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this post was submitted on 24 Sep 2023
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I hadn't even thought about getting HH:MM from a sundial, that's brilliant! Then getting seconds and the meter from a pendulum is just straight up elegant.
I thought this was worth a callout for being a really important consideration in this thought experiment. Understanding that larger scale measurements generally reduce error, and perhaps also repetition with averaging of results, would be incredibly useful in fast tracking the redevelopment of precision.
This one I wondered about more because of the effect of atmospheric pressure(?) on melting point, such that I wondered if it would be worth using Fahrenheit's Weird Brine ice slurry to get ~ -17.778 ° C instead. But that's ofc also subject to air pressure influencing melting point so I'm unsure if it'd be worthwhile.
Relatively constant 9.81 m/s² gravity is also useful for deriving force as you mention, though it reminds me of learning, to my abject horror, in undergrad physics that gravity does vary quite a bit by geolocation :'D 9.81m/s² is a better starting point than nothing though
Varying air pressure is certainly a concern, but repeating the experiment, as you said, would help to reduce the error, as would being as close to sea level as possible. Interestingly, if you have your meter measure you could use that to measure atmospheric pressure by seeing how far you could raise water in a column by suction. At standard atmospheric pressure you should be able to lift fresh water 10.3m.
Gravity is altogether too unreliable and should be abolished. Failing that, You could measure the local gravity by measuring how far a rock falls in a fixed time, say one second, and calculating back from that. If the rock is heavy enough we can ignore air resistance as the effect will be smaller than our measurement error.
Oh yeah! I should have remembered that actually, since I was just rewatching an episode of Connections 2 that mentions this height limit in the context of vacuum pump history (I think it's detailed more in season 1 but I forget which episode). So 10.3 m is another key measurement that you want at least one human to have memorized :]
This reads like a Douglas Adams quote and I love it.