Center for Science Information Working Group

15 July 2004

DISCOVERING THE LIMITS OF THE BOX

Physics/physicists are not in fact committed to time irreversibility - 22 June

Hence, **investigators of other phenomena ought not to presume that time reversibility is necessarily applicable in, or should be taken as a model for, their own inquiries**.

"Important" in the sense that such numbers are a consequence of any formal axiomatic system adequate to support arithmetic. Perhaps also important in that such numbers can be generated in other ways and so may play a role in "reality".

Arithmetic is not "complete". Hence, **investigators of other phenomena ought not to presume that either arithmetic (and, by inference, formal mathematics generally) or "Turing-computability" is necessarily applicable in, or should be taken as a model for, their own inquiries**.

Hence, **investigators of other phenomena ought not to presume that formal axiomatic systems are necessarily applicable, or should be taken as a model for, their own inquiries**.

**"Reality" may or may not be the playing out of a formal axiomatic system but, regardless, trying to understand it in terms of formal axiomatic systems will inevitably fail in the long run.**

If "reality" is not a formal axiomatic system, then the conclusion follows directly.

Ergo ..... it is time to stop trying to "ground" inquiry/exploration on some foundation of "certainty", ie on any principle or set of principles which are not themselves subject to inquiry and change

The best known tools derive from one or another form of the presumption that there is a solid starting point or set of starting points from which everything else derives/can be understood.

The best known tools clearly generate things they are unable to handle, at least in some cases because of self-referencing.

"Maybe its time to seriously entertain the possibility that looking for a single solid starting point just isn't the right way to go, that one has to find another, different way to proceed." ... Letter to René

Logics/mathematics beyond formal axiomatic systems?

IRREVERSIBILITY, INCONSISTENCY, INDETERMINACY, SELF-REFERENTIALITY (RECURSION) AND THE BRAIN

__One Trick:__ Look at your starting points and see what you can change ...

(Ralph Waldo Emerson,

Shakespeare, Hamlet

- Irreversibility already established (eg lateral inhibition network) (reservation: local vs global irreversibility)
- Inconsistency already established, is in fact a "neural uncertainty principle", comparable to the uncertainty inherent in quantum mechanics? and with same implications re reversibility? advantages re "computing"?
- Indeterminacy .... likely (VERY likely)
- Improved "completeness"?
- Roger Penrose, The Emperor's New Mind, 1990
- Four color problem
- "provable"? no ... "likely"? yep (product of Chaitin's "experimental math")

- Human brain is both iterative and recursive/self-referential (others?)
- Iteration (Wolfram) - deterministic but not compressible (Chaitin)
- Iteration plus - indeterminate and not compressible
- Iteration plus model model-building
- Iteration plus etc. and recursion/self-referentiality?

- Has both multiple "model building" and compressive/self-reflective ("story telling") capabilities
- Has distinctive "agency" capabilites vis a vis outside world: to conceive/bring into existence what would not result from "model building" (iterative change) - "free will"
- Has distinctive "agency" capabilities vis a vis itself: to conceive/bring into existence what would not result from "model building"
"I am, and I can think, therefore I can change who I am"

How to proceed in face of "profound skepticism"?, ie with no fixed starting point that one can treat as unquestionable ...

- The universe happily iterated/evolved without formal axiomatic systems (recursion/self-referentiality?) for billions of years
- Humans have the capability to do so without formal axiomatic systems ("treeness")
- Humans also have the capacity to conceive/make use of AND modify formal axiomatic systems
- The combination gives us unusual capabilities IF we make use of both
- Whether "reality" a formal axiomatic system or not, create/use/modify formal axiomatic systems, but don't "believe" in them.

AN UPDATED THEORY OF INFORMATION?

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