[Inquiry] Re: Information = Comprehension x Extension -- Discussion

[Jon Awbrey]

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ICE.  Discussion Note 48

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Ach = Achilles
DH  = Douglas Hofstadter
HT  = Hugh Trenchard
Tor = Tortoise

Re: ICE Dis 48.  http://suo.ieee.org/ontology/msg05350.html
Hx: ICE Dis 47.  http://suo.ieee.org/ontology/msg05348.html

HT, quoting DH, quoting Ach:

    | What happens if you then find a picture inside the picture which
    | you have already entered, and take another swig of pushing potion?

HT, quoting DH, quoting Tor:

    | Just what you would expect:  you end up inside that picture-in-a-picture ...

Cf: DH, "Little Harmonic Labyrinth", in 'Godel, Escher, Bach'

HT: I love the concept of recursivity.  I have a number of
    reasons for this, not the least of which is that it
    is  central to conscious thinking (to follow the
    school of Hofstadter).  I'm not sure yet how it
    relates to abductive reasoning, but I can hardly
    wait find out.

Hugh,

Here are a couple of excursuses (excursi?) on inquiry oriented systems,
in which the duchy of abductive reasoning forms a third of the kingdom:

INT.  Introduction to Inquiry Driven Systems"
      http://stderr.org/pipermail/inquiry/2003-March/thread.html#6

PRO.  Prospects for Inquiry Driven Systems
      http://stderr.org/pipermail/inquiry/2003-March/thread.html#50

Hofstadter's "GEB:EGB" is off course a whole lot of fun to read, but ...

All those divertimentoes (divertimenti?) on strange loopiness
tend to benuance the issue of what recursion is really about,
and even to confound it almost beyond recognition with the
closely related but very discernible topic of reflection.
The theory of recursive (partial) functions, otherwise
known as "computability theory", is really about what
all is definable by mathematical induction, and this
depends on how all those recursive rings and loops
and bubbles eventually touch down on solid ground.

Film at leventy leven ...

Jon Awbrey

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http://www.cs.bsu.edu/homepages/mighty/history.html
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