Experience: Table of Contents
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The Pride of Reason
This is part 6 of the discussion on experience. As most people know, 7 is considered a “lucky” number: there are 7 colors in the rainbow, 7 notes to a major scale, 7 days in the week, 7 planes of nature, God created the world in 7 days, etc. etc. 7 is consider the number of wholeness and completion.
The number preceding 7, 6, is therefore associated with incompleteness, the state of “not quite there yet”. That is our topic now, to build on the previous observation that infinity, in the sense of a never-ending progression, is in fact the very embodiment of, perhaps the purest expression of incompleteness. Infinity is not a thing. It is something that promises to be a thing, but never is.
I did not plan that Part 6 of Experience would be about incompleteness, but it is, and I find myself coming back to Chapter 6 of Alister Crowley’s Book of Lies, which I wrote about many years ago in Chapter 16 of Beyond The Physical. Crowley’s chapter is so short it can be reproduced here in full:
“The Word was uttered: the One exploded into one thousand million worlds.
Each world contained a thousand million spheres.
Each sphere contained a thousand million planes.
Each plane contained a thousand million stars.
Each star contained a many thousand million things.
Of these the reasoner took six, and, preening, said: This is the One and the All.
These six the Adept harmonised, and said: This is the Heart of the One and the All.
These six were destroyed by the Master of the Temple; and he spake not.
The Ash thereof was burnt up by the Magus into The Word.
Of all this did the Ipsissimus know Nothing.”
Crowley’s commentary contains one of my all-time favorite lines:
“The Rationalist takes the six …and declares them to be the universe. This folly is due to the pride of reason.”
Taking six things out of the kazillions of things that exist and declaring them to be everything could almost almost serve as the psychiatric definition of insanity in the DSM. Anyway, I wrote about this in Beyond the Physical years ago and won’t traverse that ground again here.
The point of citing Crowley here is that, as you see, the number 6 is portrayed as the infinity of things that make up the manifested universe. These were discussed last time as a never-ending progression of forms, all of which are characterized by the fact that they promise, but never give, fulfillment.
We now consider a less poetic and a more intellectual exposition of infinity.
Infinity as Math Object
There is much written on the topic of the flirtations of Western civilization with the concept of infinity. Well-known stories begin at the ancient Greeks, wind their way through Nicholas of Cusa, Saint Augustine, Galileo, Leibniz, and many, many others, and culminate in the work of Georg Cantor, from whence a downhill progression brings us to now.
The story often starts at Aristotle’s distinction between potential and actual infinity. The counting numbers, 1, 2, 3… are potential infinity. They imply infinity as a potential state (notated by the “…”), but one never gets to infinity. Instead, one seems to be able to get as close as one wishes by just counting higher and higher. However, the end, infinity, is never reached.
Further, the idea that one seems to get closer to infinity by increasing numbers is purely illusory. For no matter how high we count, we can then double this, multiple by 10, by 1000, by 1,000,000 and we are no closer to infinity than when we were at 1, 2, 3… . As Cantor himself showed, no matter what magnitude of number we consider, that magnitude is exactly zero next to infinity. Which is to say, the concept of “magnitude” makes no sense in the context of infinity.
Actual infinity is the idea that we can hold something infinite in the finite palm of our hand. Cantor was the first mathematician to formalize how this could happen. This led to paradoxes that made Russell look like the intellectual amateur he was, and generated the foundations of mathematics, which Wittgenstein thought were a complete travesty of the intellect. Wittgenstein, being a philosopher and not a mathematician, was mostly ignored, and people like Gödel and Turing did their paradoxical tricks showing how, with mathematical certainty, we can define incompleteness and unknowing, based on ideas analogous to Cantor’s.
All of this led to computers, which led to the widespread appreciation of chaos theory and fractals, which previously existed only in the minds of “special people” like Poincare, Cantor and a handful of others.
Now, we can indeed hold a simple equation in our hand, like zn+1 = zn2 + c, which is the equation of the Mandelbrot set, an infinite entity we can, so to speak, hold in the palm of our hand, or at least grasp in our mind as an infinite thing that occurs in a finite space.
The main reason for the above is to lay out a little about Western Civilization’s notions of infinity so we can contrast them to Hindu ideas of infinity. They are similar, but different. In Hindu thought, a distinction like potential and actual infinity also exists. But it is interpreted in a different fashion. Each are given a status as real or unreal, but in the opposite way from the Western ideas.
