Phi and Infinity, etc., Part I
My basic premise (assumption) is that infinity is.
Either infinity is, or is not.
Logically, there can be no intermediate possibility. A mix of "infinity" and "finitudes" is oxymoronic. In order to be "finite," an entity must have clearly-defined boundaries. At such a "boundary," "infinity" would of necessity come to a halt. This imposes, in fact, a "boundary" on the "infinite," in which case it is no longer "infinite." It cannot be unending if it has an end anywhere, and that is what such a "boundary" would be.
On the other hand, if existence is therefore "finite," it must exist in some context. If there is a "boundary," what is on the other side? "Nothing?" Problem: "nothing" cannot be "nothing" except in relation to "something." Therefore, "finite" must also exist in relation to "something," even if that "something" is "nothing." Assuming there is a "boundary," that this existence in which we are caught up is a "finite" entity, and that "nothing" is on the the other side of the "boundary," "nothing" must also be a "finitude," as it demonstrably has at least one "boundary." (I.e., the edge of our "finitude," i.e., our "something.")
So what then? A series of "finitudes?" And--where does this series end? Obvously, it cannot, because however far it continues, if an attempt is being made to justify the concept of "finitude," there must ultimately be a "nothing" at the end, in which case one ends up at the same place.
Again, logically, there can be neither end nor beginning to such a series, because "nothing" is at some point a necessary postulate. Therefore, one is left with an "infinite" series of "finitudes,"
thus, "infinity." This is obviously self-contradictory: "infinity" ipso facto precludes "boundaries," a necessary condition of "finitude." "Finitude," therefore, is in appearance only.
It will be found that no entity in our extant universe is in fact "finite." It is really a matter of scale. For example, an apparently solid table on a different scale is a swirling mass of atomic and sub-atomic particles with enormous spaces in between, and merging with the surrounding atmosphere. Neither are words, numbers, ideas, and so forth, sharply defined: their "boundaries," upon closer examination, prove to be fuzzy given the right scale. Music and the other arts are precisely imprecise.
Much of the issue is semantic. Mathematicians (Geometricians, et al.) speak of a variety of "infinitudes," various "infinite" sets, etc., etc. However, these, I am convinced, will prove at some perspective to simply be "segments" of "infinity," with "fuzzy edges," i.e., "boundaries" (delimitations) that are ultimately imprecise and merging with the surrounding "infinitude" of which they are part and a human attempt at expression thereof.
For example, consider the "infinite" ratios, Pi, 3.1416..., and Phi, 1.618... I have come to think that the latter "Golden Ratio" is, in the numeration available to us, the fundamental ratio of "infinity." Further, I now assume that Pi is a "segment" of Phi as it exists--as a descriptor--of our universe. The extrapolation of these ratios, and that of their relationship to one another, into not only three dimensions but into the larger multi-dimensionality projected onto our universe by, e.g., astronomers and other scientists, will provide, I believe, a more accurate descriptor of what I can only speak of as the "convergence" of "infinitudinal segment 'vectors,' "
i.e., "infinite" sets and the like, geometrical projections, parallel straight lines, the observed expansion of the "Big Bang" (hypermolecular hypothesis), the continually "im"-panding [coined antonym of "expanding"] world of sub-atomic particles, and on and on...
This also connects with the ideas I have expressed elsewhere about the general concept of "swarms," and it seems logical to me that Phi would play a role in this matter, especially as a descriptor of the average rate of proliferation and resultant coalescence of various phenomena.
If one considers the vastness of the "universe" outward, one should also consider the vastness of the "universe" inward. The logarithmic spiral deduced from Phi does a nice job of modelling this view of "infinity." One must, I think, also be led to ask if one can really appropriately speak of a larger or smaller "infinity?" Is the sub-atomic world, for example, realy smaller than the galactic world IF both are indeed "infinite?" [N.B.--If my conjecture is accurate, somehow expressible as positions on that "infinite" Phi-based logarithmic spiral.] Which is "up" and which is "down" is really just a matter of perspective and, for want of a better word, "direction," if the concept of "inifinity" has as much a valid basis in reality as I assume it does.
(to be continued)
Either infinity is, or is not.
