In 2002 a reclusive Russian mathematician known as Grigori Pereleman solved the Poincare Conjecture. This arcane topological conjecture describes the boundary - or surface - of a three-dimensional sphere within the same limits of a simply connected, compact mathematical object known as a "2-manifold". The brilliance of Grigori's elegant solution used something known as "Ricci Flow" that is often used to describe the movement of heat, and his accomplishment represents a paramount advancement in mathematics. While the significance of a solved Poincare conjecture may evade even the most ambitious armchair professor, the significance of “The Boundary” as a descriptor has corralled and confounded humankind for eons.
If only the boundary of a 2-manifold would have been resolved sooner, perhaps nautical advancement would have ventured Europeans beyond the "flat world" well before 1492, thereby redirecting the course of history. Or maybe the quantum mechanical probabilistic orbits would have already intersected with the Standard Model to provide us with fusion power. Even more exotic are thought experiments testing the synecdochical boundary from neuron to consciousness. Where is it, precisely, that an electrically active neuron bestows the synchrony of "thought"? Where is it, precisely, that my atoms end and the keyboard’s atoms begin? ...Where is it that anything really ends and everything really begins?
Zeno of Elea asked similar questions long ago, questions that would employ mathematicians and philosophers for millennia. And some of these questions remain unanswered despite Grigori’s best attempts. But is it possible that the nature of a boundary is purely semantical? Our touted “intelligence” as a species is attributed by most anthropologists and biologists to our ability to communicate through language. This evolutionary feature, many would argue, was our best weapon against the odds of extinction; yet, the innate irony to this notion is that language itself is a boundary. And a rigid one at that.
The same sphere that Grigori masterfully described may as well be a “circle,” or a “horse,” or a “really complicated thing that I don’t really understand so I’m just going to use it as a metaphor for my next blog entry because I can spin it around to get at what I’m really talking about”: “The Continuum”. The Continuum in which we think-therefore-we-exist is beyond mathematics, beyond science, and certainly beyond language. We may have an arsenal of words at our disposal, ready to strike the beleaguered mystery of the Universe, but their firepower is only as powerful as the boundary by which they describe. That is to say, words can only describe themselves in the context of other words. A lightbulb is an object that emits light, which is the spectrum of radiation that our photoreceptor cells can recognize, which is a continuum of radiation defined by different frequencies, which are periodic oscillations defined by T = 1/f...but do we now know anything more about the nature of a lightbulb at this point? We do only if we understand the definition and the context of all the subsequent words. But even then we find ourselves jumping from one claustrophobic boundary to the next, and so on until the nature of the original observation -- that of the lightbulb -- is lost.
The Continuum, then, is but the elegant nature of “something we really don’t understand,” and so we are left in a padded room with a few toys (i.e. words) to distract us. Unfortunately, the human brain seems incompatible with this maxim, so much so that we often seek answers in black-and-white absolutes and not in the gray honesty of The Continuum. This discontinuous, myopic perspective is ironically provided by words. To bring another philosopher into the discussion, Einstein provided us with possibly the most elegant step beyond The Boundary by leaving us with E = mc^2. This simple equation defines the contiguous nature between energy and mass -- both of which our flesh resonates. Where, precisely, these two entities merge into one is, again, a consequence of semantics.
And so to define something is to surrender its true nature. Just as the Heisenberg Uncertainty Principle states that the observation itself of a photon collapses that photon’s wave function, a definition itself of The Continuum collapses the nature of The Continuum. We cannot, however, live completely outside our quarantined existence -- at least not if we want to live in sanity. I am a student. I am a scientist. I am a musician. But one cannot adhere to these semantics as though their nature is static. The words themselves must by dynamic in order to adhere to their intended meaning. What it means to be “student” must be able to adapt, as I may some day still consider myself a “student (of the sciences),” even though I am a professor. And what we know now as “Christian,” or even “right” or “wrong” may change -- and should change -- as knowledge and technology advance our species into the nascent 21st Century. Surely it was once a “curse” of the demons for one to have delusions and hallucinations, whereas now it known as “schizophrenia;” and perhaps one day schizophrenia will be known as an abstraction of one’s dimensional existence that is ill-defined by a 2-manifold in the quantum consciousness of humankind’s realm. It would be black-and-white hubris to think otherwise, as what is true is what is continuous, not what is defined.
