On Feb 9, 10:28 am, "galathaea" <galath...@gmail.com> wrote:
why were many of the mathematicians
that worked on the foundations of randomness and stochastic process
also constructivist
( kolmogorov, markov )
or computer scientists
( chaitin )
or both
( martin-lof - and of course the first two above go here )
?
even my hero poincare goes here for ergodic research
i have my ideas
but i wonder if this seems counterintuitive to others...
in particular
i think this has to do with typicality and information
the mereology of typical and specific cases
carries meaningful information through complexity
..
kolmogorov complexity has been used recently
for a whole range of problems in typicality
especially proficient in this
has been the team of jiang, li, and vitanyi
who have been recently exploring
the foundations of formal languages
http://arxiv.org/pdf/cs.CC/0110040
where they derive chomsky-like linguistic hierarchies
and other useful porders
earlier they had used similar methods to
solve the typical heilbronn-triangle problem
(random structures and algorithms, vol20 i2 p206-19 )
which also has uses in testing monte carlo algorithms
for the fair market value of derivatives
as mentioned in the paper
the typical structures the particular
it is where its information content arises from
constructivists seem adamant
about meaningful exchange of information
and understanding that
deterministic models are not necessary for this
is key to realising that
information transfer does not require causality
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galathaea: prankster, fablist, magician, liar
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