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The ecological thought—an infinite interlude

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Cantor set

I've been writing a bit about infinity, so I thought it might be good to take a step aside and look at this some more.

Imagine a line. Now remove the middle third. You have two shorter lines with an equal-sized space between them. Now remove the middle thirds of the two lines you have left. Keep going!

You are creating something like a Cantor set. It was discovered by the brilliant mathematician Georg Cantor in the 1880s. Cantor got into a lot of trouble for his thoughts on infinity. But his discoveries laid the foundations for set theory, Gödel's Incompleteness Theorem, and Alan Turing's thinking on Artificial Intelligence.

If you think about it, the Cantor set contains an infinite number of points. Yet it also contains an infinite number of no-points! It appears to contain two different infinities. Does this make it weirdly larger than an infinity of points alone?

Talk about holding infinity in the palm of your hand. A two-dimensional version is known as Cantor dust: infinite dust, and infinite no-dust. If you make a three-dimensional version, you will produce something like a Menger sponge, a fractal object with infinity spaces and infinity points. You can't squeeze a Menger sponge. But there's something there all the same.

Menger sponge

The strange stranger I referred to in the last posting is like the Menger sponge. Somehow, we have discovered infinity on this side of phenomena.

Who or what is a strange stranger? The category includes, but is not limited to, “animals,” “nonhmans,” and “humans.” In The Ecological Thought I refrain from using the word “animals” (unless in quotation marks). “Nonhumans” strictly refers to the set of those entities who are not Homo sapiens.

Now behold this Menger-sponge-like strange stranger, Astrophyton darwinium:

Astrophyton darwinium

O happy living thing! What a wonderful drawing by Ernst Haeckel, the man who gave us the word “ecology.”

Alain Badiou refers to his Lacanian “set theory” as “pre-Cantorian.” (See Kenneth Reinhard's essay in The Neighbor.) Now I'm not convinced you can actually have pre-Cantorian set theory—this would be like having pre-Newtonian gravitational theory (strike one against Badiou!). But you can have a non-Cantorian set theory. This has to do with whether or not you accept Cantor's Continuum Hypothesis, a project that ended up driving him insane. The Continuum Hypothesis states that there is no set whose size is strictly between the set of integers (1, 2, 3...) and the set of real numbers (rational numbers—integers and fractions—plus irrational ones like pi). As far as I know (I'm no mathematician) the issue is open right now. I'd like to know more about this, and I'd like to know why Badiou and Lacan appear hostile to Cantor.

Intuitively, I find Cantor's view of infinity (nay, infinities) very satisfying. Since I am by no means a mathematician I can't explain this properly. Still, I believe that the kind of infinity to which Lévinas refers when he writes of the other (autrui)—my strange stranger—is not “beyond” this side of reality, if by “beyond” we mean an outside. An outside would imply an inside—and this would imply a metaphysical system. Inside–outside distinctions are the basic ingredients of metaphysics.

I find the idea of an ontologically incomplete Universe where there is no neat holistic nesting of parts in wholes very satisfying, though at present I lack the precise language in which to articulate this idea.

Rigorous materialism must take seriously the seemingly theological idea that infinity is on this side of reality. I believe that work on infinity will counteract the Heideggerian tendency in ecological discourse. Since I hold that we cannot avoid a form of fascism unless we circumvent Heidegger, I also believe that this work is of the utmost political significance.

Burying our heads in the vulgar materialist sand, or the utilitarian environmentalist sand, won't do.

In general, we humanities scholars need some remedial math and science lessons. I'm dismayed that I have nothing but vague intuition to go on in suspecting Kenneth Reinhard's essay (noted above) of Badiou hagiography—mostly the preponderance of “According to Badiou”s in it.

I would love it if a kind Romanticist would help me. Paging Arkady Plotnitsky...

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2 Comments

Some rough comments/concepts:

Some rough comments/concepts: I don't think everything in Heidegger can be dismissed as fascist; however, the privileging of humans and persistent belief in systems (even in the wake of the end of philosophy) does create a hierarchical, transcendence, in Heidegger's path of thought [weg] that could be taken as anthropocentric and also a leaning toward fascism. In The Open, Agamben does a fine hit job on this line of thinking. To "counteract the Heideggerian tendency in ecological discourse" Agamben brings in the animals. One could as well add other agencies of the non-human. The idea is to create multiple centers of non-human discourse and a thinking outside of language and the human. (See, for example, Graham Harman's Guerrilla Metaphysics.) The infinity you seem to be talking about is one of immanence rather than transcendence... Here I'm thinking the detailed look at fractals, etc. in Deleuze and Guittari's Thousand Plateaus. (Much of this in William Blake but also possible to see this in Clare and a love of the infinite in the very small.)

I agree with Ron that Agamben

I agree with Ron that Agamben shows some interesting divergent pathways through, and possibly around, Heidegger. I’m afraid I’m one of those people who like Adorno think Heidegger was a Nazi down to the very commas he used—but unlike some people who think that, I believe we should go through and down below Heidegger—literally to subvert his text. I believe that the two writers who enable this subversion are Derrida and Lévinas. The way the open is “tracked” in Heidegger is astonishingly rendered in the latter’s Otherwise than Being—it’s a passage that makes me think of Heidegger as Elmer Fudd, viz. “Be vewy vewy quiet—I’m hunting a wabbit…”

You may gather from this that I don't believe a pro-animal interpretation of Heidegger is available. I shall clarify this in my posts, I hope.

I’m not sure Agamben’s passageway through profound boredom and désoeuvrement gets us all the way out. I’m opposed to the “environmental” art of Gelassenheit—the “Let it be, let it be” variety. In the end this art mystifies life forms in an upgraded version of objectification. Stay tuned, for I’ll try to address these issues in later postings.

Yes, Deleuzo-Guattarian or fractal infinity is interesting, but it lacks a certain disturbing dimension that for want of a better word we might name “theological.” There is a trace of a familiar aesthetic in fractal infinity—think of all those cool college posters. Instead, the kind of infinity I’m trying to think ecologically is the Lévinasian one. There are lines of affiliation from Cantor to the cool posters, which I am ignoring!

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