Once you can get a good reference for one unit ypu can start to use it to determine the others. None of these are going to be perfectly accurate, but they should be good enough for day-to-day use.
I’d start with time. We’re going to make a sundial. To do this you need to make a drawing compass and some flat ground with plenty of sun. Find a v-shaped stick, or lash a couple together so you can scribe circles in the ground. Start by making one circle around a well marked centre point, then using the same compass, draw another circle centred on the edge of the first. Draw two more circles where the second crosses the first, and two more where those cross it. You should now have a central circle with the perimeter divided into six segments (this is the same technique for drawing a hexagon inside a circle). Put another stick upright in the centre and you have a sundial with 2 hour segments. You can bisect the lines between each of the points to get 1 hour segments, and if it’s big enough, busect again to get 30 minute segments. We’ll get shorter time measurements later.
The next unit to find is the meter. A one meter pendulum completes a swing from one side to the other every second. In order to minimise the effect of air resistance, find a heavy, but not too large rock and tie it to the end of a rope. Measure out approximately out meter of rope (measured from the centre of the rock) and tie it to a solid branch. Next is the tedious bit. Set it swinging as the sundial hits one of it’s marks and count the number of swings until the sundial hits the next mark. You should get 3600 per hour. If you get too many, lengthen the rope and try again, if you get too few, shorten it. Once you have the right number you have both your meter measure and your one second.
You can get a metric tonne, and thereafter a kilogram, by building a balance weigh beam, and a cube shaped container that is exactly one metre on a side. Attach the container to obe side of the beam, and a second container exactly the same distance away from the pivot on the other side. Add rocks to the second container until it balances with the empty first containor. Now fill the first with cold water. Add more weight to the second until it balances again. The additional weight should be exactly one metric tonne. By careful geometry you could reduce tge size of your first container to make this easier, but keeping it big and then dividing the result minimises measurement errors.
Temperature is harder to measure, but you can build a thermometer with any liquid that changes density with temperature. Even water works, although adding alcohol helps I believe. So, while you’re finding the meter, get some fruit and let it ferment. Use the resulting liquid in your thermometer. If you don’t have a glass tube, and can’t make one, use an opaque one, and float a light reed or similar on the liquid, with the end sticking out of the top. Calibrate it with boiling water for 100c, and, assuming a reasonable climate, wrap it against your body for a goid long while to get 37c. If you have accesd to ice, letting it just melt gives you 0c. Dividing the marks you get like this would involve some careful geometric construction, but should yield a usable thermometer. Converting that to Kelvin, as the SI unit, involves adding 273.16.
The ampere and candela are probably of less use in this situation, and are going to be tricky to measure. By assuming gravity is 9.81m/s^2 and using the kilogram you can derive the Newton. From that you have the Joule, and one Joule per second is one Watt. Assuming you build a generator, you can derive the Ampere from it’s older definition relating to the force, in Newtons, between two parallel wires. From there the volt can be derived.
Beyond that, I think you should just hope for rescue!
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.
By careful geometry you could reduce tge size of your first container to make this easier, but keeping it big and then dividing the result minimises measurement errors.
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.
If you have accesd to ice, letting it just melt gives you 0c.
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
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.
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.
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
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.
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.
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 :]
Gravity is altogether too unreliable and should be abolished.
This reads like a Douglas Adams quote and I love it.