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**Flat Earth Debate / How to argue about perspective (I'm looking at you, Tom)**

« **on:**December 22, 2007, 10:57:11 PM »

I already posted this is another thread, but it deserves its own I think. In addition to the FAQ we really need a FPBA (Frequently Posted Bullshit Arguments) so that we can refer people to it.

I honestly cannot believe that this perspective argument is still coming up. "Basic laws of perspective" they say, "obvious empirical evidence" they say. Even if the FEers are correct about the whole "sinking into the ground" thing, it cannot be due to perspective. Perspective is nothing more than the appearance of objects becoming smaller as they move further away. All of the "laws" of perspective that people love to reference so much are simply due to trivial trigonometry. I'm even going to demonstrate with a picture.

Diagram 1: Here the object's actual distance from our center of vision is y. Its apparent distance is theta. Even as y remains constant, as x approaches infinity, theta approaches 0. That is, the object appears closer to the center of our vision as it moves further away even though it is physically not moving closer. This is because theta = arctan(y/x) and arctan(0) = 0.

Diagram 2: Here the object's distance from the observer is x, it's actual height is y, and it's apparent height is theta. Yet again, as the object moves further away y remains constant, x approaches infinity, and consequently theta approaches 0. To simplify the math, let's just assume that the object is vertically centered in our vision (this only affects the coefficients). We can split the triangle in half along the horizontal and thus get theta/2 = arctan(y/2x) and yet again arctan(0) = 0. So as the object moves further away, it appears to be smaller even though its actual height is not changing.

See? All that there is is relative position and trigonometry. Now whenever you crazy FEers bring up "perspective" you have to argue it with only those two things: relative position and trigonometry. Use math, use pictures, do NOT cite Samuel "Rowboatman" Rowbotham.

I honestly cannot believe that this perspective argument is still coming up. "Basic laws of perspective" they say, "obvious empirical evidence" they say. Even if the FEers are correct about the whole "sinking into the ground" thing, it cannot be due to perspective. Perspective is nothing more than the appearance of objects becoming smaller as they move further away. All of the "laws" of perspective that people love to reference so much are simply due to trivial trigonometry. I'm even going to demonstrate with a picture.

Diagram 1: Here the object's actual distance from our center of vision is y. Its apparent distance is theta. Even as y remains constant, as x approaches infinity, theta approaches 0. That is, the object appears closer to the center of our vision as it moves further away even though it is physically not moving closer. This is because theta = arctan(y/x) and arctan(0) = 0.

Diagram 2: Here the object's distance from the observer is x, it's actual height is y, and it's apparent height is theta. Yet again, as the object moves further away y remains constant, x approaches infinity, and consequently theta approaches 0. To simplify the math, let's just assume that the object is vertically centered in our vision (this only affects the coefficients). We can split the triangle in half along the horizontal and thus get theta/2 = arctan(y/2x) and yet again arctan(0) = 0. So as the object moves further away, it appears to be smaller even though its actual height is not changing.

See? All that there is is relative position and trigonometry. Now whenever you crazy FEers bring up "perspective" you have to argue it with only those two things: relative position and trigonometry. Use math, use pictures, do NOT cite Samuel "Rowboatman" Rowbotham.