073a-Approaching a basic model: where is the commutative property? [20120905]

a + b = b + a

Many algebras have the commutative property.  though not all of them (binary combinations do not, 10 01 != 01 10  different hexadecimal numbers)

but where is this commutative property?  in what form the does the commutative property exist?  Is the commutative property a "feature" of numbers?  if it is, what other features do numbers have?  

these kinds of questions point us to the fact that the commutative property is not a feature of the materials (numbers).  But is a representation of a process we apply to the materials.   We have this process we call the commutative property.  We apply this process to numbers, or symbols.  Sometimes the application seems appropriate, and sometimes it is not appropriate.  

In an automata(material) system,  what is the form of the commutative property?   It exists as an executable code or computation that converts one number set into another number set.  In short, the process which performs the commutative property is a rule about sets of numbers, that applies to that set  . 

But where in this automata system does the rule of the commutative property exists?  The rule, doesn't exist in the material that is the automata system.  even if there is a code process which performs the rule, this is just an automatic action.  the rule itself, is not in the automata system at all.  It is a mental conception we have a function or process that happens to the material of the system (the numeric values).   But this mental conception is not in the automata or the calculations or functions or processes at all.   

For the commutative property to become a feature of the automata system, it must be represented in the automata system.  the automata system must be expanded to have values upon which processes act and representations of those processes.   There must be  a relationship between a value (a commutative process that can be performed on that value) and that representation of that commutative process (some material or structure).  once the commutative process is stored as a representation in the automata system, then we can show where the commutative property is.  

until that point, the automata does not have a commutative property, it performs an action that we refer to as the commutative property.  the property, that representation, is in us, while a function of that property is in the automata.  it is only by making a linkage from data, from values, to the commutative property, and then to the function that property represents that the automata itself can perform the function, AS the commutative property.  otherwise, otherwise, the automata is acting without any meaning... the meaning is found outside the automata in us, where we have a representation of the commutative property.

Now it stands to reason that this automata system must represent more than just the commutative property, it must represent all it's functions.  otherwise, with only one function represented, the automata is making only a binary distinction of processes.  is commutative property or is not(all other functions).  the system must have a richer representation to have a richer understanding and response and action in the world. 

consider an automata that performs processes that are commutative.   can we introspect that automata for that property or do we see a process and then say that process is commutative?

when a person uses a commutative process, and we introspect the person, the person reports that they are using a commutative process.  an automata or computer program does not report on it's processes because they are unrepresented... only functional, automatic. the person introspects themselves whereas the automata is analyzed from outside, by a programmer.  the automata cannot introspect itself.  

unless an automata makes representations of it's own processes and has processes to express and analyze those representations and processes, an automata cannot introspect.  and perhaps by the time one does, we would not think of it as an automata, but as sort of body of automata.

moreover, for an automata to introspect, it's computational contents must be introspectable.  by what?  we see both the shades of stigmergy (introspection signals) and of duality.  what is the other thing, the other automata that is introspecting?  by definition an automata cannot introspect.  a body of automata could introspect it's parts
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