A mishna on Eiruvin 41b tells of a ship that was coming into harbor at dusk coming into Shabbat. Since Shabbat had already begun when the ship docked, those on board asked R. Gamaliel if they could disembark. He said yes, because he had observed that the ship was close enough before Shabbat started.
Obviously R. Gamaliel wasn't in a position to actually measure the ship's distance from the dock; he estimated. This leads me to wonder on what basis R. Gamaliel could make that ruling:
Perhaps the ship was obviously close enough. In that case I would have expected the answer he gave to say something about "yes you can move from a vessel to land", rather than bringing up the distance.
Perhaps R. Gamaliel, being a sage, had an ability to make these kinds of judgments that we can't assume anybody else has -- he could make this determination, but a regular person could not.
Perhaps R. Gamaliel had some relevant background that increased his ability to measure distances, sort of like how archers become good at estimating ranges. Under this reasoning someone with relevant skills could make this judgement but a regular person couldn't.
I'm curious about both R. Gamaliel's ruling and whether there is application beyond him (can people in general rely on estimation?).
Here is the passage:
פעם אחת לא נכנסו לנמל עד שחשיכה אמרו לו לרבן גמליאל מה אנו לירד אמר להם מותרים אתם שכבר הייתי מסתכל והיינו בתוך התחום עד שלא חשיכה
And from the Soncino English translation:
Once [on a Sabbath eve] they did not enter the harbour until dusk. "May we disembark?" they asked R. gamaliel. "You may", he told them, "for I have carefully observed [the distance from the shore and have ascertained] that before dusk we were already within the Sabbath limit".