The flat-earth community is actually kind of fascinating. Someone recently paid to fly some flat-earthers down to Antarctica to witness the 24-hour sun which is impossible under most flat-earth models [1]. The trip was extensively documented, and one of the flat-earthers who made the trip actually changed their position. The result, predictably, was that this person was ostracized from the community. The intellectual backflips that the flat-earth community are making to try to debunk this experiment is simultaneously fun and disturbing to watch.
The easiest way to debunk the flat-earth model is simply to observe that that 1) the sun sets below the horizon and 2) this happens at different times in different locations. On a flat earth, if the sun is seen at the horizon in one location it has to be seen at the horizon everywhere.
Something doesn't sit right with me. I would expect that the semicircle would be reflected nonlinearly. That would imply the reflection is not a true circle. Am I wrong?
I'm also a little skeptical with this approach, as it's not taking into account the curvature of light through the atmosphere. In reality, when the photo was taken, the sun was already fully below the horizon. It just looks like it isn't because the atmosphere is bending the light a little ways around the earth. (As a rule of thumb, the amount of bending is coincidentally nearly equal to the apparent size of the sun's disc, so as soon as the bottom edge appears to touch the horizon, that's the moment it has actually fully dropped below the horizon, and would be totally obscured if the light were travelling in the straight line paths assumed by this article.)
Bravo. A very nice article comparing and contrasting standard trig methods and geometric algebra methods.
And as a bonus, it compares both with Dr. Wildberger's Rational Trigonometry. (Side note: I've known a few Australian mathematicians who embrace some very non-standard methods in mathematics, and I think it's great. We need people to shake up our thinking bout Math every once in a while.)
A very nice piece for some relaxing weekend recreational math.
awesome article. Do you know how to access the other articles in the series that are linked (dead) in the first paragraph? Would be great to read if still available.
I posted the following the other day -- and if you like this post and the maths involved - you will really enjoy Randall Carlson's Sacred Geometry lecture whereby he talks about all the Ancient Sacred Geometry and how it was used to measure the earth, moon, sun, stars and Earth's precession -- and how it all relates down to the measurements from the Human Body - whereby the 12-inch foot comes from, Cubits, etc.
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>Speaking of "feet" as a measurement - Randall Carlson has an AMAZING video[0] on the source of the 12 inch foot.
>And how its all related to the measurement of the precession of the earth. And yes - its specifically how to measure things in space. And its all from Sacred Geometry.
The flat-earth community is actually kind of fascinating. Someone recently paid to fly some flat-earthers down to Antarctica to witness the 24-hour sun which is impossible under most flat-earth models [1]. The trip was extensively documented, and one of the flat-earthers who made the trip actually changed their position. The result, predictably, was that this person was ostracized from the community. The intellectual backflips that the flat-earth community are making to try to debunk this experiment is simultaneously fun and disturbing to watch.
The easiest way to debunk the flat-earth model is simply to observe that that 1) the sun sets below the horizon and 2) this happens at different times in different locations. On a flat earth, if the sun is seen at the horizon in one location it has to be seen at the horizon everywhere.
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[1] https://www.the-final-experiment.com/
A list of urls from the beginning of post that don't seem to work anymore:
* Measuring the Earth’s Diameter from a Sunset Photo: https://vanderbei.princeton.edu/tex/sunset/ms.pdf
* The Earth is Not Flat: https://vanderbei.princeton.edu/tex/sunset/34-39.OPN.1108two...
* Sunset: https://vanderbei.princeton.edu/tex/sunset/sunset.pdf
* The Earth is Not Flat: An Analysis of a Sunset Photo: https://vanderbei.princeton.edu/tex/talks/sunset/sunsetTalk_...
Something doesn't sit right with me. I would expect that the semicircle would be reflected nonlinearly. That would imply the reflection is not a true circle. Am I wrong?
I'm also a little skeptical with this approach, as it's not taking into account the curvature of light through the atmosphere. In reality, when the photo was taken, the sun was already fully below the horizon. It just looks like it isn't because the atmosphere is bending the light a little ways around the earth. (As a rule of thumb, the amount of bending is coincidentally nearly equal to the apparent size of the sun's disc, so as soon as the bottom edge appears to touch the horizon, that's the moment it has actually fully dropped below the horizon, and would be totally obscured if the light were travelling in the straight line paths assumed by this article.)
Bravo. A very nice article comparing and contrasting standard trig methods and geometric algebra methods.
And as a bonus, it compares both with Dr. Wildberger's Rational Trigonometry. (Side note: I've known a few Australian mathematicians who embrace some very non-standard methods in mathematics, and I think it's great. We need people to shake up our thinking bout Math every once in a while.)
A very nice piece for some relaxing weekend recreational math.
awesome article. Do you know how to access the other articles in the series that are linked (dead) in the first paragraph? Would be great to read if still available.
https://web.archive.org/web/20160325085811/http://orfe.princ... https://web.archive.org/web/20160508114924/http://orfe.princ... https://web.archive.org/web/20170809073230/http://orfe.princ...
This is great!
I posted the following the other day -- and if you like this post and the maths involved - you will really enjoy Randall Carlson's Sacred Geometry lecture whereby he talks about all the Ancient Sacred Geometry and how it was used to measure the earth, moon, sun, stars and Earth's precession -- and how it all relates down to the measurements from the Human Body - whereby the 12-inch foot comes from, Cubits, etc.
---
>Speaking of "feet" as a measurement - Randall Carlson has an AMAZING video[0] on the source of the 12 inch foot.
>And how its all related to the measurement of the precession of the earth. And yes - its specifically how to measure things in space. And its all from Sacred Geometry.
[0] https://www.youtube.com/watch?v=R7oyZGW99os
One year of Sun movement captured in a single long exposed photo: https://wesely.org/2019/flughafen-tempelhof-berlin-1-7-2008-...
I wonder how 14 bln years of Sun movement will look if you stand somewhere on the equator?