I. THE STRANGENESS OF UNTOUCHABLE NUMBERS
The strangeness of untouchable numbers lies within their inability to be held. Zero and infinity reside outside and above human understanding. Neither may be truly imagined, fully perceived, and thus we allude to their sense of presence. They are two brilliant ideas which seem to elude concrete fact and traceable logic. Ages pass before zero and infinity are recognized and named. It is as if a declaration of the obvious requires an elegance of perception. Between these polarities exist our tangible realm of numbers. One might question the stability of numbers if these two foundations were the last to gain recognition.
Numbers are concrete, basic, and tangible to the grasp. An ethereal quality that exceeds appeal has embodied zero and infinity. It is as if the tangible and real were born from the dreamt and ghostly. If the spiritual had formed the visible, then where does the basis for our reality begin and end? These two numbers are an essence of mathematics and yet their pedigree seems elusive and mystic. How does one derive clarity’s proof of assurance if such foundations lie within the mysterious?
If the foundations of science reside upon mathematics, how reliable is that stability? A fundamental of science is accountability. Every step must be consistently traced from inception in order for hypothesis to be deemed as theorem, then law, and then into fact. All of this must be in accordance to their defined purpose, yet mathematics remains haunted by the vague. Zero and infinity are a symbolized rationale that has been placed for acceptance. In truth, both concepts retain an air of the vague. Does the nature of paradox consistently inhibit our midst? If paradox maintains a consistency of presence, then why does consistency itself become thwarted? If paradox has held our steps, if mathematics has ghosts and holes: then what of science?
II. EXISTENCE WITHIN AN ENIGMA
Infinity is a number that remains uncountable. It is not truly grasped and therefore it retains a symbol to assure us that it remains in a place reasonably close to our suspicions. It lies beyond imagination and above reason. We are not sure what it is, but it is sensed to such a degree that we proclaim the knowledge of its presence.
The breadth and depth of numbers are held by human understanding, yet infinity resides within the inverse of holding us. We lie within its whelm, overcome by a glance cast from its horizon, we are lost within the details of its epic. Our lives reside beneath the cast of its shadow, mere and atomic within a scope that exceeds our sight. We are particles against a giant that exceeds reason and its expanse maintains invisibility. It may have been frustration, utility, a corrective oversight, or a declaration of the obvious that led us to name what we did not fathom. It was a conciliatory gesture for understanding. That acceptance of reality shifted our perceptions. Our expectations changed when we gave the uncountable a name.
III. DUELS OF THE INFINITE
Picture a number line that is centered around zero. The positive numbers emerge when zero ascends to your right. The negative numbers occur when zero ascends to your left. Both sides of zero approach infinity. The positive numbers allow one to be led into macro-infinity, while the negative numbers stretch into micro-infinity. The macro-infinity is infinity on a larger scale and this is how we commonly think of infinity.
Life is big and this would be obvious if one were thrown into the depths of another galaxy. The approach of macro-infinity envelopes one through a sense of awe. Awe occurs because words fail to describe what lies before us. Awe is also the prime ingredient to aspects of wonder. Wonder occurs when beauty is so striking that you become enveloped by awe. Whether we realize it or not, the secret pursuit of humanity is that state of awe. Macro-infinity produces awe as well as fear and insignificance. When Neil Armstrong went into space, he had no other choice but to believe in God. Awe had eliminated all other options except for the obvious.
Micro-infinity is infinity on a smaller scale. Assume that one is looking at an organism through a microscope. As one increases the zoom, one realizes that there are worlds within worlds through this venture of perception. The approach of micro-infinity may envelope one in madness. Micro-infinity holds an expectation of a solid finality. To discover another road that veers into the endless is a frustrating drive into crazy. We are hesitant to realize that the common avoidance of humanity are states of delirium. That madness is derived by the microscopically infinite.
