Date: Wed, 28 May 2014 16:09:30 -0700 (PDT)
From: curtis.w.franks@gmail.com
To: lojban@googlegroups.com
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References: <CAO7bV+jcS8JFEY8=XnGbsbecuASN4Les8oDPGcwNXfh-cAT7rg@mail.gmail.com>
Subject: [lojban] Re: Geometry shapes categorization
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I have issues with *bolci, cukla, *and several other terms when it comes to 
lining them up with mathematical definitions.  A circle is one-dimension 
(but lives in two dimensional space), since it is defined only by its 
radius (once the center is fixed and specified); a circle cannot be "filled 
in", since it 1) is already filled in (it is defined as the set of ALL 
points equidistant from the center by some fixed length) and 2) if we mean 
"filled in so as to produce a disc/disk", we no longer have a circle. A 
disc is a region (set) that is two-dimensional. Its boundary is a circle. 
 They are fundamentally different things.  Likewise, a ball is a volume 
(three-dimensional region) while a sphere is its two-dimensional surface. 
The definitions as presented by the gimste are ambiguous in a technical 
way. Moreover, there is no nice way to generalize to higher (or lower) 
dimensions.  Also, how does one say that something is round (say, within a 
neighbourhood of a point) without saying that it is a circle/globe? 
(There are several solutions for fixing these issues.  We could make these 
words have non-technical definitions (related more to the concept of 
"roundness" than to any particular shape), which is the current track (but 
we should clearly mention that these definitions are strictly non-technical 
and get rid of an allusions to technical stuff); meanwhile, we would 
introduce a whole slew of new gismu/zi'evla that are technical (which is 
going to happen anyway). Or, we could more clearly, technically, and 
(hopefully) generalized-ly specify which particular definition these words 
reference, and introduce the rest. Or, something else.)

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<div dir=3D"ltr">I have issues with <i>bolci, cukla, </i>and several other =
terms when it comes to lining them up with mathematical definitions. &nbsp;=
A circle is one-dimension (but lives in two dimensional space), since it is=
 defined only by its radius (once the center is fixed and specified); a cir=
cle cannot be "filled in", since it 1) is already filled in (it is defined =
as the set of ALL points equidistant from the center by some fixed length) =
and 2) if we mean "filled in so as to produce a disc/disk", we no longer ha=
ve a circle. A disc is a region (set) that is two-dimensional. Its boundary=
 is a circle. &nbsp;They are fundamentally different things. &nbsp;Likewise=
, a ball is a volume (three-dimensional region) while a sphere is its two-d=
imensional surface. The definitions as presented by the gimste are ambiguou=
s in a technical way. Moreover, there is no nice way to generalize to highe=
r (or lower) dimensions. &nbsp;Also, how does one say that something is rou=
nd (say, within a neighbourhood of a point) without saying that it is a cir=
cle/globe?&nbsp;<div>(There are several solutions for fixing these issues. =
&nbsp;We could make these words have non-technical definitions (related mor=
e to the concept of "roundness" than to any particular shape), which is the=
 current track (but we should clearly mention that these definitions are st=
rictly non-technical and get rid of an allusions to technical stuff); meanw=
hile, we would introduce a whole slew of new gismu/zi'evla that are technic=
al (which is going to happen anyway). Or, we could more clearly, technicall=
y, and (hopefully) generalized-ly specify which particular definition these=
 words reference, and introduce the rest. Or, something else.)</div></div>

<p></p>

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