Previously in the Premiseless Imperative Series:
Kimetikos I: Foundations
Kimetikos II: Theory
Kimetikos III: Practice
Anagoge I: If You Want to be Saved, Admit That You’re A Sinner
Anagoge II: Achtung, Babies!
“The fear of infinity is a form of myopia that destroys the possibility of seeing the actual infinite, even though it in its highest form has created and sustains us, and in its secondary transfinite forms occurs all around us and even inhabits our minds.”
– Georg Cantor
The idea of God as Infinite is one of the oldest cliches in the book. It’s a basis for most religious systems in which God is all-knowing, all-seeing, all-powerful, and bigger than a breadbox. The idea is also a basis for all kinds of crazy philosophical speculation surrounding the idea of the “infinite regression,” which essentially involves every single dichtomy’s capacity to regress into an infinite number of permutations. An excellent example is Philip K. Dick’s Infinite Theophany, highly recommended for our purposes. Consider it a reading assignment!
Gnostic mythology also acknowledges the infinite nature of God– not the creator God, but the God above and beyond everything else, that to which we sometimes refer as the “Limitless Light,” or “The Great Invisible Spirit,” or “The Unknowable God.” Because it’s so freakin’ huge, so utterly infinite, it can’t even be described, because as soon as you start trying to describe it, you’re giving it a name, and giving something a name limits it. As some old buffalo-riding bat once said, “The Tao that can be named is not the Eternal Tao.” For this reason, in Gnostic literature, we often find this Ultimate God discussed in negative terms, such as the following from The Secret Book of John:
He is eternal, since he does not need anything. For he is total perfection. He did not lack anything, that he might be completed by it; rather he is always completely perfect in light. He is illimitable, since there is no one prior to him to set limits to him. He is unsearchable, since there exists no one prior to him to examine him. He is immeasurable, since there was no one prior to him to measure him. He is invisible, since no one saw him. He is eternal, since he exists eternally. He is ineffable, since no one was able to comprehend him to speak about him. He is unnameable, since there is no one prior to him to give him a name.
“He is immeasurable light, which is pure, holy (and) immaculate. He is ineffable, being perfect in incorruptibility. (He is) not in perfection, nor in blessedness, nor in divinity, but he is far superior. He is not corporeal nor is he incorporeal. He is neither large nor is he small. There is no way to say, ‘What is his quantity?’ or, ‘What is his quality?’, for no one can know him. He is not someone among (other) beings, rather he is far superior. Not that he is (simply) superior, but his essence does not partake in the aeons nor in time.
There’s a whole discussion we could have about describing God in the negative (“Via Negativa”), but we’ll leave that aside for now.
Getting a real, honest to goodness sense of this limitlessness can help us produce, within ourselves, an “existential buzz”– an indescribable feeling or awareness of the nature of the infinite. It’s like gnosis-lite, and it’s useful to occasionally shoot for an existential buzz, and recognize it when it happens. To shoot for the buzz, let’s take a look at infinity itself and see what we can do with it as a concept. Since infinity is pretty much one of the most common properties of God, getting to know infinity can really help somebody who is attempting to get to know God.
Infinity wears just as many masks, and is especially useful for those who pursue gnosis because of its wonderful predilection for paradox. Take good ol’ Zeno of Elea, famous for coming up with some excellent paradoxes that have boggled minds for millenium.
Suppose a very fast runner — such as mythical Atalanta — needs to run for the bus. Clearly before she reaches the bus stop she must run half-way, as Aristotle says. There’s no problem there; supposing a constant motion it will take her 1/2 the time to run half-way there and 1/2 the time to run the rest of the way. Now she must also run half-way to the half-way point — i.e., a 1/4 of the total distance — before she reaches the half-way point, but again she is left with a finite number of finite lengths to run, and plenty of time to do it. And before she reaches 1/4 of the way she must reach 1/2 of 1/4 = 1/8 of the way; and before that a 1/16; and so on. There is no problem at any finite point in this series, but what if the halving is carried out infinitely many times? The resulting series contains no first distance to run, for any possible first distance could be divided in half, and hence would not be first after all. However it does contain a final distance, namely 1/2 of the way; and a penultimate distance, 1/4 of the way; and a third to last distance, 1/8 of the way; and so on. Thus the series of distances that Atalanta is required to run is: …, then 1/16 of the way, then 1/8 of the way, then 1/4 of the way, and finally 1/2 of the way (of course we are not suggesting that she stops at the end of each segment and then starts running at the beginning of the next — we are thinking of her continuous run being composed of such parts). And now there is a problem, for this description of her run has her travelling an infinite number of finite distances, which, Zeno would have us conclude, must take an infinite time, which is to say it is never completed. And since the argument does not depend on the distance or who or what the mover is, it follows that no finite distance can ever be traveled, which is to say that all motion is impossible.
This paradox shows us not only that infinity can be based on addition (i.e. infinity is everything all added together– it’s huge!), but can also be based on division (i.e. it’s theoretically possible to divide something an infinite number of times– it’s tiny!).
Look at it another way: suppose we want to measure a one-dimensional line. To do so, we first divide the line into halves. We then divide each half into another half, repeating ad infinitum. Do we ever reach a point at which we can add up all of the segments of the line and arrive at a single conclusive measurement? Since a point, an object existing in no dimensions, has no measurable length, any given one-dimensional surface contains an infinitely small number of zero-dimensional points. Extrapolating from this, since any one-dimensional surface has no measurable width, any two-dimensional object contains an infinitely small number of one-dimensional surfaces. And, of course, any three-dimensional object contains an infinitely small number of two-dimensional surfaces.
