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From: Colin Hales <colin.domain.name.hidden>

Date: Thu, 28 Nov 2002 14:43:22 +1100

Russell Standish wrote:

*>> Colin Hales wrote:
*

*>> Hi Folks,
*

*>> I have chewed this thread with great interest.
*

*>>
*

*>> Our main gripe is the issue of emergent behaviour and the mathematical
*

*>> treatment thereof? Yes? This is the area in which Wolfram claims to have
*

*>> made progress. (I am still wading my way through his tome).
*

*>>
*

*>> ***Isn’t the 'algorithmic revolution' really a final acceptance that
*

there

*>> are behaviours in numbers that are simply inaccessible to "closed form"
*

*>> mathematical formulae? - That closed-form mathematics cannot traverse
*

the

*>> complete landscape of the solution space in all contexts?
*

*>>
*

*>
*

*>If this were the case, the 'algorithmic revolution' is at least 200 years
*

old, as people have

*>known at least this long that most integrals cannot be written in "closed
*

form".

*>
*

*>Of course, from a practical point of view, it was so expensive to solve
*

mathematical problems numerically,

*> that hardly anyone bothered until the advent of the electronic computer.
*

Since then, of course

*> computational science has taken off like a rocket, and keeps the likes of
*

me employed. But this is

*> hardly new news, or philosophically interesting.
*

*> Cheers
*

We have a small confusion here (probably caused by my own choice of words).

I’m not talking about the numerical solution to a given mathematical

formula. Agreed: Mundane++. Memories of laboriously iterating on my

calculator come to mind! :-)

What I’m saying (as you seem to agree) is that for some aspects of the

universe (including those aspects we identify as emergent phenomena) there

are no formulae possible in the first place. I think I find the answer to my

original question in the last 2 paragraphs of your paper section 2.

http://life.csu.edu.au/ci/vol09/standi09/, as well in your ‘emergence’

thread para where I think you have ‘nailed it’:

………. “As to mathematics predicting emergent phenomena, I believe that the

answer is categorically no. Emergent phenomena are a result of a modelling

process - eg what a brain does, not an analytic process. Mathematics can be

used to describe the emergent phenomenon after it is discovered, but I don't

think the discovery process can really be called mathematics”…………..

Here is another possible confusion: ‘emergence’ as a descriptive artefact vs

‘emergence’ as real layered behaviour in a real system. The wording

initially looks as if you think emergence is not real. The emergence is real

(whatever we consider real is!). Example: There are at least 6 fundamental

layers of emergence from quantum froth to mind. The agreed view appears to

be that any formal mathematics of each layer stops at each layer whereas an

algorithmic approach generates/spans the layers, which are delineated by an

appropriately sensitised observer. Both styles of description seem

appropriate and able to coexist provided their character is understood.

I think we do have a ‘revolution’ and it is a revolution that will force us

to use a wolfamesque rule-based numerical combination descriptive/predictive

method to deal with emergence whether we like it or not because it’s the

only technique that can traverse the layers and there are a multitude of

problems where we need to do exactly that. It seems more than a passing fad.

I can foresee industry based on derivation of elaborate CA to fulfil useful

requirements that cannot be achieved otherwise. I can see scientific method

and Cog. Sci. in particular undergoing a transformation of a sort as a

result.

Not really TOE stuff, so I’ll desist for now. I remain ever hopeful that one

day I’ll be able to understand Bruno…. :-)

Cheers,

Colin Hales

Received on Wed Nov 27 2002 - 22:49:12 PST

Date: Thu, 28 Nov 2002 14:43:22 +1100

Russell Standish wrote:

there

the

old, as people have

form".

mathematical problems numerically,

Since then, of course

me employed. But this is

We have a small confusion here (probably caused by my own choice of words).

I’m not talking about the numerical solution to a given mathematical

formula. Agreed: Mundane++. Memories of laboriously iterating on my

calculator come to mind! :-)

What I’m saying (as you seem to agree) is that for some aspects of the

universe (including those aspects we identify as emergent phenomena) there

are no formulae possible in the first place. I think I find the answer to my

original question in the last 2 paragraphs of your paper section 2.

http://life.csu.edu.au/ci/vol09/standi09/, as well in your ‘emergence’

thread para where I think you have ‘nailed it’:

………. “As to mathematics predicting emergent phenomena, I believe that the

answer is categorically no. Emergent phenomena are a result of a modelling

process - eg what a brain does, not an analytic process. Mathematics can be

used to describe the emergent phenomenon after it is discovered, but I don't

think the discovery process can really be called mathematics”…………..

Here is another possible confusion: ‘emergence’ as a descriptive artefact vs

‘emergence’ as real layered behaviour in a real system. The wording

initially looks as if you think emergence is not real. The emergence is real

(whatever we consider real is!). Example: There are at least 6 fundamental

layers of emergence from quantum froth to mind. The agreed view appears to

be that any formal mathematics of each layer stops at each layer whereas an

algorithmic approach generates/spans the layers, which are delineated by an

appropriately sensitised observer. Both styles of description seem

appropriate and able to coexist provided their character is understood.

I think we do have a ‘revolution’ and it is a revolution that will force us

to use a wolfamesque rule-based numerical combination descriptive/predictive

method to deal with emergence whether we like it or not because it’s the

only technique that can traverse the layers and there are a multitude of

problems where we need to do exactly that. It seems more than a passing fad.

I can foresee industry based on derivation of elaborate CA to fulfil useful

requirements that cannot be achieved otherwise. I can see scientific method

and Cog. Sci. in particular undergoing a transformation of a sort as a

result.

Not really TOE stuff, so I’ll desist for now. I remain ever hopeful that one

day I’ll be able to understand Bruno…. :-)

Cheers,

Colin Hales

Received on Wed Nov 27 2002 - 22:49:12 PST

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