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Thursday, March 6, 2008

Limits vs. Hard Limits

I found the following pages (links below) about physical and logical
limits. The author posits that true limits are frequently and
practically the result of knowledge systems themselves. My take on
his argument is that even where true limits exist (Godel, Penrose,
Turing) the limits in our own notational, logical and processing
systems prevent us from ever experiencing the true innate limits in a

My guess is that Godel's incompleteness limit and Turing's halting
problem, and even Penrose's arguments about self same limits imposed
by the false mapping of one computing or mapping system onto a domain
with its own (incompatible) processing system. Again, these logic
and processing system miss-mappings may present false limits that are
fundamentally different from any true limits that may exist, and
importantly, one might mistake the false limits for the real one(s).

Interestingly, Turing's process halting proofs prove that all of his other work on computing system equivalence may never be conclusively
applied to a given process (as it is impossible to say whether or not
a given process is computable (will not halt) and his equivalence law
depends on a process being computable.

The work of most theorists depends on the notion that the universe is
computable, is Turing complete, is not a member of the group of
programs that will halt. Even more problematic is the work of theorists who attempt to build ad hoc simulations of the most causal layers of the universe, of its origin, in which case both the simulation and what it simulates must both be Turing complete and not a member of the set of halting programs.

My mind is whirling around all of these issues. Plus, I am noodleing around the notion that the lowest levels of hierarchies of influence
cones (more later) necessarily share commonalities (even become
equivalent) at their lowest or most causal point. If that is indeed
the case, then there is a reason that I am seeing such parallels
between GUTs, information science, thermodynamics, linguistics,
bioinformatics, genetics, genomics, evolution, and AI. The other
less appealing possibility is that these apparent similarities
between the base of all domains is a byproduct of the ignorance that
is a natural byproduct of exploring an edge of what is known.

Note: The author of these linked pages is JOHN L. CASTI a professor
at the Technical University of Vienna and at the Santa Fe Institute.

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