The Measure of All Things
To the West, potential infinity is real because we can write down equations of all types for which we can imagine what would happen at infinity, even if, by any practical means we cannot get there. We can deduce what would happen at infinity, which is the mathematical idea of a limit, and we then say an equation “converges” to a finite solution, even though, in principle, an infinite amount of calculation would be required to actually compute the limit. For readers who have never seen a limit before, I’ve prepared a small example to illustrate the concept.
The idea of a limit is important. It, perhaps more than any other, is responsible for the technological world we now inhabit.
In this sense, potential infinity is real to the Western mind, but actual infinity does not exist, except in the imagination as a limit of a potential infinity, or in the imaginations of Cantor’s followers.
[For the mathematically sophisticated: I’m going with Wittgenstein and Leopold Kronecker and treating Cantor’s “Paradise” as a delusion. Writing a finite symbol and saying it is infinite is nonsense. No practical procedure can ever realize infinity. I agree with Wittgenstein that the diagonal method is flawed. Somehow this all links back to the real numbers. But not being a professional mathematician, I am in no position to technically argue the point. However, Poincaré in Science and Hypothesis speaks of mathematical thinking as “reasoning by recurrence”. Poincare’s sophistication on this matter led him to reject Cantor. Demonstrably more practical good came from Poincaré than Cantor. In addition, the Hindu ideas are quite clear there is only one infinite (Brahman). To debate the issue further is not something I will do here and may serve as a topic for a future post].
Contrary to the Western notions, to the Hindu mind, actual infinity is literally real and potential infinity is literally unreal.
Actual infinity is called Brahman, and it is spoken of in terms of what it is not. Brahman is not any finite attribute one can imagine. Therefore, even though Brahman is real, in fact the only reality there is, it is not something a finite being can experience or comprehend.
The idea is not confined to Hindus. Nicholas of Cusa described the situation with great beauty and penetrating insight and you should read what he had to say about “Learned Ignorance”.
To the Hindu mind, potential infinity is similar to the Western idea of potential infinity as something that goes on forever: a thing that cannot be thought of, or described, or calculated in a finite way.
In the simplest of terms, any approach to infinity, any potential infinity, is always a process or procedure that can, in principle, repeat forever, like adding 1 to the previous number to generate the counting numbers.
This is the well-known idea of an algorithm: a series of steps that generates an output. Some algorithms have a finite number of steps. Others, such as counting by 1, can go on forever. The algorithm is the real thing (by “real” I mean “it exists” and am not referring to real numbers). If an algorithm repeats forever, its output, some potential infinity, is also real. But the actual infinity implied by the algorithm is not real; it is not something that can be made to exist.
But while potential infinity is real for Westerners, it is the very definition of unreal for the Hindu mind. The Hindu word for potential infinity is “Maya”, which is translated in a variety of ways: magic, illusion, Mother, measure, ma = “man”, the measure of all things.
The latter, “measure”, from the root “ma-”(the source of the word “man”), is perhaps the clearest because it implies the essence of the idea: that which is relative. Where Brahman is absolute, Maya is relative.
Man is the measure of all things. Things are bigger or smaller than us; faster or slower than we move, heavier or lighter than we can lift, brighter or darker than we can see, louder or quieter than we can hear, and so on. “Ma”, “man” “measure”, “maya”.
Relative means that the thing only makes sense in comparison to something else of like quality but different quantity. We cannot know what “bigger” means unless there is something of a different size. We cannot know what is good unless we know evil. We cannot know what is intelligent unless we know what is ignorant.
The implications of the Hindu view are well-known to anyone who studies Hindu or Yogic thinking, but they are generally unknown to those familiar with only the Western understanding of infinity, at least nowadays. People like Leibniz and Nicholas of Cusa, were Westerners with ideas very similar to the Hindu notions, but they are rarely read today, let alone taken seriously, and are exceptions in Western thinking. Had their ideas caught on, Western thought would today more resemble Hindu thinking.
The implication was alluded to previously and is now stated: we only know by contrast. If there is no contrast, then there is only blankness, a nothing.
