3 ms·

> 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 cir

by 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.
  - erikerikson 2y ago
    That would be something else if I had written it. I accept that one can mean a great circle on a 2 sphere when they write "straight".

by pdonis 2y ago

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.
- erikerikson 2y ago
  That would be something else if I had written it. I accept that one can mean a great circle on a 2 sphere when they write "straight".