Logically, there can be no intermediate possibility. A mix of "infinity" and "finitudes" is oxymoronic. In order to be "finite," an entity must have clearly-defined boundaries. At such a "boundary," "infinity" would of necessity come to a halt. This imposes, in fact, a "boundary" on the "infinite," in which case it is no longer "infinite." It cannot be unending if it has an end anywhere, and that is what such a "boundary" would be.
On the other hand, if existence is therefore "finite," it must exist in some context. If there is a "boundary," what is on the other side? "Nothing?" Problem: "nothing" cannot be "nothing" except in relation to "something." Therefore, "finite" must also exist in relation to "something," even if that "something" is "nothing." Assuming there is a "boundary," that this existence in which we are caught up is a "finite" entity, and that "nothing" is on the the other side of the "boundary," "nothing" must also be a "finitude," as it demonstrably has at least one "boundary." (I.e., the edge of our "finitude," i.e., our "something.")
So what then? A series of "finitudes?" And--where does this series end? Obvously, it cannot, because however far it continues, if an attempt is being made to justify the concept of "finitude," there must ultimately be a "nothing" at the end, in which case one ends up at the same place.
Again, logically, there can be neither end nor beginning to such a series, because "nothing" is at some point a necessary postulate. Therefore, one is left with an "infinite" series of "finitudes,"
thus, "infinity." This is obviously self-contradictory: "infinity" ipso facto precludes "boundaries," a necessary condition of "finitude." "Finitude," therefore, is in appearance only.
It will be found that no entity in our extant universe is in fact "finite." It is really a matter of scale. For example, an apparently solid table on a different scale is a swirling mass of atomic and sub-atomic particles with enormous spaces in between, and merging with the surrounding atmosphere. Neither are words, numbers, ideas, and so forth, sharply defined: their "boundaries," upon closer examination, prove to be fuzzy given the right scale. Music and the other arts are precisely imprecise.
Much of the issue is semantic. Mathematicians (Geometricians, et al.) speak of a variety of "infinitudes," various "infinite" sets, etc., etc. However, these, I am convinced, will prove at some perspective to simply be "segments" of "infinity," with "fuzzy edges," i.e., "boundaries" (delimitations) that are ultimately imprecise and merging with the surrounding "infinitude" of which they are part and a human attempt at expression thereof.
For example, consider the "infinite" ratios, Pi, 3.1416..., and Phi, 1.618... I have come to think that the latter "Golden Ratio" is, in the numeration available to us, the fundamental ratio of "infinity." Further, I now assume that Pi is a "segment" of Phi as it exists--as a descriptor--of our universe. The extrapolation of these ratios, and that of their relationship to one another, into not only three dimensions but into the larger multi-dimensionality projected onto our universe by, e.g., astronomers and other scientists, will provide, I believe, a more accurate descriptor of what I can only speak of as the "convergence" of "infinitudinal segment 'vectors,' "
i.e., "infinite" sets and the like, geometrical projections, parallel straight lines, the observed expansion of the "Big Bang" (hypermolecular hypothesis), the continually "im"-panding [coined antonym of "expanding"] world of sub-atomic particles, and on and on...
This also connects with the ideas I have expressed elsewhere about the general concept of "swarms," and it seems logical to me that Phi would play a role in this matter, especially as a descriptor of the average rate of proliferation and resultant coalescence of various phenomena.
If one considers the vastness of the "universe" outward, one should also consider the vastness of the "universe" inward. The logarithmic spiral deduced from Phi does a nice job of modelling this view of "infinity." One must, I think, also be led to ask if one can really appropriately speak of a larger or smaller "infinity?" Is the sub-atomic world, for example, realy smaller than the galactic world IF both are indeed "infinite?" [N.B.--If my conjecture is accurate, somehow expressible as positions on that "infinite" Phi-based logarithmic spiral.] Which is "up" and which is "down" is really just a matter of perspective and, for want of a better word, "direction," if the concept of "inifinity" has as much a valid basis in reality as I assume it does.
(to be continued)
posted by Monte at 9:58 a.m.
1 Comments:
Dr. Pishny-Floyd, you have a vast collection of deep thoughts. Unfortunately I don't have a lot of time to read through them now, nor do I know if you'll see this comment. But I'll make sure to go through these posts in the near future.
Shame you haven't updated it in over a year. You have a great deal of interesting things to say...more so than the nonsense I've posted on my blog.
Later!
-Matt Becker
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