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I think there are two separate cognitive skills involved in correctly answering a trick question like this - both important, but the mix of them can make the results a bit confusing. One is the general intelligence to come up with and understand the right answer. The other is the social intelligence to recognize that you are being asked a trick question, and should round off any confusion you have to that trick question and not to the non-trick-question it's mimicking. It's common for models to give a trick question like this the wrong answer, while noting in their reasoning that the question is trivial as written and they assume whoever wrote it made a mistake.
Note that this second skill, of trick question detection, varies highly among humans as well. It's common for simple trick questions to go viral on social media as a kind of ragebait. And in addition to the throngs of people who fail the first-order IQ test and give the wrong answer, there's often a bizarre number of people who fail a second-order IQ test and somehow miss that the question was deliberately constructed as a trick.
I'm not an expert, but I think the key aspect of intelligence here is the ability to model the world. I am a little hung over and off my game this morning and I did not immediately recognize this as a trick question. Rather, in a split second I imagined myself walking to the car wash; realized that I didn't have my car; and realized that this was a problem. Only then did I see it was a trick question.
My sense is that LLMs don't really model the universe. I would be very impressed to see an LLM correctly answer a question which was novel and for which the correct answer requires modeling the world.
A year or two ago I would test LLMs with the following question: 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?
The LLM never got the correct answer (New Jersey) presumably because they are unable to model the situation. I would think that by now, this question is now in the training data, but still, these sorts of quick fixes don't solve the general problem.
Okay what am I missing here. Isn't the correct answer New York?
No, because you are traveling West at a slightly higher latitude than your latitude when you are traveling East. So you will end up going a bit further West in terms of degrees longitude. The Empire State Building is in Manhattan so it's very close to the New Jersey border.
Doesn't this only hold if you're measuring the direction at each juncture rather than working from the NSEW coordinates of the Empire State Building?
Maybe that doesn't sound like the most intuitive way to think about it, but in my defense it's kinda similar to how bullseye navigation works.
(Also, since we're in an aircraft, pedantically we would need in theory need to account for the rotation of the Earth, which we can't do without knowing the airspeed.)
I don't understand. Let's suppose the helicopter has completed the first (northbound) leg of its journey and is about to turn West. To me, "west" would mean that the helicopter turns 90 degrees to the left. What direction would the helicopter go at that point if one were "working from the NSEW coordinates of the Empire State Building"?
If the helicopter makes 90 degree turns at each turn, it will return to the Empire State building, making a square with 300 miles to a side, right? Helicopters fly, so they don't need to respect the Earth's curvature - they can fly in a plane, at least until they exceed their operating altitude. So the 2D map view would be basically correct (if we don't worry about the Earth's rotation). This is the mental model I had in my head that told me we would return to New York (which now I feel a bit dumb about.)
But when after turning West, we turn back South, if we flew to the South pole from our location, we would collide with (intersect) with an aircraft flying due South from the Empire State Building (at the South pole). The lines aren't parallel; they intersect. So when we made our turn South, we will fly a different course if we turn "South" as in "South by compass" or if we turn "South" as in "parallel to a line extending due South from the Empire State Building." And if we fly South by compass, we won't be making a 90 degree turn, for the same reason that squares of latitude and longitude aren't perfect squares.
...I think that's all correct, but it's been a long time since I've thought about this, so thanks (it's good for me).
Ahh, I understand. Except that compass directions such as "north" are typically understood in respect of the Earth's curvature. So for example consider the following questions:
(1) A helicopter starts at the equator. How many miles due north does it need to fly before it reaches the north pole?
(2) A helicopter starts in NYC. How many miles due north can it fly before it is impossible to fly any further north?
Most people would reasonably understand these questions to have straightforward finite answers. But if "north" is understood to be on a plane which is tangent to the Earth at the point of departure, then answers are (1) it will fly forever without reaching the North Pole; and (2) it can fly North forever.
Yes, I think this is all right. The more erudite reason I can give for my initial interpretation is that in certain contexts (such as the military) navigation is done in reference to a fixed point (bullseye). But probably I was just having a grug-brained moment!
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