various fuzzy matters

["Steven M. Belknap" <sbelknap@UIC.EDU>]

>Ahem.  This is, people, the Lojban list.  There is no Lojban gismu for
>"tall"; the job is divided between "condi" (deep) and "clani" (long),
>each of which has a place for "by standard".  (Why "deep"?  Because depth
>and height are both vertical size, but one is measured from the top, the
>other from the bottom; cf. Latin "altus mons" 'high mountain' vs. "altus
>mare" 'deep sea'.)
>
>So when you say "John is long" or "John is deep" in Lojban, you IMPLICITLY
>are speaking with reference to a standard of length or depth that you may
>make explicit if you will.  "Long" and "deep" are not one-place absolute
>terms!

 Although it is not an exact fit, <clani> seems more appropriate for
describing "vertical height of a person when standing," because it has a
place for dimension, the default being the "longest dimension". However,
<clani> is a general gismu, not one just applied to people, and when used
for people therefore does not specify whether the person is supine, seated,
or standing; the supine length of a person is slightly greater than the
standing height because of compression of the intervertebral disks.
(Additionally, standing height will decrease by approximately 1.5 cm or so
in a 180 cm tall person who remains vertical for several hours, so when we
try to pin down height, we are trying to hit a moving target. :-) )

<condi> does not explicitly specify dimension; if you were going to use
this to describe a person's vertical height when standing, I would think
you would have to explicitly add the condition that John is standing. (If
John were supine on the ground, and the origin were the ground, then
<condi> would refer to John's thickness)  Also, since <condi> is also used
in the sense of the vertical depth of a container, one might think that
condi is referring to the length of John's gastrointestinal tract, which
might lead to some interesting translations in the chinese whispers game!

Actually, I'm not sure what

la djan clani

means. (I was so interested in fuzziness, that I confess I did not look up
the definition of <clani> when and gave it as an example.)

Would this translate as "John has height."?

la djan cu barda le clani

seems closer to "John is tall." in the sense of an unspecified external
standard.

How about

la djan barda le clani mi

"John is tall compared to me."

To get fuzzy, I would use an interval scale; if the proposed selma'o <xoi>
is to be used:

la djan pi mu xoi barda le clani le cnano

"John is to fuzzy extent 0.5 taller than normal."

In non-numerical terms, I would understand this to mean, "John is
moderately taller than normal." Obviously, one could use the sumti of
<cnano> to more explicitly specify the norm.

If John were 240 cm tall, ("circus-tall" in my idiosyncratic English), then
I might say:

la djan papino xoi barda le clani le cnano

"John is fuzzily 1.0 taller than normal."

which in non-numerical terms, I would understand to mean:

"John is definitely, no question about it, tall."

Note how numbers are being used here. There is not a 1:1 correspondence
between height and the fuzzy tallness <xoi bardi le clani> of the person!
(There seems to be a pervasive misunderstanding of this point.) If we were
explicitly specifying a fuzzy tallness function, it might be something
like:

0 for all persons shorter than 160 cm
1 for all persons taller than 200 cm

linearly increasing from 0 to 1 for all persons between 160-200 cm in height.

Thus, this is an interval scale, not a ratio scale, as we are using
arbitrary cutoffs for fuzzy tallness. But where did the specific choices of
160 and 200 cm come from? From a prior implicit or explicit understanding
between speaker and listener, of course! I might imagine the following
conversation:

Person 1: I want to talk about human tallness.

Person 2: O.K. What fuzzy norm should we use?

Person 1: I think that anyone shorter than 160 cm is definitely not tall,
and that anyone taller than 190 cm is definitely tall.

Person 2: Actually, I would choose 200 as the top cutoff.

Person 1: O.K. And I want to use a linear function for instances of tall in
the interval 160-200 cm.

Person 2: O.K., I accept that. So we agree on a fuzzy norm.

Person 1: la djan papino xoi barda le clani le cnano

Person 2: go'i

Of course, speaker and listener might choose to leave the exact fuzzy norm
unspecified, or might use a different function; in this case, any
monotonically increasing function mapping [0,1]:>[0,1] will do. I am unsure
how to elegantly describe the fuzzy function explicitly in lojban.

co'o mi'e. la stivn



Steven M. Belknap, M.D.
Assistant Professor of Clinical Pharmacology and Medicine
University of Illinois College of Medicine at Peoria

email: sbelknap@uic.edu
Voice: 309/671-3403
Fax:   309/671-8413