On Tue, October 30, 2012 06:48, Andries van Renssen wrote:
> On 26 september 2012 at 19:50, doug foxvog wrote:
>> On Wed, September 26, 2012 11:44, Andries van Renssen wrote:
>> > John F Sowa on 26 september 2012 at 15:53 wrote:
>> >> On 9/26/2012 8:53 AM, Andries van Renssen wrote:
>> >> ...
>> >> > But the piece of land that is defined by that boundary is
>> >> > nevertheless a physical object, and it has a mass, although
>> >> > its value is unknown and not of interest. (01)
>> >> Space is physical, but it doesn't have a mass. An area is
>> >> a two-dimensional region. The political subdivisions only
>> >> specify coordinates that determine the area at the surface,
>> >> and they are silent about depth or height. (02)
>> > [AvR] I hesitate about the mass of a physical space, and whether the
>> > gas in a space is part of the space or just occupies the space. (03)
>> Occupies. (04)
> [AvR] Why? In geometry we make a distinction between a hollow sphere and a
> solid sphere. (05)
I'm just using the standard English definition. (06)
> By excluding the content of a space from the definition of the space you
> seem to define a physical space as a hollow space, whereas
> I think that the analogy is more with the solid space, including the
> content. (07)
The concept of the English word "space" is that of a volume, excluding the
material in the volume. This concept is of a spatio-temporal entity without
mass. It is not the hollow sphere -- which is a 2D surface curved in
3-space.
It is not something necessarily hollow -- although spaces with holes in them
can be defined. (08)
The concept of a volume including the matter present in it is also a useful
concept. The first concept does not change as something moves into and
out of the Space, while the second concept does. (09)
>> > But if the space is
>> > not empty, the mass may be of interest such as in the interior of a
>> > balloon and a submarine. (010)
>> Sure. (011)
>> > ...
>> > I question whether a physical area is by definition two dimensional. (012)
>> I'm not sure what you mean by "physical area".
> [AvR] See below. (013)
I prefer a definition to guessing a meaning from an example. (014)
>> > Mathematical area's are two dimensional. But two dimensional area's in
>> > physical reality seem to be abstractions. They are at least curved in
>> > the third dimension. (015)
>> Fine. Math allows this. It also defines planar 2D areas. (016)
> [AvR] Which implies that two dimensional area's (which are abstract) do
> not belong to the physical domain, but to the mathematical domain. (017)
Mathematics works at two levels.
1) A logical system of symbols and rules for their manipulation.
2) Mappings of portions of the logical system to specify properties of a
system outside of mathematics (whether physical or not).
A description in 2) seems to me to be able to be partly in the physical
domain
and partly in the mathematical domain. Mathematical descriptions of the
count, speed, location, volume, etc. of something i would treat as being in
both domains. So i consider located 2D areas to be in both the physical
and mathematical domain. (018)
>> > But more important: if you walk on them, they compress
>> > under pressure and they provide an upward force on you. (019)
>> The areas don't compress. The physical surface does. (020)
> [AvR] In my view a (physical) surface is a kind of (physical) area. If a
> surface compresses, that implies that the area compresses. (021)
I find the name "physical area" for whatever you mean here
to be misleading. (022)
>> > If you buy them (023)
>> You don't buy an area (or volume). You buy physical land or part of
>> a physical structure or rights to take certain actions within some
>> volume (spatial or physical). (024)
> [AvR] I don't understand what is wrong with the statement to buy an area. (025)
Although early definitions of "area" according to the OED are various types
of plots of land, the word isn't used with such a narrow meaning any more.
A term such as "geographical region" would be more easy to understand
if a definition is not provided. (026)
> I make a distinction between two homonyms: (physical) area
> as a physical object with a shape (027)
I'm trying to figure out what a physical object without a shape might be --
how it could be physical. If this is your definition, why not use the term
"physical object"? (028)
Or would you want a narrower definitition than "physical object with shape"
for "physical area" -- perhaps something to do with surfaces? (029)
> and (property) area as an aspect (e.g. of a physical area),
> measured as a two dimensional integral of distance. (030)
This is a third and fourth meaning, neither of which we have been discussing. (031)
Connected Abstract Space -- a connected massless volume defined by the
coordinates of its limiting abstract surfaces.
Physical Space -- a Connected Abstract Space along with all the matter within
the space.
Physical Object -- a connected body of matter with a shape.
Connected Area -- a connected two dimensional surface, which may be curved
in 3-space
Area Quantity -- a quantity dimensioned as a distance quantity times
a distance quantity
surface Area Of Object -- a property of a spatial object relating the
surface of
that object to an Area Quantity. (032)
> I discussed the first concept. You seem to argue on the basis
> of the second concept. (033)
I haven't discussed either the relation or the quantity. (034)
> My impression is that you do not make the distinction. (035)
My distinction is different -- that between something spatial and massless
and
something spatial that includes the mass within the space. (036)
>> > then you also possess a mass with volume below and a space above it, (037)
>> If you buy a physical object, then you own (a social property) the mass
>> that comprises that object along with associated rights as defined by
>> society. (038)
>> > although constrained nowadays by government rules. (039)
>> and before that by societal rules. (040)
>> > Although they are typically defined in two dimensions only,
>> > their third dimension is recognized and
>> > constrained by government rules (as you describe below). (041)
>> It appears that you are referring to plots of land here, not "two
>> dimensional area's in physical reality". (042)
>> > ... (043)
>> > We are probably
>> > influenced by the abstract mathematical concept of dimensions.
>> > In practical physics, every physical point has a size that is non
>> > zero, although nearly infinitesimal. (044)
>> What do you mean by "physical point"? (045)
> [AvR] With "physical point" I means a volume of negligible small size, but
> not of zero size. Because things of zero size cannot be observed nor
located (046)
They cannot be observed, but certainly they can be located. (047)
Are your "physical points" cubes/spheres/indeterminate shapes with
a size of the Planck distance? (048)
-- doug foxvog (049)
> and therefore do not belong to the physical domain.
> However, mathematical points with zero size do exist in the
> mathematical domain.
... (050)
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