Paradox Number 



1. 
Arrow Paradox There is no motion since what is moving must arrive at a midpoint before arriving at an endpoint. Henri Louis Bergson describes this as a self~absurd dialectical, formal, canonical, mathematical, mechanical "movement by immobilities." See Bergson's Time and Free Will, Creative Evolution, and An Introduction to Metaphysics. Doug  19Mar2010. 
This paradox makes a deluded classical presumption that reality is both an infinitely divisible spatial extensity and that infinitesimal reductions of that infinitely divisible extensity are demarcable by ideal 'dimensionless' classical 'points' and that a moving object can 'stop' at classically demarcated points. (Classically 'stop' means zero momentum.) Another way to make our statement is that this, Zeno's first, paradox assumes that classical motion and time are subject to analyticity. Via that assumption, any classical motion is, due its spatial extensity, thus stoppable for purposes of analysis, and not continuous. Similarly for time. Stoppability of continuous motion is source of this proposition's paradox. We see here two separate contexts treated as one:


1. contd. 
continued... 
In Quantonics, we choose to view Zeno's first paradox as his own derision of classicists' assumptions of both analytic motion stoppability and analytic temporal stoppability in a single context. Our chosen views derive from our studies of works of Henri Louis Bergson, William James, et al. (See links below.) Readers should know that our choices/views run wholly counter to classical interpretations of Zeno's intent. An implication of our quantumenhanced version of Zeno's view, assuming we are correct, is that he intuited macroscopic quantum uncertainty of any moving entity's position and momentum. To a classical mind, absent quantum thinking modes, noncommutativity of Poisson's bracket of position and momentum is a paradox. We infer that Zeno intuited this issue. Most classicists today are incapable of this level of intuition. 

1 contd. 
continued... 
Most physicists, today, view quantum uncertainty as only a microscopic phenomenon and describe it mathematically/analytically like this: where p, q, i, and h are classical objects (see dichons) and [p, q] is Poisson's bracket AKA a classical analytic commutation relation. Most physicists presume this expression is only valid at physical atomic and subatomic 'levels' of classical reality. Zeno, in our view, and agreeing with Quantonics, is saying that Poisson's bracket, AKA quantum umcærtainty applies at all levels of quantum reality.
In Quantonics we quantumly/quantonically apply our hermeneutics to achieve a more quantum real: where p, q, i, and h are quantons and our quantum BAWAM, EIMA hermeneutic for i is a recursive quantum square root. (We assume all 'mathematics' in our Quantonics notation are ~quantum. E.g., classical concept 'minus' and quantum meme 'minus' are entirely omnifferent one another.) 

1 contd. 
continued... 
Zeno, in our view, is telling us that: Arrow_Momentum: A_M form a Poisson bracket: where, in anihmatæ quantum macroscopic reality, which really has absolute motion, we may may n¤t kn¤w A_P and A_M classical analytic, stoppable 'states.' Also see our Boolean Logic is Distributive. Readers can infer, for macroscopic sensibilities, scaled multiples of h above. Insertion of, say N, may suffice. 

1 contd. 
continued... 
A very easy solution to this paradox is similar to our TRUE/FALSE 'paradox' and our CHIMERA 'paradox:' create a motion context and a stoppability context. Read detail of these solutions at our SOM Connection. A graphic of these bicontextual solutions appears here: Many Truths to You. This approach permits solution of paradice 2 and 3. See Bergson in his Creative Evolution topic 40 (large page with animations) and his Time and Free Will topics 15, 19, 22, 23, and 34 on Zeno's paradice. One renowned quantum physicist has been shown by James Gleick to understand thoroughly what Doug means by quantum~ "many truthings:"


1 contd. 
continued... 
Zeno's 1^{st} paradox offers some vague yet unsubtle sensations of Bohrian complementarity. Allow us to make a similar nexus via a quotation from Max Jammer's The Philosophy of Quantum Mechanics, pp. 9293:


1 contd. 
continued... 
Having read that quote, you may be asking as we have, "How could Bohr have ever viewed quantum complementarity as 'exclusive?'" We believe that he did n¤t. His use of "exclusive" was merely a palliative for his then overwhelmingly classical peers, like Einstein. See our Absoluteness as Uncertainty. Subsequent remarks by Jammer bring back Bohr's own special brand of exclusivity. Classical languages are traps which impose exclusive dialectical predilections on their users. Beware all analytic languages! (Question: Was William James Sidis' Vendergood an analytic, dialectic language? Does anyone know? Contact us if you do know. We currently do not have access to Vendergood.) Also, you should be able to make a very strong nexus of your own with Zeno's 1^{st} paradox. 

2. 
Achilles Tortoise Paradox That which is running slower shall never be passed by that which is running quicker. Why? Quicker must arrive at a point where slower already departed and thus slower must always maintain a distance advantage over quicker. 
See our comments above regarding paradox 1. See Bergson's Time and Free Will, Topic 23. See James' Some Problems of Philosophy, Chapter X., and Chapter XI. Surrounding pages in these two chapters are worthy of your further study. 

3. 
Racetrack Paradox That which is at a place cannot move at a place which it is not. That which is at a place cannot move at that place where it is. But a moving object is always at the place at which it is. Specifically, said object is, at any instant, at rest. But if said object is not moving at any instant then it is at rest. 
See our comments above regarding paradox 1. See Bergson's Creative Evolution, Topic 40 (large page with animations) on Zeno, "...movement is made of immobilities." Ponder how this paradox's assumptions outright deny quantum reality's probability distributions of 'place' and 'motion.' You may be able to QTM relate this putative as akin Aristotle's excludedmiddle. In quantum reality, 'place' and 'motion' analogues have quantum anihmatæ EIMAs. 

4. 
Stadium Paradox Allow three objects of equal dimensions called A, B, and C. A at velocity x and C at velocity x are passing B in opposing directions. A requires t to pass B's dimension and 1/2T to pass C's dimension. Implication: A requires both T and 1/2T to traverse an identical size. 
Even to classicists this is no paradox (unless we assume A, B, and C are classically dimensionless point objects). Classical velocity is dx/dt. Opposing velocities traversing an equal 'stopped' distance A require 'identical' time. Opposing velocities traversing their mutual equal 'moving' distances A each require half of A's stopped traversal time. Here we have at least three separate velocity contexts, and even classicists treat them as separate subcontexts (stopped, +dx/dt, and dx/dt) within a larger framework context (which classically assumes common, homogeneous, independent classical 'time'.) If time were indeed heterogeneous and different (see omnifference) for each 'velocity' context, but treated as homogeneous then we, from any classical conspective, would have a temporal paradox. An example might be time as stable/stopped for B, futureistic for A, and pastistic for C. Results in this case would be paradoxical when 'analyzed' in one global temporal context. 
Paradox 1  Reality is n¤t classically
stateic. Paradox 2  Reality is n¤t classically analytic. Paradox 3  Reality is abs¤lute quantum flux. Paradox 4  Reality is n¤t classically analytic. 
Notes:
Note 1  For alternate, more classical perspectives see: Ancient Greek Philosophy  From Thales To Aristotle edited by S. Marc Cohen et al., The Cambridge Dictionary of Philosophy edited by Robert Audi, The Oxford Dictionary of Philosophy by Simon Blackburn, etc. Also, use Google to search for: "Zeno of Elea".