[Inquiry] Re: Doctrine Of Individuals -- Discussion

[Jon Awbrey]

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DOI.  Discussion Note 7

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JA = Jon Awbrey
JC = John Collier

JA: Are there things in reality that would require
    an unlimited amount of information to specify?
    Probably -- but we don't really know for sure.

JC: A necessary condition for a system to require an infinite amount of information
    to specify it is that a) it has at least one infinite dimension, and b) there
    is no effective statistical procedure that could distinguish it from random.
    Condition (b) is equivalent to it not having a complete representation that
    is compressible in the sense of algorithmic information theory.  No fully
    regular system requires infinite information to specify, and, furthermore,
    if a system can be specified with finite information, then there is a rule
    to specify it.  So, if there are real systems that require infinite
    information to specify, then they are not fully regular.  To the
    best of my knowledge, the issue of whether or not a system is
    regular is in general undecidable.

JC: We do know (Shannon) that the information capacity of a channel is
    always finite (a channel must be regular -- see Barwise and Seligman,
    'Information Flow').  On this basis, we can say, assuming our information
    about the world comes by way of channels, that if there is a real system
    with infinite information, then it will make no difference to any possible
    experience we could have (we can't tell by any test if the cause of the
    experience has a compressible representation or not).  I find this
    conclusion unpalatable, and I have been looking for ways around it,
    and I think I have a set of cases of systems in which we would
    expect the information generated by the system is more than
    we could ever receive.  It is reasonable to believe that 
    such systems exist (some of them are very simple).

After three or four readings that starts to make sense to me.
Bur can you say more about what you mean by a regular system?

The fact that channels have finite capacity --
it seems like channels were defined in such
a way that this would be so -- means that a
source of infinite information would take an
infinite amount of time to transmit all of its
information through the channel, but couldn't
there be definite hypotheses about the system
that are settled in finite time, in effect,
non-retractable bits?

Jon Awbrey

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