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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Turning the Page on Locke: Private Property in the Coming Age

John Locke (1632-1704) left quite an intellectual legacy for modernity to brood over. He was a founding figure of the empirical age, arguing that all knowledge begins with the input of the five senses. (“Perception . . . [is] the first step . . . towards knowledge, and the inlet of all the materials of it” [1].) He applied this to psychology [2], arguing that the mind at birth is a tabula rasa or blank slate (a psychological theory that coincidentally supported the views of his Whig patron, Shaftesbury, who despised the old views of inborn superiority of rank and innate ideas about social hierarchy). Indeed, Locke says point blank that there are no innate ideas “as it were stamped upon the mind of man” [3]. And then of course there’s his political theory, with ideas about the government’s role in protecting life, liberty, and property [4], which would be applied by Thomas Jefferson 100 years later in the founding documents of the US. Jefferson, of course, cagily substituted “pursuit of happiness” for “property” [5], but it’s the “property” idea that concerns me here.

The same ideas that supported Locke’s epistemology (empiricism) and his psychology (tabula rasa) fed into economics. Instead of the old economic system based on landed hierarchies, suddenly you have “economic individualism” as the cornerstone idea. Each individual is a self-contained unit with a right to their individual property. For “the ingenious Mr. Locke,” as he was often called in the 18th century, ownership was the cornerstone of all social relations. Indeed, Locke argued that ownership over one’s own body is given in the very state of nature, and that all appropriation of additional properties is a natural extension of that relation. (“Everyman has a property in his own Person … [and] the labour of his body, and the work of his hands, we may say, are properly his … Whatsoever then he removes out of the state that nature hath provided … [and] mixed his labour with … [is thereby] his property,” [6].)

Thus we come to a world where social relations take the form of individuals accumulating and competing for property, and governments organically emerge in defense of “life, liberty, and property.”

If I may take what 18th-century wit, Henry Fielding, said of a certain philosophy of the day, and apply it to Locke’s theory, I might say it is “a very wholesome and comfortable doctrine, and to which we have but one objection, namely, that it is not true” [7].

OK, I can’t quite make the claim that Locke is wrong, but I can raise the question: What if this cornerstone idea of modernity and capitalism, this idea about the primacy of personal ownership, is false? Or perhaps not false, but at least not logically necessary. What if it is but one way of looking at things, and a way that is perhaps no longer the most serviceable?

My alternative would start here. My interlocutor might grant me that the idea of ownership as the primary relation between oneself and one’s own body is speculative and not in any way self-evident. But, my interlocutor might say, the relation between a person and land or objects – there, ownership seems to naturally apply. Surely ownership is fundamentally a relationship between individuals and the things that they own, no? My counterargument is this: Ownership is not fundamentally a relation to self, nor is it fundamentally a relation to objects or natural resources. Ownership at its most fundamental is a relationship between people. “Mine” is a nonsense concept in isolation. “Mine” always means, a priori, “mine and not yours.” Or, one could perhaps narrow that still further and say that (“mine” = “not yours”), and that this is the fundamental equation of ownership. With all due respect to Locke’s contemporary Daniel Defoe and his Robinson Crusoe, an isolated individual cannot own anything [8]. That individual can use resources, can deploy them in the hunt for food and shelter, but cannot own them because there is no “mine and not yours” line to be drawn.

So am I just quibbling or are there consequences to this revision of the ingenious Mr. Locke? I tentatively suggest there are consequences. Once you see ownership and private property in this light, as relations between people and people, not between people and things, it can plant the seed for a new vision of how things could work.

Marx said that the capitalist world of commodity-values converts social relations into the “fantastic form of relations between things” [9]. With social identity thus alienated, we compensate by creating a wedge between “social” and “private” identity, and start to treat private identity as “real” identity.” But what if that world view is coming to an end? Under the pressure of income inequality and ecological imperatives, it seems capitalism must break or evolve into some new form. At least the prevailing definition of human identity and human fulfilment in terms of private identity and private property must break. If we can reverse the Lockean trajectory – instead of casting social relations into terms of private identity and private property, what if we recast identity and property into relations between people?

From Locke to Adam Smith to Marx to Thomas Piketty, we have been in the age of homo economicus, where homo sapiens are defined fundamentally as economic units and human relations fundamentally as economic relations. But is that necessary or is it just the signature paradigm of the 17th – 20th century? I won’t say 21st, because I think it is finally time for a paradigm shift out of the age of homo economicus. Increasing inequality (well-documented in Piketty as an intrinsic feature of capitalism, despite spikes and troughs [10]) and ecological imperatives require it. If we can reconceptualize ownership and private property into the fundamental social relations that they are, perhaps we can start to turn the ship. Perhaps we can redefine human identity and human fulfilment in terms that render the obsessive desire to accumulate private property for one’s own self into a historical curiosity. There are enough resources to go around. As Russell Brand points out in his cheeky anti-Establishment manifesto, Revolution, “a bus with the eighty-five richest people in the world on it would contain more wealth than the collective assets of half the earth’s population” [11]. Stripped of the debilitating definition of human identity as private self and private property, a technology and a sharing economy in the service of something larger than personal gain might flourish – not that ownership will disappear, but it will be conceptualized differently. Instead of “owning” being an absolute relation between individual and thing, a removal of the thing from the field of social relations for oneself, owning would be seen as something provisional and embedded in social relations, an ongoing negotiation, evolving and flexible as our relations to others are evolving and flexible. This way of looking at things is not only possible but as the current cycle keeps turning, it will become more and more a practical necessity.

  1. LockeEssay on Human Understanding, II.ix.
  2. LockeEssay on Human Understanding, I.ii.
  3. Locke, Essay on Human Understanding, I.i.
  4. Locke, Second Treatise on Government, Chap 7, parag. 87.
  5. U.S. Declaration of Independence.
  6. Locke, Second Treatise on Government, Chap. 5, Parag 27.
  7. Henry Fielding, Tom Jones, Book 15, Chap. 1.
  8. The Lockean sense of ownership Defoe gives to Crusoe is almost unintentionally comical as Crusoe surveys the island with “pleasure . . . to think that this was all my own . . . and [over it I] had a right of possession” (Robinson Crusoe, 1985 Penguin ed., pp. 113-14).
  9. Karl Marx, Capital, 1906 Random House ed., p. 83.
  10. Thomas Picketty, Capital in the 21st Century. The documentation referenced runs throughout the book.
  11. Russell Brand, Revolution, p. 8.

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Money (and Somerset Maugham)

As I recall, Larry, the protagonist in Somerset Maugham’s “The Razor’s Edge,” is a vagabond spirit, a backpacking nomad with friends of all classes on different continents. At one point, a rich friend who enjoys philosophical discussions with Larry offers him a job at a high salary with little or no actual work. He is surprised that Larry turns him down. How could he resist such an offer? Larry responds succinctly:

“Money to you means freedom; to me it means bondage.”

He says this, as I recall, with no arrogance but a genuine appreciation of their differences. That pretty well sums up the two key viewpoints on money. Most everyone’s attitude can be placed in relation to those two poles. And if I got some of the context wrong, well I haven’t read the book in a while. That’s the way I remember it.

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