INFINITIES! CERTAINLY SIR! HOW MANY WOULD YOU LIKE! SHALL I HELP WRAP THEM UP OR DO YOU WANT THEM PUT ASIDE INDEFINATELY ON LAYAWAY! OUR SPECIAL TODAY IS AN UNMARKED LINE IN WHICH YOU CAN NEVER SEE THE END! *.................. FRAMING OF INFINITIES |____________________________________________________| ABSTRACT: THERE IS NO PARADOX, EXCEPT IN THE WAY THE HUMAN MIND APPROACHES CONCEPTS ABOUT INFINITY. The concept of infinity (or infinities) seems to continually blow the minds of thinkers. There seems to be a problem originating in the way the thinkers use their minds. In every real sense, a breath cannot exist until the action of making a breath occurs. That is, that a breath cannot of itself stand apart from any breathing apparatus, such that the breath itself can be discussed meaningfully. In order for the breath to be discussed at all requires it to have been taken, or to be taking place, or that it will be taking place. But then, in order to recognize it, some event external to the breath must also exist in order to make comparisons with which to indentify what the breath is, was, will be, or should be. Similarly with many human thoughts regarding infinity, the insights which identify thoughts as concepts are in effect 'framing' instruments by which each thought is articulated. For example, the concept of infinity is identified by the insight that, in comparison, finiteness is not infinite. Also, an infinity is typically seen as being impossible for its end to be seen, whereas anything that is finite has some describable bound, or end-time. Many paradoxes arise in attempting to establish infinities within recognizable bounds. In this brief discussion it is suggested that not enough about the 'framing' of the concept of infinity is typically taken into concideration by thoughts which have no reasonable basis in the grounds of Reality. It becomes obvious that arguements involving infinities become tautological when phenomena are involved. The only proviso is that a real universe is herein concidered to be physically finite in some way. Zeno's paradox, in asking that an infinite number of halved steps be taken between two points separated by a given distance, cannot be contemplated without there being an external apparatus making the steps, otherwise, each step (like a breath without cause), is meaningless without some external apparatus giving existence to each step. Unless it has been made, is being made, or is going to be made, a step doesn't exist. In every case, knowing about the step requires that it be articulated in some way, such as in being a measure. The question then resolves to: Is there some way for an external apparatus to make an infinitely small step, or, also, is there an external instrument capable of observing an infinitely small measure. It happens that some space or event must exist between each data point said to be a designator in an infinite series, otherwise the points would be physically joined, describing nothing but an unmarked straight line. However some distinguishing features may be spelled out involving the line. When consisting of a series of dots; in which dots are said to occupy areas, and any two dots must have a non-dot measure between them; dots become beads when no measure separates them, forming a beaded line, although it can be argued that the periodic greatest length hence comprises the infinite series. On the other hand were the line to designate a vector of time in which some event periodically peaks, then the series of peaks might be said to be possibly infinite in number, but only when in a universe which is known to be infinitely wide and infinitely long lasting, assuming such a universe is also large enough to hold within whatever manner is used to graph the periodicity. The peaks themselves are connected by lulls such that the peaks and lulls are continuously an action of time. In any case of a marked line, a measure is said to distinguish any two marks or events. In an infinite series of dots, the spaces in between in toto are another whole series, except that the spaces are 'framed' by the first and continuously last event or mark, and hence cannot be inifinite in number. Similar arguements dealing with infinities arise when an infinite number of points is said to be put on an inch-long line, then another inch is added onto the line giving, or not giving, another infinite number of points. What is missing from generalizations per such arguements is the 'whatever' it is that is used to mark the points. Even infinitely small points must be distinguished by a 'whatever it is' that exists between each point. In other words as an abstract idea, in an illusionary universe having any properties which the mind wishes to concieve of, an infinite number of points can be thought of in the confines of an inch. But in a real universe no points can exist on the line without the point being both made or marked in some way. In tota, there is but one measure that identifies the concept per se, known as an inch. Subdividing the inch toward infinity requires input from an external measure source to compare before to after each subdivide. There is not enough room even in an infinite universe to handle all such apparatus, without which, the infinity of dots simply doesn't exist. The apparatus itself would end up taking up more room than the universe itself. In another example, gravitational black holes are said to be mathematically consistent of point source centers which are also called singularities, infinity