A critique of Chaotic Dynamics of Nonlinear Systems

A critique of Chaotic Dynamics of Nonlinear Systems

A critique of Chaotic Dynamics of Nonlinear Systems by Thomas McClure I

Introduction

This paper is written on A critique of Chaotic Dynamics of Nonlinear Systems.

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A critique of Chaotic Dynamics of Nonlinear Systems

https://www.academia.edu/19672656/Nonlinear_Systems

Thomas McClure

A critique of Chaotic Dynamics of Nonlinear Systems should include three examinations:

(1) Cataloging (2) Elaboration (3) Demonstration

Rasband has provided a sufficient number of examples of nonlinear systems in a catalog. (1) He has elaborated this catalog with graphical maps and mathematical derivations. (2) And he has demonstrated a few applications of the theoretical aspects of Chaotic Dynamics. (3)

What he has not done is to provide a Popper-like falsification of the theory by experiment. Comparing his efforts to the theory of Einstein for the bending of light around

Mercury, he has yet to provide an experiment which will prove his theories by falsification of his premises. Walter Isaacson. Einstein: His Life and Universe, c. 2007, paper, 675 pp. shift in Mercury's orbit predicted to be 43 arc-seconds per century. (p. 218) The corrected prediction was most satisfying of his life. Two postulates (p. 191) (1) principal of relativity - all the fundamental laws of physics ... are the same for all observers, moving at constant velocity relative to each other. (p. 118) (2) principle of the velocity of light - the speed of light was a constant, 186,000 miles per second, irrespective of the source that emitted it .... (p. 119) Two minimal programs: (1) the same for all observers (2) speed of light was a constant Godel numbering (1)

2^4* 3^6* 5^2* 7^5* 11^10

S(21)

(2)

13^8* 17^1* 19^7* 23^3* 27^0* 29^9

0

a

1

of

2

for

3

was

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the

5

all

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same

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light

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speed

S(29)

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constant

10

observers

Chaotic Dynamics of Nonlinear Systems By S. Neil Rasband, paper, c. 1990 Rasband (1990) has provided a plot of (Fig. 10.1) The approach of complexity of an n-digit binary string to the theoretical values as a function of digits in a string. (p. 209) The LZ complexity c(S) of the string S is the number ... (p. 210) Now the procedure is clear for comparing the LZ complexity of a given string to the LZ complexity of random strings of the same length. [random meaning algorithmic complexity (p. 206)] The algorithmic complexity of a string is defined to be the length in bits of the shortest algorithm for a computer to produce the given string. (p. 206) The measure is c(S)/b(n) in the linear plot as (c/b -1), where b(n) = h_n/{log (K) n}, where K denotes the number of the elements in alphabet A and h denotes the normalize source entropy. Taking the portion of the plot 10^-1 (c/b - 1) {0.25,0.33} and 10^4 n{0.0,0.33} then in the interval n{0,3300}, where N=47; 2^5.6 = 48; {10^4 5.6*10^-4 = 5.6 binary digits} (c/b - 1) = 0.25*10; c/b = 26; c(S) = 26 b(n); b(n) = c(S)/26 (c/b - 1) = 0.33*10; c/b = 34; c(S) = 34 b(n) ; b(n) = c(S)/34 Taking the two postulates of Enstein S(21) and S(29): b(n) = 21/26 = 0.80; b(n) = 29/34= 0.85 Then plot the pairs n{5.6*10^-4} and (c/b - 1){0.25,0.33}. This falls into the interval {0.0,0.33}. Hence, the LZ complexity is validated. In short, Rasband has created a way to falsify his hypotheses with experimental data from random strings from postulates.

Like Einstein before him, this should be a most satisfying finding.

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Conclusion

This paper is written on A critique of Chaotic Dynamics of Nonlinear Systems.