Rene Descartes wrote of the unique idea of infinity.  Infinity is a word that we know and use.  Even more, today we would say that calculus is the math of infinities.  Yet, according to Descartes, infinity is a notion that overflows itself.  Of necessity, it is a word that must be what it isn’t.  A word or an idea is finite.  Yet, the idea of infinity is a placeholder for what it cannot be.  It is not like the ostensive definition of a cat.  The word cat points directly to a cat.  The word “infinity” does not point directly to any such “thing” as an object.  However, it is a word that gets its meaning by negating itself not for some mystical reason but for something as real as the mathematics of calculus.

The Greeks were very taken by the geometry of the triangle.  Even more, Plato spoke of the forms, the ideal perfection, the real of everything we see.  Everything we see is murky and shadowy.  We know from Einstein that there is no such thing as a perfect triangle.  Space-time is warped and curved by mass so, while we might imagine a straight line, a straight line does not exist.  The real strait line only exists in concept form.  The real triangle is an ideal form but has never existed.  Yet, we use the idea practically all the time.  It is a concrete ideal or as Hegel might phrase it a concrete universal.

While language is a system of signs, signs are not all made the same.  Some signs have a real, ostensive object like a cat.  Others can only point to something concrete by dismantling themselves, by holding the “not” more closely they point to ideals that never “are” in existence and yet “are” as real, concrete and practical as a cat.  What should be observed is that they are what they are by being what they are not.

Perhaps this could be said of all words and ideas to some degree.  They designate over and against to function.  They instantly define by negating what they are not.  Some words and ideas can function as ambiguities, metaphors, poetry, art, etc.  Similar to infinity they can simultaneously hold various systems of thought, ideas or get reduced to a myriad of words.  Take this poem I wrote a while ago:

Oh wistful night of a million suns.
Spawn dancing shadows from nameless orbs.
Through stellar darkness light years are thrown.
Perchance dark grace our sun or moon
And primal night fire my heart drum.

Oh wistful thoughts of a million souls
Spawn dancing shadows from nameless histories.
Through unconscious darkness years are thrown.
Perchance dark grace our I or other.
And primal projections fire my loves

This poem speaks of a natural phenomenon, an eclipse.  Yet, it also holds with it a primal humanity, an archaic origin.  These are not systems of signs that would normally go together but in the metaphor of poetry that can actually elucidate or bring to presence a “reality” of who we are. 

Words can also be mistakes. We can say that a square is a circle or that A is not A but it is simply wrong to insist on such a thing.  In a more sophisticated fashion we can all freely develop ideals or ideologies in politics, religion, morality, etc. that are simply based on wrong facts.  We can put together ways of thinking that do not belong together.  As in evolution, we can make mistakes that can take on a life of their own.  When Einstein first came out with what we now call relativity more physicists opposed him than agreed with him.  Many thought that the universe Einstein envisioned was a step back to the hocus pocus of the dark ages, a step away from the concreteness of Newton.  Over many decades the doubters became less and the believers increased.  Einstein had a set of facts that he observed keenly that embodied many wrong perceptions (see “Einstein’s Mistakes”) but held together enough of unexplained phenomena that the Newtonian physics could not hold together to provide a more plausible showing of our universe.  The point here is that while language allows us to put together systems of signs that do not go together, that are wrong, not based on “facts”, they can also hold enough of a truth, a cohesion that does hold together to make them plausible.  This does not mean that a square will ever be a circle but in curved space-time it is possible to pick a coordinate system in which an object could be described as a square or a circle.  A cylinder can be sliced as either.  Yet, the idealized concept of a square and a circle will always be fundamentally at odds with each other.  To insist that A is not A is opposite to a tautology, an absolute contradiction.  The idea holds together concepts that are absolutely incompatible.  In its “wrongness” the idea comes to be.  Its “wrongness” is always contingent.  It can only be wrong by proclaiming it, by naming it and what it necessarily entails.  It abstractly “nots” itself while at the same time asserts itself.