small. However, it is said that each hole also consists of an event horizon in which, once inside, normal emission spectrum radiation or any radiation cannot escape, due to the assumption that emmitting atoms cannot exist within the hole due to an overpowering crunch of gravity that destroys atom constructs, and can relativistically countermand the outward transmission of photons and energy as well as mass. If the event horizon is included as a property in a real universe, it is difficult to concieve of an infinite number of mutually hungry black hole point sources being laid along a line without each being separated at arms length by the cross sectional diameter of each event horizon. In fact, it is difficult to think of point sources at all, except as mere mathematical conveniences in abstract logic, since in real terms, the point source is 'something' surrounded by an event horizon which is its 'frame'. For example, relative to itself, a planet has a gravitational field consisting of several discussable features, mainly, that the greatest field density is at the outer boundry of the mass causing the field. In other words the field strength is greatest at the Earth's surface. A plunge toward the Earth's point source center means that immediately the surface is penetrated, the mass behind the penetrator subtracts from the mass in front of the penetrator, so that at the exact Earth center there is no Earth gravity at all and anyone in a small cavity at the gravity-free Earth center would be free to float around as if in the freefall of outer space. Ideally, the causative mass now extends in all directions by equal amounts, with up and down, left and right, and rear and frontal directions all cancelling each other's gravity. In any multiple body system the gravitational feature is distinctly different. Mathematically, the gravitational attraction between any two bodies can be handily demonstrated as measurements from a point source to a point source. Even physically, when sufficient distances are involved as between the Earth and Moon, the gravitational distinction between the Earth and Moon's surfaces, vrs center to center, is negligable in ratio to the distance between the two bodies. This insight makes a speculator wonder if a gravitationally infinite crunching black hole point source center really exists. Inside the event horizon, or at least inside some place involving the hole, an up-down, left-right, and rear-frontal architecture may take over so that the internal field of a black hole may be geometrically articulate in some manner analogous to the internal architecture of a star or planet with no gravity at all at the body's point of center relative to an observer there. And that these architectural contructions have features that are measurablable by comparisons of one feature against another to mark and/or reveal their differences. And so there is the basic insight, in infinity arguements, that whatever is used for marking, must have a measure or structure. A dot, for example. In the abstract, each dot can be infinitely small, but in every real sense an infinitely small dot would be without a finite measure; having no measure to speak of; and so an infinite number of infinitely small dots on a line would be unexistent, in any physical manifestation in which a mark to reveal differences is applied. Always, it is apparent that paradoxes resolve themselves into contradictions as to whether the markers themselves have, or do not have, measure. When infinitely small, a dot cannot be measured except by some yardstick which is capable of making an infinitely small measure and is external to the dot. And so there is the statement that an infinitely small mark can only be identified by an instrument having an infinitely small measure. This includes the case of mathematical point sources, such as black holes, which are theoretical phenomena which can never be placed closer then the spaces comprising the radii of their event horizons while still remaining countable separate entities, without merging into one. Getting back to the paradox about the infinite line itself; each of the infinite points on an inch-long line has to consist of data points each consisting of some finite measure. But since any finite measure, no matter how small, voids the possibility that it contributes to an infinite series set within a finite bound, the paradox of an infinite number of points within each of two inch-long lines finally disappears when the question of the size of each point is concidered. The paradox actually dissolves when it is claimed that were there to be an infinite number of things along any line, an external apparatus capable of each and every infinitely small event, or an external instrument capable of each and every infinitely small measure, must be required to distinctify each and every REAL thing. However these externals are possible only in thought. Even though any infinity can be thought of, most all thoughts of infinities vanish when the means for achieving the infinity is concidered. There is a range of paradox concepts, but only in the way the human mind traditionally approaches concepts about infinity. A human mind which avoids an illusionary universe usually has more creative scope in tackling problems associated with understanding the real universe, and usually is willing to appreciate more framing in concidering each concept. In peace, such a mind can be kept very busy just thinking of the non-paradoxical nature of Cause and Effect. The