"Whereof one cannot speak, thereof one must remain silent." – Ludwig Wittgenstein

I gaze outwards unto the overhanging gray skyscape. Stretching above me is a gigantic, ebon trunk rising into the heavens. Across the plains I see a further two trunks stretching proudly into endless skies and yet another adjacent to the one I'm closer now. At each one I see the Physicist, the Biologist, the Chemist, and the Mathematician climbing, mere ants crawling upon these gargantuan celestial conduits. Each climber shouts to his adherents, they report their findings, they help each other take a further step upwards. It's a difficult, cold and lonely task; the higher they get, the thinner the air, the harder the climb. He's almost there but not quite yet, he gazes downwards, down, on the bottom ground, a herd has gathered, the weak turn their heads in fear of the terrifying, vertiginous heights; they shout words of discouragement in a vain attempt to cover their own cowardice. "How small are they from up here!" he gasps and yet the questions still echo in his fervent mind: Is there an end? Is there a summit that each climber in his own right will reach? Is there a Form to this four-legged Divine Table of knowledge? In Reason we trust...

For centuries man has engaged in efforts to understand the world he inhabits, a world bounded by his reason. Knowledge increases at exponential rates, science perpetually revises itself, worldviews are re-interpreted and re-analysed while we try to find a meaningful place for Man in the infinity of the cosmos. "And yet it moves!" whispered Galileo circa 1616; perhaps the quintessential act of one man's tenacious grasp of Truth, or rather scientific truth. From Aristotelian cosmology to Ptolemy and from there to the Copernican revolution and Darwin's "Origin of species" as our knowledge of the world expands we mortals come to understand more and more of the laws that mould our physical and biological reality. With all this progressions the very notion of God (or rather the Judeo-Christian God) has retreated from being an all-powerful, intelligent artificer of the Universe, to something completely incompatible with what the world appears to be through the eyes of Reason.

When taken en bloc science seems to slowly unravel a universe that at one level is coldly indifferent to our existence, that we are nothing but another continuation on this endless cause and effect chain of events. Yet at another level it reveals a universe whose amazing complexity is reciprocally reflected in the mind that ponders it. Where is science really taking us on this cosmic journey? What is it exactly that we are trying to understand? Indeed, what is really more mysterious: the observable world or the observer who observes it? As we take this inward shift it would seem that the only epistemic tools in our possession, namely our senses and our reason - our sacred reason - are themselves active participators in this mystical dance. Perhaps we are no longer the detached observers of the outside world that we thought we were, perhaps the enigma that we are is much more intricately bound to the Universal mystery than what our previous conceptions would have us believe.

Philosophy has always dabbled in such question begging so it would be no surprise that it is in philosophical works that we find the first serious inquiries into the limitations of Reason. It was Aristotle, the first great Naturalist, who espoused that the Truth lay in the World much like Leibniz who hoped for the eventual subsuming of Nature into a rigorous, mathematical whole. Aristotle was antithetical to his teacher's conception of a Perfect netherworld of Forms, which in itself transcended Reason. I for one, and apparently I might not be alone, lean towards to the Platonic ontology. The most known vanguard of rationalism, Rene Descartes (1596-1650), escaping the insidious pit of hyper-pensive skepticism in which he fell, established, quite vigorously, that reason is the irreplaceable foundation of reality and a necessary condition for it to exist in the first place.

Although his impassioned rationalism paved the way for a more secular and hence more quantifiable understanding of the universe his apotheosis of Reason was later on to be vehemently attacked by the great skeptic David Hume (1711-1776). For him the role of reason is limited and the deductive reassurance of an external reality is in principle misguided thus firmly placing him in the empiricists' camp. Amidst the ruins of the Cartesian citadel of Reason left by the relentless attacks of pernicious Humean skepticism it was the Prussian giant of German idealism, Immanuel Kant, who would resurrect it but on a very different foothold by a conflation of both his rationalist and empiricist antecessors.

Immanuel Kant (1724-1804) is generally regarded as one of the most important if not the most important thinker of modern philosophy. His ideas are pertinent to the issues herein because he himself upon inquiring on the nature of human Reason was the first, to my knowledge, to rigorously infer the repercussions these limitations would entail for our understanding of our cognitive abilities and how this reflected on the apperception of the World. I won't dwell on his idealism, since it reaches far and beyond the spotlight of this essay, or the subsequent philosophical movement that he instigated but rather focus on his groundbreaking ideas in the role of mind as an active 'painter' or artificer of reality. Kant states that objects that are conceived through our sensorium are themselves constructs of our cognitive apparatus; different features are imposed on the "object" allowing us to intuit it (in Kantian terms) as a cognizable object.

