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Sep 28, 2022, 6:06:04 AMSep 28

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ART MATRIX PO 880 Ithaca, NY 14851-0880 USA

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'The Paths of Lovers Cross in the Line of Duty.'

THE THEORY BEHIND 'THE CELL AND THE WOMB'

An example of a NON Fractal system.

Copyright (C) 1990 by Homer Wilson Smith

All Rights Reserved

We have learned in early school that the equations relating

distance to velocity and acceleration is:

D = 1/2*A*T**2 + V*T + D

V = A*T + V

Easily enough what this says is that after time T your distance

away from your starting point will be your original distance D away from

D = 0, plus distance gained by virtue of your original velocity V at T =

0 plus distance gained by virtue of added velocity caused by

acceleration.

No problem. Further a graph of D vs T will show a non linear plot

basically like Y = X*X.

Being non linear one might immediately wonder if there is potential

for fractal behavior in this system.

The answer is no.

To start with, the system as modeled here is not iterated, it is

merely evaluated. We can however turn it into an iterated system by

choosing a unit of time to match the unit of iteration. Let's choose

our unit of time to be 1.

Thus the preceding equation can be remodeled and iterated as

follows.

D = 1/2A + V + D

V = A + V

D is the iterating variable in the first equation, and V is the

iterating variable in the second equation.

If D and V both start off with value of 0, and A is a constant

acceleration, then each iteration will give us new values for D and V

for each second down the road.

This is an iterated system and not an evaluated system because you

can't just plug in the number 10 and get the final distance 10 seconds

down the road. You have to operate the pair of equations 10 separate

times to get the final answer.

PAGE 2

However you will notice that both equations are now linear. Thus

there is no fractal behavior evident.

The equations have to be non linear in the ITERATING VARIABLE in

order for fractal behavior to be manifest. Our original equation was

non linear in T but iterated in D. That is why it is non fractal.

However consider the situation where the acceleration is no longer

constant but is a function of D itself such as in a spring system or a

gravity field. If A is a non linear function of D, then indeed the

equation in D is non linear and will show fractal behavior. If we

consider relativistic effects, it is possible that the acceleration will

also be a non linear function of V too. Then BOTH equations have non

linear terms in the iterating variables D and V and will show dualistic

fractal effects.

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Wed Sep 28 06:06:02 EDT 2022

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================== http://www.lightlink.com/theproof ===================

Learning implies Learning with Certainty or Learning without Certainty.

Learning across a Distance implies Learning by Being an Effect.

Learning by Being an Effect implies Learning without Certainty.

Therefore, Learning with Certainty implies Learning, but

not by Being an Effect, and not across a Distance.

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