## The NSTP Theoretical Resolution of Zeno's Paradoxes

Written by Dr Kedar Joshi

Zeno of Elea's (b.490 BC) arguments against motion precipitated a crisis in Greek thought. All of these, concerning motion, have had a profound influence on development of mathematics. They are described in Aristotle's great work 'Physics' and are presented as four arguments in form of paradoxes, stated below :

1. The Racecourse or Dichotomy Paradox -

There is no motion because that which is moved must arrive at middle of its course before it arrives at end. In order to traverse a line segment it's necessary to reach halfway point, but this requires first reaching quarter - way point, which first requires reaching eighth - way point, and so on without end. Hence motion can never begin.

This problem isn't alleviated by well - known infinite sum ½ + ¼ + 1/8 ... = 1 because Zeno is effectively insisting that sum be tackled in reverse direction. What is first term in such a series ?

( See David Darling : The Universal Book of Mathematics, 2004. )

2. Achilles and Tortoise -

This is perhaps most famous of Zeno's paradoxes.

The slower when running will never be overtaken by quicker; for that which is persuing must first reach point from which that which is fleeing started, so that slower must necessarily always be some distance ahead. Thus, Achilles, however fast he runs, will never catch plodding Tortoise who started first. And yet, of course, in real world, faster things do overtake slower ones.

3. The Arrow -

An arrow cannot move at a place at which it is not. But neither can it move at a place at which it is. But a flying arrow is always at place at which it is. That is, at any instant it is at rest. But if at no instant is it moving, then it is always at rest.

4. The Moving Blocks or Stadium -

Suppose three equal blocks, A , B, C, of width 1, with A and C moving past B at same speed in opposite directions. Then A takes one time, t, to traverse width of B, but half time, t/2, to traverse width of C. But these are same length, 1. So A takes both t and t/2 to traverse distance 1.

( See Simon Blackburn : Dictionary of Philosophy, 1996 )

The German set theorist Adolf Frankel ( 1891 - 1965 ) is one of many modern mathematicians ( Bertrand Russell is another ) who have pointed out that 2,000 years of attempted explanations have not cleared away mysteries of Zeno's Paradoxes : "Although they have often been dismissed as logical nonsense, many attempts have also been made to dispose of them by means of mathematical theorems, such as theory of convergent series or theory of sets. In end, however, difficulties inherent in his arguments have always come back with a vengeance, for human mind is so constructed that it can look at a continuum in two ways that are not quite reconcilable."

## The NSTP (Non - Spatial Thinking Process) Theory as a Masterkey : Non - Spatial Universal Mechanics

Written by Dr Kedar Joshi

The NSTP ( Non - Spatial Thinking Process ) theory, a published invention (2002) of Kedar Joshi ( b. 1979 ) (i.e.Myself), a Cambridge ( England ) based philosopher, is a position that, in computer terminology, regards Universe as a Non - Spatial Computer and Space as a Virtual Reality (UNSCSVR). This model of reality can resolve mysteries surrounding quantum mechanics ( e.g. wave - particle duality, EPR ( Einstein - Podolsky - Rosen ) paradox, Schrodinger's cat paradox ), Zeno's paradoxes, biological phenomena of 'protein folding' and 'cell development and differentiation', relativity, action at a distance ( which is a rehabilitated mystery through Joshi's work ), etc. All these mysterious phenomena are, in fact, multiple aspects of a singular underlying structure, composed of four conceptual elements : 1.impossibility of spatial mechanism 2.space as a form of illusion 3.phenomenal mind as non - spatial 4.intelligent orderly execution of spatial events through non - spatial mechanism

The NSTP theory is unique theoretical representation of that structure. The NSTP theory is a philosophical / scientific masterkey that unifies apparently diverse phenomena through its powerful non - spatial mechanical framework.

The NSTP theory is based on

A] Three axioms ( i.e. self - evident truths ) :

(One's objection that these propositions are not axiomatic is nothing but one's inability to perceive truth. These propositions are clearly axiomatic to author.)

1) Phenomenal mind ( or feelings or qualia ) is non - spatial. i.e. No kind of feeling, e.g. feeling of colour blue, can be represented by any spatial structure.

2) All kinds of experiences, even thoughts I know I am having, are feelings or qualias.

3) A phenomenally conscious self is a temporal stream of non - spatial phenomenal mental events. ( A Non - Spatial Thinking Process (NSTP), as every feeling is itself a thought or idea. )

B] And two hypotheses :

1) Space ( as a room or void out there : whether three or higher dimensional, bounded or unbounded ) is a virtual reality ( i.e. a form or projection of non - spatial mind, a kind of feeling ).

2) Individual or local NSTPs are orderly ( or thoughtfully ) executed by a gigantic, central, or global NSTP ( rather a group of NSTPs ), representing superhuman thoughts or ideas, in order to account for order in universe, e.g. gravitational phenomenon. ( The central non - spatial superhuman thoughts are processed in zero time because of no spatial limitations; e.g. in space it takes time to transfer data from one spatial location to another. Although a conscious human is nothing but an NSTP it is, at least partially, conceptually, as opposed to physically, bound to spatial biochemical brain, and thus core NSTPs introduce time lag in processing of individual NSTPs, where appropriate. )

Further, existence of central NSTPs is assumed for two reasons :

i) In any machine where its peripherals are not intelligent enough to modulate ( or be able to account for ) their own behaviour there has to be some central intelligent part in machine to bring out peripheral happenings or phenomena.

ii) As laws of physics ( or any other than those of pure mathematics or logic ) are not logically or conceptually necessary there has to be a way to change ways individual NSTPs are generated ( or produced or executed ). And for that to be possible there has to be some central intelligence existing in form of ( non - spatial ) mental events, which itself could be modulated to alter modulation of individual NSTPs.

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