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 onrepparttar development of mathematics. They are described in Aristotle's great work 'Physics' and are presented as four arguments inrepparttar 127622 form of paradoxes, stated below :

1. The Racecourse or Dichotomy Paradox -

There is no motion because that which is moved must arrive atrepparttar 127623 middle of its course before it arrives atrepparttar 127624 end. In order to traverse a line segment it's necessary to reachrepparttar 127625 halfway point, but this requires first reachingrepparttar 127626 quarter - way point, which first requires reachingrepparttar 127627 eighth - way point, and so on without end. Hence motion can never begin.

This problem isn't alleviated byrepparttar 127628 well - known infinite sum + + 1/8 ... = 1 because Zeno is effectively insisting thatrepparttar 127629 sum be tackled inrepparttar 127630 reverse direction. What isrepparttar 127631 first term in such a series ?

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

2. Achilles andrepparttar 127632 Tortoise -

This is perhapsrepparttar 127633 most famous ofrepparttar 127634 Zeno's paradoxes.

The slower when running will never be overtaken byrepparttar 127635 quicker; for that which is persuing must first reachrepparttar 127636 point from which that which is fleeing started, so thatrepparttar 127637 slower must necessarily always be some distance ahead. Thus, Achilles, however fast he runs, will never catchrepparttar 127638 plodding Tortoise who started first. And yet, of course, inrepparttar 127639 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 atrepparttar 127640 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 atrepparttar 127641 same speed in opposite directions. Then A takes one time, t, to traverserepparttar 127642 width of B, but halfrepparttar 127643 time, t/2, to traverserepparttar 127644 width of C. But these arerepparttar 127645 same length, 1. So A takes both t and t/2 to traverserepparttar 127646 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 awayrepparttar 127647 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 asrepparttar 127648 theory of convergent series orrepparttar 127649 theory of sets. Inrepparttar 127650 end, however,repparttar 127651 difficulties inherent in his arguments have always come back with a vengeance, forrepparttar 127652 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 resolverepparttar mysteries surrounding quantum mechanics ( e.g.repparttar 127621 wave - particle duality,repparttar 127622 EPR ( Einstein - Podolsky - Rosen ) paradox,repparttar 127623 Schrodinger's cat paradox ), Zeno's paradoxes,repparttar 127624 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 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 isrepparttar 127625 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 perceiverepparttar 127626 truth. These propositions are clearly axiomatic torepparttar 127627 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 forrepparttar 127628 order inrepparttar 127629 universe, e.g.repparttar 127630 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 torepparttar 127631 spatial biochemical brain, and thusrepparttar 127632 core NSTPs introduce time lag in processing of individual NSTPs, where appropriate. )

Further,repparttar 127633 existence ofrepparttar 127634 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 inrepparttar 127635 machine to bring outrepparttar 127636 peripheral happenings or phenomena.

ii) Asrepparttar 127637 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 changerepparttar 127638 ways individual NSTPs are generated ( or produced or executed ). And for that to be possible there has to be some central intelligence existing inrepparttar 127639 form of ( non - spatial ) mental events, which itself could be modulated to alterrepparttar 127640 modulation of individual NSTPs.

Cont'd on page 2 ==> © 2005
Terms of Use