astro picture of the day

Credit & Copyright: Gemini Obs., AURA, NSF

------------------------------thought for the day extra-------------------------------------------------------------------Stephen Wolfram revisit---------------------------------------------------------

I don't want to repost that video.  The link at my first post of Wolframs video still works.

I want to say what I think solves Wolfram's problem.  Kurt Godel published his incompleteness theorems in 1931.  Since then, mathematicians and others have made a lot of it.  Stephen Wolfram seems to me to want to suggest that nature taps into some extra computational ability.  I'm not going to argue against Kurt Godel; those theorems are proved logicaly.

Let me just say what Jacob Bronowski says.  Jacob in his "Origin of Knowledge and Imagination" argues that a theory established finite boundaries in the infinit continuum of the universe.  These finite boundaries are inevitably incorrect somewhere.  Inevitably, we have to question our assumptions and expand our axioms, define our concepts more precisely. This corresponds to what Kurt Godel shows.  That a finite set of consistent axioms cannot prove an infinity of truths.  Eventually, in order to prove some theorem that cannot be proven in our finite set of axioms(our finite cut in the infinit continuum of the universe), we have to add in some axiom.  And, we have to do it off to infinity.

Wolfram is saying we just mine these things that are past our finite set of axioms.  I'm saying we just add another axiom.  But, I've gone further.

Jacob Bronowski considers a machine like a finite set of axioms; there's things it's good at and things it is not good at.  Any machine pushed beyond a certain limit breaks.  When a dynamical system is pushed beyond a certain point, it often reorganises itself, it often evolves new structureal order. I'm suggesting a correspondence between dynamical systems, bifercations to new states of order and adding new axioms.  This is how dna is imprinted as well. What was previously 'computational complex whole' that is unfathomable in a previous finite set of axioms is now a new syntheses and that 'computational complex whole' is now understood in a new higher framework.