Re: "Inevitable Illusions"

From: ca314159 (ca314159@bestweb.net)
Date: Thu May 31 2001 - 13:07:53 MET DST

  • Next message: Sidney Thomas: "Re: "Inevitable Illusions", Law of Excluded Middle etc."

    P. Sarma wrote:
    >
    > This is precisely what fuzzy systems are all about. Notice, for example, how
    > the natural linguistics are instrinsically fuzzy themselves ... there's
    > nothing exact about the word "precisely"! It is also true that precise
    > measurements are artificial. If anything, there is a cost associated with
    > increasing precision or crispness, which was clearly observed in Zadeh's
    > 1973 IEEE SMC paper. The most direct example, of course, is the rapidly
    > increasing word-length for a digital computer to represent increasingly
    > precise real numbers.

    This is definitely an interesting area. Particularly in terms
    of data compression where Shannon-Fano codes were followed by
    Huffman codes and then arithmetic coding in reals:
     http://www.google.com/search?q=arithmetic+coding
    but even then the reals met up with finite word sizes so
    the solution became an inverted cosmology so to speak.
    Instead of a contracting universe such as in a chinese box
    or russian doll, information black-hole models,
    arithmetic coding turned into an expanding universe model
    to make the algorithm practical under finite wordsizes.

    In classical computers, Transmeta's hybrid software-hardware
    Crusoe processor demonstrates fuzzy to some extent. There
    the distinction between software and hardware as finitely
    bounded states becomes blurred in the general case;
    although these processors are necessarily deterministic
    in the special cases.

    A demonstration of fuzzy in quantum computers would be an
    even more direct example since they are non-deterministic
    computers with (ideally) deterministic states.

    An even more extreme example of fuzzy states is an
    optical illusion such as:
      http://members.aol.com/Ryanbut/profileblk.gif
    Which could be said to fuzzily compose two categorical states
    as a whole, with the assignment of membership to those states
    at the subjective discretion of the observer.

    >
    > Each subsystem, artificial, natural or hybrid has it's own internal
    > precision limiting bound. Practically, even this bound is often not reached
    > or really used. For a simple semi-numerical example, consider an important
    > measurement in the chemical process industries - one of measuring and
    > inferring the success of an acid/base type of neutralisation process ...
    > from high school chemistry we know that "perfectly neutral" has a pH = 7.0.
    > The extreme precision limit could be, say, the sensor with |error| < 0.05.
    > However, for the true process downstream it does not care as long as the
    > |true error| < 0.2, say. Then the hidden cost of excess precision is clear
    > and economic: the entire process control system sort of exponentially zooms
    > up in cost for every order of magnitude in precision (close to the truth).
    > Finding the "optimal" configuration ... it's all in the soft heuristics of
    > an error variable that ranges from -0.2 to +0.2. It's also a severely
    > nonlinear process. In fact, even the crisp controllers are gain-scheduled
    > for this. Fuzzy methods appear just right here for measurement and control.
    >
    > The broadly qualitative equation is
    >
    > heuristics + crisp logic = fuzzy logic
    >
    > Very informally, one can also use quasi-quantum mechanics, particularly
    > Heisenberg's uncertainty principle:
    >
    > dx * dp >= Ksys
    >
    > where dx is the precision error, and dp some relevant energy-cost function,
    > such as
    > price, and Ksys is system-specific. It could also be viewed as a crude model
    > for an appropriate version of Goedel's Incompleteness Theorem - which really
    > puts a "universal limitation spanner" into crisp logic and its mathematical
    > works.

    It's more of a dimensional problem. A moebius strip could
    be said to be paradoxical in two dimensions (intersects itself)
    but not in 3 dimensions. Likewise the representation of a Klein
    bottle in 3 dimensions is 'paradoxical' (intersects itself):

      http://www.kleinbottle.com/

    but not in 4 dimensions.

    Boolean logic can be said to be 'dimensionally challenged'
    in base 2, in the general case, but in ever higher dimensions,
    it maintains its rigorous nature. This is the essence of
    Godel's Theorem that there will always be a need for those
    higher dimensions (basis extensions) at the highest resolutions.
    This same idea is present in terms of 'hidden variables'
    concept in quantum mechanics. There are many ways to bypass this
    limitation in the lower dimensions. See quantum lithography for
    the latest applications of subwavelength imaging using quantum
    entanglements.

