CHASING INFINITY
If there is one thing our basically empirical culture does not do well, it is the concept of Infinity. Mention it and you’ll probably encounter quite a few raised eyebrows. It is, after all, largely associated with religion – or at least with the idea of an infinite God. But it seems to me that the idea of God is something we human beings have given shape to, while the infinite is without any shape or form whatsoever. In other words, our collective imagination has domesticated the concept of infinity through its picture of God – the Loving Father, The Compassionate and Merciful Allah, the Vengeful Jahweh, or my own Divine Joker. Infinity itself has never been given a space of its own to expand in without being yoked to someone’s idea of an ‘infinite God’.
I have suggested elsewhere that the number 5 – or any number you can name – implies a series that stretches from zero to infinity as its background. Yet that infinity is an impossibility, a paradox – a point which Kant made in the Antonomies section of his Critique Of Pure Reason. What is paradoxical about it is that from any empirical perspective, infinity cannot exist, because, however far you take your series of numbers, you can always go further and never reach the end and complete it. Empirical thought loves things with limits, and with infinity you encounter something without limits. On the other hand, Logic demands that infinity must exist for precisely that reason. Cannot and Must are therefore in conflict. What is scandalous about Infinity is that it constitutes an absence of closure – a negation, if you like, of everything finite and familiar. It does to thought, therefore, what Pi – or any irrational number - does to an algorithmic equation. In other words, it is the dark shadow of everything finite, like some kind of trace it will never get rid of. Imagine being shadowed by that which negates you by surpassing you towards an always receding horizon. It is bound to make you feel somewhat superfluous.
But so far, we have only dealt with the Infinite as a mathematical concept, which is purely skeletal and lifeless as far as it goes. Surely, there must be more to the concept than this, something which gives flesh to it and also breathes life into it, filling it out, connecting it to ourselves as living beings and the whole of the cosmos of which we are a part – if by the term “cosmos” we imply something more than the physical universe(s) that scientists study. (I say nothing of String-Theory, Brane-Theory, ten, eleven or more dimensions, or the infinite number of parallel universes which split into two or come into being whenever decisions are made involving an either/or choice.)
It is on this level of putting flesh onto our mathematical skeleton of infinity that we might be tempted to bring back the hypothetical notion of “God”. I have no objection to this, as long as it is the “God” of Spinoza (or the Spanish Sufi, Ibn al Arabi) – that is to say the “God” which equates with everything else that is normally considered not to be “God”. Spinoza put it this way. “God” and the universe – or, in our case, the cosmos – are one and the same, and they logically must be, because an infinite “God” could not co-exist with anything else. If a separate infinite “God” existed, the universe itself would be pushed out of existence – unless, of course, the universe was an integral part of that infinite “God” – another mode of ‘his’ being as it were. A very logical chap was Spinoza, not really cut out to believe in the mumbo-jumbo most religious people believe in – in fact he said as much himself, “Religion is organized superstition. It is based on the fears of naive ordinary people in the face of unpredictable nature, and clever power-hungry leader-types use those fears to control people.” – and this fact has made him persona non grata to priests and rabbis ever since. (He was excommunicated from the Amsterdam Synagogue.)
It is through “God”, by way of Spinoza, that we might come back to the idea of more a rounded infinity permeating every finite part of itself, myself included, along with the pen I hold in my hand. It makes sense to me to think of everything as part of a continuum which absorbs everything else. What I have never found convincing in the natural and physical sciences is the way everything seems to be neatly divided from everything else – dogs from cats, atoms from other atoms, plants from animals, rocks from water, water from air, me from you and ultimately what people tend to call ‘mind’ from something else they tend to call ‘matter’ and place them all in discrete categories, thereby putting them into neat little boxes. The only relations such discrete things can have with each other in such a cosmos could be ‘interactions’ with other discrete things – that is to say relations that come from outside. This paradigm appears to be breaking down in Quantum Mechanics with ideas like Quantum Entanglement, but it is still very entrenched elsewhere in science.
But back to infinity. I am far from believing in any kind of God. Would ‘God’ not also be another discrete entity, separate from everything else? The point that it is important to establish is that if “the infinite permeates every finite part of itself,” the finite and the infinite must be of the same basic nature with the same characteristics. The only difference is that one has been raised to an infinite power, while the other’s powers are finite. We are assuming, of course, that the cosmos was not created by a creator ‘God’ who pre-existed ‘his’ creation and continues to exist outside of it, having framed its laws and set its co-ordinates to ‘his’ satisfaction and then, to quote Antonin Artaud, “gets the fuck out and leaves the cops to keep an eye on things.”
We cannot, of course, reduce even the finite parts of this infinite whole to our own perspective. What we might perceive and what actually is can never be identical. We see through a glass darkly as it were. The thing-in-itself, to borrow from Kant, is inaccessible to us. Nevertheless, I believe that we can infer from the fact that the infinite permeates everything finite that the cosmos in both its finite and infinite modes remains the same cosmos and shares the same nature – one in a finite mode and the other in an infinite mode. Reality is everywhere the same, in other words, and this everywhere extends beyond finite horizons.
If this is true, everything in the cosmos – including whatever it is that underlies our own consciousness – is shared by everything else. All ‘matter’ in other words has a ‘mental’ or ‘proto-mental’ dimension. The difference is only one of degree, not kind. For example, what organises matter on an atomic plane is of the same nature as what organises matter in the human brain, giving rise to human consciousness. Atoms are simple, though they may well be complex compared to the sub-atomic particles of which they are composed. The human brain, on the other hand, is much more complex – as befits the tasks it has to perform and functions it has to fulfil. However, brains and atoms share in the same underlying nature, and embody the same impulse towards self-organisation. And that is probably true throughout the whole infinite cosmos and not just our finite section of it. The whole of being, therefore, is, to use Sartrean-Hegelian terms, in some way being-for-itself when viewed from within and only being-in-itself when it is viewed from the outside.
Hegel distinguished between Good Infinity and Bad Infinity. Good Infinity was apparently circular, doubling back on itself, while Bad Infinity was linear and just went on and on and on forever – as a kind of interminable extension of the finite. I am not sure, but in suggesting that the infinite permeates every finite part of itself, I basically agree with Hegel's Good Infinity rather than his Bad Infinity, and that’s certainly a turn up for the books because I never thought I’d ever agree with Hegel on anything.
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