*"If you were looking for any glimpse into the mind of Microsoft, this is it: the company has completely abandoned Windows XP, and it has absolutely no plans to ever ship an XP SP3. My guess is that Microsoft will do what it did with the final Windows 2000 Service Pack: claim years later that it's no longer needed and just ship a final security patch roll-up. This is the worst kiss-off to any Microsoft product I've ever seen, and you'd think the company would show a little more respect to its best-selling OS of all time."*

To view parent comment, click here.

To read all comments associated with this story, please click here.

I'm sure it won't be too much of a problem for one more post here.

(please excuse the use of wikipedia for convenience)

Firstly, keep it simple. A straight line is a pretty generalised term, there are many more precise ways of defining a path, there probably isn't any one unified comprehensive definition, but this is how I understand it:

My claim is that a line is **always** the shortest distance between 2 points[1]*. If that is true, then it will always hold true, you can never shorten a straight path between fixed points, ever. If you define a straight line( f1(y)=mx+c ) in 2d euclidean space and then change the metric such that the 'distance function[2]' changes, then the line f1(x) will no longer be straight. As I understand it, then if you define a non-metric or discontinuous space, the entire concept of a straight line becomes patchy anyway.

This becomes useful in the physical world. You can specify that light[3] always travels in a straight line. Therefore when light bends around a planet, the definition still holds. Even a black hole doesn't stop light traveling in straight lines . I'm not sure how this definition holds up when taking about dif/refraction.

I can't find any reliable source to back up my claim that a straight line is always the shortest path. I imagine that there is no properly agreed definition in this case. But I know that it is used in Physics.

* The article only claims this fact when in euclidean space, Physicists believe that this holds in any space.

[1]http://en.wikipedia.org/wiki/Line_(mathematics)

[2]http://en.wikipedia.org/wiki/Distance_function

[3]http://en.wikipedia.org/wiki/Light#Optical_theory

Member since:

2006-01-21

As this is already getting to far off-topic, I would suggest we discuss this further in private if necessary.

It may very well be, that I have worded my argument too sloppy, and it is definitly possible, that your knowledge in this field surpasses mine, so feel free to correct me, as I'm very eager to learn if I have made any stupid mistakes.

Say I limit my set of objects to a curved subspace of lets say the R^N with an euclidean metric (prime example: a closed spherical surface R^(N-1) ), then (again to my knowledge) the straight line definition from the R^(N) is no longer the shortest path

withinthe curved space that connects two points. It is in this example the shorter of the two pieces of the grand circle, that goes through both points.I have approached this whole thing from the variational calculus point of view, where one tries to minimise the

functional of the action

onthe curved manifolds that result from the (holonomic) constraints, that one has to obey that I'm used to from classical mechanics.Feel free to correct me here if I have made any obvious mistakes, otherwise I would ask you to contact me at mfschwin [at] gmx [dot] at

to discuss this further. Thanks in advance!

Regards

Edited 2007-04-08 09:14