Asymptote + Intuition = Leap of Faith
Perceiving, on any determinable level, has an asymptotic nature. The closer the trajectory of the curve of clear understanding gets to the tangential angle of the asymptote of enlightenment, the closer we get to objective truth--reality. Infinity can be considered as equivalent to the inherent nonlinearity orchestrating the complex web of physical interdependent interactions taking place in space and time, the emergent identity of the universe. On the other side of this coin, however, if we could but also see the nonlinearity as the fundamental source of the universe, as one whole unto itself and as it transformed from moment to moment, we would then be in that state the ancients called enlightened. The main problem with that, however, from a logical point of view, is that we'd have to leave ourselves out, and thus the perception would necessarily be incomplete in a way that would make it meaningless. The eye that cannot see itself -- how can we know this eye?
Prajna is defined as direct seeing into the nature or soul of things, thereby transcending perceptual reality. But is this possible? In the West it's loosely translated as or compared to intuition. But I don't believe that captures the gist of it. Intuition is usually defined as knowing something without the recourse to reason, immediate cognition. But is that direct seeing into its nature? I think Prajna goes deeper than intuition insofar as the inner nature we speak of is the bare bones expression of primordial reality. It's knowledge of the cosmic essence in those terms and from that mutual perspective, which is a higher consciousness than the profane or mundane apprehension of a thing's earth-bound identity. Prajna is four-dimensional; intuition is three. Handicapped as they've been and continue to be by Aristotle and the Age of Reason, Western philosophers are constitutionally incapable of coming up with a concept equivalent to that of prajna. They, along with theologians, talk around it, the most they can do.
Regardless of the mode of perception, I side with the Chinese poet Basho on this. With all his genius and insight, he did not believe in enlightenment, at least as it was understood in his time, which, we'd like to think, is the same as now. I have my doubts. Everything evolves. Western psychology, Jung and Freud, other schools of thought and theories of the mind and consciousness have been appended to and complement the philosophy of enlightenment. Nonetheless, the asymptote can never be realized, always it remains just out of reach. The distance separating the trajectory that is your life and the asymptote of enlightenment can be rendered inconsequential only by an act of faith. But faith in what? God or gods? No. Some credo or book of dogma, moral rules of behavior, codes of conduct? No. Faith in science? No. Nothing objective.
When we read descriptions of the Pure Land or No-Mind of Buddhism or some other religion's description of analogous illuminated states of mind, we use that for a guide, trying to emulate the arrived state. This is a time-honored practice of all religions, specifically laid out as such in Buddhism. But, that path will only take us so far, and the negative impact on our minds and hearts when we fail to live up to these impossible self-regulating standards can take a heavy toll.
At the start of this searching we make the assumption that enlightenment is realizable. If we abandon that false assumption--based on nothing more than hope and a touch of arrogance--that is, the idea that we can realize the state of enlightenment and subsequently everything we do is accepted, validated and even encouraged by the Grand Universe itself, or God, Allah, Atman, and so forth, then, in fact, we come closer to the asymptote. It's a paradox, of course. What is unknowable is forever so; to strive to attain it, to see the ineffable in the mind's eye--to realize reality--wanting to feel convinced that our will and the will of God [however you define that term] are one and the same is identifying with the asymptote at every point along the curve. An illusion instigated by the will to power, to fearlessness, to certainty, and to control. Ironically, this self-justified delusion of absolute lucidity leads to self-destruction on a grand scale as narcissism takes hold. All personal relationships lose their depth of meaning, becoming instead merely transitory and self-gratifying experiences, of no significance; not something we need respect as doing so would inhibit our god-sanctioned action.
The distance from the curve of your life to the asymptote of enlightenment is infinite in the sense of nonlinearity. Infinity is not a true measure of length, the notion of length subsumes the idea of linearity. The qualitative difference between linearity and nonlinearity consists in a level of dimension. The leap must therefore be one of faith.
Huineng stated that the self is realized in the act of action. He didn't say anything about the possibility of seeing life and reality as a god would. He didn't promote godhood. Focusing on the moment without second-guessing--comparing actions to some god-like standard based on a false assumption--frees the mind and heart. When that happens, the curve of your life approaches the asymptote of enlightenment across the chasm separating perception and identity, out into empty space.
The Many become the One by a shift in perception. Topology is concerned with continuity which is determined by the closeness of separate points. And in the quantum world, how close do two spatial fluctuations have to be for the continuum to arise?
Intuition plays a vital role in the understanding of the natural world through the medium of mathematics.
A Leap Of Faith
It's a hot August afternoon. I was lying in bed. Thinking and imagining. I was thinking about the classical and quantum ways to measure the surface area of a cylindrical can, open at both ends. I know, I don't have a life. Nonetheless, classically, we'd measure the circumference of the circle and multiply it by the length of the can. Simple enough. But where did that come from, mathematically, and how do you do it quantumly?
The answer to both questions is the same. With calculus, one must first delineate a representative unit, then sum an infinite number of those between the limits set forth. Say what? Sum an infinite number of them? Yes. Our circle has only one dimension, remember. It has zero thickness. Placing one next to the other all along the length of our can will get us nowhere. We need another dimension, a circlular band cut from the can. To do that so that each band is identical, we first must decide on a gauge; an extension along the length-line that can be normalized as one unit. In that case, each circle has a thickness equal to one over the length of the can [1/lg.], and the surface area of a single one (they're all the same) is the circumference times that thickness, our gauge of 1/lg.. And how many of these circles are there? Well, there can only be the number length; the total sum of each circle's thickness must add up to one.
With calculus, what we do is sum all those circles while gradually decreasing the thickness we've arbitrarily chosen, let it grow ever smaller, until, puff, it's gone--zero. We take a circle, and remaining in the world of the finite, keep making it thinner and thinner. We take the limit, in other words, as the thickness approaches zero. We make a leap. It's as though, at the very last, when the thickness has entered the quantum realm, we pull the rug out from beneath finiteness, and before infinity can notice, we've integrated. It's kind of exhilarating. Like quantum mechanics, it's right because it works in the real world. Leaping across chasms of discontinuities, non-differentiable holes in space, impossible to metricize, only topologically viable is what applied mathematics is all about. But without quantification--the result of measurement--nothing can be predicted, you say.
I might point out that the spectacular bull's-eye landing of the rover Curiosity recently was the result of the brilliant work done by talented engineers, scientists, mathematicians, and programmers, among others. They hit the nail on the head, after traveling some 50 million miles, through evershifting gravity-well fields, while everything was in relative motion, moving and turning and changing position. Yet, it landed with precision in the crater they wanted. The mathematics, the celestial navigation, that went into that feat was ultimately based on an imaginary summation of circles with zero thickness.
Once the summation is intiated, the process continues within no-time, and the thickness of our circles is reduced continuously. What's being taken to the limit as delta x (thickness of circle) approaches zero (is reduced) are the separate circles. In the process of adding more and more circles, the thickness decreases. Both processes go on simultaneously, until we make the jump from a very large number to a union of all the circles into a single integrated whole. They're smeared into one piece. The One has engulfed the Many. It's like shifting from algebra to topology at some critical point. In Topology, continuity is ascertained by a degree of closeness. Within that closeness--that Planck length--two blend into one, are identified as one. The total mass of the sun, considered as a continuum of shells, like an onion, equals the sum of the separate shell masses, no gaps allowed.
It's pure magic, nothing less. We take it on faith.