A common sense example is how we move about in the gaseous atmosphere of the Earth. We look forward and see nothing between us and other objects. We feel no resistance to moving forward (only the downward pull of gravity). Therefore, we consider the space around us to be empty, though it is not, and we only need feel the wind to know something invisible is there buffeting us.
Of course it is common knowledge we live in the atmosphere, but in our day-to-day existence, we take the air for granted because it is the only condition we experience. We can, in a manner of speaking, subtract it out of our moment-by-moment considerations.
This same logic was used in part 5 to describe “normal people” who only know the surface mind. Again, without the contrast of experiencing an altered state of consciousness, the “normal” person takes their conscious state for granted and makes the (incorrect) inference that it is all that exists (That pesky “pride of reason” thing).
The point is that what we call “knowledge” or “information” is an expression or manifestation of contrast. Contrast implies difference. Difference implies relative-ness. Therefore, all we sense, all we think, all we know, all we experience is relative. This is what Hindus call “Maya”. Our entire existence is of a relative nature.
This does not change when the curtain gets pulled back. The inner realms are also relative: expanded being, greater consciousness, more awareness. The adjectives are the giveaway.
The key point I wish to convey, perhaps the central insight of this essay, is the following:
When we recognize that existence always has the quality of being beckoned by promises that never fulfill, this has the same form, the same “shape” as “1, 2, 3…”, particularly the “…”. The “…” is the promise. It seems like it will give to us, like it will fulfill, but it only goads us on to something else. “…” is not a sign of fulfillment, it is but a road to a different promise, and then the cycle repeats.
In short, potential infinity is the nature of the relative, and it is always incomplete, and most important: this is the nature of experience.
All Conditions Each
Perhaps the most important implication of realizing that existence is relative is to realize that any one thing depends on everything else for its definition, for its being, for its existence. To be more precise, given that all relative things are in a constant flux, it’s not even correct to call relative existence “being”. As Western philosophers have recognized for over two millennia, the state of things must instead be called “becoming”. It is always in a process of transformation.
I will not dwell on this point here, but leave it to the Reader to consider how, when in the relative condition, any seeming separate thing depends, ultimately, upon all other seemingly separate things. The end conclusion is there is no such thing as a separate thing; only the appearance of separate things, due to ignorance of not seeing the total picture.
From Whence the Relative
It doesn’t take much mental power to understand and accept that all experience is relative. Once it is pointed out, once all the terms are defined and the picture drawn, it is all pretty obvious. Self-evident actually. Axiomatic. What requires mental power and effort is to think through the implications.
Particularly if we are honest: nothing we can do in actual fact can make an actual infinity. A fractal is infinite in our imagination, not in fact. A convergent series is infinite in our imagination, not in actual fact. No one has ever written down an infinite set of symbols. (Please, if you are so smart, write me an infinite set. I will be impressed and you will get a Fields Medal). No amount of “…” can change the fact. That was Wittgenstein’s point: “…” is simply dishonest. It is a lie, a sham, and a scam. Be that as it may, it is not the point I want to dwell on here.
The issue to consider is: from whence has this condition arisen? We stated the answer in the first post on Experience:
“When the ultimate cause of a particular experience is discovered, it will be found that the cause lies in the recognition of the Self in the not-Self.”
When the cause of a particular experience is discovered, the cause of all experience is discovered. Since all experience is relative, the cause of the relative condition is discovered.
The cause is found to be a process of projection, a trick, like a mirror image. It looks like the reflection is there, inside the mirror. But it is not. It is just a trick of how light reacts with mirror surfaces.
Something analogous happens in consciousness. Then, that which is doing the projecting begins chasing its projection, like a dog chasing its tail. The tail chasing process behaves like a potential infinity: it seems to go on forever and ever, it always promises but never delivers. From this tail-chasing process emerges what we in our ignorance call “reality”, “existence”, and “experience”.
It has to do with “being” because, although I said all experience is becoming, behind the becoming is being, without which becoming would be impossible. It is like watching a movie at the theater. The movie must be projected on a white screen. The white screen is the “invisible” background, invisible in the sense that it is not to be paid attention to while focusing on the move. But without it, there would be no movie.
This is the relationship between being and becoming. Being is the background, the substrate onto which becoming is projected. We experience becoming. But we only do so because we are. The actual infinity, which is being, projects itself and makes seemingly infinite potential infinities that spin round and round in the process of becoming, trying to achieve a satisfaction that can never come.