are all one and two dimensional spatial regions part of some three dimensional spatial region?

[Alan Ruttenberg]

If not, could I have a counterexample?

Thanks,
Alan

[Pierre Grenon]

yes

most properties of space are left open by bfo but in this case it
should follow from the fact that all spatial regions are part of space
(the universal spatial region) and this is 3-d

i imagine that doesn't prevent you from taking some lower dimensional
regions in isolation for some purpose

pierre

[Michel Dumontier]

On Tue, Aug 18, 2009 at 1:47 PM, Pierre Grenon <pierre...@gmail.com> wrote:

yes

most properties of space are left open by bfo but in this case it
should follow from the fact that all spatial regions are part of space
(the universal spatial region) and this is 3-d

i imagine that doesn't prevent you from taking some lower dimensional
regions in isolation for some purpose

yes, and the discussion stemmed from the assignment of coordinates to entities in lower dimensional regions. For instance, should i refer to a point on the 2D surface of a 3D table with a 3D coordinate (X,Y,0) or with a 2D coordinate (X,Y)? Or to refer to a point on the edge of the table with a 3D coordinate (X,0,0), a 2D coordinate (X,0) or a 1D coordinate (X)?  Usually, we use the appropriate coordinate system given the spatial region in question, even if it is a lower dimensional region.

-=Michel=-

 

pierre

On Tue, Aug 18, 2009 at 6:12 PM, Alan
Ruttenberg<alanrut...@gmail.com> wrote:
>
> If not, could I have a counterexample?
>
> Thanks,
> Alan
>
> >
>

--
Michel Dumontier
Associate Professor of Bioinformatics
Carleton University
http://dumontierlab.com

[Pierre Grenon]

i think you *could* do any of this although the choices you have left
are dependent on your initial choice of a reference system

what you need will depend on the context and what it requires you to
express. This may guide your choice of a reference system. But in
general I would make sure that all points are given by default all the
coordinates they may have in a context or another and always start
from a 3-d coordinate system.

If you work under the assumption that all your points share the same
coordinate along a given axis, you can reduce your representation by
defining 2-d vocabulary, but you define it based on the 3-d. You fix a
value for the 3rd coordinate and that's part of the definition of your
vocabulary. But in effect, you're just contextually dropping a
dimension.

If you want to refer to a point on the planar surface of a table and
there's no reference to anything else out of this space, then your
space is contextually 2-D and you can drop the third coordinate. But
if the space is not 2-D and you need to refer to something else, I
would go for having the 3rd coordinate. This is because it makes more
sense to say that (X,Y) locates a line (parallel to the z-axis) rather
than any particular point on it...

In short, a 3-d representation, even for planar or linear contexts is
preferable for it is more precise and is more general as it allows for
defining specialised vocabulary.

hope this helps, although perhaps i'm building too much in the example
of the table...

p

[Michel Dumontier]

Absolutely helps!!!

-=Michel=- 

[Alan Ruttenberg]

On Tue, Aug 18, 2009 at 5:52 PM, Pierre Grenon<pierre...@gmail.com> wrote:
>
> i think you *could* do any of this although the choices you have left
> are dependent on your initial choice of a reference system
>
> what you need will depend on the context and what it requires you to
> express. This may guide your choice of a reference system. But in
> general I would make sure that all points are given by default all the
> coordinates they may have in a context or another and always start
> from a 3-d coordinate system.
>
> If you work under the assumption that all your points share the same
> coordinate along a given axis, you can reduce your representation by
> defining 2-d vocabulary, but you define it based on the 3-d. You fix a
> value for the 3rd coordinate and that's part of the definition of your
> vocabulary. But in effect, you're just contextually dropping a
> dimension.
>
> If you want to refer to a point on the planar surface of a table and
> there's no reference to anything else out of this space, then your
> space is contextually 2-D and you can drop the third coordinate. But
> if the space is not 2-D and you need to refer to something else, I
> would go for having the 3rd coordinate. This is because it makes more
> sense to say that (X,Y) locates a line (parallel to the z-axis) rather
> than any particular point on it...
>
> In short, a 3-d representation, even for planar or linear contexts is
> preferable for it is more precise and is more general as it allows for
> defining specialised vocabulary.

Hey buddy, you're on an ontology discussion list!
What are these things of which you speak: Reference system, coordinate
system, axis, context, dimension ?

