Message-Id: <199509241911.PAA22672@locke.ccil.org>
Date:         Sun, 24 Sep 1995 19:50:33 +0100
Reply-To: ucleaar <ucleaar@UCL.AC.UK>
Sender: Lojban list <LOJBAN@CUVMB.BITNET>
From: ucleaar <ucleaar@UCL.AC.UK>
Subject:      Re: direction, dimension
To: John Cowan <cowan@LOCKE.CCIL.ORG>
Status: OR

> > In the case of the pencil lead, it is rigid along two paths, the one
> > defined by its longest dimension ("lengthways"), and the other defined
> > by its shorter dimensions ("sideways").
> But that's either not enough or too much. If we allow {tinsa} to include
> resistance to stretching/compressing, then how do you know whether
> "sideways rigid" means resitant to sideways stretching/compressing,
> or resistant to sideways flexing/bending?
> If we separate the concept of {tinsa} from stretching/compressing
> (which is already taken care of by {tcena}), then there is only
> one way in which a 1-d object can be tinsa, and the direction place
> is always redundant.

It seems like a good idea to define {tinsa} as resistance to bending
and {tcena:pruni} as resistance to stretching/compressing. I think
that you could always paraphrase {tcena} by something involving
{tinsa}, though, e.g. if tcena then the surface is tinsa in direction
inward or outward or both.

I don't understand what I said about a pencil lead being rigid in 2
directions. What you say makes much more sense.

But this still leaves room for x2 ("direction") of {tinsa} and
x3 ("dimension") of {tcena}.

> A similar thing happens for 2-d (or quasi 2-d) objects. If we don't
> consider stretching/compressing, the only direction in which they
> can be tinsa is away from their plane.

That's right. But the sagging can be in one or both dimensions. The
shape of the sag can be like half a sphere or it can be like half
a cylinder. (I don't see that it depends on the object's symmetry;
a square of corrugated cardboard would tend to sag "hemicylindrically".)

> I'm still not sure what are the three things that are the only
> dimensions of three-dimensional objects that don't have well
> defined length, width and thickness.

It can happen that there are suoremei such that you can't distinguish
one member from another. Take the earth's orbit of the sun, or its
rotation around its axis - you can tell how many days and years pass,
but not where each one starts and ends (unless you arbitrarily choose
a delimiting point (midnight, Jan 1st)).

Is it therefore wrong to say {ci da cimde lo bolci}? I don't know.
Maybe {li ci memcimde lo bolci} would somehow be more meaningful?
I don't know how much an expression like {ci da} relies on
individuability. But at any rate, whichever locution is appropriate
for cimde & bolci is also appropriate for {djedi} and {nanca} (or
related concepts denoting a 24 hour and 365.x day period).

---
And