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Wednesday, April 13, 2011

Notes on Russell's Paradox

 Bolyai and Lobachevsky


I am using the blog as my own, private Notebook again, so skip on if you do not wish to dither along with me.

Last paragraph in the post about Russell's Paradox:

I have often wondered "I wonder what it was like for the first men or women who uttered speech? Was there anyone else around to understand them?" Scenarios like this, dealing with the first occurence, are very, very foggy. Was there a "first" person to speak? We often talk as if there were...
Yadda-yadda-yadda...

It is important that the First Speaker needed a First Listener. The entire Scenario of "The First Occurrence of X "  where X is some process for which we posit a "beginning" ... I have not thought about it enough. It is interesting.
Notice we are talking about complex systems composed of complex subsystems. I believe the example of Eyesight has been used in arguing for Intelligent Design.... sort of logic of the Frankenstein monster: brute matter baaaad.... and dumb; can't create the Eye all by itself, since the Eye is a complex system containing many complex subsystems, and only God can juggle all the variables...
(Which in itself is a logical howler and depends upon a certain frame-of-mind approach to complexity... God is He who is Necessarily the Un-Baffleable!!  In its simplest expression, Intelligent Design asks the question: Can the Divine Dictionary figure out the Unsolveable  Crossword Puzzle? )

In Particle Physics we are searching for the Beginning or the Ground: the set of basic building blocks particles and forces.
My question is whether there may be such. The basic particles hitherto discovered are complex enough to baffle me, and each complex entity seems to need some complex set of subsystems... are we correct is postulating that there need be a "beginning" or a basic foundation for the world? Or for anything, for that matter?

Is the search for a Basic Foundation essentially a stepping backwards down an Illusory Great Chain of Being? What if the concepts "Basic Foundation", "Beginning", or "Singularity" are not suited for such knowledge structures?
Now it will be said that Physics has met this very objection from people like,  oh, say Fred Hoyle and his theory of Continuous Creation, and has refuted them.
However, it seems to me that Hoyle was refuted in the context of a system which allowed for Singularities, which - like magnetic monopoles - are the very stuff of Paradox. Consider Hoyle to be saying that he wished to establish Non-Singularity Physics, just as Bolyai and Lobachevsky created Non-Euclidean Geometry...

Certain processes cannot exist without enormous complexity:  speaking requires listening, else language dies with the passing of First Speaker.
Is there an end to complexity: a simple and basic foundation upon which everything is built?
So far, I only see an infinite regression of complexity in Physics.
Singularities are where science fizzles out, not necessarily where mystery reigns.
Besides, if the universe is constantly expanding, so is the potential for knowledge.

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