate motivation happiness (following Aristotle) or the satisfaction that comes with living a good life (following Plato); is there any comparable motivation for AI?

2. Transcendental Fulfillment

Or how about this take on the AI/human difference. What humans are always seeking, the grand dream under it all, is fulfillment liberated from the anticipation-fulfillment cycle, a sense of contentment that gets us out of the rat race of endless desires and partial fulfillments. For a correlative to the visual perception model, picture yourself gazing at a painting, motionless, without any interest in increasing perspectives, just having the static fulfillment of the beauty in front of you for a certain duration of time. What elapses in that duration of time may be an expression of the thing that is inaccessible to AI. What humans really want is not a sense of fulfillment that is indefinitely deferred by endlessly proliferating perspectives – the never-ending drive for more data that might occupy the AI entity. We want THE sense of fulfillment that comes when you opt out of the cycle of proliferating perspectives, a sense of fulfillment that transcends process. So whereas the anticipation-fulfillment cycle is an end in itself for AI, for humans all such processes are instrumental; the end in itself, that end which motivates the whole process, is that which falls outside of the process, a kind of static contentment that in inaccessible to the AI.

3. Singularity, or Singularities

The concept of singularity might help to clarify the distinction between fulfillment embedded in the anticipation-fulfillment process and transcendental fulfillment, fulfillment liberated from the cycle. Transcendental fulfillment is, let’s say, a metaphysical singularity – the space of infinite oneness alluded to by many philosophers and mystics, indicating escape from the rat race. Compare that to technological singularity, the critical mass at which artificial superintelligence would eclipse all human intelligence, rendering homo sapiens superfluous. Perhaps fears about the technological singularity, about an external AI dislodging us, are misplaced. I will tentatively side with those who say that computers do not really have their own motivation, their own autonomy. The risk then is not of some external AI overtaking us; the risk lies rather in the porosity between human reality and AI. The risk is not that AI will defeat us in some battlefield Armageddon but rather that it will bleed the life out of us, slowly, imperceptibly, until we go limp. We have already ceded quite a bit of brain activity to the machine world. We used to have dozens of phone numbers in our heads – now all stored in our “external” brains.” We used to do a lot more math in our heads. (Try getting change today from a teen worker without the machine telling them how much to give.) World capitals? In the external brain. City map layouts in one’s head? Replaced by GPS real-time instructions.

“So what?” students today might say. “Memorizing all that stuff is now a waste of time?” And they may be right. But as the porosity increases between human reality and the computerized ether we live in, we cede more and more of our basic survival skills to the ether. I don’t expect malice on the part of AI (although the HAL 9000 was a cool concept), but there may come a tipping point at which we have ceded the basic means of species survival to the machine world. And in ceding more control of our inner lives to the external brain, we become more embedded in the anticipation-fulfillment cycle. Even basic human activities take on a query-and-report format. It becomes increasingly difficult to “opt out” of the processing apparatus and find that space of reflection that transcends the endless proliferation of future-directed perspectives.

4. The Historical Side: Dystopic or Utopic

All this talk about homo sapiens being bled out sounds quite dystopic, and perhaps dystopia is the endgame. But not all possible futures are grim. First of all, in structural terms, porosity is two-directional. Ever since the invention of writing, we have transferred information into the external media of books, giving subsequent generations the capacity to “upload” that information and store it in their brains when the books are removed. This prompted Clark and Chalmers, as far back as 1998, to theorize about the “extended mind,” in which the space of the mind is shared by internal processes and environmental objects that work in tandem with those processes. Another parallel is in Wittgenstein’s Blue Book example wherein we use a color chart until we “learn” our colors, and then throw the chart away. In these cases, the external device provides intermediate information storage. We use the Internet in this fashion all the time. Nothing dystopic here. But is it different when the device becomes capable of evolving its own algorithms, generating its own information, and using it to implement tasks that go far beyond mere storage? Perhaps so, but it is not yet clear that the dystopic end is inevitable.

