Pat, (01)
> It always bothered me that dimensional analysis made angles
> dimensionless, when they are of such profound physical significance.
> Clearly, direction of length matters. The fact is, 'length' should be
> treated as a vector rather than a scalar. This also, btw, helps with
> distinguishing length from width from height. BUt this is probably
> going too far out in left field for this forum :-)
> (02)
I guess from your example that it is not angles per se that you miss, but
the information that they provide. (03)
Could your suggestion for length be similar to the difference between
velocity and speed? (04)
Could there be vector lengths (where the physical instances of lengths as
categorised by 'length' and direction) and then the sum across all
directions to give you the bare length. So, for example there is 1 foot
upwards (wrt some reference frame) - the class of all particular 1 foots
that point upwards (I am not sure that the analogy completely holds as would
one distinguish between upwards and downwards - we do not with height, etc.
measurements). And the 1 foot forwards length. And the the 1 foot length
which has as its instances the sum of the 1 foot direction lengths. (05)
I think that the analogy holds better if one sees the velocity vectors as
vectors in 4d space (so the speed is built in), then the vector with a
direction London to Cambridge is clear distinguished from the Cambridge to
London direction. (06)
Regards,
Chris (07)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
Shared Files: http://ontolog.cim3.net/file/work/UoM/
Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard (08)
|