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Comment by cush | Hacker News Reader

Travel exactly due East. Now, ignore what East means. Then, ignore the giant white arrow pointing East into Montana in the image we've created to illustrate this question. Also, don't worry about anything called a Great Circle, it's completely unimportant. What country would you first encounter?

Did you get it, idiot? No? Let me explain to you why you're wrong.

First, you completely missed that the Great Circle I told you not to worry about doesn't actually follow along the white arrow I used to illustrate the problem. Clearly, if you completely ignore all the information that was given to you, and what East is, the answer is obviously Australia. Because if you were at the North Pole, a line going East would be a tight circle.

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> Travel exactly due East. Now, ignore what East means.

It's "face east, then travel in a straight line," not "travel due East" (though I agree that the title itself is misleading).

IMO, it's a cool thought experiment because it demonstrates that an instruction to "travel in a straight line" is incompatible with an instruction to "travel due East" (unless you're on the equator!) - as the North Pole example illustrates. Start 3 feet south of the North Pole and face east, then start traveling in a straight line. Obviously after 10 or 100 or 1000 miles of travel you'll be essentially due south of the pole - and in fact, if you take a single step to the left, you will be exactly due south of the pole!

Everyone's replying as if the title and image don't exist

> It's "face east, then travel in a straight line," not "travel due East" (though I agree that the title itself is misleading).

It's a fun and interesting problem, but just to be the contrarian:

The solution didn't travel in a straight line any more than the alternate (incorrect solution), both resulted in arcs.

Any straight line that's tangential to the surface of a sphere will lead off the sphere.

Author here — I agree the image is misleading (and added a caveat to be clearer, though I could have made the arrow smaller).

I don't think the question requires the reader to ignore what ‘east’ means, however. There is unambiguously one direction at Seattle (tangent to the Earth's surface) which is facing due east.

I also didn't mean to take a patronising/arrogant tone to the reader and I'm sorry if that was the impression I gave.

FWIW I did not get that impression at all, and I'm bewildered by all of the combative comments here. It's a cool thought experiment!

The article and title have changed in response to the comments.

I read it after your caveat was added, but I didn't find it intentionally misleading, from the very strong response (which is doing what it accuses the post of doing by claiming it reads 'travel due east') I get the feeling someone may be a bit peeved they didn't 'get it's and instead thought the answer would be some embassy that happens to be directly east of Seattle.

> There is unambiguously one direction at Seattle (tangent to the Earth's surface)

and that tangent is the straight line, at least it is within the R^3 spatial universe I live within.

There's confusion here as the article presumes humans to be bound to an S^2 manifold and to consider a Great Circle to be a "straight line" which it certainly is not unless one lives within an S^2 Flatland.

My immediate guess was England or maybe a bit lower and France, but then I saw the arrow and thought "DOH! Canada"

The way I'd explain it is:

You have a perfect paper airplane. It flies in a straight line regardless of wind, rain, hail or snow. And it keeps in the air a really long time.

You get into an air balloon over Seattle and launch your paper airplane directly East.

The plane descends so slowly it can leave North America and go over the ocean and eventually will reach another country and still not touch the ground. What is the first country it will reach?

This is so much better. I'd remove even more and forget about descending.

You have a perfect paper airplane. It flies in a straight line regardless of wind and never descends, staying a constant height from the ground as it flies. You get into a hot air balloon over Seattle and launch your paper airplane directly East. After leaving the USA, what is the next country that the plane will fly over?

No, it says face due east and travel in a straight line. Sure, the wording could have been clearer, but you're seeing misdirection that isn't there.

A straight line would extend into space.

The instructions state the following:

> 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 does it say to "travel exactly due East"?

The instructions are impossible to follow, since there are no straight lines (in all three dimensions) along the Earth's surface.

And if it's supposed to mean "a straight line when projected onto a map", I'd like to know: Which map projection? :)

Imagine you're on a snowmachine 10 feet south of the North Pole pointing due east. I tell you to ride for 10 miles without turning. You don't need to worry about map projections or anything - just don't turn. When you stop, are you still 10 feet south of the North Pole? Clearly not, you'll be about 10 miles south of the pole.

It's exactly the same if you start in Seattle. If you drive for 10 miles without turning, when you stop you will no longer be at Seattle's latitude - you'll have gone south.

I know, but that's not what TFA demands. Going 10 miles without turning is not "traveling in a straight line"; it's at most "traveling along a great circle line"!

And even that would require an unusually well aligned steering on a snowmobile :)

Impossible to follow if you are thinking Euclidean geometry, but a great circle is a straight line in spherical geometry. The earth isn't a sphere, but it is much closer to one than it is a plane.

Certainly not the map projection used to illustrate the question with the giant straight line on it. Not that one

I'm glad I read this comment first. This blog post is terrible and you saved me time.

It really isn't, at least with the author's clarification that the arrow isn't the path. It might sound like it if you misread the instructions as 'travel due east' as the parent comment did.

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