Re: Neighbors in Space
- From: nance@xxxxxxxxxxxxxxxxxxx (Anthony Nance)
- Date: 30 Apr 2009 12:43:05 GMT
Michael Stemper <mstemper@xxxxxxxxxxxxxxxxxxxx> wrote:
In article <zswIl.16970$D32.2996@xxxxxxxxxxxxxxxxxxxx>, Rebecca Rice <rebecca_rice@xxxxxxx> writes:
I have been pondering whether physical location or ease of
access is the more important part of determining what spots
are "near" each other, and whether that would change if we
get to a future where space travel occurs by wormholes, jump
points, or other discrete routes.
Now, if someone asked you what the closest city to Los
Angeles was, would you say San Diego (because of the
geographic distance), or Las Vegas, because it's the easiest
city to get to? And when you start extrapolating this out
to stars, does it start to make physical proximity even more
meaningless, since "close" physically is still lightyears away?
You're discovering the concept of "metric function", which is a
generalization of what we commonly call the distance between two
points. There are lots of different metrics that we commonly use
in normal life:
1. The Euclidean, or "straight-line" distance, which is the
one that you probably learned in high-school algebra, based
on the Pythagorean theorem.
2. The Taxicab distance is how many blocks east-west plus how
many blocks north-south, and is useful in major metropolitan
areas that have their streets laid out in a rigid grid.
3. "Great Circle" distance is what steamship operators and airline
pilots use to figure the distance between two points on the
Earth's surface.
As you (and others) have noted, various methods of passing through
something like "hyperspace" give other metrics. Stars that are far
apart in Euclidean space might be neighbors in the Wormhole Nexus.
Another metric that I haven't seen mentioned yet is the "Perfect
Teleportation Metric" [1]. If you can teleport with equal ease
from any point to any other point, then the distance between any
two different points is the same, namely one trip.
Another strange one is the TARDIS metric, which is Euclidean outside
the TARDIS, and is Euclidean multiplied by <bignum> inside, with it
being necessary to pass through the door of the TARDIS to go from
one to the other.
We can make things more fun by having one-way wormholes, such as in
_Red-Limit Freeway_ or _The Avatar_. But, then we don't have a metric
function, as it's normally defined, any more.
Good andinteresting points all. Relative to your last two sentences,
I just want to add that relaxing the symmetry requirement can be very
useful and practical. In everyday driving, for example, whenever
people factor in time (or one-way streets, or...) they're basically
using "metric functions minus symmetry".
Tony
.
[1] Officially known as the "Discrete Metric".
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