explain this:

If I travel ten thousand kilometers, make a 90 degree turn, travel ten thousand kilometers, make a 90 degree turn, and travel 90 thousand kilometers, i will end up back where i started, with a path in the shape of a triangle with three 90 degree angles.  This would be geometrically impossible on a flat earth, so please debunk.

Seems legit. Have you tried this?

If you haven't actually done it, what are we supposed to debunk again?

Surely, bluerabidrabbit can at least post some sources where people have performed this, right?

Also, 90 thousand kilometers for the last leg sounds a bit off.

apologies, 10 thousand kilometers.

and know i have not done this, but even if i had would it matter? would that be enough to actually satisfy you or would you question the reality of my journey? also what if i were to ask you to produce a travelled square with 10000 kilometers along each side of the perimeter.

You are trying to use a hypothetical concept as proof. 

Do you not do the same thing?

No.

Check it out.  You go 10 thousand kilometers.  You turn 60 degrees.  You go another 10 thousand kilometers.  You turn 60 degrees.  You go another 10 thousand kilometers.  And then you're right back where you started!  This is only possible on a flat Earth.  Please debunk.

If I travel ten thousand kilometers, make a 90 degree turn, travel ten thousand kilometers, make a 90 degree turn, and travel 90 thousand kilometers, i will end up back where i started, with a path in the shape of a triangle with three 90 degree angles.  This would be geometrically impossible on a flat earth, so please debunk.

First of all, there's no such thing as a triangle with three 90-degree sides. What I think you're trying to say is if I walk to the north pole, turn 90 degrees, walk back to the same latitude I started at and then return to my home position, I'll have turned 90 degrees 3 times and gotten back to where I started, right? Trouble is, you haven't walked in a triangle, you've walked on a globe and none of your lines are actually straight.

If you were to walk the same journey on a flat earth, you'd be walking a non-linear path, and you'd still be doing the same thing. The same can be said vice-versa for Roundy's counter-argument. Both work.

Quote from: bluerabidrabbit on March 27, 2013, 09:42:33 PM

If I travel ten thousand kilometers, make a 90 degree turn, travel ten thousand kilometers, make a 90 degree turn, and travel 90 thousand kilometers, i will end up back where i started, with a path in the shape of a triangle with three 90 degree angles.  This would be geometrically impossible on a flat earth, so please debunk.

First of all, there's no such thing as a triangle with three 90-degree sides. What I think you're trying to say is if I walk to the north pole, turn 90 degrees, walk back to the same latitude I started at and then return to my home position, I'll have turned 90 degrees 3 times and gotten back to where I started, right? Trouble is, you haven't walked in a triangle, you've walked on a globe and none of your lines are actually straight.

It is still a triangle.  Without even realizing it (since he just parroted it from that stupid video) bluerabidrabbit was describing a typical construction of Non-Euclidean geometry in which the three angles of a triangle add up to more than 180 degrees.

My bad, I should have said planar triangle.

On a sphere your angles might not each be 90 deg exactly, using 10,000 km sides.

But it makes sense to do three 60 deg turns and see where you end up. It would be interesting to work out what's the smallest triangle you'd need to see the difference between flat and round.

it would seem to me none of the proposed experiments would be of a good scientific standard as application in/on the real world would require a smooth, whether flat or spheroid, surface upon which to execute precise angular changes of direction.

the altitude and attitude of the three points, both in relation to the horizontal plane and in relation to one another, would not be constant or therefore consistent with the basic scientific method (repeatable, with the same results).

so if some intrepid investigator set off with a protractor and some suitable transportation whether on a flat or spherical earth, they would be doomed to failure.

90 degrees relative to what?  And in which direction will you turn each time?

it would seem to me none of the proposed experiments would be of a good scientific standard as application in/on the real world would require a smooth, whether flat or spheroid, surface upon which to execute precise angular changes of direction.

the altitude and attitude of the three points, both in relation to the horizontal plane and in relation to one another, would not be constant or therefore consistent with the basic scientific method (repeatable, with the same results).

so if some intrepid investigator set off with a protractor and some suitable transportation whether on a flat or spherical earth, they would be doomed to failure.