How does this then relate to “higher” dimensions? Well, each three-dimensional object exists in what we might call an “instance”– an infinitely small measurement of time. In other words, we measure time in hours, which are divided into minutes, which are divided into seconds, etc. etc. etc. Following the above logic, there are an infinite number of “instances” within each experience of space/time. Or, to turn this idea on its head, you are an infinite number of instances of a single four-dimensional object which is the sum of your instances! Were we able to look at you from the standpoint of a 4-d object, you’d resemble a sort of snake-like blob that simultaneously filled every single spacial location you occupied during your life. And a 5-d object would contain an infinite number of these snake-like blobs, ad infinitum!
Now toss motion into the mix. Suppose we have a cylinder, like a soda can, and it’s painted blue on one third (vertically), red on one third, and yellow on the other third. Now suppose we lay this cylinder on its side, horizontally, and rotate this cylinder. How would this motion appear to someone on a two-dimensional plane which intersects the cylinder along its axis of rotation? The 2-d denizen wouldn’t see the entire cylinder, nor would she be able to percieve the motion of the rotation. Instead, depending on the speed of the rotation relative to the observer, she would see a series of colored lines flashing in a pattern: blue, red, yellow. If the cylinder rotates fast enough, the 2-d person wouldn’t see anything but a fuzzy gray line! With this in mind, what would a 4-d object look like to someone in the third dimension? What would 4-d odors smell like? Would we be able to “feel” a 4-d object?
Got that buzz yet? No? Let’s keep trying.
Our pal Georg Cantor, quoted above, is the father of set theory, and spent a hell of a lot of time thinking about infinity. He came up with the concept of the measurement of infinite sets using the Hebrew letter Aleph (א). Although the idea of a “set” of infinite items seems odd, Cantor, a devoutly religious man, had an interesting way of looking at the relationship between humanity and the universe using the language of infinite sets.
To Cantor, the human and the universe were equally important, and equally infinite. The macrocosm, thought Cantor, contains an infinite number of points. If we start with the universe, or God, and divide into two, and continue this process of division, we would never stop– we could go on for an infinite amount of time. However, said Cantor, the same can be said for any single object within that macrocosm, humanity included! No matter where one starts within the great chain of being, one can arrive at a manifestation of infinity! Every portion of infinity, said Cantor, contains infinity itself!
This is how infinite sets manifest; the infinite set of points within a human, for instance, is an infinitely large subset of the greater infinite set which contains the infinite set of points within the universe.
So, to continue, infinity is present within everything that exists. If God is infinite, then God is manifest within everything that exists. As a being with infinite dimensions, God transcends space and time to such an extent that what we perceive as motion, change and time would by necessity appear as a single unit to God, as God would perceive every instant simultaneously. Thus, Existence as what has been, is now, and will be, as we perceive it, is defined by our own limitations! Now, if God exists outside of space and time and percieves it as a sort of motionless block, then God has access to any “instance” within space and time regardless of what we perceive as some kind of linear order.
Here’s an interesting exercise: find a brick, or brick-shaped object, and draw a line from one end to the other. At one end write the number one. At the other, write the number 1000. Now make a few points on the brick with chalk– doesn’t matter where. Once you’ve made your points, touch each with a finger. Some points will be closer to one, some to 1000, some on top, some at the bottom. Do any of these points exist “before” the others? Is it more difficult to touch the points closer to 1 or to 1000? Is it tougher to touch the points on the top, or the bottom? What would the brick look like if you drew a dot on every single individual point on the brick’s surface?
Here’s another exercise: find a block of Swiss cheese– the kind with holes. Mark the cheese’s surface with the same 1-1000 line you made on the brick. This time, mark some increments on the line as well, say steps of ten or one-hundred. Now, carefully slice the cheese into sandwich-sized slices perpandicular to the line. Now, on each slice, assign each hole a distinguishing mark– let’s say letters. So on any given slice you’ll have hole A, hole B, hole C, etc. Try to make sure the holes you mark match their counterparts on the other slices. Now for the fun part: get some thread, and cut enough lengths of thread to represent each hole. So if you have six holes in each slice, you’ll want six pieces of thread. Label each piece of string A, B, C, etc., and then begin reconstructing the block of cheese by threading each piece of string through its corresponding holes in each slice.
And another exercise: try to come up with an algebraic formula representing God, the universe and humanity. Spend as much time as you like.
Eventually, at some point, all of this contemplation of the nature of infinity will give you that buzz. You’ll have a weird ideation about your relative location in the whole scheme of things, and sense the vastness as part of yourself. This isn’t some namby-pamby New Age “all is one” craziness– the idea is to cultivate the ability to call up this feeling at any time, in any place. Using the skills you’ve been developing, pay strict attention to this feeling, and you’ll begin to experience it more often, sometimes in relation to other objects around you.
When you can call up the existential buzz at will, you’re ready to continue.
Finally, another reading assignment: if you haven’t yet, read Flatland by E.A. Abbott. It’s a pretty fast, easy and funny read, well worth re-reading if you so desire!