*.................. THE EXTENCE OF 'FRAMES' |_______________________________________________________| It has to be ahem, well, oops, fuzzy logic. But nonetheless it winds its way through a philosophical arguement regards the fact that INFINITIES don't exist, in that any way required to express an infinity involves the infinity being FRAMED in some kind of artifact in order for the apparent infinity to be identifyable in the first place. Wherein the infinity's apparentness has to vanish, due to the existence of the FRAME in the first place. For instance, Infinities may seem to exist just about anytime you do a mathematical equation, but CAN'T occur unless expressed in some way, such as by a string of digits, or bits of a measure repeated. And yet, the digits are arbitrary to human narrow thought views, and bits of a measure can only occur from one place to another, which is axiomatically within a FRAME. A piece called INTRINSIC STATUS VALUE which follows next, discusses aspects of FRAMES as the embodiment of û2, seemingly Infinite but not, in the diagonal of an ordinary square. Its poetic style gives a sort of Infinite look, to the contents. ============================ INTRINSIC STATUS VALUE ============================ It is futile contemplating images that are impossible. Zen buddists do this Sitting strung out on mountain tops all over the planet puzzling through the next step puzzling how to achieve a handclap with only one hand to make it happen. The Zennist has galled on a concept thinks an eyblink can't happen unless an eyball sees the lid slick over the view and sits on the pinnacles unable what to do to make the fateful wink link to what goes on in Reality. In existence there cannot be anything real without there being at least one real other thing that is different in order to notice the first thing's difference. Thoughts can imagine infinities in endless variety. However there are no real infinities and apparent infinities are re-usable only when embodied in something else. A part might seem infinite when in isolate then becomes a step along the way when structured in other parts that are finite. Root 2 is said to be infinity in number value and irrational though it is not instantly argued if it's infinity is in the number of digits of the number or the length the digits make when strung together in a line. Root 2 is actually a measured hypotenuse found as the finite diagonal of a square of 1 per side. The measured hypotenuse bisected yields two new infinities in isolated parts; the two finite and linked halves of the diagonal seem to become two infinite measured halves that are irrational when taken apart, having infinite digits and infinite length of digits in two strings within the single infinity known as root 2 if each new half is concidered by itself as separate. These infinities in root 2 are actually co-incidences in the base 10 number system used to measure the hypotenuse and two hypotenuse half parts. Given many other number bases those infinities would vanish simply by the miracle of changing the way the thoughts want to count. For instance if the thought base was said to be a hypotenuse equal to 1; then the link that was root 2, and the length of and number of digits in its measure all sum to a 1 with identical link, length, and measure half parts also finite. But watch this, the four equal sides inscribing the hypotenuse now each carry the mark of a measured 1 over root 2 value, ie. the reciprocal of root 2, ie. one half root 2 (no surprise), ie. one minus (1 over root 2) (plus 2), ie. 1 minus (root 2 plus 1 minus 3/2 root 2), etc., (each one constructable each procedure different in plane geometry techniques when you know how to construct reciprocals) since all are a measure value yet appear to be the same number value as the diagonal of 1, ie. 1, since the square root of 1 is 1. But when measured the digits change to those that seem infinite in a variety of trigonometry sources each itself an infinity for each of the count of, the length of, for value of, the digits comprising each side measured, since each digit has to occupy a space, no matter how big or small the size of each digit as the number continues forever to be written out by hand if ever an infinite number is quote: to be written in full. Four sets of infinities? and a multiplex of infinite sources in the sides of a simple square? Not so, and no paradox. It's all in human thought of, but not the Reality of, Creation. The problem is resolved by realizing that measures are arbitrary, selected by choice to note a non dimensional finite diagonal that is already framed by the existence of the finite square that contains it. Even if one measure crossed a universe and is selected as a constant the measure of the diagonal and the measure of the square might seem irrationally infinite in some marker value when scaled to the constant but this is not the case because the square is already a framed finite entity existing in the realm of the universe. The hypotenuse would and the sides would appear as mere parts of the constant; proportionate segments of no other value until a human said measure is given to the constant. The infinities appear only when attempts are made to arbitrarily put a value on the frame itself, using arbitrary secondary techniques such as those