Work with the smaller triangles idea, and do it at sea using INS to hold your course. My proposed experiment along these lines:

Start from an island (perhaps Hawaii? Might as well go somewhere nice to do this!) and set off into open ocean. Travel a straight line for 1000km, then turn 60 degrees. Travel a further 1000km, then turn 60 degrees again. Travel another 1000km, and if you arrive exactly where you started, the earth must be flat. If not, then it is round. To be able to trust these results though, your straight lines must be straight, your turns must be exact, and visual navigation should only be used for safety, not course.

If you don't know what INS is, please look it up. It is the only way I can think of to do this experiment accurately and without bias.

If the Earth is round, how far away from your origin would you be after finishing the third leg?

If the Earth is round, how far away from your origin would you be after finishing the third leg?

Not sure. I'll have a go at working it out after breakfast and edit this to let you know.

EDIT: Oh man, 3 dimensional trig gives me a headache! Anyway, by my calculations, you should end up about 12km away from where you started, definitely far enough that you'd notice!

Thanks

Thanks

No worries! Helps keep the brain active

Just because you can't do the experiment doesn't make it a lost cause.  If you look at the "Impossible requirements" thread that I've started, I use this interesting phenomenon to deduce that the earth must be round.  So far, no one has offered a complete explanation for the discrepancy I point out.

So, let me get this straight.  If we start at Oahu, Hawaii, go north for a thousand kilometers, turn 90 degrees and head east for a thousand kilometers, and then turn 90 degrees and head south for a thousand kilometers, I will be back at Oahu?

So, let me get this straight.  If we start at Oahu, Hawaii, go north for a thousand kilometers, turn 90 degrees and head east for a thousand kilometers, and then turn 90 degrees and head south for a thousand kilometers, I will be back at Oahu?

That is not what he wrote. Although what you propose should be possible on a round Earth. Maybe not with the legs of the triangle at only 1000kms in length, but certainly at much longer lengths.

So, let me get this straight.  If we start at Oahu, Hawaii, go north for a thousand kilometers, turn 90 degrees and head east for a thousand kilometers, and then turn 90 degrees and head south for a thousand kilometers, I will be back at Oahu?

No. I think you need to go back and re-read the relevant posts.

My proposal involves 1,000km legs, and 60 degree angles (actually a 120 degree turn), with the net result that, on a flat earth, you arrive where you started, or on a round earth, you arrive at a point about 12 km from where you started.

The original proposal was for 10,000km legs and 90 degree turns, which would get you back to where you started on a round earth, but put you at a point 10,000km away on a flat earth.

Two separate proposals, which you have confused with each other.

12kms seems like a small margin of error. Perhaps longer legs to exacerbate the difference?  Can an INS account for drifting off course because of ocean currents or wavefronts?

Yeah, it's not much of a margin, but with a good INS it should be possible to do it with enough accuracy. Longer legs would definitely help too. And yes, INS can account for any course deviation at all, that's the whole idea of the system.

Yeah, it's not much of a margin, but with a good INS it should be possible to do it with enough accuracy. Longer legs would definitely help too. And yes, INS can account for any course deviation at all, that's the whole idea of the system.

INS has a margin of error of 0.6km per hour.  How many hours would it take to complete this experiment?

Quote from: jroa on April 06, 2013, 04:40:22 AM

So, let me get this straight.  If we start at Oahu, Hawaii, go north for a thousand kilometers, turn 90 degrees and head east for a thousand kilometers, and then turn 90 degrees and head south for a thousand kilometers, I will be back at Oahu?

That is not what he wrote. Although what you propose should be possible on a round Earth. Maybe not with the legs of the triangle at only 1000kms in length, but certainly at much longer lengths.

My statement would work on a spherical Earth if the second leg ended up at a place where it made a complete 360 around the Earth.  Otherwise, this theory is full of shit.  Sorry for my language.