Monday, July 25, 2011

The Structured Use of Randomality

Derived from Comments made to : Neither D or R by Wm Jas

This seems like ( upon greater reflection ) a much more interesting consideration than i originally granted it.
What needs to be done is to define a continuum of How Determinism & Randomality may be mixed together in various ways.

i continue to believe that this isn’t going to help The Problem of Freewill one iota, but i also believe that there are several distinct classes of how randomality may effect a classical deterministic model.

The Continuum would consist of a Perfect & Simple ( Dominoistic ) Determinism
on One Side ( On The Left ) And Perfect Randomality on The Right Side.
Holistic Determinism, When Every Particle in The Model is Affecting Every Other Particle, Via Instantaneous Forces, would be at The Middle.

A Holistic Deterministic Universe, with Forces acting at The Speed of Light Would be Just to The Left of That. ( Very Close to Our Observed Reality )

What really got me going on this ‘ReConsideration’ was that i thought of an Example, that i’d played around with on The Computer, that would satisfy this Definition; Of An Orderly Structure that ‘Evolves’ with A Distinct Random Element regularly interjected into it.

The Orderly Structure Contains ( Constrains ) The Randomality,
So that, In this Example, The Structure ( Overall ) is Not changed in The Least.
If The Random Element was replaced with The Fibonacci Sequence, or any other Mathematical Series, The Net Result would Look Pretty Much The Same.
Indistinguishable from one another if you stepped back from them.

The Example that i’m thinking of for this case;
Would be to arrange any number of Dots on A Field, ( 3 is Clearest ),
( In roughly a Circular Form, with an Open Space in The Middle )
Then Randomly Select an (x,y) Coordinate inside this space, Position (A)
- Start of Loop -
And Additionally Randomly Select One of The Other Dots,
Previously Defined, Position (B)
Then Apply The Simple Rule, of Determining The Point, One Half of The Distance from Your Original Position (A), To Position (B) And Placing a Dot There.
This New Dot is Now Position (A)
- Repeat Several Thousand Times -

( The One Half Rule can be any Fractional Value,
So long as it’s The Same amount of Each Itineration )

The Result will be ( ± ) a Sierpinski Triangle ( The Triangle of Pascal, Modulo 2 )

Vaguely Like this :

Sierpinski Pyramid (version 1)

Borrowed from : YoyoBandalore's Flickr Album ( without Permission ! )

i am also fascinated by Chaos, which i understand to be Orderliness of such a extreme complexity, that it is indistinguishable for Randomality.
Curiously; These Chaotic Systems Are completely unpredictable when examined in small boxes, but when you allow them to run around in The Back Yard, and Film them with a Time Lapse Camera, They reveal a Very Distinct ‘Macro Pattern’ of somekind.
What is so remarkable about these Chaotic Systems is that they are able to Return to Their ‘True Nature’ while Internally, They seem Completely Random.

This also brings to mind Scanning Electron Microscopic Pictures of Some QuasiRegular Crystals. These are Crystal Formations in which A Regular Pattern is Revealed, But can only be Examined at a Comparatively Large Scale.

A ‘Normal’ Crystal, like Salt or Diamond, will look like Salt or Diamond, at Whatever Scale you Examine Any Number of NaCl Molecules or Carbon Atoms.

But a QuasiCrystal will look like one thing, such as a perfectly flat plane for several thousand atoms, Then Suddenly manifest itself as tower structure, then return to The Plane, and Then after awhile, Make another Tower, exactly like The One that we just examined.
What is Amazing ( ? ) is that The ‘Instructions’ for how to make The Tower, were hiding in The Flat Plane.
All The While that The Atoms were laying there so peacefully flat, They were counting off how many atoms from The Last Tower, before Starting a New One.
How can they do that?
Are they all just a teeny tiny bit out of angular registration,
or is there a musical tone that they are holding onto, that contains that secret information?

Is this sort of thing Extremely Common?
Is there ‘Secret’ Information hiding in Everything?
Layers & Layers of ‘Causal Determinism’ that is hiding from view.

So that besides The Holistic Interactivity of All The Particles in The Universe ( Pretty much so ) Interacting with Each Other,
There is Another Layer of Causal Determinism hiding inside All These Particles, That are telling them how to create MacroScopic Objects & Effects.

The point being;
If you’re sure that ‘Randomality’ is Necessary to Create The Complexity of The Observed Reality;
That’s probably not necessary.

Recursive Chaos is Completely Orderly;
But is Indistinguishable from Any Theoretical Randomality that you might wish to Imagine.

And how does this help Freewill?
Not in The Least.

Given all The Information that’s Available;
The Only Way that Freewill makes sense,
Is to Equate it with Autonomy,
And Define The Universe itself as Autonomous,
And Then Claim that Every ‘Node’ of Consciousness
Is Sharing The Autonomy & Freewill of The Universe.

Sharing Autonomy may sound like an oxymoronic statement,
But it also seems to make sense in a perfectly kooky kind of way.

But it still doesn’t allow for Deterministic Determinism.
That is something that no Example of has ever been observed under Laboratory Conditions.

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