[asa] Lorenz equations and fine tuning (was Results of Cameron's Survey)

From: Don Nield <d.nield@auckland.ac.nz>
Date: Mon Jun 29 2009 - 21:16:01 EDT

Sorry, Iain, but you are off the beam. The parameter rho that appears in
the Lorenz equations is not a fundamental constant that can be thought
of as being fine tuned. Rather, it is a parameter like a Reynolds number
that can be varied continuously. In the original Lorenz paper on
convection in the atmosphere it appears as a sort of Rayleigh number
that measures the ratio of factors associated with the causes of
convection (a temperature difference between the top and bottom a layer
of fluid, expansion , gravity) and properties. of the fluid that hinder
convection (viscosity, conduction). For small values of rho one has no
convection, for intermediate values one has laminar convection, and for
large values one has turbulence. The value 28 (in conjunction with the
values of sigma and beta) is a typical value for the the transition to
turbulence.
Don N.

Iain Strachan wrote:
>
>
> Ah yes, of course I'd forgotten the quantum uncertainty. But that
> only applies to things like position and momentum (which would of
> course apply to my Lorenz Attractor example - initial conditions).
> However it would not apply to the fine-tuning of the constants of the
> universe. Hence there are constants in the Lorenz attractor (this
> from the Wikipedia page):
>
> ## Lorenz Attractor equations solved by ODE Solve
> ## x' = sigma*(y-x)
> ## y' = x*(rho - z) - y
> ## z' = x*y - beta*z
> function dx = lorenzatt(X,T)
> rho = 28; sigma = 10; beta = 8/3;
> dx = zeros(3,1);
> dx(1) = sigma*(X(2) - X(1));
> dx(2) = X(1)*(rho - X(3)) - X(2);
> dx(3) = X(1)*X(2) - beta*X(3);
> return
> end
>
> Note that the line starting rho = 28 specifies not the initial
> conditions, but the constants of the system. One might imagine there
> is much greater scope for fine adjustments of these. Different values
> of rho give very different behaviour of the system.
>
> So generalising to the Universe, maybe the Creator has much more fine
> choice over things such as Planck's constant , or the Fine Structure
> Constant than would be allowed by Quantum uncertainty.
>
> Iain
>
>
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Received on Mon Jun 29 21:16:50 2009

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