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 (5th 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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The Language Matrix

When you ride the subways in Tokyo, it might strike you that the signs and the books passengers are reading require special language skills. The signs are sometimes written in Kanji, sometimes in Katakana (the two Japanese writing systems), and sometimes in English:

無料配達
むりょうはいたつ
Free Delivery

Sometimes they seem to mix Kanji (the one that looks like Chinese) and Katakana in the same message:

とは? 使い方や敬語表現

Also, the books are typically read in vertical lines, top to bottom, right to left, but the newspapers seem a fairly even mix of horizontal and vertical text passages.

I know little of Japanese languages and culture, but let my thoughts run wild for a minute. Learning from infancy to be equally comfortable in all these language systems – vertical readings, top to bottom, right to left; horizontal readings, left to right; Kanji and Katakana, separately and mixed; and English text and Western numerals as well – this must affect how your brain gets wired. It’s like language is a layered matrix with all these synchronized modes operating (or rapidly engaging and disengaging in the brain) at the same time.

Here’s a hypothesis. As I said, I’m a novice at Japanese culture, so my hypothesis may have some empirical support, may have no empirical support, or may, to the legions of easily mortified souls in today’s debauched intellectual climate, merely prove me an unregenerate racist. But it seems that if you learn language from the start as this kind of many-tiered system, your brain wiring will be really good at “matrix thinking” – math, manifold arrays of logic, etc. Rigorous might be the right word. A people raised in this kind of multi-dimensional language field should, by my hypothesis, be good at math, programming languages, etc. (not universally, but on average). When it comes to more chaotic, creative, rule-breaking, outside the box thinking – people in the US (in the aggregate) might have an edge. To wit, wiring your brain via language requires less rigor in the US, which means you’re wired less for rigor and more for open-ended thinking – more mistakes and more creative tangents.

Of course, none of this is meant to indicate universal traits but just a tendency on average to lean a little bit this way or that in your signature strengths as a culture. (Western Europe, in my experience, would be in between the Japanese and US poles, but maybe closer to the US side. I am not a psycholinguist. I base this on the purely anecdotal evidence of three years’ residence in Europe, 12 countries hitchhiked in Europe, and the half-baked ideas flowing through my brain as I sit here in a quiet neighborhood in Tokyo.)

If you think this is bad, you’ll hate my psycholinguistic foray into Mexican vs German and English language students.

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From Kant to Chomsky (with a plug for Fr–d)

h/t Matt McManus on Noam Chomsky’s Theory of Human Nature (04/16/20), from which much of this is taken

Descartes famously argued that all our empirical knowledge may be an illusion, so it can never provide a basis for absolute certainty. By contrast, we can be certain that we are thinking (“I think, therefore I am”), and so glean some certainty about the nature of cognition.

Kant goes a step further. True, all empirical knowledge may be an illusion, but there is a universal structure to the human mind by which we all perceive the empirical world in more or less the same way. E.g., all human beings see the world in terms of space and time. And since we see the world in the same way, we can gain knowledge that would be accepted by anyone. However, this doesn’t mean we gain knowledge of the world “in itself.” Our knowledge is only of the world as it appears to those structures of the mind (what Kant calls the “phenomenal world”). The world of actual things may or may not match the phenomena we experience, but we’ll never know.

Chomsky applies this toggle from empiricism to Kant to linguistics. McManus mentions how Chomsky’s linguistic theory (beginning in the late 1950s) pushed against such behaviorists as B. F. Skinner. Skinner and the behaviorists assume, like the old empiricists, that the mind is initially a blank slate, and only learns things like language from the experience of being taught. To Chomsky, this behaviorist/empiricist approach falters if we look at language acquisition. If we accept the blank slate premise, he argued, it leads to the conclusion that if one left a rock, a tomato and a baby with a family in London each of them would be equally likely to learn English, since each of them would experience being exposed to that language. The reason that a baby can pick up a language—even several languages—very quickly is that her mind is a priori capable of learning a human dialect. This language faculty also explains why human languages have many deep similarities. Not only do we largely perceive the world in the same way, as Kant points out, but our language faculty generates universal grammars, and much of Chomsky’s linguistic theory is about unraveling those universal grammars.

As with Kant’s theory, this position implies an upside and a downside. The upside is that human beings are capable of understanding one another, and even translating their various languages between each other. The downside is that we are still operating exclusively in the phenomenal world, as our mutual understanding, including cross-cultural communication, is based on the universal structures of how our minds process the world, not on any direct experience of the world “out there.”

I will go the extra step here and align Chomsky in this way with Freud. (As my loyal readers know, I am always eager to shore up Freud’s place in the history of ideas over and against his pitiful detractors, albeit with an occasional concession to those detractors.) What Chomsky rejects in the field of linguistics, Freud rejects in the field of psychology. The behaviorists shunned Freudian psychoanalysis, shunned talking about the internal structure of the mind as if there were something in there anterior to our experience of the world. As in Chomsky the mind has an a priori structure that facilitates language acquisition, so in Freud the mind has an a priori structure that facilitates similarities in development of the psyche across human populations. Whether you see that structure in terms of primitive drives along with mechanisms that develop to inhibit those drives, or as a gradient structure moving from the conscious mind down deeper and deeper into unconscious layers of motivation, Freud’s psychology and Chomsky’s linguistics both defy the “blank slate” theory by positing some internal structure, something intrinsic about the human mind, what Kant might call subjective universals that shape how humans process the world, irrespective of the range of individual human experiences.

