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**These are excerpts and elaborations from my book "The Nature of Consciousness"**

Emergent computation is to
sequential computation what nonlinear systems are to linear systems: it deals
with systems whose parts interact in a nontrivial way. Both Alan Turing and John Von Neumann, the two mathematicians who inspired the creation of the computer,
were precursors in emergent computation: Turing formulated a theory of
self-catalytic systems and Von Neumann studied self-replicating
automata. In the 1950s Turing introduced the
“Reaction-diffusion Theory” of pattern formation, based on the bifurcation
properties of the solutions of differential equations. Turing devised a model to generate
stable patterns: ·
X
catalyzes itself: X diffuses slowly · X catalyzes Y: Y diffuses quickly ·
Y
inhibits X ·
Y
may or may not catalyze or inhibit itself Some reactions might be able
to create ordered spatial schemes from disordered schemes. The function of
genes is purely catalytic: they catalyze the production of new morphogenes,
which will catalyze more morphogenes until eventually form emerges. Von Neumann saw life as a particular class
of automata (of programmable machines). Life's main property is the ability to
reproduce. In the 1940s Von Neumann had already proven that a machine could be
programmed to make a copy of itself. Von Neumann's automaton was conceived to absorb matter from the environment and
process it to build another automaton, including a description of itself. Von
Neumann realized (years before the genetic code was discovered) that the
machine needed a description of itself in order to reproduce. The description
itself would be copied to make a new machine, so that the new machine too could
copy itself. In Von Neumann's simulated world, a large checkerboard was a simplified version
of the real world, in which both space
and time were discrete. Time, in particular, was made to advance in discrete
steps, which meant that change could occur only at each discrete step, and
simultaneously for everything that had to change. Von Neumann's studies of the 1940s led to an entire new field of Mathematics,
called "Cellular Automata". Technically speaking, cellular automata
are discrete dynamical systems whose behavior is completely specified in terms
of a local relation. In practice,
cellular automata are the computer scientist's equivalent of the physicist's
concept of field. Space is represented by a uniform grid and time advances in
discrete steps. Each cell of space contains bits of information. Laws of nature
express what operation must be performed on each cell's bits of information,
based on its neighbor's bits of information. Laws of nature are local and
uniform. The amazing thing is that such simple "organisms" can give
rise to very complex structures, and those structures recur periodically, which
means that they achieve some kind of stability. Von Neumann understood the dual genetics of
self-reproducing automata: namely, that the genetic code must act as
instructions on how to build an organism and as data to be passed on to the
offspring. This was basically the idea
behind what will be called DNA: DNA encodes the instructions for making all the
enzymes and the protein that a cell needs to function and DNA makes a copy of
itself every time the cell divides in two.
Von Neumann indirectly understood other properties of life: the ability
to increase its complexity (an organism can generate organisms that are more
complex than itself) and the ability to self-organize. When a machine (e.g., an
assembly line) builds another machine (e.g., an appliance), there occurs a
degradation of complexity, whereas the offspring of living organisms are at
least as complex as their parents and their complexity increases in
evolutionary times. A self-reproducing machine would be a machine that produces
another machine of equal or higher complexity.
By representing an organism
as a group of contiguous multi-state cells (either empty or containing a
component) in a 2-dimensional matrix, Von Neumann proved that a Turing-type machine that can reproduce itself could be simulated by using a
29-state cell component. Turing proved that there exists a
“universal computing machine”. Von Neumann proved that there exists a
universal computing machine which, given a description of an automaton, will
construct a copy of it, and, by extension, that there exists a universal
computing machine which, given a description of a universal computing machine,
will construct a copy of it, and, by extension, that there exists a universal
computing machine which, given a description of itself, will construct a copy
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