re: Baseball rpi

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It's like the curvature of the earth. We all just accept it as fact despite being unable to provide evidence

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I can provide evidence of the curvature of the earth. I've see the earth's shadow on the moon. I've seen ships sailing into the distance gradually disappear.

I've never done the experiment myself, but I've read about Eratosthenes' calculations...

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The measurement of Earth's circumference is the most famous among the results obtained by Eratosthenes,[13] who estimated that the meridian has a length of 252,000 stadia (39,060 to 40,320 kilometres (24,270 to 25,050 mi)), with an error on the real value between -2.4% and +0.8% (assuming a value for the stadion between 155 and 160 metres (509 and 525 ft)).[2] Eratosthenes described his arc measurement technique,[14] in a book entitled On the measure of the Earth, which has not been preserved. However, a simplified version of the method has been preserved, as described by Cleomedes.[15]

The simplified method works by considering two cities along the same meridian and measuring both the distance between them and the difference in angles of the shadows cast by the sun on a vertical rod (a gnomon) in each city at noon on the summer solstice. The two cities used were Alexandria and Syene (modern Aswan), and the distance between the cities was measured by professional bematists.[16] A geometric calculation reveals that the circumference of the Earth is the distance between the two cities divided by the difference in shadow angles expressed as a fraction of one turn.

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If you don't consider these things evidence than there is no evidence for anything.