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> A straight line along a constant latitude is a perfectly valid interpretation of the words. It's a perfectly understandable interpretation, and I wouldn't be

> A straight line along a constant latitude is a perfectly valid interpretation of the words. It's a perfectly understandable interpretation, and I wouldn't belittle anyone who read it that way, but it can't be correct. A line of constant latitude cannot be straight unless it's on the equator. (Of course technically no line that remains on the Earth's surface is truly straight, but the puzzle's definition of "straight" meaning "turning neither left nor right" does seem like the best interpretation overall.)

erikerikson 2y ago
> it can't be correct You are making a good point and I feel like I understand the basis of the original article's definition of straight as well as its basis for that definition. However, it does not seem to fully define the frame. If it had disambiguated the underlying terminology and assumptions, I'd maybe think some of the definitions unintuitive but ceded their right to define. The way I would regard my interpretation to be valid is to take the sphere and slice it at the current line of latitude. That seems like a historic if not reasonable interpretation of "exactly due East". Then for further visualization, consider a cylinder that is perpendicular to and centered on the edge of the flat surface. If you cut the cylinder at the starting point and unrolled it, the resulting path to the other end would be a 2D ray. Traveling the center of that cylinder along the ray seems like a way to go "exactly due East". As a bonus, the tradition of following a compass would take you on the same path. Given the ambiguity and what I think are reasonable interpretations of some of the terms, I believe that this is a reasonably reachable result that can be called valid and/or correct. The challenge here is the underdefinition of and opportunity to attach different semantics to the words in use.
- pdonis 2y ago
  > The way I would regard my interpretation to be valid Involves getting rid of the 2-sphere and substituting a cylinder. Which changes the geometry. Yes, a circle cut in the way you describe out of a cylinder is a geodesic on the cylinder. But that doesn't mean it's a geodesic on a 2-sphere. It's not. > That seems like a historic if not reasonable interpretation of "exactly due East". It's a reasonable interpretation of "exactly due East", yes, but it's not a reasonable interpretation of the directions the article actually gave, which are: "Imagine you begin a journey in Seattle WA, facing exactly due east. Then start traveling forward, in a straight line along the Earth’s surface." So you start facing "exactly due East", but then you travel "in a straight line along the Earth's surface". The most natural interpretation of "in a straight line" is "without doing anything to change direction", i.e., just "put one foot in front of the other" continuously. And if you do that, you will follow a great circle, not a curve of constant latitude. To follow a curve of constant latitude, you would need to be making a conscious effort to turn left as you went. That's not traveling in a straight line.
  - erikerikson 2y ago
    The author admits that: > "by ‘straight line’ here I really mean ‘geodesic’" In other words, the puzzle hinges on one's interpretation of "straight line". I am merely asserting that other valid interpretations exist even if you are correct and geodesic is "the most natural interpretation". Incidentally, the article appears revised and seems far more intellectually honest now (thank you Fin, that's a lot more fun!) Consider the tomato. Classified as vegetable by the culinary discipline based on its use in the kitchen, it is classified as a fruit botanically based on the characteristics of the plant[0]. Neither is correct over the other, they are both frames for understanding the world and a classification can be correct (or not) according to the definitions of each. In the same way, I described a means of acquiring a line that I believe most would accept as meeting our ideas of "straight" that was consistent with my interpretation. It made how I failed to understand the author's intention for the puzzle exceedingly clear which can be beneficial for anyone debugging their thoughts and/or social patterns. Do you tend to get into conflicts instead of expanding your perspective? Mine doesn't seem to be the best interpretation and it certainly wasn't that intended by the author but it seems a valid interpretation, especially given the brevity of the problem statement. I find this is generally a forum where we discuss the meaning we intended and benefit from the varieties of perspectives available. Of course we are unified on almost nothing. [0] https://www.eufic.org/en/healthy-living/article/is-a-tomato-a-fruit-or-a-vegetable-and-why https://www.eufic.org/en/healthy-living/article/is-a-tomato-...
    - pdonis 2y ago
      > I described a means of acquiring a line that I believe most would accept as meeting our ideas of "straight" that was consistent with my interpretation. Which, as I said, involves throwing away the 2-sphere and substituting a cylinder. Which does not strike me as a valid interpretation of anything. There is no cylinder anywhere in the problem. Saying "I will only count a Euclidean straight line going off into space as a straight line" would be one thing--still not really applicable to the problem, but the Earth is embedded in a Euclidean 3-space so at least you're dealing with something that's actually there. But saying "I will not count a great circle on a 2-sphere as straight, but I will count as straight a circle drawn around an imaginary cylinder that I just made up" is something else.
tacitusarc 2y ago
This is not how three dimensional Euclidean geometry works! Please see https://en.m.wikipedia.org/wiki/Geodesic https://en.m.wikipedia.org/wiki/Geodesic Geodesics are “straight” along a curved surface, regardless of if they follow the circumference. Edit: The above is an incorrect description of geodesics, which must follow the circumference. Perhaps a more accurate description of the problem would be to say that it is impossible to have an easterly vector field except at the equator, and Seattle is not at the equator.
- pdonis 2y ago
  The GP is correct. Only great circles on a 2-sphere are geodesics. Curves of constant latitude, except for the equator, are not. I'm not sure why you referenced the Wikipedia article you did, since it supports what the GP says and contradicts what you say.
- lxgr 2y ago
  In Euclidean geometry, one generally does not return to the point of departure in finite time when following a straight line! So is a geodesic a straight line?
lxgr 2y ago
No interpretation can be correct, since there are no straight lines on the surface of the earth.

