“The shortest distance between two points is a straight line” looks true, even for “curved” spaces.

But a shortest line MEANS a straight line. It’s a grammatical, not an empirical necessity that a shortest line is the straightest line.

Let’s clear up this mess, these old platitudes about lines. Here is the correct formulation::

All “shortest” lines are the same length because The shortest line is the line with the least number of events on it. Straightness has nothing to do with it.

In so far as events take time—and it would be quicker not to have to go to events—I am in general agreement that the shortest affair is the one with the least events, and this would hold for lines as well.

I have also verified the hypothesis that one can draw a curved line that’s shorter than a straight one—insofar as one draws the straight one longer. So I agree with that as well.

In fact, I’m not aware of anyone who ever thought the shortest line ‘meant’ a straight line, and that there couldn’t be a curved one shorter.

Lines are to distance like bread is to sandwiches.

I never thought I’d say this, but Monooq, you’re completely wrong, and JohnJones is completely right. You might think you two are in agreement, but as far as I can tell, you’re talking about different things. John Jones is correct when space itself is curved and distorted by gravity, which it frequently is.

My point applies to time as well. The shortest time is the time with the least number of events.

In fact, “the shortest line is the line with the least number of events on it” IS a temporal description as well. All shortest temporal events are the same duration.

Nope, I disagree. A straight line could be anything, including time, but possibly a road. The comments before are fine as they are, not standing for time. Btw, time can be circular, that much is clear.

if you draw two points on a paper, and then draw two “lines” (using the word line in the loose form), one of them a straight line and one of them a curved line, the straight line WILL be measurably shorter than the curved line. go ahead, monooq, try the experiment and get some measuring tape. when you find a curved line that connects two points that is shorter than a straight line that connects the same points, i’ll give you a million dollars.

no. they don’t hold. we’re not jsut talking about drawing a random straight line and a random curved line. if that’s what you think this is about, like i said, you’re misunderstanding what this thread is about.

This is what this thread is about. Connecting Point A and Point B. Are you starting to see what’s going on here? Go ahead and print this image and measure the two paths. Tell me which one is longer.

The ONLY way to make the curved path the shorter path, as I said before, is if space itself is distorted.

You’re the one whose misunderstood the thread. The thread is not about the shortest distance between two points. It is about whether the shortest-ness of a straight line is analytic or empirical. I proved the assertion that it is not empirical, by verifying via my page that a curved line could have less events on it.