-Alan

[Michel Dumontier]

Hi Alan,

A coordinate system is a information-based system for assigning an n-tuple of numbers to each point in an n-dimensional space. In Cartesian coordinate systems, the position of a point is given by an n-tuple of real numbers. A coordinate gives the distance from the point to a fixed line of reference, called an axis.The dimension of an object or space is given by the number of coordinates required to specify each point within it. Thus, a three dimensional object (a table) requires three coordinates to specify the position of any point in/on the object. A two dimensional object (the surface of a table) or spatial region (a plane) requires only two coordinates to specify a position of a point - and thus the context is about which dimensional object or space you need to place a point.

Cheers!

-=Michel=-

[Pierre Grenon]

On Wed, Aug 19, 2009 at 1:14 AM, Alan
Ruttenberg<alanrut...@gmail.com> wrote:
>
> Hey buddy, you're on an ontology discussion list!
> What are these things of which you speak: Reference system, coordinate
> system, axis, context, dimension ?

they're weird stuff mate

i wasn't using 'context' technically but for the rest i think there's
a genuine alternative between taking the coordinate system apparatus
ontologically seriously or as a mere system of representation akin to
labelling and naming. It's fun but tough to do it ontologically, I'd
be tempted to call these things 'abstract' but I'm not too sure what
to make of it. Is the IAO trying to deal with them?

p

[Phillip Lord]

Alan Ruttenberg <alanrut...@gmail.com> writes:
> If not, could I have a counterexample?
>

A singularity, which is a zero-dimensional spatial region has no three
dimensional spatial region which contains it. I'm not enough of a
physicist to know whether this can be true for 2D and 3D SpatialRegion;
I think in some accelerative frames of reference, you would get 2D
SpatialRegions which would not map to any 3D SpatialRegions in that same
frame of reference.

I'd also worry about using "part_of" as defined for this relationship,
for a number of reasons.

First, I think that the relationship between a 2D and 3D space is
different from a normal partonomy; you can have an infinite number of
distinct, non-overlapping 2D spaces in any 3D space, which I don't think
is true in general of things related by part_of.

Secondly, BFO makes play of the distinction between fiat and not fiat
object parts; this distinction makes no sense, I think, for 2D and 3D
spaces. So, I'm not clear that it's the same relationship.

And, finally, aside from these worries, while part_of might work for the
relationship between a 2D SpatialRegion and a 3D SpatialRegion, it does
not work for the relationship between a 3D SpatialRegion and a 4D
SpatioTemporal region; the former is a continuant, the later an
occurrent, so as I read the part_of relationship definition a
SpatialRegion cannot be part of a SpatioTemporal region.

Obviously, this discussion does not apply in general to Spaces in the
mathematical sense which can be n-dimensional. It's not clear how
"part_of" applies there, because the relationship is defined over
instances and the distinction between an universal and particular is, to
my mind, not useful for mathematical spaces.

Phil

[juliant...@gmail.com]

On Tuesday, August 18, 2009 at 10:12:20 AM UTC-7, Alan Ruttenberg wrote:

If not, could I have a counterexample?DRFFUFF

Thanks,
Alan

[juliant...@gmail.com]

On Tuesday, August 18, 2009 at 10:12:20 AM UTC-7, Alan Ruttenberg wrote:

If not, could I have a counterexample?

Thanks,
AlanDYFUFUYFY

[Barry Smith]

From the current BFO perspective (in which the issue of frames of reference has not been incorporated) all spatial regions are part of the largest three-dimensional spatial region.

BS

On Sat, Jun 11, 2016 at 7:48 AM, juliant...@gmail.com <juliant...@gmail.com> wrote:

On Tuesday, August 18, 2009 at 10:12:20 AM UTC-7, Alan Ruttenberg wrote:

If not, could I have a counterexample?

Thanks,
AlanDYFUFUYFY

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[juliant...@gmail.com]

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[juliant...@gmail.com]

On Tuesday, August 18, 2009 at 6:15:37 PM UTC-5, Michel Dumontier wro reference system. But in

general I would make sure that all points are given by default all the
coordinates they may have in a context or another and always start
from a 3-d coordinate system.

sggddgdgdfdm4hdghdj3

[juliant...@gmail.com]