What chance do I stand, my trusted reader, what chance do I stand against this marvelous force? What odds do I have at accomplishing a strenuous task bequeathed to me as if in the act of mockery and derision? I should admit, dearly, that I'm failing, failing miserably at this undertaking.
How to traverse the uncharted waters where the sight of shores is far more evanescent than some distant dream, and the bearings provided by the learned ones are not less ephemeral than the clusters of fog in the open seas?
Such were the thoughts, my confidant, the thoughts that came and went like tidal waves leaving exposed this drained and barren reality of belonging from which I cannot escape, neither afloat, nor sinking. And where would I go even if I had the maps, the compass and all the gear? I would want to get lost instead, drift, be carried by the current rather, being able not to tell up from down and the East from the West. But none of this appears to be within my possibilities; no more can I pretend, no more can I elude or procrastinate. And it has no difference that the task has never been revealed to me, nor have I been given the slightest idea of what is required and which direction to head. “Forget, forget”, the sound of gentle waves would whisper to me, “let go and dissolve, dissolve in us, we accept...”.
I would not be surprised if you go on saying that I have taken upon myself what I shouldn't have, that the struggles of mine are self-imposed and the worries are overinflated, and I wouldn't be able to argue: what material proof do I have in support of my claims – none! My task has no valid substance, no mapped location and cannot be subjected to reliable measurement, yet it sits there as concrete as bedrock covered by miles-thick antediluvian waters, submerged deep beneath the currents of everyday affairs and barely touched by the torrents of the worldly life as we know it. And what can I expect when we are all taught to stay afloat before we ever consider the abyss beneath us and dare to notice the vertiginous quintessence of the firmament. So are our units of measure and the milestones: not dissimilar to navigational usefulness of the froth in the high seas.
My attempt is petty and trivial, the task, however, is insurmountable. Yes, it weights on me, weights with the mass of condensed silence, always there, looming like an unfinished theorem: inapplicable yet grandiose. Do you have the words to describe silence, do you know the colors that can paint emptiness? At times I come very close, I feel the breath of an inexplicable, begin distinguishing the colors of the dark and hear the silent melodies... You can duly equate this with madness and thus elegantly complete the unfinished theorem, and this is the beauty of it: irrationality expands the reality to the uncountable infinite continuum just like the one described in a flash of genius by Georg Cantor. But this is the whole issue, this is the exact issue I am having with all of you, past, present and future: misunderstanding.
Since when understanding became an accomplishment, since when we mistook proof for a fact? And if I can't present valid proofs of my own, what proofs you, yourself have, say of your own existence?
My task is beyond proof, beyond validation. Sorry, Georg, but the infinite uncountable set is empty: thats what you have indirectly proven but few understood. Can we now stop pretending to hypothetically count the hypothetical members of the hypothetical sets? Reality is irrational and the reality of the real numbers is made of irrational numbers. “Almost all”, I hear someone correcting me! Now stop where you are, infinity doesn't know 'almost', infinity is 'all', and if an infinite part is 'all', then the whole is also 'all'! There is no hypothetical point on a hypothetical line, and this is what irrational numbers show without further proof. There is no point of fixation neither in numbers nor in existence. All we deal and dealt with is the semantic consistency, consistency of a point of view over a point of view over a point of view. Take any integer, or better natural number, no you can't, because there ain't no number, it is only a consistency, a matter of unified opinion. I applaud ancient Greeks for doubting that one is at all a number. So, can 0.999 be 1? what about 1.001? How about the infinite decimal expansion of those two? How close will they come to number 1? And will there be any 'space' at all left for our glorious numerals after all? Even our trusted mathematics is an ephemeral concept devised over a concrete task of continuity. All numbers are an infinite interpolation of an empty set. Numbers interpolate the abstract ideas from the zero far-ends and into the infinite continuum of the center. Several ancient languages, especially the derivatives of Aramaic, are written in sinistroverse (right to left) likely for this matter. But even more likely, most ancient languages were first written in symbols arranged in multidirectional circles, like, say, mandala or Tzolk'in wheel, then squares, take 'sator square' until later becoming boustrophedon (bi-directional or snaking) as found in old manuscripts. When did we flip? When did we begin substitution of concrete for abstract and abstract for concrete? Remember, emptiness has the shape of a boundless sphere. We simply don't have anything more objective than that. Nothing is more unbiased and concrete than the empty set. The fact that emptiness cannot be measured translates into its greatest quality: unprovability. Every point of coordinate, every line, edge or angle is only an abstract and can only be measured in relation to some other abstraction in order to be “provable”. Emptiness, in contrast is objective and is not “provable” based on concepts of abstract. An empty vessel/container can be “proved” and “measured” against other vessel, but not the emptiness inside the vessel. Even if you can measure the degree of emptiness, it is only measuring the inclusions and not the emptiness per se.
Thus we now appear with you on crossroads, my fellow traveller, but trust, these crossroads are just a plot of imagination, an abstract concept, semantic consistency, so to say. There is hardly any intersection in the plane of objective reality; the roads there go in circles, and are not likely to lead anywhere at all to begin with. Put it simply: movement is not necessary if the center is indistinguishable from the fringe. That is what the infinity of an empty set is. Emptiness is truly infinite.
