It is interesting what a "straight line" really means, though, in different contexts. I would have to say this is a poor puzzle, though, filed under cheap word tricks & ambiguities.
I'd also point out that it's a puzzle, not a standardized test question. Wordplay, tricks and ambiguities are par for the course.
It's also why the question is (paraphrased) "start facing east and go in a straight line", and not "go east in a straight line".
Emphasis mine.
> 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.
where there isn't any wording saying "go east in a straight line".
Edit: Ok, the latitudinal geodesic only exists at the equator, so the question is fundamentally impossible, with how the author defines a straight line.
There is no such thing. A curve of constant latitude on Earth, except for the equator, is not a geodesic.
> You cannot claim that one geodesic is more “straight” than another in 3d Euclidean geometry
In terms of 3D Euclidean geometry, neither a curve of constant latitude on Earth's surface nor a great circle on Earth's surface is a straight line/geodesic. Both are curved.
If you restrict to the 2D surface of the Earth, a great circle is a geodesic but a curve of constant latitude, except for the equator, is not.
Wrong. There is a perfectly good great circle passing through Seattle and pointing due east at the point where it passes through Seattle. The author showed it to you in the article. That geodesic does not always point due east, but nothing in the article said it had to. The article only said you have to face due east at the start, not that you need to continue facing that way.
If you're working within a 2-sphere, such as the Earth's surface, or indeed any non-Euclidean geometry, they mean the same thing. More precisely, there are no "straight lines" in the exact sense you mean in a non-Euclidean geometry, but there are geodesics that satisfy all of the geometric properties of "straight lines" within that non-Euclidean geometry.
"Then start traveling forward, in a straight line along the Earth’s surface."
Historically, maintaining constant latitude (colloquial "Go East") was straightforward.
By contrast, maintaining a Great Circle Route other than the equator was effectively impossible until the 1800s. It requires the ability to track longitude which requires the invention of the marine chronometer.
It was at sea because the sea is constantly forcing your ship to change heading (wind, currents, etc.), and you have to compensate for that, and before the required navigation techniques were developed, there was no way to know what heading you should be on at any given time to maintain a great circle route.
But the article is asking you to imagine that you don't have to worry about that--which, if you're just walking across flat land, you don't. You can just "put one foot in front of the other", doing what comes naturally, and you will follow a great circle--not a curve of constant latitude.
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.)
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.
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.
> "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-...
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.
I accept that one can mean a great circle on a 2 sphere when they write "straight".
Please see 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.
I'm not sure why you referenced the Wikipedia article you did, since it supports what the GP says and contradicts what you say.
So is a geodesic a straight line?
On a sphere, you have to pick one: Stick to the surface or follow a straight line.
If you are working in the 3D Euclidean space in which the Earth is embedded, yes.
But not if you're working within the 2D non-Euclidean space of the Earth's surface alone. Within that space great circles, geodesics, satisfy all of the geometric properties of "straight lines".
In other words, the geometric properties that define "straight lines" do not actually pick out the precise concept that Euclid thought they did. They pick out his intended straight lines in Euclidean space, but they also pick out great circles on 2-spheres, and hyperbolas on a hyperboloidal 2-surface. This discovery was made in the 1800s by several different people, and it led, among other things, to the theory of General Relativity in physics, so it's not something that can just be put aside.
You live in both. In your daily life, you're restricted to the Earth's surface, and if someone asks you to walk in a straight line, you will walk in a straight line (geodesic/great circle) along the Earth's surface. You're not going to walk off into space, and you're not going to constantly be turning to maintain constant latitude. Over short distances the difference is negligible, but the article is not restricting you to short distances.
For everything beyond that, I'd need a compass or GPS and map, and then... I'd ask them to clarify if they meant a rhumb line, great circle line, or something else :)
Why? If you just put one foot in front of the other, you will naturally walk along a geodesic--a great circle.
https://www.sciencedaily.com/releases/2009/08/090820123927.h...
You can't walk in a universally straight line on the planet. You can only walk in a straight line relative to something. In their example, when they say "walk in a straight line" they really mean something more-like "walk in a radially straight line, relative to the center of the earth, assuming the earth is a perfect sphere, etc"
My assumption when reading the text of the question, which I think is most peoples' very reasonable assumption, is that you are traveling straight relative to the eastward direction; meaning, you're re-adjusting to continue to travel east, because that is a reasonable extension of the pretense "you leave Seattle traveling east".
Its a bad question that is purposefully bad to trick people.
To me "go east" means something more like "travel with a velocity vector that is always aligned with east on a compass", not "travel with a velocity vector that is fixed with east from your initial position"