erikerikson 2y ago

> it can't be correct You are making a good point and I feel like I understand the basis of the original article's definition of straight as well as its basis for that definition. However, it does not seem to fully define the frame. If it had disambiguated the underlying terminology and assumptions, I'd maybe think some of the definitions unintuitive but ceded their right to define. The way I would regard my interpretation to be valid is to take the sphere and slice it at the current line of latitude. That seems like a historic if not reasonable interpretation of "exactly due East". Then for further visualization, consider a cylinder that is perpendicular to and centered on the edge of the flat surface. If you cut the cylinder at the starting point and unrolled it, the resulting path to the other end would be a 2D ray. Traveling the center of that cylinder along the ray seems like a way to go "exactly due East". As a bonus, the tradition of following a compass would take you on the same path. Given the ambiguity and what I think are reasonable interpretations of some of the terms, I believe that this is a reasonably reachable result that can be called valid and/or correct. The challenge here is the underdefinition of and opportunity to attach different semantics to the words in use.

pdonis 2y ago
> The way I would regard my interpretation to be valid Involves getting rid of the 2-sphere and substituting a cylinder. Which changes the geometry. Yes, a circle cut in the way you describe out of a cylinder is a geodesic on the cylinder. But that doesn't mean it's a geodesic on a 2-sphere. It's not. > That seems like a historic if not reasonable interpretation of "exactly due East". It's a reasonable interpretation of "exactly due East", yes, but it's not a reasonable interpretation of the directions the article actually gave, which are: "Imagine you begin a journey in Seattle WA, facing exactly due east. Then start traveling forward, in a straight line along the Earth’s surface." So you start facing "exactly due East", but then you travel "in a straight line along the Earth's surface". The most natural interpretation of "in a straight line" is "without doing anything to change direction", i.e., just "put one foot in front of the other" continuously. And if you do that, you will follow a great circle, not a curve of constant latitude. To follow a curve of constant latitude, you would need to be making a conscious effort to turn left as you went. That's not traveling in a straight line.
- erikerikson 2y ago
  The author admits that: > "by ‘straight line’ here I really mean ‘geodesic’" In other words, the puzzle hinges on one's interpretation of "straight line". I am merely asserting that other valid interpretations exist even if you are correct and geodesic is "the most natural interpretation". Incidentally, the article appears revised and seems far more intellectually honest now (thank you Fin, that's a lot more fun!) Consider the tomato. Classified as vegetable by the culinary discipline based on its use in the kitchen, it is classified as a fruit botanically based on the characteristics of the plant[0]. Neither is correct over the other, they are both frames for understanding the world and a classification can be correct (or not) according to the definitions of each. In the same way, I described a means of acquiring a line that I believe most would accept as meeting our ideas of "straight" that was consistent with my interpretation. It made how I failed to understand the author's intention for the puzzle exceedingly clear which can be beneficial for anyone debugging their thoughts and/or social patterns. Do you tend to get into conflicts instead of expanding your perspective? Mine doesn't seem to be the best interpretation and it certainly wasn't that intended by the author but it seems a valid interpretation, especially given the brevity of the problem statement. I find this is generally a forum where we discuss the meaning we intended and benefit from the varieties of perspectives available. Of course we are unified on almost nothing. [0] https://www.eufic.org/en/healthy-living/article/is-a-tomato-a-fruit-or-a-vegetable-and-why https://www.eufic.org/en/healthy-living/article/is-a-tomato-...
  - pdonis 2y ago
    > I described a means of acquiring a line that I believe most would accept as meeting our ideas of "straight" that was consistent with my interpretation. Which, as I said, involves throwing away the 2-sphere and substituting a cylinder. Which does not strike me as a valid interpretation of anything. There is no cylinder anywhere in the problem. Saying "I will only count a Euclidean straight line going off into space as a straight line" would be one thing--still not really applicable to the problem, but the Earth is embedded in a Euclidean 3-space so at least you're dealing with something that's actually there. But saying "I will not count a great circle on a 2-sphere as straight, but I will count as straight a circle drawn around an imaginary cylinder that I just made up" is something else.

tacitusarc 2y ago

This is not how three dimensional Euclidean geometry works! Please see https://en.m.wikipedia.org/wiki/Geodesic https://en.m.wikipedia.org/wiki/Geodesic Geodesics are “straight” along a curved surface, regardless of if they follow the circumference. Edit: The above is an incorrect description of geodesics, which must follow the circumference. Perhaps a more accurate description of the problem would be to say that it is impossible to have an easterly vector field except at the equator, and Seattle is not at the equator.

pdonis 2y ago
The GP is correct. Only great circles on a 2-sphere are geodesics. Curves of constant latitude, except for the equator, are not. I'm not sure why you referenced the Wikipedia article you did, since it supports what the GP says and contradicts what you say.
lxgr 2y ago
In Euclidean geometry, one generally does not return to the point of departure in finite time when following a straight line! So is a geodesic a straight line?

lxgr 2y ago

No interpretation can be correct, since there are no straight lines on the surface of the earth.