[ExI] symmetrical 11-Venn discovered

[Anders Sandberg]

On 14/08/2012 16:28, scerir wrote:
> Anders writes:
>> In general, I expect that fractals often emerge because the universe 
>> also tends to follow simple rather than complex programs. Even when 
>> these programs make organisms it is easier to grow and evolve 
>> recursive structures than non-recursive ones. So the important and 
>> deep question is what forces affect what programs get run, and what 
>> kind of simplicity is optimized for.
>
> That reminds me of a paper by Berry showing that a quantum wave
> in a box evolves from a uniform state and the graph of the evolution
> of the probability density is both fractal in space and in time. There 
> are, in addition to these time and space fractals, infinitely many 
> 'quantum revival' times, when the probability density is constant.
> http://www.phy.bris.ac.uk/people/berry_mv/the_papers/Berry275.pdf
>
> But there are chances that Anders already knows all that :-)

I knew the rough outlines, but it is nice to see the paper. And it gets 
some elegant results with seemingly no effort.

In this case quantum mechanics adds an infinite series of periodic 
functions with a particular wavelength relation set by the boundary 
conditions: the fractal happens because there is energy at all scales 
(because of the uniform initial condition). The finite energy case is an 
approximate fractal.

I wonder if these fractals can be seen as the quantum mechanical analog 
to a random walk of a particle?

A new kind of science: sure, lots of complexity from short programs. But 
where do we get the programs from, and what is the measure?

-- 
Anders Sandberg,
Future of Humanity Institute
Philosophy Faculty of Oxford University