sneaking creeping decimals snowballing across the cosmos in someone's thought whim ad infinitum. Savvy? Simple rules for simple messages is the escape from ideas which can never finish because they have no reason for existing other than being buffeting mistakes in lazy thinker's or urgent stinker's promiscuous thought balloons. "This is very surprising"... the person says putting the manuscript down and looking across the coffee table to the associable professor "...how did you get it? "You gave it to me last week at the conference"; says the Professor "Oh," says the person. "Did you get a chance to read it? "No", the professor says. "I'm giving it back to you. After all it must have taken at least a few dollars to make the photo copies and that at the least must mean something "Go ahead kid, lump your swallows, then, swallow your lumps Gustily, with singleword empahsis intended; "EARTH QUAKE" ! "Nonsense, the world is calm "Anybody know what twaddle is well this ain't some of it! Socialite Eagerton 111 the infinity specialist slowly stirs a cup of tea giggling everything in the room but the teacup jiggling "What I want to know is, what is the underlying theory Well, ah, er, gee, shucks, you see, you're twisting my insights deliberately so tight that like right now you can't even think of anything I want to tell you Gravitational Ho Ho? Funny how a single insight can slow the game Come off it you mean blow the mind Disrupt the brain chatter? What? Careful you'll spill your tea if you keep jiggling to avoid the earthquake OOPS Here is an earth joke, or, here's a joke on the planet earth: what is renowned by Hindus is brown, round, and sounds like a bell rung DUNGGG! After a brief lull after a brief murmer of the class in response has subsided the person adds I guess you'd have had to have been there to appreciate the joke on the planet. This time the response is more like it Greydon Moore March 23, 1993 ÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄÄ Appended February RE: ZENO'S PARADOX There are two major apparents regards the simple solution taken to be that 'paradoxal infinities' do not exist because the length being subdivided by contiguous 1/2 slices are contained in a 'frame' being the start and end of the 'unit'. The first 'major' is the FACT of the UNIT itself. It is NOT dimensionless. Dimensionless implicits comparative rates, for instance comparison of two sizes one over the other to produce a 'dimensionless' ratio having no systems of units. A unit itself on the other hand, is its own system of units, i.e this length being contiguously divided by Zeno is one 'unit' long The second major is where an action is involved, for instance a walker crossing the length being subdivided. By 'walking' is a way the 'paradox' is often stated, that the walker takes steps until 1/2 the length has been crossed, then more steps until 3/4 of the length has been crossed. In the games of paradox the walker is percieved never to be able to complete the crossing because an increasingly small portion of the length still remains. But woah, pause, time out. The paradox stated this way implies that the walker's own steps are also diminishing in size, which they are not, they begin as one SIZE as the FIRST step, and continue same size through proceeding steps, the crossing of the length completeted when the length of the last needed foot step exceeds the remaining 'unit' being crossed. In other words the walking monkey element of the paradox is just plain hoax. The event starts with a length of one 'X 'unit' wide, to be crossed by steps of one 'Y' unit per each step. Only a few accumulates of steps of 'Y' units each reaches a lineal sum total that will exceed the total length comprised in the one 'X' unit being crossed by footsteps. How the fact that the action is twofold - one unit of diminishing remaining length, and many units of identical accumulating footsteps in the action, can be merged into a paradox of many centuries duration, is the real mystery. Slow thinking, or is it slow witted, humans The only co-incidence can be if the length sum of 'N' number of steps happens to exactly equal one 'X' unit, then the walker will land exactly on the far edge of the length being crossed. You can argue if it is toe or heel touching the far edge after the co-incidental crossing the detail does not matter. The next step, again a single repeated 'Y' unit, automatically takes the walker past that edge. If you can see any paradox existing in the fact of accumulating singular measures ('Y' units) cropping a fixed original length 'X' unit you can probably also teleport by throwing the light bulb at the wall. The point is there are two dissimilar systems of units in the action; 'X' and 'Y'; and with the two there cannot be any possible paradox, since any 'action' involves ratios between the fixed length, and the increasing tally of foot steps, to change constantly in ways that have nothing whatsoever to do with the nature of the original fixed 'X' length itself. The ratios of change exist only in the action occuring between the walking and the direction in which the 'walk' takes place between two goal posts. Fundamentally, the two 'goal posts' are not a part of the action and so fall out of the mix, instantly dissolving the paradox DONE Greydon Moore greydon@look.com