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PaperclipPerfector  21hr ago (text post)   3142 thread views

Culture War Roundup for the week of February 16, 2026

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A helicopter takes off from the Empire State Building, flies 300 miles North; 300 miles West; 300 miles South; 300 miles East; and lands. In what US state does the helicopter land?

Assuming I'm understanding this correctly, doesn't this depend pretty heavily on your choice of definitions and assumptions? If you trace it out on a cylindrical projection map (most options) and follow that on the ground, you'll end up where you started. If you follow a magnetic bearing (and if the compass is actively followed, or a "straight line" great circle from the starting bearing), you'll get a different set of answers than using a GPS and travelling true lines of latitude and longitude. For more subtle details, your choice of reference datums and even the flight altitude will matter slightly.

Assuming I'm understanding this correctly, doesn't this depend pretty heavily on your choice of definitions and assumptions?

Well, if I state that a helicopter takes off and travels "north" for "300 miles" what does that mean to you? Same question for "west," "south" and "east"?

Well, if I state that a helicopter takes off and travels "north" for "300 miles" what does that mean to you? Same question for "west," "south" and "east"?

That's a different question than the one upthread. If you're running laps around the pole, then you're going west for 300 miles, but you did not fly 300 miles west, you flew in a circle.

Do you really want chatbot outputs to be that sensitive to your exact phrasing, or would you prefer reasonable interpretations?

That's a different question than the one upthread. If you're running laps around the pole, then you're going west for 300 miles, but you did not fly 300 miles west, you flew in a circle.

It's interesting you should make this point, because the OG puzzle question goes like this:

A hunter is tracking a bear. He travels 1 mile south; 1 mile east; 1 mile north and discovers he is in the same place he started. He then shoots the bear. What color is the bear?

The answer, of course, is "white." To me, that's both correct and a reasonable interpretation of "east." I take it you disagree?

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". Compare to a winding trail: You can go 10 miles North by travelling North for 20 miles.

Both the bear and the helicopter are point-to-point (destination = distance+direction), while your followup question was path-based (travel mode and path, for a distance). The bear hunter walked in an equilateral triangle with approximately 119.9 degree corners.

If it had been "He travels south for one mile, east for one mile, and north for one mile", then it would be a 1 mile line, a 90 degree corner, a 1 mile arc with radius 1 mile, another 90 degree corner, then a 1 mile return line that's 122.7 degrees off from the first line.

I haven't mathed it out, but I suspect both versions involve the helicopter landing in New Jersey, but in different locations.

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.

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

I'd assume statute miles (although aviators might assume nautical miles), and I would probably assume true north for all bearings, but would prefer to ask for clarification: it's about a 12 degree difference in New York City. If you asked me 30 years ago (before everyone had a GPS-enabled map in their pocket), you'd probably have gotten magnetic, maybe with a fixed local adjustment (although declinations change over time, so it might be a different value).

I'd assume the altitude was negligible.

I'd assume statute miles (although aviators might assume nautical miles), and I would probably assume true north for all bearings, but would prefer to ask for clarification:

I think by "north," most people would interpret this to mean "in the direction of the north pole" which seems to be in agreement with your assumption.

Anyway, to answer your question, it looks to me like the puzzle depends heavily on definitions and assumptions just as every puzzle depends heavily on definitions and assumptions.

So for example, if I were to ask "what number, when multiplied by 2, is the same number," most people would correctly answer "0," but perhaps some smart-ass in the back of the class would say "12, if we are using clock arithmetic"

I think by "north," most people would interpret this to mean "in the direction of the north pole" which seems to be in agreement with your assumption.

There's two reasonable choices for North -- in the direction of the north magnetic pole, and in the direction of the geographic north pole. These are significantly offset (about 12 degrees) at the ESB, but not enough to change the answer I don't think.

Anyway, to answer your question, it looks to me like the puzzle depends heavily on definitions and assumptions just as every puzzle depends heavily on definitions and assumptions.

Sure, but any answer that would make sense to a helicopter pilot is going to put the landing point west of the starting point. Except the even more pedantic answer that there's no helipad on the ESB, so it can't happen. Or the point that very few helicopters can go 1200 miles without refueling.

Sure, but any answer that would make sense to a helicopter pilot is going to put the landing point west of the starting point. Except the even more pedantic answer that there's no helipad on the ESB, so it can't happen. Or the point that very few helicopters can go 1200 miles without refueling.

As a side note, I think one thing LLMs seem to do really well is reasonably interpret words. Whenever I've asked something like "what does phrase X mean" I've gotten answers that seem very good.

If you use a cylindrical projection and follow true rhumb lines, you'll end up west of your original course. If you follow magnetic rhumb lines (that is, you keep your compass bearing constant) you still do but with some south or north deviation as well. The reason is that the north-south rhumb lines are closer together as you go north, no matter which datum you choose. I think you'll end up in New Jersey regardless of your choice.

I think you'll end up in New Jersey regardless of your choice.

Unless you take a wrong turn, then somehow you'll inexplicably end up in Dundalk.

You'll just think you're in Camden.

The existence of map projections does not make the Earth flat.

Right, and the existence of a spherical geoid-shaped Earth doesn't well-define "flies 300 miles North" either.

Whether you're using geographic or magnetic compass directions, east and west do not cancel each other out that way.

There is enough of a gradient in magnetic declination in the NY area that magnetic "north" and "south" are up to a couple (true) degrees different if you travel 300 miles. I'd have to do some math I don't feel like at the moment, but it might dominate the spherical error term.

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