# Re: Fractal Foundations of mathematics: Axioms notions and the set FS as a model

http://www.fractalforums.com/index.php?action=profile;u=410;sa=showPosts

## The Ill Conceived Second "Law"

The second law of thermodynamics is a misconception that arose from a naive apprehension of God, Space, Time and Complex dynamical Systems. Few have dared to challenge it because the big guns come out and if you are a serious scientist etc your reputation is besmirched. However, this does not make the law immune from critical analysis.

The vested interest in keeping the law as it is are in fact not that great and the research that would easily sweep it away is in fact formidable. The three important Figures in correcting this law are Einstein, Alan Turing and Ed Lorenz.

A brief sketch. Einstein in solving the problem with regard to Brownian motion found it required the concept of variable time rates. The actual soution in the formula depends on the fractional surd power of time.
Ed Lorenz established a set of simple dynamical equations that demonstrated the complexity of particulate motion in a seemingly easily apprehendable system. He recognised that this is what people called Chaos in the collective subconscious, so he introduced the God of chaos into supposedly determined systems.

Alan Turing suspected that pattern emerges out of the natural processes by some set of dynamical equations that underpin it. His equations for diffusive motion within a complex system introduced the notion of emergent properties from complex systems which demonstrate patterned behaviour.

Thus the evidence, the empirical evidence for "order" arising out of "chaos" , and "chaos " inhering within "order" is clea and demonstrable.

The second Law of thermodynamics is a similar system of equations, and yet it is used to support only one side of the observed effects. The reason is that in the time it was conceived, the religious notions of the conceivers would not allow them to posit order arising without the immateria hand of "God", nor would it allow themto alter "god's" prdained sequence of "Time", or even to question it.

Lord Kelvin, an otherwise serious critiquer of "wrong" ideas, was unable to criticise his own fundamental assumptions in this regard, and he admired Fourier to such an extent , regarding him as a genius who laid bare the methods for tackling complex dynamical systems of heat flow through his Analytical system(Fourier Analysis) Which developed during his lifetime: he admired him so ardently that he uncritically accepted his assumptions about heaflow.

Of course the layman has no right to criticise mathematical formulations he does not understand, apparently. But oftn the "ignorant" can point out the obvious, the emperor has no clothes!

Technically Entropy is the change in a "measure" called the specific heat of a given substance. The substance is usually specified by a chemical name or formulation and the 3 dimensional arrangement of the molecule is only briefly taken into account, and to be blunt it is mostly ignored, because the development follows a kinetic theory argument which is really a modified version of the gas laws(Kelvin contributed much to the kinetic theory of gases). The weakness of this approximation is the major flaw in the concept of Entropy or specific heat.

Specific heats are very important and useful, and so deserve to be treated better than this. As i have sketched out Einstein, Lorenz and Turing have provided a model for developing a better development of specific heat, if indeed that is necessary, and thus revising the Concept of Entropy on a more secure empirical basis, if inded it is deemed worth keeping the idea.

We have moved on since those times, and fractal geometrical ideas underpin the notions of dynamical systems, and indeed all of so called mathematics. I go further: Fractal Geometrical notions underpin all our human apprehension of the space "in which we live and breath and have our very being".
December 2013
S M T W T F S
1 2 3 4 5 6 7
8 9 10 11 12 13 14
15 16 17 18 19 20 21
22 23 24 25 26 27 28
29 30 31