Using solution to a famous physics problem in trying to explain the relativity of the future and the past leads to a possible Zeno’s paradox... original problem has a bird flying between two trains on a collision course (Ref: Monologue in a cab while returning home on a Friday night, documentary on E=mc^2). One way to calculate the distance traveled by the bird before it gets squished between the trains is by the infinite series method (had to struggle a bit to understand the whole solution... didn't realize one would have to use mathematical induction as well.. funny how much easier it was when I studied it earlier). Of course, there is the infinitely simpler method using basic algebra (the speeds of the bird and the trains, the distance between the trains and relative velocity)............................................
Let the solution to the original problem be the first axiom. Second, that you are your thought. Third, that the perception of thought is a directional force, and a corollary, that relative perception parallels relative velocity (perception of the future relative to the past and vice versa, equal in quantum, for the present purpose.) From these we deduce a new problem - when you think what you think when you look ahead and when you look behind, into the future and past alternatively, the future and the past are technically on a collision course within every infinitesimally small period of time (in discrete time, the past is following you and the future is moving away from you.) In it, your thought is the bird; the future and the past are the two trains traveling towards each other with the relative force of perception.
For the solution to this problem - by the first axiom, the solution, by alternating the thought of the future and the past in an infinite series and combining the perception of the two, by the second axiom, you travel the distance from your starting point (your past), to your destination (your future), while sitting right in the middle of the distance between the past and the future, at that infinitesimal speck of the present, at the point of collision of the thoughts traveling with relative perception towards the future and away from the past.
If D is the distance between your destination in the future and your starting point in the past, the distance your thought will travel in alternatively looking into the future and the past equals D. In letting your thought travel the distance D, by the second axiom, you have traveled the distance from your past to your future, in effect, reaching your future. That is to say, when you think about the future, you have reached the future, or are in it. The same argument holds for the past. Hence, the present is at the same moment the the past and the future.
(.... discovered not much later that this is a restatement of one of Zeno's paradoxes of motion, possibly the Arrow Paradox - “If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless." I could not find any authoritative view that linked the problem to this one, but quite a few that hinted at it being a likely parallel. Their counter-intuitive nature is probably why these paradoxes were major problems for ancient physicists and philosophers - they called into question concepts and ways of thinking without which normal existence became difficult, and as Ulam . They still are discussed at length, but more because they often led to interesting intellectual discoveries and less as an attempt to resolve the problems. As I understand, most physicists these days are quite comfortable with Heisenberg's version of uncertainty and the idea that position, time, and speed can never be exactly determined; in this light the paradoxes which deal with time and motion are kindly looked upon as rudimentary applications of reductio ad absurdum. Where this method of proof stands in modern day mathematics is something I will have to investigate another time. The Arrow Paradox is inherent in the derivation of the original solution involving the infinite series, which is ignored in order to reach it. So without ignoring the famous paradox in the original solution (which is what we did in our first axiom), the solution to the new problem, which is a re paradox, cannot be reached. That is, in ignoring the paradox, we prove it. Another paradox?)
:) Ayyo.
This thread is interesting - http://www.imminst.org/forum/index.php?s=&act=ST&f=9&t=1491&st=0
3 comments:
I don't quite understand this paper by Peter Lynds. The semantics (perhaps necessary?) is terribly confusing!
As I understand, most physicists these days are quite comfortable with Heisenberg's version of uncertainty and the idea that position, time, and speed can never be exactly determined; in this light the paradoxes which deal with time and motion are kindly looked upon as rudimentary applications of reductio ad absurdum.
So I now understand from Lynd's paper that while Heisenberg's uncertainty has its origins in the limitations of measurement the static arrow in Zeno's paradox has its origin in the absence of a 'static time', i.e., it is inherent to the nature of time itself. This latter is responsible for motion and an inherent absence of precision in all physical values, on both a macro and micro scale, although they are determinable to within the limits of Heisenberg's uncertainty.
I didn't read the whole paper. :D What do you think they teach us in an MBA?
Did read the main parts though, didn't find the main views as path breaking as some of the people who commented on the thread said it was... these thoughts have been thought before, I know it. But the thread itself was fun to read... complete and unabashed intellectual masturbation. :D
I'm not sure that Zeno's paradox indicates that the inherent status nature of time is "responsible for motion" - I think it negates the the idea of motion itself. Lynds resolves the paradox by saying that since time is not a succession of instants (the basic premise of many paradoxes of motion), but is a 'flowing' entity based on indeterminacy within precise physical magnitude.
Have other thoughts on this, but will have to save them for when I have time to ruminate. :)
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