number, root 2, (also other roots including root 3 and 5 because they also occur as proportions in perfect geometric constructions), can be used as an example to show how frames provide external apparatuses for many non-paradoxical real situations. Given only root 2, and presuming that it is truly an irrational number in which, no matter how accurately the number may be determined there is still another digit which can go onto the tail of the number, then arguably such a number is in some way infinite, and arguably, such a number cannot be divided in half. However in a square whose four sides are each equal to 1, the diagonal of the square is equal to root 2, and a criss-crossed pair of diagonals cuts both root 2(s) exactly in half, yielding two reciprocals of root 2. Therefore, with this external apparatus, the framed digital number is not indivisible, even though it can be argued again that each of the two halves of root 2 are themselves irrational therefore consistent of an infinite number of digits, hence by cutting in half the irrational number indefinately by repeatedly reconstructing smaller squares and criss-crossing the resulting diagonals, that an infinite series of irrational numbers results, potentially. Since neither half of a criss-crossed diagonal consists of an infinite set of real digits but only of an exact length, it is clear that several nuances to infinity problems are again at hand. One nuance is that an infinite number does not existentially exist in a real universe whenever the number is 'framed' in any finite bound, such as a square. A second nuance is that the diagonal itself is marked by the characteristics of being a diagonal, as distinctified abruptly by the existence of the four sides whose consequence is the existence of the diagonal. In other words, the square 'frames' the diagonal, which does not exist outside of the 'frame' identified as the square. Which brings into focus the question of what means are to be used to identify the 'infinityness' of the diagonal's root 2 measure. The digital expression of the number is non infinite in any usual context. The infinity of the number is a potential, and not an actuality, until work is done to bring forth the digits to express the number. Suppose that each digit when expressed occupies a measure set within the strung out number, eventually the physical tally of digits would extend beyond bounds of any physically finite universe. In other words, a number expressed accurately toward an infinite set of real digits, must exceed the bounds of a real universe in order to be physically expressed, because of the space that is occupied by the size of each and every digit used to express the totality of the number ad infinitum. And so the finite size of a real universe provides at least one frame, in the form of a self evident bound, which automatically limits the expression of so-called infinite amounts, including digits. Once again referring to the example of a square's diagonal: the diagonal itself (for a square whose sides each = 1) is an Absolute Cosmic Constant without infinity of any kind. It is only when an abstract concept is attached, that it seems to take on an infinity in value, for instance in applying the arbitrary digit values from the 10 base number system, in which case it is just a mentally abstract number not attached to anything, the number root two becomes an abstract term not attached to anything except itself. Even if it is abitrarily used to try and describe an absolute value for the diagonal of a square. In conclusion, no number can be infinite until it is actually expressed by some external apparatus, but no number can be physically expressed to extend beyond any finite bounds of a real universe. Infinitive potentials are all over the place, but these are actually expressed no place, in a real universe. At this point it is clear that infinite numbers, or infinite amounts, and infinite proportions, can exist unfettered in consciousness, of which abstract mathematics is a part. Human thought provides a co-creative frame which establishes abstract infinities as potentials which are distinct from actual infinities thought to be occurring only in a real universe. However a real universe's 'frames', precludes that things within are finite. Fundamental paradoxes involving infinities are resolved by the awareness that infinities are possible in potential form within the capability of thought, and are manifested as potentials embodied within frames of a real universe, (root 2 in a diagonal), but cannot exist as any physical expression within a finite universe (the digits needed to express root 2's alledged numeric infinityness). With these dignified insights, it is now possible to concider some of the physics of God. Assuming there to be a God existing in the form of an expressor of a Creation, it is now understandable that the expressed cannot be infinite in all aspects. Rather than God, a more appropriate designation is the Supreme Creators, in fact a male/female unification in consciousness, so that as one, they contain the embodiment of all possible infinite and finite potentials, but that whatever is expressed is finite, determined by frames of the chosen Creation itself. In putting meaning to the word eternal, expressions of the Supreme Creators could continue indefinately when the Supreme Creators continue to change the range of their chosen Creation. In Peace Greydon Moore greydon@look.com Drafted: Ottawa, Ont. 1983. Revised: Ottawa, Ont. 1994.