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Flat Earth? Sure, Why Not?

@Geek_0nline offered to clean @GerbusJames’ house, if he could prove that the Earth is flat. I don’t care about this flat Earth nonsense, but I do want a clean house, so here’s my proof of a flat Earth.

So first consider “flatness.” Is a table flat? Most people would say yes, but there are certainly imperfections in the surface. Yet it is still flat. So what is flatness? Consider some mass. Now consider some point on the surface of the mass, and a plane passing through the center of mass, with a normal which is parallel to the shortest vector between the plane and the point. We will call the distance to that point, the shortest distance from the point to the plane. Finally, we can say that the mass is flat if and only if, for any two points on the surface of the mass, the absolute difference between the distances for each point is less than one percent of the average distance for all the points on the surface of the mass.

Now, science accepts that the Earth is roughly a sphere. It has a radius of about 3,959mi. Now consider the highest point on Earth, Mt. Everest, and the lowest point on Earth, the Mariana Trench. The distance for each of these points is just the distance from the center of the Earth to those points, and the difference between those distances is the distance between their height or depth above or below sea level. The average distance of all points would be the radius of the Earth. That difference is about 65,000ft. That comes out to a little over 0.3% of the radius. So the Earth is indeed flat.

Now, I did prove that the Earth is flat, but I only did so up to definition and axiom. It is reasonable, to me, to consider the Earth flat, as a surface which is relatively smooth is, for practical purposes, flat, and I even showed that many people consider things to be flat, even if they have imperfections. The imperfections just need to be small enough. But if those definitions and axioms are not accepted, then my proof falls apart.

That is the issue with evidence. All evidence is analyzed with respect to some axiomatic framework. There is no universal norm for evidence. And variations in epistemological frameworks is what makes it so difficult to discuss topics like flat Earth concepts, gods, etc. We do not share a common foundation, at least not completely, and there is rarely an attempt to seek one out. Still, I did provide evidence, so I think it’s now time for Geek to fly over and clean out this house. It really needs a good cleaning.

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