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. (01)
The basic issue is the definition of a physical object
and its relationship to a privileged time called 'now': (02)
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. (03)
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. (04)
3, In 3+1 D, the object undergoes various changes, which
cause some properties to become true or false at different
times called now. (05)
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. (06)
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: (07)
1. Lagrangian coordinates are like a 3+1 D system: the
observer follows a particular parcel of fluid as it moves. (08)
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. (09)
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*. (010)
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. (011)
John (012)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/
Config Subscr: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/
To join: http://ontolog.cim3.net/cgi-bin/wiki.pl?WikiHomePage#nid1J
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx (013)
|