[ExI] symmetrical 11-Venn discovered

[Anders Sandberg]

On 2012-08-15 09:49, scerir wrote:
> Anders:
>> I wonder if these fractals can be seen as the quantum mechanical
>> analog to a random walk of a particle?
>
> Actually if one looks at those "quantum carpets" (link below)
> http://www.phy.bris.ac.uk/people/berry_mv/the_papers/berry329.pdf
> one has the perception of a sort of "walk", more ordered than random.

Yeah, quantum mechanics is very ordered and "clean". It is ironic in the 
same way as relativity theory is about the things that are absolute to 
all observers.

Quantum chaos and whether it was "real" chaos or not was rather ho6tly 
discussed when I was doing a bit of dynamical systems. It still seems to 
be an active problem: it is not obvious how you can get sensitive 
dependence on initial condition out of a system where everything is 
essentially linear.

My own take on it is that the sloppiness and uncertainty we have about 
not just initial conditions but the exact system we are dealing with (we 
can never make exact boxes, there are slight disturbing external fields 
etc) produces more than enough randomness to smear out the nice quantum 
carpet regularities.

But the underlying mathematics of why we get such random structures as 
are shown on http://en.wikipedia.org/wiki/Quantum_chaos still remains 
unclear: it might just be that it is a consequence of "borrowed" 
nonlinearity from force laws that makes the quantum states behave 
chaotically.

-- 
Anders Sandberg
Future of Humanity Institute
Oxford University