Principia Complexica

1. Crutchfield's computational mechanics
• Advantages
• Based on computational understanding (mathematical logic, theory of computation)
• Provides the notion of the edge-of-chaos
• Uses statistical measures (We can make measurements)
• Shows the way to representing the informational processes underlying Quantum Mechanics
• Lucidates the relationship between information and statistical mechanics
• Disadvantages
• Uses statistical measures (e.g., cannot blunt Prigogine's and Rosen's arguments against reductionism)
• Limited functional abstraction
• Does not explicitly address the problem of Quantum Mechanics

 
2. Bohm's ontological quantum theory
• Advantages
• Alternative to Quantum Mechanics: explains quantum effects
• Clearly makes sense in the physical sense, gives you reason to hope that we can find something about what underlies the quantum level
• Disadvantages
• Limited abstraction
• No notion of complexity

 
3.   Category Theory (John Baez   Robert Rosen)
• Advantages
• Functions of Functions: Functors (Processes of Processes)
• Abstraction/Generalization of Process Structure
• Mathematical approach to go beyond reductionism
• Disadvantages
• No computational constructs
• Obtuse


4.   Fontana's compositional dynamics
• Advantages
• Based on proof theory and lambda calculus, models of computation
• Has symbolic notion of composition and decomposition
• Lucidates the notion of organization
• Disadvantages
• Limited abstraction of process structure?
• Limited notion of levels of complexity

 
5.  Prigogine's Laws of Chaos
• Advantages
• Based on dynamics, the foundation of physics
• Has functional composition and decomposition
• Functional analysis of coupling and decoupling (Poincaire resonances)
• Lucidates time, irreversibilty, entropy and how to get order out of chaos.
• Disadvantages
• Limited abstraction
• Limited information/computational representation
• Limited notions of levels of complexity

• The edge-of-chaos region
• Langton (phase transition - life)
• Crutchfield, Mitchell (physical computation)
• Kaufmann (autocatalysis)
• Braeiss (optimal capacity of network)
• Levels of Complexity
• David West Keirsey (what is the context?)
• Langton (edge of chaos)
• Hegel (three - thesis (chaos), antithesis (order), synthesis (edge of chaos))
• Quantum Replication
• Why big bang
• Crutchfield (physical computation)
• Functional Shift
• Adam Smith, Darwin (function, form)
• Gould (pre-adaptation, punctuated equilibrium)
• Prigogine (Poincaire's resonances)
• Rosen (functional composition, decomposition)
• Levels of Selection Process
• Leo Buss (levels of selection)
• Prigogine (chemistry selection)
• Smolin (physical selection)
• Maynard-Smith (linear encoding)

• Advantages
• Outlines the structure of existence
• Lucidates the relationship between information and physical existence
• Has notion of levels of selection processes
• Explicit relationship between death, growth, and physical computation.
• Lucidates a better notion of complexity than conventional measures and common usage.
• Methodology of analysis and synthesis
• An approach to naming abstract function
• Disadvantages
• No precise mathematics or computational models, except vague combination of work of above
• Underlying process still unexpressed (random vacuum, replication of quantum information, encoding of information in rest mass and charge)
• No clear representation of processes of processes.
• Methodology of analysis requires understanding all levels of complexity.

 Assumptions

1. Meta-Universe composed of random communication "states"  (but non-State, because they don't contain invariant information)
2. Rest "Mass" has some type of invariant information, but is encoded as part of a process.
3. The invariant information in "Mass" encodes information for communication and can be transmitted
4. The creation of "mass" is some type of "replication" process, the replication process is also encoded as part of the State.
5. There is no absolute space, all states are relational and depend on process.
6. The relationship between State and energy(in space-time) is constant.
7. Invariant information is increasing in our universe

You can think of our universe as being created by the infection of a "reality virus"  A set of random bits of information that happen to encode replication of itself in a random sea of state: energy.   This replication spreads and replaces randomness (chaos) with unfolding order.

Massive Replicative/Dissipative Structures