John, (01)
I am sure other people will go into the details, but I think your
description below does not follow the standard uses. It seems to be more
like plain 3D than 3D + 1 - recall Ian asked for 4D, 3D and 3D +1 to be
disambiguated. (02)
3D/4D are different approaches to time or change - see
http://plato.stanford.edu/entries/time/. (03)
AFAIK 3D + 1 is a restricted version of a kind of 4D view, where the basic
objects are (from a 4D perspective) time slices.
The time dimension is then added using a time index (rather than mereology
as in pure 4D).
This structure has a nice mapping to some ways of using time indexed logic.
Whether anyone actually uses natural language that way - well, it seems
unlikely. (04)
Regards,
Chris (05)
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F. Sowa
> Sent: 27 January 2011 17:05
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] 3D+1 (was presentism...was blah blah blah)
>
> On 1/27/2011 11:17 AM, Ian Bailey wrote:
> > I get 4D, finally, after years of hanging on Chris and Matthew's
> > coattails, but the 3D+1 thing is a mystery.
>
> The basic issue is the definition of a physical object and its
relationship to a
> privileged time called 'now':
>
> 1. In 3+1 D, which is the implicit assumption in ordinary
> language, an object (human, animal, plant, or artifact)
> comes into existence at some time t1 (e.g., birth),
> ceases to exist at some time t2 (e.g., death), and
> for each now between t1 and t2, all parts of it
> exist together now.
>
> 2. In 4D, a physical object extends over a 4D volume, whose
> lower and upper time coordinates are t1 and t2 and whose
> spatial coordinates trace out a volume that spans the
> object's travels.
>
> 3, In 3+1 D, the object undergoes various changes, which
> cause some properties to become true or false at different
> times called now.
>
> 4. In 4D, the object doesn't change, but it has time-dependent
> parts (slices or stages) at which various properties may be
> true or false.
>
> The analogy I prefer (since I studied fluid mechanics at one time in my
life) is
> between Lagrangian and Eulerian coordinate systems for representing and
> computing fluid flow:
>
> 1. Lagrangian coordinates are like a 3+1 D system: the
> observer follows a particular parcel of fluid as it moves.
>
> 2. Eulerian coordinates are like a 4D system: the observer
> sits on the side and watches the flow of all the fluid
> as a whole.
>
> In our ordinary language, we talk about our bodies in Lagrangian terms.
We
> observe our own motion through space and time, and relate everything else
> to where we are *now*.
>
> An Eulerian system is like a God's eye view of the universe.
> God sees everything spread out in all dimensions of space and time. There
> is no privileged point of time or space.
>
> John
>
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