1a) What Does It Mean “Computing”? or Evolution and “Intractable Mathematics”

- Bremermann’s Limit of Rate of Information Processing

2 x 1047 bits/s-g

2 x 1047 x (age of the Universe) x (mass of the Universe) = 2 x 1047 x 1017 s x 1057 g =
= just about 10122 bits

F = number of possible values of a function measuring the human genotype fitness
10 = 210
if all nucleotide bridges (105 per gene) are taken into account;

F = 210,000 = about 103,000
if genes only are taken into account

– The Lesson of Flight Controllers

# 1,000 planes arriving per day

# input to controllers plus their devices,
designed by human beings for their own use
= 21,000 bits/day

# amount of Shannon’s information
1,000 = log2 (22 ) = 21,000 = 10301 bits

i.e., 179 orders of magnitude greater than the information processed
up to the present time by the whole Universe if taken to be a computer

- Some Basic Conclusions

– Computation in an evolutionary system means “non-syntactic (extralogical) transformation of the system in state space”

– Self-organizing evolutionary systems are far-from-equilibrium dynamic systems of hierarchical levels, at least two levels being required for “cognition”, i.e. self-awareness and self-description, this cognitive pair of levels consisting of a structural level (hardware) and a functional level (software) which make up a solidary unity as a holistic system. Stated otherwise, the energy of the dynamic structural ongoings is actually indistinguishable from function, or their symbolic description

– This structure-function solidarity processes the information time series from the environment (i.e., computes) through convolution of them with its own internal dynamics and compressing information into asimulation (representation) of the environment as a closed chain of

syntax <=> semantics <=> pragmatics

embodied in a set of levels featuring increasing degrees of abstractness of representation (symbolics) of and ways of acting (pragmatics) on the environment

– The holistic solidarity of structure — function wholeness, and the closed chain of the physics of information processing mean that cells, and even the first biota, not only process information, but they also are their own interpreters, e.g. in simulating the environment, and the recognizers of that information. They create new information, i.e. information not present in the initial conditions

- 2a) Two basic remarks:

– an isolated material system undergoing an isentropic transformation meets the conditions of Turing’s halting problem and Gödel’s incompleteness theorem for abstract systems: the flow of information in the state space of a “mechanistic”, i.e. syntactic, computer does not reach any state corresponding to new information. The process is a purely syntactic one (mathematics is tautological)

– openness and dissipation through the coupling with the environment is of the essence to create new information: dissipative chaos, not Hamiltonian chaos, is a loophole out of self-reference paradoxes. In the case of Generalized Quantum Holography, the loophole out of abstract logic paradoxes is synchronous cooperativity by linear superposition throughout the levels, from the nano to the macroscale: information compression, storage and transmission are just the same unique process

– openness and dissipation through the coupling with the environment is of the essence to create new information: dissipative chaos, not Hamiltonian chaos, is a loophole out of self-reference paradoxes. In the case of Generalized Quantum Holography, the loophole out of abstract logic paradoxes is synchronous cooperativity by linear superposition throughout the levels, from the nano to the macroscale: information compression, storage and transmission are just the same unique process

- 3a) What Is “Information”?

– For a physical description of life and biological intelligence, this term must be given two closely interrelated meanings:

1] to have knowledge
and
2] to give a format or “shape”

i.e., it designates both a state and a process

or:

information is the process by which the form of an object of knowledge is impressed upon the apprehending mind so as to bring about the state of knowing

– all that can be physically embodied by the notions developed above, following a suggestion by G. Bateson:

“Information is any difference which gives rise to a difference”

– Stated otherwise:

For any mark (the first difference) to become information there must be something or someone (the observer) interpreting that mark through interaction with the observed system, thus creating the second difference. So any mark actually becomes physical information as an emergent property from the conjugation of the observing and the observed system internal dynamics

Accordingly, information is not contained in any source, nor is it contained
in the receptor, and it is an objective physical phenomenon arising from interactions. Source and receptor can work just as metaphors in case of systems at equilibrium

– From the nanoscale to the microscopic level, toward fundamental physics

According to A. Zeilinger’s team experiments, virtual information, just like the virtual particles of quantum field theory, is revealed when one member of an entangled pair interacts with real information.

The “mark” locked in a quantum state of a particle C becomes an emergent objective property through the entangled pair A <=> B as a channel and through the observer in a measurement performed on C

At the quantum level, matter and information would become blurred into a kind of supersubstance, a matter-information solidary agency which is reminiscent of Bohm’s view of quantum mechanics underlying reality according to A. Zeilinger’s thought quoted in transparency no. 1

These points deserve further illustration for the full understanding of the weird link between the objects of our experience. We have to venture now into the strange, and yet real, world of Quantum Mechanics; it shows that there is a real link, mysterious though it may be at present, which substantiates the Bohmian view of an

“Undivided Universe”