    R.I.P. Douglas Adams

    > Fairly clearly, fuzzy logic is a little more than somewhat natural.
    >
    > Pramit
    >
    > -----Original Message-----
    > From: Wise <weiz@spam-block.sympac.com.au>
    > To: Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>
    > Date: Monday, May 21, 2001 7:33 PM
    > Subject: Re: "Inevitable Illusions"
    >
    > >I nursed for a while and we often needed to dip
    > >a plastic stick, containing a number of chemically impregnated
    > >pieces of paper up the length of the stick, into a urine sample.
    > >
    > >These sticks gave us an indication of sugar, proteins, etc found in
    > >the urine sample. Inevitably they were graded not just true or false
    > >indications.
    > >In real life the diagnosis and treatment of disease is not just true or
    > >false.
    > >
    > >Your example talks about an absoluteness in having a disease which is
    > >inevitably not always the case.
    > >
    > >We can have a person who can belong to the fuzzy set of diabetics who we
    > >would think
    > >of as having diabetic tendencies. In fuzzy terms they have a small
    > >membership value
    > >in the diabetic set.
    > >
    > >The classical logic would have us render them as diabetic or not diabetic.
    > >The artificial
    > >preciseness is actually a dangerous circumstance because now we have to
    > >treat or
    > >not treat. Real life actually uses fuzzy logical strategies to handle these
    > >people and their
    > >treatment.
    > >
    > >A full on, full blown diabetic (a real life description) is someone who, in
    > >fuzzy set
    > >terms, has a high membership value in the diabetic set.
    > >
    > >The words (descriptions) are optional, the fuzzy math under the bonnet is
    > >consistent.
    > >
    > >I think that a lot of discomfort with fuzziness is its ability to
    > >accommodate the superficial, the changing
    > >and very malleable language layer. They are only descriptors used to label
    > >both the sets and then the
    > >extent of membership in those sets.
    > >
    > >As descriptors ....slightly diabetic, less diabetic, diabetic tendencies
    > >...
    > >allows me and
    > >you to put our heads at the lower end of the spectrum (low membership
    > >values) of diabetic types.
    > >
    > >We do need to be on the same page with respect to our fuzzy set
    > definitions,
    > >our fuzzy value universe,
    > >etc... if we jointly intend doing any thing more precise, but often to hold
    > >a conceptual conversation
    > >a lot of this stuff is just not required, it is implied.
    > >
    > >If I tendered the following advise
    > >
    > > to treat your diabetic tendencies patient with diet and review
    > >after a while
    > >
    > >without a lot of definitions, to prop up the words tendencies and review
    > or
    > >the word while you would get the drift of
    > >what I recommended.
    > >
    > >Now if you wanted to meter out a precise dose of chemical A for particular
    > >Diabetic lets talk about the
    > >membership value of that person in the diabetic set and then using fuzzy
    > >mathematics calculate the
    > >dose and frequency of chemical A.
    > >
    > >Fuzzy control systems work today that achieve this type of precision.
    > >
    > >
    > >And that my friend is TRUE in a fuzzy kind of way.
    > >
    > >Rob W
    > >
    > >
    > >Chris De Voir wrote in message ...
    > >>> -----Original Message-----
    > >>> From: fuzzy-mail@dbai.tuwien.ac.at
    > >>> [mailto:fuzzy-mail@dbai.tuwien.ac.at]On Behalf Of Wise
    > >>> Sent: Wednesday, May 16, 2001 6:31 PM
    > >>> To: Multiple recipients of list
    > >>> Subject: Re: "Inevitable Illusions"
    > >>>
    > >>>
    > >
    > >>My question is: Supposing that all the data in the above example take on
    > >>Fuzzy values, how does one maintain logical clarity of Bayes to make good
    > >>predictions/decisions using Fuzzy still subject to limited rationality?
    > >>
    > >>Regardless, the answer may still be, no, this has not been studied. But
    > >>thanks for the response.
    > >>
    > >>Chris.
    > >
    > >
    > >
    > >
    >
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