So, set a point, plant a flag rather, let's make it point zero; from here and so forth shall all distances be measured! How grandiose, yet nothing is accomplished. Someone else is needed to endorse your claim: it takes at least the two to validate the one. Be honest to yourself, your coordinate makes no sense all by itself: a pointless zero in the endless sea of void. But don't be saddened by this fact, there are still a few tricks at your disposal; go on make a step. Now you have a point two. Success, this will have proved your point one and vice versa. Both validated in one go! How great, you also have a measure and in fact a line. Hence, movement is itself a proof, a tool of validation. No wonder someone has proclaimed: “Life is movement!”.
Any abstraction requires a passage or a movement between A and B, which are otherwise indistinguishable from each-other. The word 'abstract' itself means to 'draw off' implying a starting point and the prescribed direction. This passage is here a 'validating' vector, a proper genesis of an abstract, a definition of subject from the otherwise undefinable object. Hence distance and duration are the definitions of an abstract. Object requires none of these as it's validating mechanisms. It is self-validated with any distance and duration being equal to zero. The direction is only towards or from the abstract, other than that, objectivity is directionless.
Infinity, on the other hand, cannot be abstract, since it don't have a departure point or a starting coordinate – the prerequisite of abstract. By elimination, the infinity thus must be axiomatic, objective and concrete. An abstract vector can be extended to infinity, but it cannot 'begin' from the infinite even though it originates 'in' the infinite (and remains there).
If we consider two opposite rays abstracted from the common coordinate and forming an infinite line, a dimeter of a boundless circle. The line is a subject since it is 'abstracted' and can be 'measured', i.e. direction; the circle has to be the object since it is there 'by itself' and is not capable of measurement. Don't get confused, the diameter 'defines' and 'relates' to the circle's circumference and its area but it is not the same as being measured and being proven. The diameter doesn't “measure” the circle, instead it is the circle that provides the scope to measuring and abstracting of anything in relation to its bounds. You can look at my friends, relatives and 'define' who I am, but this doesn't prove who I really am. Definition hardly goes beyond opinion and opinion is only a matter of consistency, with another opinion. Therefore, there isn't any plausible way of squaring a circle as there is no way of proving the object with the subject, concrete with abstract. You do have better chances of squaring the circle outside of Euclidian geometry, but not until you completely move away from the subject-driven realms and into the pure object geometry to which circle duly belongs.
See it for yourself:
Being 'boundless' this circle has no specific center, any point along the diameter can serve as a center, neither the size of the center any longer matters and a center can potentially be infinitely large, as large as the circle itself, or infinitely small, nor the location of the center matters any more. Therefore, the infinite circle 'fits' inside the zero center as well as the zero center 'expands' to the infinity of the circle. Does this not mean that the vastness of infinity is inherently empty? If zero is empty, than the infinity has to be empty, or if infinity is 'full' than zero has to be 'full'. Which one you choose, up to you, but let's conclude: infinity=zero, and zero is measureless. Being measureless is being objective, thus infinity is non-abstract.
e^(pi*i)+1=0 How beautiful! Like a flower unwrapping its petals amidst swamping marshes. A pure music. I imagine Euler walking along with Pythagoras, oh how much in common they see inside this equation! Yet, one tiny bit still disturbs wise Pythagoras, still boggles his mind: this “+1” has to be wrong, out of place, out of tunne.
Function is the mathematical interpretation of movement. Exponential, a non linear function is the movement from/to an abstract as seen by the outside observer. It is in essence a rotational impulse, however not completely circular: it is a rounding elliptical ever approaching circular if from the abstract or a flattening elliptical if moving towards the abstract. Euler's identity shown above is a 'pure' circular rotation outside of abstract .
E constant is the time interpolation of object, pi is the space interpolation of object, i, the imaginary number, the unrealized dimension, dark matter acting from outside space-time. Bring the exponential of time to the power of space (Space cedes the power to Time as we also know from the Uranus-Cronus metaphor) multiplied by the imaginary number and you have a steady rate of circular rotation. An imaginary number ensures a continuous 90degree push towards the center thus countering the otherwise exponentially increasing escape velocity (or preventing the pure object from grossing in to matter of the subject, preventing the manifestation so to say) and allowing the movement to proceed steadily in a perfect circle: Musica Universalis as the brazen serpent would have called it. +1 is the abstract of our world, the motion and the act without which the beauty of the entire existence would remain unrevealed, ever whirling in the pristine domain of the un-manifested object. +1 is the breakout, a daring of a seed to protrude and grow into a mighty oak, it is life as we know it.
So what is continuum? Continuum is a circular vector of object-subject-object, or concrete-abstract-concrete, ever bridging the two. The only reason, sine qua non for a continuum is subject or the abstract, i.e. the world of numbers, the world of ideas and representations. Pure object is directionless, distance-less, so no continuum, no movement, where to go then? Into abstract, as the only way. Why at all bother? Because there is a face in the emptiness, there is a mind in the object looking for exit. And after it has searched the infinity it failed to establish its own omniscience. No, absolute is further than infinity, beyond reach. Rightly, to know everything is to know nothing.
Aye, do you even know how profoundly depressing it feels: to search and discover, to play knowing the outcome? The last thing that was left is to create a 'different' game, a game where you'll pretend to really play it, to really search and to really find. Dismantle – gather – reestablish, this is the scenario of this game. Repeat until nothing makes sense, until order becomes chaos and chaos becomes a new order. Forget and remember, remember and forget. Recycle memories like rags, until they turn into ethereal dreams solidifying back into ideas, take material shapes... Proceed, create, amalgamate! Heat, boil and evaporate. Split, join, join and split. Condense the steam from sunlight beam: this process is alchemist's dream.
