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Re: [ontolog-forum] Axiomatic ontology

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Barker, Sean (UK)" <Sean.Barker@xxxxxxxxxxxxxx>
Date: Tue, 12 Feb 2008 10:14:28 -0000
Message-id: <E18F7C3C090D5D40A854F1D080A84CA4AECBEE@xxxxxxxxxxxxxxxxxxxxxx>

This mail is publicly posted to a distribution list as part of a process
of public discussion, any automatically generated statements to the
contrary non-withstanding. It is the opinion of the author, and does not
represent an official company view.    (01)

Sean Barker
BAE SYSTEMS - Advanced Technology Centre
Bristol, UK
+44(0) 117 302 8184    (02)

BAE Systems (Operations) Limited
Registered Office: Warwick House, PO Box 87, Farnborough Aerospace
Centre, Farnborough, Hants, GU14 6YU, UK
Registered in England & Wales No: 1996687     (03)

Comments on Pat Hayes' reply to Rob Freeman    (04)

Radar signal processing <B>theory</B> treats signals and noise as being
random, but with different probability distributions. The probability of
detection of a signal is a trade off between two types of error:
identifying a detection when there is no signal, and failing to identify
one when it is present. Given a set of observations, there is no way of
minimising both simultaneously. The only way to improve performance is
to make more observations (which is in practice what is done).    (05)

The problem is complicated by the physical processes involved, which
usually shows up as a rapidly decaying auto-correlation function (i.e.
the function of the correlation co-efficient between one observation any
subsequent observation of the same phenomenon). There are a number of
techniques, such as changing frequencies each pulse, that have the
effect of more-or-less eliminating the auto-correlation tail - that is,
making the signals appear random (though without changing the
distribution function), since this makes processing more reliable.    (06)

Also, early signal processing systems used "hard limiting", that is,
reducing the input signal to a stream of 1's and O's. These systems were
still able to detect targets in the presence of noise, although with
some performance loss arising from the quantisation noise.    (07)

Pat's claim "The definition of a random sequence is that no matter how
much of it you have, there is no way even in principle to compute any
information about the next item." is true only where you exclude
probabilistic estimates (which you might do depending on how you
interpret "information"). For example, if you encode the tosses of a
coin as a bit stream, as you continue to observe the bit stream, you
will be able to make increasing accurate estimates of the probability
that the next bit will be a 1. Given the additional knowledge that this
is the encoding of coin flips, you will also be able to estimate the
probability that it is a fair coin.    (08)

This certainly leads on to the question, "what is the ability of
statistical techniques to learn things from the web?" Indeed,
statistical based hypotheses such as "Sean Barker the baseball player"
is different from "Sean Barker the science fiction character" could
probably be substantiated on the basis of the differences in the
populations of terms found on the different sites.    (09)

However, this is a separate question to axiomatic ontology.    (010)

________________________________    (011)

        From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Pat Hayes
        Sent: 08 February 2008 17:21
        To: Rob Freeman
        Cc: [ontolog-forum]
        Subject: Re: [ontolog-forum] Axiomatic ontology    (012)

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        At 6:48 PM +0800 2/8/08, Rob Freeman wrote:    (015)

                On Feb 8, 2008 2:21 PM, Pat Hayes <phayes@xxxxxxx>
                > I take it to be obvious that a random sequence cannot
encode information
                > about anything other than itself. Right?    (016)

                I think I understand what you are suggesting. I think
you are
                suggesting that while a random string is very complex,
it can't
                actually code anything. If I drop my coffee on the floor
the mess
                might be complex to describe, but it won't tell me
anything.    (017)

                I think that is intuitive, and the way we normally see
randomness. But
                I'm not sure that its true, not for all random systems,
anyway.    (018)

                Maybe it comes down to the way the random pattern is
created. Say you
                code one signal. Then you code another using the same
elements. The
                second one will interfere with the first one a little,
but it need not
                obliterate it. If you push enough signals on eventually
the overall    (019)

                pattern might appear random.    (020)

        But if you can extract information from it, it isn't in fact
random. The definition of a random sequence is that no matter how much
of it you have, there is no way even in principle to compute any
information about the next item. This is why their information capacity
is as high as it can get, because you can't compress them into a smaller
package. But this also means that you can't in any sense parse them: you
can't find any structure in them to utilize to say something about
something else. They are entirely used up being themselves. All they can
do, as it were, by way of communication, is to exhibit themselves and
then stop.    (021)

        I had better stop this conversation myself, as I am getting to
the point where I have no confidence that I know what I am talking about
:-)    (022)

                In fact from the point of view of each
                individual element it will be random, because there will
be no way to
                decide given only a single element, which pattern it
belongs to (it
                will belong to many.) But combinations of elements will
still reveal
                patterns. The key is using combinations to select, when
                the distribution is random.    (023)

        I think there is an important distinction between appearing
random and actually being random. You seem here to be talking about
something like a hologram (?)    (024)

                What will happen is you will get a whole lot of patterns
using the
                same elements. And because they use the same elements
you won't be
                able to form more than one at a time. But they will all
be there.
                Different combinations will "resonate". And because you
can have many
                more combinations of n elements than n, you will be able
to have many
                more "resonances" for a given number of elements than
you have
                elements (if the distribution for each element is
random.)    (025)

                It is that "more combinations for n elements than n"
that gives you
                the extra storage space. (Some suggest it is this kind
of "larger than
                itself" ability which might give the mind its ability to
                the universe, when the mind is itself smaller than the
universe.)    (026)

                BTW This "not being able to form more than one at a
time" starts looks    (027)

                a lot like an uncertainty principle, or at least
Chaitin's Omega.
                Which is what I thought you might be alluding to.    (028)

        No, and indeed I don't know that term. I will go and find out
more about it, thanks for the pointer.    (029)

        Pat    (030)

                -Rob    (031)

        --     (032)

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