Re: Chez Watt: Entropy in crystalization: up or down?

On Oct 25, 3:50 pm, c...@xxxxxxxx (Richard Harter) wrote:

Oh?

As the universe, by definition, contains everything there ever was or
will be, it contains your binary string.

The universe that we know and love and live in does not necessarily
contain all that there was or ever will be. Ever hear of the multi-
universe or multiverse hypothesis?

How is this binary string represented in your binary string which
contains all the information in the whole universe over time?

The universe, if finite, can be represented by a finite string. Even
an infinite universe could be represented by a single infinite string.

Well, no, this isn't right at all. It is open to question what
the cardinality of the universe is, but unless it is composed of
discrete entities, it is C, the cardinality of the continuum
which is uncountable, i.e., it cannot be represented by even an
infinite string of bits.

It is conceivable that it could be approximated by discrete space
time meshes to any desired degree of precision, but even that is
not plausible because of quantum uncertainty in small regions of
space-time.

Looks like you are bringing in a variant of Zeno's paradox.

Zeno's paradox, when it comes to physical systems like the universe,
depends on if the universe is or is not composed of discrete entities.
It also depends upon how you defined the "information" created or
represented by the universe. In any case, there seems to be a bit of
debate, even within mainstream physics, when it comes to the question
of if the universe could be represented by a string of digits.
"Treating the universe as a [finite] computer has been advocated by
Fredkin, Lloyd and Wolfram among others." (3)

In fact, some scientists suggest that your arguments, when applied to
the "real universe", do not apply; that they are "mere fiction".

"In other words, in a universe limited in resources and time - a
universe subject to the information bound in fact - concepts like real
numbers, infinitely precise parameter values, differentiable
functions, the unitary evolution of a wave function - are a fiction: a
useful fiction to be sure, but a fiction nevertheless, and with the
potential to mislead. It then follows that the laws of physics, cast
as idealized infinitely precise mathematical relationships inhabiting
a Platonic heaven, are also a fiction when it comes to applications to
the real universe. Landauer's proposal that our theories should be
constrained by the - possibly finite - resources of the universe has
been independently developed in recent years by Benioff." (3)

"All physical systems register and process information. The laws
of physics determine the amount of information that a physical system
can register (number of bits) and the number of elementary logic
operations that a system can perform (number of ops). The Universe is
a physical system. The amount of information that the Universe can
register and the number of elementary operations that it can have
performed over its history are calculated. The Universe can have
performed 1e120 ops on 1e90 bits ( 1e120 bits including gravitational
degrees of freedom)." (1)

"'Jacob Bekenstein has claimed that our universe might be an
illusion, perhaps consisting of 10100 bits of information that can be
stored on a disk.' . . . Kaku cites the calculation by Bekenstein, who
with Stephen Hawking developed the theory of black hole evaporation,
that a black hole with a 1 centimeter diameter can store 1e66 bits of
information on the event horizon, and that the number of black holes
within the observable universe is sufficient to store 1e100 bits." (2)

"If Laplace's argument is taken seriously, on the assumptions
adopted, then everything that happens in the universe, including
Laplace's decision to write the above words, my decision to write this
article, Chaitin's beautiful work on Omega, etc. are all preordained.
The information about these events is already contained in the state
of the universe at any previous time. To get some idea of the demon's
gargantuan task, note the following. If the demon overlooked the
gravitational force of a single electron located at the edge of the
observable universe, then his prediction for the motion of a given
molecule of air in your living room would be rendered completely
uncertain after only 12 intermolecular collisions.6 This arresting
example reveals how exquisitely sensitive to error predicting the
future can be. . .
A completely different view of the relationship between
mathematics and physics comes from Chaitin's development of
algorithmic information theory, from which he was drawn to the
conclusion, "A scientific theory is like a computer program that
predicts our observations." For example, in Newtonian mechanics the
initial positions and momenta of a system of particles serve as input
data, the laws of mechanics are the program, and the final state of
the particles at some later time of interest corresponds to the
output. In this manner, the universe processes information
automatically as it evolves. So we might envisage the laws of physics
in terms of software, as a grand cosmic computer program. This shift
of perspective, simple though it may be, has profound implications,
which are immediately apparent when we ask what is the hardware on
which the cosmic software is being run? The answer is, of course, the
universe itself. And by this I mean the real, physical universe. I am
not referring to some imaginary cosmic hardware in a Platonic heaven,
but the real universe we observe. The significance of this last point
is that the real universe might very well be *finite*, that is, have
finite resources and age, and thus be subject to restrictions on what
it can accomplish in regards to computation.
The region within our particle horizon contains about 1e80
particles of matter, and about 1e90 photons and neutrinos. If the
system is treated quantum mechanically, with information encoded in
discrete bits (e.g. spin up, spin down), then the maximum number of
bits of information contained in a horizon volume at this time is
about 1e122 according to Seth Lloyd." (3)


1. S. Lloyd. Computational capacity of the universe. Physical Review
Letters, 2002, vol. 88, issue 23, 4 pages
http://www.ltn.lv/~podnieks/gt1.html

2. http://www.astrophysicsspectator.com/commentary/commentary20040908.html

3. http://cosmos.asu.edu/publications/chapters/chaitin_book.pdf

Richard Harter, c...@xxxxxxxxxxxx://home.tiac.net/~cri,http://www.varinoma.com
In the fields of Hell where the grass grows high
Are the graves of dreams allowed to die

Sean Pitman
www.DetectingDesign.com


.

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