On 27 Feb 2012, at 12:16, Alberto G.Corona wrote:

Perhaps a more basic, and more pertinent question related with
entrophy and information in the context of this list is the relation
of computability, living beings , the arrow of time and entropy,

What the paper (http://qi.ethz.ch/edu/qisemFS10/papers/
81_Bennett_Thermodynamics_of_computation.pdf)  that initiated the
discussion suggest is that in practical terms it is necessary a
driving force that avoids random reversibility to execute practical
computations, this driving force implies dissipation of energy and
thus an increase of entropy.  This is so because most if not all
practical computations are exponentually branched (Fig 10).

But all computations can been done in a non branched way.
There exists reversible universal machine, and indeed a quantum computer is such a machine. From Bennett 73, (Logical reversibility of computation, IBM, J. Res. Dev., 17, 525). Energy is dissipated only when information is erased (Landauer principle), and, as the logicians already knew (Hao Wang, for example) computations can been done without erasing any information. Bennett convinced me also that we can extract work from (Shannon) information, and that energy might be a local measure of information content.

And here comes the living beings. As the paper says in  the
introduction, living beings perform computations at the molecular
level, and it must be said, at the neural level.

I am OK with this, but of course we don't know that.

Therefore given the
said above, life must proceed from less to more entrophy and this
defines the arrow of time.

Besides the paper concentrates itself in what happens inside a
computation some concepts can be used to dilucidate what happens with
the interaction of a living being and its surrounding reality.  The
reality behaves like a form of ballistic computer at the microscopic
level., with elemental particles ruled by the forces of nature instead
of ellastic macroscopic collisions.  At the macroscopic level,
however, there is a destruction of information and irreversibility.


However in the direction of entropy dissipation, it is possible to
perform calculations in order to predict the future at the macroscopic
level. That´s a critical function of living beings. An extreme example
of the difference between macro and micro computation is to "predict"
the distrubution of water in a water collector after rain.   It is not
necessary to know the position and velocity of every water molecule,
not even the position and velocity of each drop of water.  is this
erase of information  that the increase of entropy perform at the
macroscopic level (that indeed is the reason of the mere concept of
macro-state in statistical mechanics)  the process that permit
economically feasible computations.  Since computation is expensive
and the process of discovery of the world by living beings trough
natural selection very slow, (trough the  aggregation of complexity
and sophistication by natural selection is in the order of magnitude
of the age of the universe : thousands of millions years) Then the
macroscopic laws of nature must be simple enough, and there must be a
privileged direction of easy computation for life to exist.


The fact that evolution for intelligent life and age of the Universe
are in the same magnitudes means that this universe is constrained to
the maximum discoverable-by-evolution complexity in the
computationally  privileged direction of the arrow of time.

OK, in term of "this branch of the multiverse".



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