Nathan Oakley is one of the biggest flat-earth activists. He is quite notorious for being, arguably, by far the most obnoxious, smug and condescending of them all. His tone of voice, his manner of speaking, the way he expresses himself, and even his facial expressions all exude smugness and condescension. It's a very smug and hostile tone, and whenever someone doesn't agree with him, very often he resorts to just petty insults and his smugness turns into a very aggressive tone and words. Unsurprisingly, if he is in control of the conversation, eg. if it's happening during an online live stream and he has the capability of muting and kicking out the other person, he's more than happy to do that and he abuses that power very easily and often. Also unsurprisingly, when he isn't in control of the conversation, he always tries the next best alternative, ie. to control it by constantly interrupting and shouting over the other person.
He is the epitome of the Dunning-Kruger effect, and every single video I have seen of him tells me that he's an extremely unpleasant person to be around. Even most still images of him make him look like a smug and unpleasant person.
Anyway, one of his pet arguments that he loves to repeat over and over, is that all geographical measurements, be it small or big, are always done assuming a flat Earth. Anything that needs measuring distances or other geometry of the ground, according to him, is always done assuming a flat plane. According to him, the curvature of the Earth never comes into play when such measurements and surveying are done.
Well, rather obviously he is quite wrong, even though he will never, ever admit it. And here I'll present an actual practical example of this.
But before I do that, let me explain why measurements may be approximated by assuming a flat ground when distances are short enough.
Nathan, surely you understand the "8 inches per miles squared" approximation of the curvature of the Earth? This is, in fact, a quite an accurate approximation of the vertical change of a circle of the radius of the Earth, up to several miles in horizontal distance. (Of course the longer the distance, the more that approximation starts to deviate from the actual value, but it's surprisingly accurate up to even 100 miles or so.)
You might not have the mental and cognitive capability of actually using that formula to calculate the amount of drop, so here are some example numbers:
8 inches per miles squared means that if you traverse 1 mile, the ground will have dropped by 8 inches.
If you travel 2 miles instead, the ground will have dropped by 32 inches.
If you travel 3 miles instead, the ground will have dropped by 72 inches.
If you travel 4 miles instead, the ground will have dropped by 128 inches.
In other words, if you travel 4 miles, the amount of expected drop will be about 11 feet. That's not a lot.
That means that if you do Earth surface measurements that involve distances of up to just a few miles, and assume that the surface is flat, the amount of error that you will get is extremely small. Usually too small to be significant. And approximating assuming a plane results in much simpler mathematics than trying to use the surface of a sphere.
That's why a plane may be used as a more-than-good-enough approximation, as the errors introduced are usually insignificant. Measuring something a mile long assuming a plane might introduce an error of just a fraction of an inch compared to the true value.
However, once the distances start becoming larger, the errors become more and more significant. For example, if the distance you are measuring is 100 miles, the expected drop due to the curvature of the Earth is now about 1.3 miles, which starts being very significant. If with these distances you were still approximating with a plane, the errors you would be introducing would be quite large.
With such large distances you need to start taking into account the curvature of the Earth.
And unlike you love to claim, that is actually being done, all the time. Here's the practical example I mentioned before:
Take any GPS software or library, and check how it calculates the distance between two points on Earth. If the source code of the program or library is available, you can check it right from there.
Do those programs and libraries assume a plane, or do they assume an oblate spheroid?
The formulas for calculating distances are vastly different in those cases.
They cannot approximate assuming the Earth is a plane because the result you get would be very erroneous, particularly for larger distances.
You don't have to take my word for it. You can check it yourself.
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