Subj : Re: Polymorphism sucks [Was: Paradigms which way to go?]
To   : comp.programming,comp.object
From : Dmitry A. Kazakov
Date : Sat Aug 27 2005 12:19 pm

On Fri, 26 Aug 2005 13:21:30 -0500, Chris Sonnack wrote:

> Dmitry A. Kazakov writes:
> 
>> 2. "good guys" is of course fuzzy. Technically either Captain Kirk or
>> "good guys" or both should be fuzzy to get 0.85 instead of 1 or 0. Well,
>> assuming Captain Kirk being a real man... (:-))
> 
> Right.  But at some point the knife comes down and the system decides that
> this fuzzy guy, Jim, has 85% membership in this fuzzy group "good guys".
> 
> THAT is not fuzzy.

No it is. There are two variants:

1. Jim is 0.85 good is an input (term).

2. It was inferred from other inputs among which there is some fuzzy Z.

In both cases there is something (Jim or Z) which you cannot split up into
crisp sets. Fuzziness cannot be obtained from crisp data. Neither can it be
reduced to them.

>> 3. But let's forget it and say "good guys" is crisp. That wouldn't change
>> anything because Captain Kirk is still 0.85 in it. What does it *mean* to
>> be 0.85 good?
> 
> Simple.  It means you're good most, but not all, of the time.  (True for
> most of us, I imagine.)

Nope. Firstly, time is not a subject of set theory. You must be talking
about some [stochastic] process, not a set. Secondly, this way you can come
only to randomness, i.e. an additive set measure (probability.) And
thirdly, this will give you nothing, but probabilities. Because you will be
unable to answer even trivial questions like: if Stochastic Captain Kirk
was 85% of the time good, will he be the next time? The answer will sound
it will, 0.85 probably. "0.85 will" is nothing better than "0.85 is". You
still have nothing in your hands.

>> This meaning is the essence. It is uncertainty you cannot deal with in
>> a crisp framework. You can do it only symbolically by postulating existence
>> of uncertainty (either as randomness (0.85 = probability of), or as
>> fuzziness (0.85 = possibility of), or as other set measure.) But you cannot
>> look into that measure. You have to carry it with all the time. And all
>> the answers will be in the terms of that measure. So in the end after all
>> manipulations you still have: "it is 0.85 right." And? Is right or wrong?
>> See? It is insoluble.
> 
> But, like probability functions in Quantum Mechanics, as some point, to be
> useful, you have to "collapse" the function into a decision.

And as we know the decision (observation) will destroy the original system.
You loose and falsify knowledge by doing that. The same effect exists in
fuzzy systems too.

> I can no longer quote from memory accurately, but to paraphrase Jim T. Kirk
> himself, "TODAY we *decide* to be good."  (Tomorrow I might phaser you. :)
> 
> And computers--that is to say binary--can easily carry our 0.85 symbols
> around until we need to do a calculation that determines whether Kirk
> pushes the phaser button or the nice guy button.

No. 

1. You can say no more than there is some probability p that Kirk will do
this or that. You cannot create a copy of Kirk, likewise you cannot have an
exact copy of an electron.

2. The inputs you are using for your inference are uncertain. You have no
access to Kirk's brain. You have nothing but observations, which themselves
are either random or fuzzy.

-- 
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de

.