In every thought and concept there is a “not”.  The “not” has to be for the word, thought or idea to be.  Any idea must be what it is by announcing what it is not, by suggesting it is this and not that.  This may seem trivial but for Hegel the “not” was always an absolutely necessary operative in every concrete word, concept, idea, reality, etc. – the “not” is always necessarily and unequivocally implied by existence.  Post modern deconstruction might think this as the trace of the knot that always must undo itself, a sort of tangential contingency that is always taken up into our surest notions, the dark side of presence, the banal “not” of existence.  It allows and creates existence.  It is always the “other” that cannot be totalized or brought into a cohesive presence.  It must eternally be relegated to the nether region.  For the light to be, the dark must always be a close ally.  Our finitude and mortality can only be in lieu of infinitude and immortality.  Wrong must be for right to be.   This is a step into Hegel.

Knowing this play of signs destabilizes our absolutes, our forms.  This awareness curves in on itself into an absolute singularity, nonsense, a hermeneutical circle.  It frees us of logic while simultaneously necessitating logic.  Normally, only the ravings of a madman would be attributed to such rants.  Perhaps it is madness but it is a madness that must be for the sane to be.  Foucault spoke if this in “Madness and Civilization”.  There is a irrationality that necessarily plays at the roots of rationality.  It can be “deduced” and has been by philosophers and scientists.  Physicists have known about singularities for centuries.  Yet, a black hole is a singularity.  When they recognize a singularity it causes them to reflect back on their theory.  The mind necessarily turns back on itself and doubts itself, its current understanding of physics in this case.  Curved space-time was such a demonic notion for a classical Newtonian.  How can mass get larger with speed?  How can a ruler get shorter with speed?  How can time slow down with speed?  Did you know that one of the first ways relativity was proved was by synchronizing two clocks, putting one in a plane and flying it around the world several times and comparing the results when the clocks were brought back together?  Sure enough, they reported different times.  Can you image being one of the folks carrying a clock around in a airplane to see if speed changed it?  No wonder physicists thought Einstein was insane.  Need I discuss string theory?  Have you heard of the m-verse, the multi-universe?  All particles we observe in our universe are really multi-dimensional strings coming in and out of existence or our brane (membrane).  Just as a triangle can never really exist because all space is curved, our brain tells us that it is and we use it every day as an essential tool of technology. 

You may think that the way the “not” circumscribes and denotes what is is insane but the fact is that it is as a “not”.  I am not making this stuff up, only reporting it in the company of those that are much smarter than me.  Sure there are myriad other ways to process this insanity at the roots of the sane but they may only be the illusions of a brain that cannot allow the contradiction to be.  It may be that the evolution of the brain has made it impossible for the concreteness of an absolute “not” that “is”, that necessarily gives rise to “isness” to “see” what shows itself here.  This absolute fissure in achrony, time, how we perceive, understand, know, etc. is an alterity or otherness that can never be gathered or held together – and yet, it must be in its “not being”.  The sense of this is embodied in the intuition that for God to create being and existence God must be outside of being and existence.  Only by God “being” outside of existence can existence be.  This is yet another indication of the insanity that awaits us in the “absolute impossibility of the possibility of death” as Heidegger suggested.  The “me” that is to die cannot in any way conceive of death and yet death “is”.  Be careful as Nietzsche points out that if we look too long in the abyss the abyss will look back into us. 

What gives rise to the “soul”, the different kinds of awareness’s that enables humans to write books, create art, build technology, in effect, create worldhood?  It is the way that we are thrown back on ourselves in the face of the “not”.  It is the reflection that forces us to doubt our concrete perceptions, understandings, knowings.  When we doubt we re-think, we ponder, we try to make sense of, decipher and restore the cosmos to order.  This is our life long burden and we eternally are rolling the stone up a huge, never ending mountain.  While our dilemma may be insane it cannot be argued that it is not concrete and as “real” as any of our functional and assumed realities.  Only by the denial and sublimation of what the conscious cannot conceive can we have an unconscious, a dark side, a mystic writing pad that in advance of our deliberations writes our history and requires our obedience to a call that we cannot choose.  The turn here can only recognize a sort of Kantian category of knowledge.  Light is invisible and yet when it hits mass, particles it gets filtered sort of like a prism and shows color, sight, objects.  Light is not what we are seeing only the effects of the filtering of light.  Likewise, the “not” that necessarily gives rise to being, existence, concreteness is itself always never perceived but in its wake we are and have our being.