Re: fuzzy matters

[Jorge Llambias <jorge@PHYAST.PITT.EDU>]

> I really like math.

So do I, a lot. I hope you are not suggesting that you have to dislike
maths in order to dislike using numbers like that. Actually, the best
math doesn't come anywhere near using actual numbers. Numbers are for
engineers... :)

> Could the relative
> comfort/discomfort people feel with using numbers this way be a sort of
> Sapir-Whorf effect?

Could be, who knows?

> Suppose that we agreed to use three categories:
>
> slightly taller than normal
> moderately taller than normal
> extremely taller than normal
>
> Suppose then, that you and I independently assigned 1000 tall persons to
> each of these categories. I assert that there would be a correlation
> between your assignments & my assignments.

Undoubtedly.

> Would the correlation
> coefficient be 0.99? (that is, very good?) Probably not. Would it be 0.1?
> (very bad?) I would be surprised to fuzzy extent 0.9 if it were.

I, on the other hand, would be very surprised if it were. :)

> I assert
> that the correlation would be sufficiently high enough to justify using a
> numerical means of ordering this data, and that *even if we had no prior
> agreement* that we would be able to meaningfully talk about height in terms
> of:
>
> ti pafi'ucisi'e xoi bardi le clani
> ta refi'ucisi'e xoi bardi le clani
> tu cifi'ucisi'e xoi bardi le clani

In spite of what I said before, I think it should be {le ka clani},
not {le clani}. As Goran pointed out, a property can't be long.

Also, note that {pafi'ucisi'e} is a brivla, not a number. This is not
how {xoi} was supposed to work in And's proposal. You just need
{pafi'uci xoi}.

>  I also believe
> that in moving from an ordinal scale (slightly, moderately, extremely) to
> an interval scale, that the universe of potential discourse is enriched in
> a very important way.

It is enriched. If you say that 1/3-big, 2/3-big, and 3/3-big constitute
an interval scale, you are saying that the difference in tallness between
the extremely tall and the moderately tall is the same as that between
the moderately tall and the slightly tall. Is that true?

> >I just don't see the point of using the word "tall" in that case. If
> >I'm talking about objective heights, even if given unprecisely with large
> >error bars, why bring in a subjective word that doesn't add anything?
> >
> Agreed. But often we don't have exact measurements at hand, yet it might
> still be possible to convey meaningful information in the form of an
> interval or ratio scale. I think the subjective:objective distinction is a
> false dichotomy.

Ratio scales are extremely useful, that's why we use them. So are
interval scales and the others, there is no doubt about it. The problem
comes when you want to force one kind of scale onto a concept that uses
another kind. If you are successful, you are redefining the concept,
perhaps making it more objective. If you are unsuccessful, you are
misusing the scale.

> >Say that instead of "tall", which has the objective {mitre} alongside,
> >we were to talk about {melbi}.
>
> Guess what. Someone did this experiment. And guess what they found. It
> turns out that there *is* considerable consensus about some aspects of
> beauty among observers!

Of course there is consensus, or we wouldn't know what the word means!
That doesn't mean that "beauty" can be naturally fitted to an ordinal
scale.

> Using computer morphic blendings of many different
> faces, the investigators concluded that humans are quite sensitive to
> asymmetry in human faces.

Yes, and averaging the features of many beautiful faces they got even
a more beautiful one. I read an article in New Scientist or Scientific
American about it some time ago.

> Apparently assymmetry is considered ugly a priori
> by the brain. So, perhaps one could use an ordinal scale for beauty.

One could, of course. We may decide that such and such a length for the
nose is prettiest and any deviation from it gets lower points and add a
lot of other such criteria. And if our model is good, maybe the evaluations
made by the model would agree with those made by people. So what? That
doesn't make talking about 0.5-beautiful noses any more palatable to me.

> We are
> already too dominated by physical appearance as a society, so I would
> eschew doing this. I find beauty pageants and the like mildly repugnant.

So you don't mind talking of 0.5-tall but you do dislike talking of
0.5-beautiful?

> >Why not give examples using {melbi} rather than {clani}, which has no
> >objective counterpart to rely on.
>
> <clani> is simpler to explain, and people are less emotional about height
> than beauty.

Of course it is simpler, because there is an objective property very
much related to it, which you are using to arbitrarily define tallness.
If you get emotional about the beauty of people think instead of the
beauty of flowers. Let's say that we agree that a rose has 3/4-beuty and
another rose has 1/2-beauty. Does our agreement on those two points give
us a scale to determine the beauty of a third rose? Isn't it possible
that you will think the third rose is 1/4-beautiful and I would think
it is 1-beautiful?

>  Clarity is served through the use of a simple example as a
> demonstration of proof of concept.

I love examples, but you can't get attached to a single one. If your
theory is general it should work for different cases. I claim that your
theory for fuzzy tallness (the way you present it) is completely based
on the objective notion of measurement. If it is more general, it should
also work for properties like beauty that have no objective notion
behind it.

> >Dividing a continuous
> >spectrum into a discrete set can always be done, but that is not what
> >fuzzy truth values are about.
>
> We're dividing the continuous spectrum into fuzzy sets, not discrete sets.

Ok. My question is what to do when you don't have an objective continuous
spectrum from which to define the fuzzy sets.

> > For example, how would you use functions to say how beautiful
> >you have to be in order to be a model?
[...]
>  I've indicated
> above that I think this is demeaning and insulting to women, as such
> scoring implies that the chief value of women lies in their physical
> attractiveness. But that's a different soapbox.

There are male models too, why should the scale apply to women only?
So you would not use numbers with the predicate {melbi}. How can we
tell which predicates are suitable for number ranking?

>  Even if klani works (fuzzy meter zone =
> <klanimitreranji>?) it might be useful to have a separate word for fuzzy.

What place structure do you have in mind for it? Perhaps a lujvo can
be made. I have no idea what you mean by "fuzzy meter zone", but the
lujvo in any case would be {klanymitryranji}.

> We still need a formalism for handling numbers, like in this example:
>
> la xorxes pafi'ucisi'e xoi <fudjimitreranji [1.6,2.0]>

What does it mean?

        Jorge 1/3 fuzzy-meter-continuous [1.6,2.0]

Does that mean that the truth value of "Jorge is fuzzy-meter-continuous
[1.6,2.0]" is 1/3? That was And's original idea for {xoi}, but I don't
know if you are using it like that.

In fact, the truth value of my height being in that range is 1.
I don't think you can give it a truth value of 1/3. You could have
given it a certainty value of 1/3 before I told you that the truth
value is 1. Now your certainty value (if you believe me) should be 1.

> Any ideas?

I would say:

        la xorxes cu mitre li papixa ji'i repino
        Jorge is in meters somewhere between 1.6 and 2.0

But we have left fuzziness behind. If we are talking about measurement,
even with unprecise ranges, there is little room for fuzziness. The truth
value of that sentence is definitely 1. Whether that makes me tall or not
is a separate subjective call, but that seems to have disappeared from
the example. A truth value of 1/3 would be definitely wrong here.

Jorge