Hi Evgenii,
You might also find Stephen Wolfram's work with cellular automate
replete with examples of bifurcations and symmetry breaking. My thought
was considering how to construct models of the behavior of bifurcating
and symmetry breaking systems. I was thinking in second-order terms, as
it where... Thus the use of statistics...
Onward!
Stephen
On 3/24/2012 11:50 PM, Russell Standish wrote:
Look up the literature on catastrophe theory. There were many examples
of just these phenomena cooked up (particularly by Zimmerman IIRC)
some good, many not so good. I'm sure you should be able to find
something appropriate - maybe the appearance of Benard cells for
instance.
Cheers
On Sat, Mar 24, 2012 at 10:05:00PM +0100, Evgenii Rudnyi wrote:
Hi Stephen,
I am not sure if I completely understand you. My question was rather
what happens in Nature if we assume that its mathematical model
includes bifurcations and/or symmetry breaking.
Do you know a simple mathematical model with bifurcations and/or
symmetry breaking? It might be good to consider this on a simple
example.
Say, I do not understand how do you apply statistics in this case.
Either it is unclear to me how infinite computational power will
help.
Evgenii
On 23.03.2012 22:27 Stephen P. King said the following:
On 3/23/2012 3:08 PM, Evgenii Rudnyi wrote:
In physics there are bifurcations and symmetry breaking. What happens
then if I solve some transient problem for a system where a
bifurcation or symmetry breaking happens. How the choice will be made?
Evgenii
Hi!
We would use statistics to model such a scenario or, if able to access
infinite computational power, we would compute faithful simulations of
the solutions and see which best matches the environmental requirements
of the universes from which those bifurcations or any other form of
symmetry breaking occurs. Given infinite computational powers there is
no such thing as randomness in a 3-p sense. This is known as
"omniscience". We have seen it before...
One thing that most models of statistic fail to sample is the
environment in which a stochastic event occurs, thus they integrate over
them and smears out the very facts that might otherwise inform us of
exactly how and why a "choice was made".
Onward!
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