Escape Velocity |
A tangent must prevail over the forces of the circle to which it belongs and the forces that act externally on that circle. Velocity is needed to get a rocket off the ground and further velocity to get it beyond the bounds of the earth. No mean feat, the tangent's.
These forces may be variable, the rules that govern triangulation are known and constant.
Webster:
We could explain it (the right angle) as the central line between an obtuse and an acute angle, where they meet. Entirely rational, figured out using an irrational, *, pi, denoting the ratio of the circumference of a circle to its diameter, having a value to eight decimal places of 3.14159265. 22/7 if i remember rightly. Irrational because there's no such rational number, it doesn't work out exactly. Never. Not even by a ferocious analytic engine determined to outdo MAN. MAN standing for "mad as an 'atter". My minor authority on pi declares it to be a transcendental number. Out of this world, i suppose.
Getting out of a closed circle is an irrational act. Irrational in the best sense. When it's time to get out, bid goodbye. Brush off the dust. Curve headlong into the future.
Now a bridge is a connection, linking what is known with what has become known. A simple interface, there meets here, at these points. A significant connection. The adventurer or explorer who discovered this crossing place leapt from one world to the other, from the familiar to the unfamiliar, as no doubt did the errant geometer that first triangulated his way out of a circle. Presumably "his". Though a female has been known to go off at a tangent, too, to good purpose.
Reasoning led our geometer to his eureka. Practical or pure we shall never know. Is there a difference? Philosophers would have us think so. If there is, it is arbitrary. We cannot learn the unfamiliar without transcending what we already know. Oh, argument rears it inelegant head. Raises its hackles. "Peace, Man!" as the hippies would say. This is not about territory. Serious authority has not been invoked. We are asterisks questioning the text in a footnote. Travellers on foot in a country where authority rides. Pure reasoning wouldn't have got us out of the armchair and on to the soapbox. Hobby horses do that.
I want to bridge the irrational and the rational. Why so touchy? We are told we cannot go there because we don't know the maths. Does maths know the maths? And if it doesn't, who's going to lead it by the nose to the water of wisdom and make it drink? An irrational human brain has to get there first and build the bridge. Obvious, isn't it?
No place for emotion in maths, that science of necessary connections, which comes along and crosses bridges intuition has elicited, proving them licit. Did e-motion drive the inference that essayed this first passage? How many times did it fail? And faltering, resumed the search? Passion proves its place.
Intuition sails into the blue and out of the blue produces wonder. No sleight-of-hand, but true wonder. Look, Ma, triangulation, i did it! I got us off the goddamn ground. I broke the sacred circle. freedom to breathe. Inspiration in the air.
Wonder becomes the light of common day. Familiar. Old hat!
There are nets for all kinds of catch. Custom-made grids. We haven't got one big enough for the universe, but we're trying. A grid is a sieve. Ever think of that? Things slip through it. Drop your net over something. Can you tell what it is by enumerating the points where it makes contact? Fat chance. Especially if it's strange. We ask a topologist, where shall we start in building the ultimate net? Depends, they'll say. Probably shrug.
22/7. Not a round number. A number rounded out. Like the Wicked Sister's foot. The glass slipper, wonderfully transparent. Not ordinary glass. Faery glass. Neither reflecting nor refracting. Doesn't deflect light or bend it. Imagine, bending light! A faerie property if ever i met one. For that matter, occluding light. Transmitting light.
Expendable light. As far as we know, the energy in the universe could be measured. For it's conserved. Well, a pound of energy will always be a pound of energy, in whatever shape it comes. Stands to reason. Though what energy is, no-one knows.
Call energy motion. No, call it volition. Volition gets things done. Even thought of whatever stripe requires volition. Idle thoughts, too. For we permit them. You see, life is volition and life must go on, as long as it lasts. Life, alas, defies conservation. Prove me wrong!
License is common in language. It offers freedom to expression. We like to keep it out of logic and philosophy. You know, adherence to Truth. White knights, ever immaculate. Handle expression with kid gloves. Make things definite, exact, clear-cut. A maiden must be virtuous or a strumpet, no tinkering with chastity. So the absolute.
Webster:Not a long stretch to abstraction, withdrawn from reality, no context, no application, standing on its own like the Cheshire Cat's smile. Disembodied.
From extreme to extremes; logic and philosophy dote on rigour and exactitudes. No slackness, no compromise, categorical and demonstrable. How out-and-out abstractions can be demonstrable is beyond me. Wickedness and evil on a plate.