He even went a step further, postulating a distinction between what we comprehend through our senses, i.e. the phenomenon, and the thing-in-itself, which exists untainted so to speak by our cognitive "tampering". Most importantly this meant a dichotomy between the reality of the human being as a neuro-cognitive construct and the noumenal world that will remain forever unknown to us. Consequently, the notions of time and space (the forms of sensibility) are features of the world that are imposed by our own faculties, and are subjective and necessary conditions if any knowledge of the world is to be possible. The eerie world of quantum physics has made such notions at the least thinkable over the last century with the discovery of quantum entanglement and non-locality. Furthermore, logical paradoxes such as the one of infinite halves as first proposed by Zeno of Elea again raise the difficulty in defining something as basic as spatial distance when confronted with such skeptical conundrums.

Interestingly enough and when taken under a Kantian prism, developments in cognitive neuroscience have revealed that many features of object apperception are modular. For instance, there are different neural circuits responsible for extension, shape and even some form of subtle categorization (edible vs. inedible objects etc.) This gave rise to what is known as the "binding problem", i.e. how can the brain "bind" all this information as provided by each sense-data processing module into a meaningful whole as represented by the object (e.g. a rose)? It would seem that this is quite redolent of Kantianism since the active contribution of the brain in "setting-up" a visual framework for the subject to interact in was one of the prime tenets of his work. There have also been developments into how the brain processes information via neuronal communication. Up until the mid 19th century vitalism reigned supreme stating that the human body was irreducible to a complex organic machine but instead different body parts communicated with each other via some form of vital 'essences'. Neurophysiological discoveries however made later at the turn of the last century and later on in the mid 1900's, revealed that neurons communicate with each other via action potentials; small bursts or "spikes" of positive electrochemical gradients (long gone are the 'essences' of the vitalists...). Every spike is essentially a singular bit of information, a binary state of either 0 or 1. It was Lord Edgar Adrian back in 1926 whose work suggested that the spike rate of neurons might be the principal means by which a single neuron can transmit information on a certain stimulus.

For example let's say you have a neuron that is sensitive to different temperature states; hot (or rather a certain temperature range designated as hot) might elicit a spike rate of 1500 spikes/sec; cold 250 spikes/sec and so forth. However things aren't that simple since temporal features of the code in question can impinge on the quality of information transfer so it is important to look at the entire time-scale of neuronal activity to reliably understand how the neuron can readily distinguish between different stimuli. Ultimately all information that comes through our senses is reducible to an ordered sequence of action potentials or "spikes". It is not all that important to fully understand the science behind all this but what is emerging from the research is that finally neuroscience is catching up with Kant. Slowly, we are beginning to back-up Kant's understanding of our cognitive interpretation of the world with scientific data. Furthermore, the elucidation of the neural code reveals a quantifiable appreciation of the a posteriori acquisition of knowledge through our faculties of perception.

Most importantly, the phenomenon-noumenon dichotomy becomes evermore apparent since the phenomenon, the subjective representation of the object, is essentially quantifiably measurable and its units are in terms of the neural coding, i.e. a sequence of neuronal activity can be described as a function of time, e.g. rose(t) or even face(t) (this function is valid if the temporal facet of the code is thought to carry information and hence taken into account, otherwise activity could be represented as r_rose or even r_face, averaging over time and discarding time-scale variation). Now the mind-twister is what is exactly causing these particular sequences of neuronal code to manifest in our conscious experience? What is exactly causing the neural code to even represent some form of information in the first place? What is the thing-in-itself behind the phenomenon; the Rose behind rose(t)? It's like the childish question of asking what is gravity made of or what exactly IS the number 3 for example.

Childish but not necessarily frivolous in their posing because when taken in all seriousness these questions reveal a fundamental limitation to any rational acumen that we may possess. Once again Kant to the rescue where he ascertains that our capacities of reason are structured in such a way that it poses enquiries that itself cannot answer. Further blows to our deductive reasoning have come not only from philosophy but also from the fields of both mathematics and physics with Gödel's incompleteness theorem and Heisenberg's uncertainty principle. The former suggests that mathematics as a system has insoluble problems that extend far and beyond our logical formalizations and the latter that we have limitations in knowledge which again are beyond our grasp. Specifically Heisenberg's principle states that at the quantum level different states are not deterministic but rather stochastic or probabilistic such that we are inherently incapable of rationally giving a precise model of such physical state of affairs: "The more precise the measurement of position, the more imprecise the measurement of momentum, and vice versa. In the most extreme case, absolute precision of one variable would entail absolute imprecision regarding the other."

