[lojban] Re: how to say manifold

[xah lee <xah@xahlee.org>]

the "manifold" in its bare essence means a shaped space, so to speak. 
Curves for example, are 1-dimensional entities, which differs from what 
one normally thinks of 1-D space (straights lines) because it has a 
"shape" associated to it. Likewise, surfaces are 2-dimensional "skins" 
that is a plane with a shape. Similarly, there can be 3-dimensional 
entities that differs from our "straight" 3-space we live in. And so on 
for n-dimensions.

in math　technicality, manifold has more specific meaning. i.e. that it 
is everywhere differentiable etc. Or the similar notion of term 
"variety" in algebraic geometry, which essentially also means 
n-dimensional curve/surface entity like manifold, but with nuances or 
technicalities that suits algebraic geometry.

all considered, there is the basic need for a word to specify 
curve/surface entities of more than 2/3 dimensions. And i think their 
essential meaning is "shaped-space". Thus i think lojban word of 
shaped-space would be a good candidate.

i was surprised it wasn't a core word in lojban or one haven't already 
been devised and settled. At first i thought sefta was it.
sefta @ x1 is surface/face [bounded shape/form] of [higher-dimension] 
object x2, on side x3, edges x4
but as someone pointed out in previous post, sefta means a particular 
face/side/part of an n-dimensional object. (and this object has sides 
and edges, apparently referring to higher-dimensional polygons (i.e. 
polytopes)).

i thought a manifold word would have a structure like this:

x1 is a manifold of dimension x2 embedded in dimension x3 with 
properties x4

How do lojban say curves and surfaces?

  Xah
  xah@xahlee.org
  http://xahlee.org/PageTwo_dir/more.html



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