Complete and unambiguous generalities serve the fastidious mind. No quibbling. Though philosophers like to argue, it is to prove their judgment, not to test their metal. Metal is tested in the real world. In a context. These are head trips. And what more heady than a fine idea. One that can't be contested.
You see, i use "philosopher" as though they were a type. Types are easy to identify. They enjoy few characteristics. No individuality. To take a neutral example: tree. The vague idea of tree seems legitimate, unequivocal. Or bird. Again, a few sketched features: feathers, two legs, wings, a beak. We exchange it like sound currency, in good faith. And yet, neither idea of tree or bird is backed by equivalent experience. We suppose it is, because it works. Our word is not called in question. If it is, we can offer no guarantee your idea equals mine. For it doesn't! Cannot.
So philosophy lives in the clouds, never or seldom venturing on to solid ground. Always a level of abstraction between concept and embodiment.
Webster:Indefiniteness, ambiguity and uncertainty cannot be borne. Categories that are subsumed in hierarchies, terms that cannot be challenged, generalities that are absolute or universal, transpositions that are necessary and inevitable: these are the stuff of logic. All else can be dismissed as irrational, irrelevant, of no account. Tropes and figures of speech are out. Reality is made insubstantial, illusionary, and abstractions reified, more than real, transcendent.
A "thought". Catch me a thought, pluck it from your brainstem, let it settle like a polyphonous sound on your fingertip. There! By the tropes and cantrips! Imagination attends. Logic distances itself. Yet discusses thought as if it existed, in bits and bytes naturally, or unnaturally; ideas and generalities float like cartoon bubbles over philosophers' heads, and they pronounce them good.
I prefer something to fix a thought by. If i wish to offer it on the market. To realize its value. I use the trope as a ground. An illustration to fix it by. Inductive inference made fanciful. Analogy. Compared with what is.
Beauty is an abstraction. Unless you adorn a young lady with it: "She's a beauty." Others might remark: "Pretty", "fair", "comely", "attractive", "lovely", "gorgeous" and so on. Beauty applied, brought down to earth, a single instance invoked. Some might (petulantly, no doubt) declare her insipid, lacking that authentic stamp of beauty, character. We variously carry this notion of beauty in our heads, thinking it common goods. If our single instances of this general idea do not agree, what use can it be as a vehicle for the exchange of meaning?
Don't worry! We suffer laxity. Even ambiguity. We are not finicky. We are prepared to higgle-and-haggle, weigh in the balance, offering ambiguity for ambiguity if that furthers our trafficking. We don't normally trade in absolutes, for we keep in touch with what is, the staples of trade. Even our analogies. We keep our feet on the ground, joined to our heads. And our ideas, our generalities remain flexible because they must be faithful to the irrationality they represent, what we see around us, the reality of things.
Volition is not velleity nor is velleity desideration. We know the difference, yet they seem to form a murky grey continuum, baffling, when subjected to close scrutiny. Determinations are subject to reality. Definitions make objects of the subjective. The breath sucked out of them, shells. Informative. Instructive. Dead-ends. Conceived in our rational minds, that capable artificial intelligence engine, running smoothly on its gears (aka circuits), digital not analogical. Outside in the wide world of sense, sprawls infinity; inside our heads, behold the finite!
"How can the less the greater comprehend
Or finite reason reach infinity?"John Dryden, from "Religio Laici", Selected Poems, P.43 Bloomsbury Classics, 1994
In truth, rational figures are tropes, figments of the mind, abstracted from their context. A tangent is a trope. Perceptions are determined in their context. Rationality withdraws them. Hence finite. Finished. Fixed. No direct references to subject unless we apply them again, which removes them from their conceptual frame. Because finite terms are out of context they do not relate by affinity but categorically, as in attributive classes, hierarchies; membership is rigorous, uniform. Closed groups. Recursive procedures. No room to breathe. Needless.
Comes the tangent to the vicious circle. Conceived as a commensurable chord, a mechanical triangulation, brought about by these rational forces which hold it in check. Not a wayward or enthusiastic wanderer, a pioneer, no, a prisoner of its origins. Rationality serves its purpose. It imitates infinity without comprehension. The analogy made digital. Points, forces about a point, momentum, expressed in numerical figures, quaintly anonymous in the algebraic formula.
We conceived volition, velleity and desideration to advance our understanding of what takes place. They mean we can exercise choice, grades of will and wish, for they are not absolute. Nor are they grades. Graduation is rational. We can see how complexity rules behaviour. The forces are factors, influences, basically irrational. Inexpressible. We do our best with will and wish. And, being careful of our judgments, refrain from arbitrary rulings based on cause and effect. the tangent is not finite.
©Laurie Ashton, 1999
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