Second of all, in terms of social implication, technology could free us up to spend less of our lives on drudgery and more of our lives in that reflective space of self-fulfillment, working out our own electives of self-realization. Indeed, this is the signature promise of technology in the age of capitalism. Ever since the early 19^th-century Luddite rebellion, technology has repeatedly made this promise and repeatedly failed to deliver. Why would it be any different now? It could only be different if there were a fundamental shift in our perspective of what it is to be human.

When Madary exemplifies his visual perception theory with the example of a modern sculpture, he introduces what for me is the wild card in the anticipation-fulfillment cycle: the element of surprise.

“Recall a situation in which you moved to gain a better perspective on a novel object and were surprised by how it appeared from the hidden side … Modern sculpture can be helpful for illustrating visual anticipations because the precise shape of the sculpture is often unclear from one’s initial perspective. Our anticipations regarding the hidden side of a modern sculpture tend to be more indeterminate than our anticipations about the hidden sides of more familiar objects.” (Madary)

Whereas I started out by saying that Madary’s anticipation-fulfillment model of visual perception applies equally to AI and humans, I suspect we might handle the element of “surprise” differently. In the case of humans, “surprise” is a trigger for imagination, a less tractable faculty than might be intelligible to our future friends in the AI phylum. Sure, our AI compatriots might predict possible futures as well or better than we do (and thus they might best us at chess), but is that really “imagination”? Humans imagine not only possible futures, but also alternative presents and alternative pasts, using self-generated imagery to feed nostalgic visions of times gone by. There is something about the creative process of imagination that might separate us from AI and might make us less predictable in the event of “surprises” or disruptions in the normal anticipation-fulfillment process. Since technology has typically failed to deliver on its promise to enhance self-fulfillment time for personal development, we might anticipate another failure when technology says that AI will truly free us up from drudgery. But the result could be different this time if a rupture in conditions is great enough. Imperatives of income inequality and ecological destruction might be rupture enough. As we survey our predicament the way Madary’s viewer surveys the modern sculpture, we might on the other side glimpse the end of capitalism (which may sound dramatic, and yet all ages do end). Perhaps this might jolt the imagination to a new sensibility, a new subjective frame of reference for values like “work” and “technology” and “success” and “self-actualization” – to wit, a new definition of what it means to be fully human.

How rapidly and wholly we make that turn to a new definition of what it means to be fully human will lock in the dystopic or utopic endgame. In the dystopic version, homo sapiens is bled out by some combination of AI and economic and ecological calamities. In the utopic version, consciousness about what it is to be human evolves quickly enough to allay those calamities and to recapture AI as the servant of human ends and not vice versa.

Footnote on Kierkegaard’s 3 modes of lived experience: aesthetic, ethical, religious

The anticipation-fulfillment model of visual perception can be seen as the basic process of Kierkegaard’s aesthetic mode, sensory-based life. A whole life lived on the aesthetic level is lived as a continuous accumulation of equally ephemeral sensory perspectives on one’s own life.

The ethical life turns out the follow the same model but on the ethical level. The ethical life is a continual accumulation of equally provisional ethical perspectives.

The religious life, though, breaks the model. It concerns the absolute. It does not consist of accumulating perspectives but of a singularity; it eschews all the accumulations of visual or ethical perception for the singular relation between the religious subject and the absolute, a singularity which obliterates all mediate or quantitative concerns.

Michael Madary’s Visual Phenomenology

Richard Marshall’s interview of Michael Madary in 3:AM Magazine

                

 

Imagination’s role in all of this

The question: Is “reality” is limited to “all things that are actual” or does it include “all things that are possible”?

As in a previous fine entry on the topic, full of pith and wit, I choose the more inclusive definition.

If all possible futures were not part of the fabric of reality, imagination itself would not be possible.

It is, so they are.

An analogy: Microorganisms in the human body outnumber human cells 10-to-1; without those microorganisms, the human body’s ecosystem would collapse, or more accurately, would never have existed. It may be the same with possibilities folded into the world of actuality.

Here’s an article that looks at the topic from the point of view of quantum physics:

Quantum mysteries dissolve if possibilities are realities

Thanks to Wayne.

 

 

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)