I don't think it has anything to do with Gödel's incompleteness
theorems. Those are about the relation of proofs and consistency.
Minimizing Fisher information is just maximum entropy (minimal
assumption of information) when both means and variances are known. It's
going to give the exact answer whenever the underlying random variables
are Gaussian; which is why it is widely applicable.
Brent
On 3/1/2016 7:29 PM, Dan wrote:
Also- minimization of Fisher information is one shockingly effective
approach to statistic inference of models for complex natural
phenomena (e.g., ones involving multiple evolving interacting agents).
When you don't know the true probability distribution of values for
some natural process, the probability distribution which is most
likely to be accurate is the one which minimizes Fisher information
when constrained by the variance of the samples you have observed. In
other words, complex natural phenomena operate as if they were
intentionally trying to minimize our ability to symbolically reduce
them. This is, I think, is just a restatement of Gödel's
incompleteness theorems.
On Tuesday, March 1, 2016 at 10:13:51 PM UTC-5, Dan wrote:
"ELUDING THE DEMON – HOW EXTREME PHYSICAL INFORMATION APPLIES. TO
SEMIOSIS AND COMMUNICATION"
https://www.youtube.com/watch?v=zBX26OD0dXw
<https://www.youtube.com/watch?v=zBX26OD0dXw>
Has this work by Roy Frieden and Vinicius Romanini been reviewed
here already?
Also wanted to share the interview for forthcoming video game "No
Man's Sky" below for two reasons: 1) self-similarity and recursion
produced via compact program such as Lindenmayer system
(procedural generation) appear to cause so much apparent diversity
and complexity, and 2) it reveals importance of Fisher information
for understanding our universe in the following way: the world is
only rendered dynamically for a player when there is a player to
observe. Without an observer, there is no transfer of information.
Frieden's EPI variational principles reveal that the process of
information transfer itself can be used to derive solutions to
Euler–Lagrange equations such as all scientific laws in physics as
well as social sciences.
https://www.youtube.com/watch?v=h-kifCYToAU
<https://www.youtube.com/watch?v=h-kifCYToAU>
One other fascinating video! Evolving cellular automata using
genetic algorithms reveals that information transfers from
generation to generation to acheive global
coordination/computation in the form of "particle physics."
https://youtu.be/hdRTcrTYfiQ?list=PLF0b3ThojznRyDQlitfUTzXEXwLNNE-mI
<https://youtu.be/hdRTcrTYfiQ?list=PLF0b3ThojznRyDQlitfUTzXEXwLNNE-mI>
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