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PaperclipPerfector  1mo ago (text post)   25583 thread views

Culture War Roundup for the week of February 16, 2026

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I interpret them as "flies [to a point which is] 300 miles [to the] North [along the most-direct route]..." and "travels [along a path continuously facing] north for [a path length of] 300 miles".

These are the same. For North and South, all meridians are great circles anyway. For East and West, following a rhumb line (keeping your bearing constant) 300 miles East or West gets you to a point that is 300 miles East or West. There's a shorter way to get to that point but that doesn't matter.

There's a shorter way to get to that point but that doesn't matter.

How would you describe a point at the same latitude as yourself, and 300 miles away (by great circle)? "302 Miles East"?

Yes, the exact distance would depend on the line of latitude of course.

Yes, the exact distance would depend on the line of latitude of course.

For what it may be worth, I agree with this. If it is stated that someone travels (or walks, or flies, or whatever) 300 miles east, I interpret that to mean that the person follows a "rhumb line." (thank you for teaching me this phrase.)

I understand that due to the geometry of the Earth, that if you travel 300 miles along a rhumb line, you will usually end up at a point less than 300 miles from your starting point. If you had taken a great circle route, you would have gotten there quicker.

To me, when a puzzle states that a helicopter starts at the Empire State Building and flies 300 miles north and then 300 miles west, it's reasonably clear what that means. Obviously this is all semantics, but I think some people in this thread are being what we used to call a "smart-ass"

As an example, one can imagine the following question: "What number stays the same when you multiply it by 2?" A reasonable answer to this question is "zero" But a smart-ass could defend a different answer. He might say "actually, it's 12 if we are using clock arithmetic!"

So every point on this orange curve is the same distance from the yellow point? I don't think so.

86 degrees north is only 277 miles from the pole; going 850 miles in a wide range of northerly directions isn't well-defined there. That is, if I asked you from that point, "Where is a point 850 miles North?", there simply is no good answer, since there is by definition no point north of the pole.

Pick a better-behaved set of numbers and the "rhumb ring" (which doesn't seem to be a standard term) will touch the great circle ring in both the North and South directions. Every point on the "rhumb ring" will be the same distance from the origin in one particular compass direction.

going 850 miles in a wide range of northerly directions isn't well-defined there.

That's okay, those points don't appear on the curve. From eyeballing it, East-North-East is about as close as you can get to North before that becomes an issue.

Pick a better-behaved set of numbers and the "rhumb ring" (which doesn't seem to be a standard term) will touch the great circle ring in both the North and South directions.

Nah. You pick a better-behaved function, and it won't be an issue. The same distortion that causes you to measure a 300 mile distance as a 302 mile arc causes you to measure a 250 mile distance as an 850 mile spiral.

That's okay, those points don't appear on the curve.

Yes, they do, that's why there's that silly loop.

Nah. You pick a better-behaved function, and it won't be an issue.

Spherical geometry is what it is.

The same distortion that causes you to measure a 300 mile distance as a 302 mile arc causes you to measure a 250 mile distance as an 850 mile spiral.

These are different effects. One is the distortion caused by curvature, and the other is the fact that the surface is finite. You get silly answers if you ask for great circle distances longer than the circumference, too.

Yes, they do, that's why there's that silly loop.

That loop is still well-defined though. The example picture on Wikipedia shows the line spiralling around the pole, and ending near the same meridian as its starting point. A different line with the same length and starting point but a slightly shallower angle would end a bit northwest of there, and so on for the rest of the angles which would trace the loop.

If it reaches the pole after spiralling inwards for an infinite number of turns (but finite distance), then it's not well-defined. Otherwise it is.

These are different effects. One is the distortion caused by curvature, and the other is the fact that the surface is finite.

A 1% distortion is one effect, but a 200% distortion is another? What's the threshold between the two, because it sure looks continuous to me.

You get silly answers if you ask for great circle distances longer than the circumference, too.

It's simply not defined. Much like your definition is only defined for a subset of angles near the poles (which is why those points don't appear on the curve).

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