Once, one may have believed that there was one infinity, now there are two. People take solace in viewing the bound of things, it enables definition which in turn fosters the illusion of control. Definition leads to axiomatic formulas which become an ability to manipulate and we feel empowered by that aspect. It emits an illusion of control and that becomes saddled with expectations. Human beings take comfort in control because we have a lot of fears that are maintained by our numerous vanities.
A loss of control is instilled through both forms of the infinite. The difference lies within the placing of expectancy. We do not require being placed into a galactic expanse in order to realize that life is too big to control. It is an easy acceptance because the context surpasses expectations. We do not adhere to the rise of expectations. The universe is big and breath-taking. Expectation is dismissed with a greater ease on the macro-level. That ease of dismissal becomes zero expectancy. Awe becomes more facilitated to occur in that absence of expectancy. This understanding seems innate within humanity and we remain comfortable with that.
Both forms of the infinite leave us breathless. The problem lies within the expectations that accompany a micro-level’s breathless state. This usually means a panic attack keeps one gasping. We must accept the apparent that is buried within the deep down: we control very little. The problem with the micro side of life is that our expectations are hopelessly shattered to the point of madness.
IV. THE LEAGUE OF GIANTS
Both sides of zero approach the infinite. Assume that you have written this number line on various sheets of paper that are different sizes. Now bend the paper into a circle, then take other number lines of different sizes and bend them into circles of different sizes. Each circle contains a number line with zero going both ways to infinity. There is a positive infinity and a negative infinity. Their eventuality is somehow reached from zero.
The notion of shape and form has become apparent, involved, and this leads us into the notion of dimensions. These variables keep stacking their necessity. Since shape is involved and apparent, infinity is symbolized but not given. A geometric sight becomes an intuitive proof. The original scope of number lines are retained within the circles. It becomes obvious how infinities may be greater than one another and yet equal. Infinity is an idea that has been sensed, partially seen, but never viewed through its full scope. It is a symbol that represents something beyond our comprehension.
Zero and infinity loosely render themselves to religious experience. Zero would favor Eastern religions such as Buddhism, because of concepts like Nirvana. In Nirvana, one empties themselves to a state of nothingness, a selfless peace. The infinite would favor Christianity within the realm of Western religions because God is omnipotent, omniscient, and so forth. Infinity could be thought of as an impersonal paradigm for God.
Zero and infinity are ideas which are framed within a context of paradox. Paradox does not have a symbol, but it is something that goes against what we comprehend. It is similar to a matter that is counter intuitive. Logically, something should work, yet it is the illogical that makes it go.
V. A VALLEY OF UNCERTAIN SHADOWS
The wandering into philosophy is realized when fascination and madness settle into a schizoid appeal. This mode of thought may be circular motion or a deafening necessity than is unnecessary. It may also be a depth of method that shuns the expectant, a logic exotic and above our understanding. In the parting of reason, the mad may lay claim to the wake of the mind. Should reason be superceded, the philosophers depart anticipation to become pioneers.
Philosophical induction has come upon mathematics. The nature of thought itself becomes open for perusal. One may study the brain, behavior, the mind, the spirit, the soul, and these quests deepen. Medicine, biology, chemistry, physics, and other fields may also tempt mathematics. The introduction of these matters become problematic when conclusion seems endless and wandering. It is unnerving for small infinities to inhabit foundations. Foundations are supposed to be solid and stable. Madness rises from despair when the endless appears inescapable.
It is mad to fend against reason and foolish to forsake truth, but the lull of uncertainty may shake a stable mind. Leaving the old for the new is a seasonal transition. We are daunted by the forge of transcendence, the fall from its testing looms as our peril. Einstein once claimed that imagination lies above reason. Godel would require faith above all else because we are flying blind. The daunting matters of life require faith to lead us through uncertainty. If we do not seek the infinite, then we fall as nothing.
GODELIAN PSI-FI 2 INFINITE VEX THEORIA OO2