In neither Freud’s case nor Chomsky’s, it seems to me, does this leave us with an either/or dilemma. Chomsky’s theory might well elucidate the universal grammars that provide the a priori capacity for language acquisition without demeaning the contribution of behaviorist methods on the other side. Likewise, behaviorist psychology might well provide a stimulus-response model that works quite well as a mechanical operation for changing behaviors, but I see no reason (other than that academics must endlessly produce us vs them models and show the superiority of their side over the other as a way of securing tenure) that this should preclude psychoanalytic investigations of the internal structures of the mind that might underwrite human possibilities, human creativity, and human pathways of dysfunction more generally.

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Approaching cosmic oneness

The opposite of oneness is categories. The human mind sorts the chaotic flux of reality into categories to render it intelligible. But pull out the dividers that sort the categories and what you have is oneness, or rather one continuous cosmic gradient. (In my experience, psychedelics like LSD and mushrooms are one way of pulling out the dividers but not the only way.)

Some cognates:

Before Freud, there was faculty psychology. The human psyche was composed of faculties: passion, reason, appetite, etc. – like separate boxes on a shelf. Freud (not alone but he’s the one that pulled it together) switched out this category-based model for something more fluid and dynamic – a gradient moving from the conscious mind down deeper and deeper into unconscious drives and mechanisms that exert enormous though unseen influences on our behavior. Though dismissing Freud is something of an international pastime these days, I think his model of the psyche, where old and unconscious impressions continue to affect behaviors later in life, was a remarkable paradigm shift that shaped the direction of psychology. It is still perhaps the prevailing model today, and indeed Freud’s detractors often use Freud’s depth psychology model in waging their attacks. Feel free to demur in the comments.

Or how about the four sheaths in Vedantic philosophies: physical, emotional, spiritual, and intellectual. They seem like four separate categories but isn’t it more intuitive to see them as part of one rainbow continuum? Think of the emotional and physical registers during sex. Surely they are part of one gradient of response and not separate categories, unless we deliberately separate them for the purpose of analysis.

Or how about space and time. They were generally considered two separate categories – either objective categories defining physical reality or subjective categories, as in Kant, by which we organize our experience of reality. But categories. Then Einstein. It turns out space and time are not categorically separate but are part of the same continuum. Same with energy and matter in Einstein. No longer separate categories but part of the same continuum. E = mc2.

There are probably a million other instances in the history of ideas, but the point is that categories help us sort, evaluate, and make sense of things, but the categories are not the things. In fact, there are no things. Just the one big cosmic Thing. The kaleidoscope of cosmic oneness, which is of course the same thing as the kaleidoscope of cosmic consciousness. The objective world and the subjective world fold into each other at the cosmic level. There is no other way. You don’t need LSD see your way through to this vision. Well, in my case maybe that LSD trip to a remote Mexican beach helped just a little, but that was almost an accident. Almost an accident. Maybe that’s the window to the next level of discussion 😊

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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 (5th 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 5th/early 6th 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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The mathematical basis of reality

A curious note from Plato’s Timaeus on the mathematical basis of reality:

“Every sort of body possesses solidity, and every solid must necessarily be contained in planes; and every plane rectilinear figure is composed of triangles; and all triangles are originally of two kinds, both of which are made up of one right and two acute angles … the principles which are prior to these God only knows.”

So there you have it. Right-brainers read it and weep.

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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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Carving conceptual space: into rivers and blocks

This is about how we carve up conceptual space, but first it’s about language. In my case, teaching English as a second language (ESL). Why did my Mexican students have so much trouble with run-on sentences, whereas this was not an issue for my German students? Don’t get me wrong. Every student has their problems. But this difference really stood out. Sure, the German language is in some ways more closely related to English, but German word order and sentence structure can also be quite different than in English. But comma splices and run-on sentences seem to be something of a national pastime in Mexico – four, five, or six complete English sentences joined only with commas or with nothing at all. If we did an exercise, they could all grasp the concept of how to punctuate correctly with periods. But then in the midst of writing or speaking, they would revert to the endless flow without periods.

I concluded, based on my zero hours of training in psycholinguistics, that I was up against their intuition. And their intuition in this case was their way of carving up conceptual space. I tried to compare to my experience watching films in German and Spanish. I’m intermediate in German and upper intermediate in Spanish, but I can follow German dialogue better. Why? Because German is more like English? Yes, but only in a specific way. I definitely have a larger vocabulary in Spanish than in German. But the Germans pronounce every word, with clear edges at beginning and end, whereas the spoken language in Spanish flows like a river. Spanish subtitles can tell me that I know 90% of the words, but I understand 10% in the oral flow. I never know where one word ends and the next begins.

Coupled with my Mexican students’ style of writing full paragraphs with only commas along the way, I decided this is not just a speaking style. It’s the way they carve up conceptual space. Conceptual space is like a flowing river for them, whereas conceptual space for Germans is arranged into building blocks. And you can hear it in the oral flow of the language. Based on the way sentences are arranged into building blocks for paragraphs, English speakers would seem to carve up conceptual space as Germans do, into building blocks. The oral flow of English, however, may strike second language speakers differently than German, as there are so many more pronunciation peculiarities in English. I actually don’t know – I am too “at home” in English – but if any ESL speakers or psycholinguists out there want to chime in, I’m all ears.

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A revolution without enemies

With the current fervor for social transformation in the air, it’s a good time to cue an odd-sounding idea at the hidden core of the 1960s social transformation (click for link):

A REVOLUTION WITH NO ENEMIES

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