"All knowledge as binary systems are based on the law of the excluded middle, that is a statement is either true or false. This turns out to be useful, especially to science and technology because it makes the universe knowable, deterministic and predictable. Science is based on the idea of causality which in turn yields scientific laws, or rules of behavior that the universe follows in a consistent manner. It is what makes life and survival possible.

This system of causality, determinism, predictability and the excluded middle can be called logical space. Logical space is everything we know and everything we can know and it is where life evolves, sentience contemplates, lovers love and the stars explode away from the cosmic womb. Logical space is analogous to what science describes as local reality.

The second is paradoxical space and is, in principle, unknowable and non-dual, uncertain, unpredictable, random, chaotic and non-local; fundamental reality. Let it be called Apeiron, or the Boundless, which means non-dual or without logical distinction. It is a continuum meaning that it is an undifferentiated whole without constituent parts. It may be associated with Parmenides' One, Heraclitus' Logos, Anaxagoras' Nous, Lao Tzu's Tao, Samkara's Non-duality and the entire universe of quantum potentia."

"In the final analysis, we choose the ultimate belief; that there is a state beyond knowledge and uncertainty. From time to time we have given this state names and have attempted to describe it. We have called it Brahman, The Tao, The Great Mysterious, Apeiron, Nous, the less offensive and more abstract descriptions of God, and even the consciousness continuum.

But as soon as we give it a name or description, it collapses into knowledge, is bounded by paradox, and sinks into uncertainty. And still we choose to believe that by leaping that horizon again and again we may somehow leap into the unknowable, into the ecstasy.

And from time to time we do.

And of that ecstasy, we can only remain silent.

Michael Andrews, The Gnomes of Uncertainty
reprinted without permission

"It is possible to regard the history of the foundations of mathematics as a progressive enlarging of the mathematical universe to include more and more infinities. The Greek word for infinity was apeiron, which literally means unbounded, but can also mean infinite, indefinite, or undefined. Apeiron was a negative, even pejorative, word. The original chaos out of which the world was formed was apeiron. An arbitrary crooked line was apeiron. A dirty crumpled handkerchief was apeiron. Thus, apeiron need not only mean infinitely large, but can also mean totally disordered, infinitely complex, subject to no finite determination. In Aristotle's words, "...being infinite is a privation, not a perfection but the absence of a limit..."

Rudy Rucker, Infinity and the Mind
reprinted without permission

"Interestingly, apeiron did originally mean unbounded for the presocratics, but did not come to mean infinity until later, probably around the time of Aristotle's commentaries on the presocratics. The Greek scholars that I have read who have written on the meaning of the word say that it means unbounded more in a perceptual sense, but in relation to the world. For instance, if you look up at the sky on a clear night, then your vision is unbounded."

"If you think about it, there is a difference between infinity and unbounded. It is possible mathematically to have an infinite number of things in a finite space, but unbounded cannot imply finite space in relation to the world, it can in relation to perception, which is what the Greeks were working with. It is hard for us to work with their texts because they really did see the world different from us. They saw apeiron on a clear summer night in the sky not only in an abstract conception of what the cosmos (which for them was a big sphere) is."

Trey Suttle
http://home.millsaps.edu/~suttlwf/
June 9, 2001