Avira, I’m surprised that you didn’t see what is inherently unscientific in the sundial story, but before I explain allow me to summarize the pertinent parts of the story very briefly for those who are unfamiliar with it.
A poritz had a sundial that did not work correctly from 2 pm to 5 pm. The greatest professors could not explain why, but the Baal Hatanya could.
(That may sound as if c”v I’m denigrating the Baal Hatanya, but I am not at all. In fact, I seriously have no problem believing that a gaon who was so kadosh vetahor could have a greater understanding of science than even the greatest professors nowadays. It’s just that the explanation given in the story is nonsensical.)
He suggested that there were tall trees growing on a tall hill 12 to 15 miles to the south, and they were blocking the sun from 2 pm to 5 pm. The trees were cut down and the Baal Hatanya was proven right. (The story is longer and contains accounts of anti-Semitism and trickery, but in a nutshell that’s what happened.)
What’s wrong with the story?
1. The horizon on flat land is approximately 3 miles away. Due to the curvature of the earth no hill or trees 12 to 15 miles away could interfere with the sun’s rays hitting a sundial.
2. If when standing next to a sundial on a clear day (sundials require sun to function properly) you can’t see any obstruction such as trees on a hill, the sundial can’t see it either, and it would not affect the time shown. If something would affect the sun’s rays reaching the sundial at any particular time, you would be able to notice it with the naked eye without having to resort to experts or professors.