So if quantum theory reveals a microscopic world of no apparent or at least measurable order then the ordinary macroscopic world we seem to inhabit might not be all that 'ordinary' or even in every respect rational after all. Both these theorems make AI advocates cringe since they imply an un-impeachable obstacle in their quest for an algorithmic description of their notion of what intelligence is. However even if these limitations to positivistic enquiries are insurmountable there is still much to be done towards an understanding of nature not as it is anymore, i.e. as something epistemologically objective, but as it is represented to us through our sensorium. Kant and later scientific discoveries gave us a good taste of our limits; we are finally grasping on the walls of our cages and lo' behold!, we discover that there is a cage after all. It is quite an attractive idea to think of the universe as a naked edifice, open to a full and complete understanding but the consequences of such thoughts leave much to be desired in their naďve optimism.

Fundamentally it might be the case that the World as it is, is truly irrational and bereft of meaning – or at least a meaning appreciated by as common mortals. Both Heraclitus and Lao Tzu made reference to an un-nameable preternatural essence that fashioned the universe according to its Will. According to them it forms the primary substratum of our reality; it is as the Tao Te Ching describes it, the "Intangible that makes the tangible possible". At some fundamental, quantum (?) level then all is One, matter being subservient to this sublime Unity like everything else, a whole greater than its sum of its parts. Most importantly both the Logos of Heraclitus and the Tao of Lao Tzu were ascribed with no human features and dubbing either of these quasi-numenal essences as God would be too vague a term since their inner cores are fundamentally unknowable to the human intellect. For Spinoza, God is infinitely manifested in Nature, for him science is the ultimate course of theological investigation and he henceforth places all his faith in the fruits of Reason but alas denies any form of pure free will to the human being.

From this perspective we're caught in the endless maelstrom of God's -- or Nature's -- restless perturbations like an unaided man grabbing on a plank in the midst of a sea tempest. Undoubtedly, there is a sense of glumness exuded from these schools of thought and it is without surprise that the great German pessimist Arthur Schopenhauer concluded that: "In a world where all is unstable, and naught can endure, but is swept onwards at once in the hurrying whirlpool of change; where a man, if he is to keep erect at all, must always be advancing and moving, like an acrobat on a rope -- in such a world, happiness is inconceivable. How can it dwell where, as Plato says, continual Becoming and never Being is the sole form of existence? In the first place, a man never is happy, but spends his whole life in striving after something which he thinks will make him so; he seldom attains his goal, and when he does, it is only to be disappointed; he is mostly shipwrecked in the end, and comes into harbor with masts and rigging gone. And then, it is all one whether he has been happy or miserable; for his life was never anything more than a present moment always vanishing; and now it is over."

All these interpretations of the world leave the dedicated rationalist in decrial of the finitude of our capacity to understand it, as it is; that our world is but a "limited whole" in the words of Wittgenstein. Spinoza was dubbed as some sort of materialistic mystic, and it is in this brand of materialism that we could hope to marry the nature of the Infinite with our finite material world. In that effect, I believe slowly science is giving a physical rendering of what the nature of the cosmos might be, its elusive, infinite nature however will always let it have the last word.

So where does all this leave us? Brash reductionist materialism and petty, pseudo-nihilistic "nothing-but"-isms are not the best depiction of reality and they most definitely won't provide us with the necessary answers. Nevertheless when materialism is undertaken in a more calculated and concerned methodology perhaps it is the only viable means we have at the moment towards a stalwart and rigorous scientific understanding of our world. If, however, we allow orthological skepticism to ravage the very altar of Reason with the advent of this relatively recently acquired ammunition then we are very well doomed to a scientific world of no firm basis, but hopefully this isn't the case.

The questions remain though: can we ever hope to escape the Platonic cave and attain access to his mystical realm of Forms, of pure unadulterated reality? Or are we mere biological machines, bound by laws so incomprehensible and unreachable (although we may asymptotically tend towards a clarified comprehension of the physical laws that affect us directly) that any effort to helplessly fathom an Infinite world within the diminutive spatiotemporal context of our existences is by our very nature futile? While struggling for an answer I ponder our climbers who, after eons, may finally reach the summit. They will grasp for each other in fear in the thick darkness. And now... They gaze outwards into the gaping Abyss... Some crawl to the outskirts take a proud look and say, "I like it!" while others turn away in woe and despair. The tearing Silence, the sacred Silence is all that is now. And perhaps, this may be the crowning achievement of our epistemic capacities, the final Limit: that after centuries man has finally realized that he knows absolutely everything about nothing and absolutely nothing about everything.

September 24, 2007