needed to compute higher ordinals.
The sampling is not canonical, there
are lots of ways of doing it computably. This means we have an iterative
process analogous to that described
by Pinker and Damasio, which exhibits the irreversibility we expect from
Prigogine. It is a picture of definable
data represented using constructive
ordinals. Turing’s representation of
data is scientifically standard, in terms
of reals. The basic computational
structure of the connectivity is captured by functionals modeled by oracle Turing machines. The abstraction
delivers a complex structure with a
rich overlay of definable relations, corresponding to real-world ubiquity of
emergent form impacting nontrivially
on the development of the organism.
The difference between this extended
Turing model of computation, and
what the modelers deliver is that there
is a proper balance between process
and information. The embodiment
was a key problem for the early development of the computer, insufficiently recognized since the early days by
the theorists, fixated on the universality paradigm.
Rodney Brooks6 tells how embodi-
ment in the form of stored information
has reemerged in AI:
“Modern researchers are now se-
riously investigating the embodied
approach to intelligence and have
rediscovered the importance of in-
teraction with people as the basis for
intelligence. My own work for the last
25 years has been based on these two
I summarize some features of the
framework, and refer the reader to
sources9, 10 for further detail:
˲ Embodiment invalidating the ‘
machine as data’ and universality paradigm.
˲ The organic linking of mechanics and emergent outcomes delivering
a clearer model of supervenience of
mentality on brain functionality, and a
reconciliation of different levels of effectivity.
˲ A reaffirmation of the importance
of experiment and evolving hardware,
for both AI and extended computing
˲ The validating of a route to cre-
ation of new information through in-
teraction and emergence.
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S. Barry Cooper ( firstname.lastname@example.org) is a
professor in the school of Mathematics at the university
of leeds, u.K.