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Imagine you're in deserted island. You will eventually need to know how much there is of something or how long is some thing.

Is there a way to get all main measurement units (kg, m, °C, m$^3$, etc.) somehow? I know water freezes at 0 and boils at 100. Also $G=9.8$ and $\pi=3.14159$. Also probably I could do something with pendulum, because I know $G$, but I wouldnt know time (from sunset to sunset 86400s?).

Are there some other valuable equations that could be used?

peep
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Ri Di
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  • i think your question belongs on https://worldbuilding.stackexchange.com/ – aaaaa says reinstate Monica Nov 30 '22 at 20:48
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    I don't think this question should have been closed. I believe you are asking "can I recreate modern measurement devices (rulers, scales, clocks, thermometers, etc) using only the definitions of the SI base units." The answer as of 2019 is Yes. If your island has unlimited ability to build scientific equipment (lasers, circuits, etc), you can figure out what 1 meter, 1 second, 1 kg are, etc, using only physical experiments and the equations of physics. – RC_23 Nov 30 '22 at 21:01
  • I agree with @RC_23 that this a reasonable question, perhaps phrased in a fanciful way. I'd summarize it as "what are the best measurement standards you can construct using only household items." I also wanted to add that this Q&A is perhaps relevant: https://physics.stackexchange.com/questions/615177/how-do-you-make-more-precise-instruments-while-only-using-less-precise-instrumen – Andrew Nov 30 '22 at 21:03
  • Prior to 2019, you would have been stuck, because you would not have access to the kilogram in Paris to decide what 1 kg is. Unless you made an approximation that 1 cubic cm of distilled water has a mass of exactly 1 gram. In which case your gram would be slightly different from the rest of the world's – RC_23 Nov 30 '22 at 21:04
  • Temporal considerations were addressed here. I feel like there was an equivalent query for the full set of SI units, but I'm not finding it yet – Kyle Kanos Nov 30 '22 at 21:05
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    Why try to reproduce SI units? Any units will do as long as they are reasonably reproduceable. Pick a small rock and call that mass “1 rock”. Then build a balance scale. Etc. It’s not like Nature gave us kilograms. We just made them up. – Ghoster Nov 30 '22 at 21:55
  • It is an interesting an fundamental question. I prefer the starting from scratch in the stone age. You can get close to the meter by measuring the distance from the equator to the North Pole using any arbitrary length, then calculate a correction for the length. (I think there are easier ways using geometry, the Sun, and shadows.) You can then define the second by dropping something 4.9 meters. With that I think you are well on the way. Answers could explore "smart" decisions like using water to define volume and mass, etc. – C. Towne Springer Nov 30 '22 at 23:01
  • If you arrived on the island wearing a wristwatch and knowing that the circumference of the earth is darned close to 40,000km, then you could use sticks in the sun to determine what is 1 meter, and then use that to arrive at 1kg of water, and 1 degree of temperature. It's all possible from that starting point. – foolishmuse Nov 30 '22 at 23:05
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    The Mysterious Island by Jules Vernes explores this subject in depth... although on the basis of scientific knowledge from some century-and-a-half ago. Still, could be useful for thinking it through. – Roger V. Dec 01 '22 at 08:10
  • Distance, Force and Time are easy to measure. Those are the basic units of the classical world. – JAlex Dec 01 '22 at 19:28
  • To be clear, do "reinvent...units" and "get...units" mean that you want to create artifacts of known SI unit length, mass, etc., and you want to make instruments that give the same numerical readings as given by instruments used in labs around the world today? As @RC_23 said, you can do that in principle, but you have to know the definitions of the SI units. You have to know that a meter is defined to be the distance light travels in 1/299 792 458 of a second. There is no physical reason why that number is what it is. It's arbitrary. It's just an accident of history. – Solomon Slow Dec 01 '22 at 20:46

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Short answer: yes

Longer answer: yes, but it's hard

Assuming, that you somehow have accces to any information you want, you can get there but it's a long way that a single person can't do all alone. At least, if you want defined precision.

Get roughly one second: let something dense fall from 4.9m (but for this we need to know how long ma meter is). Precisely get one second: get a lab full of gear to measure the frequency of the hyperfine transition frequency of the caesium 133 atom. 9 192 631 770 of those transitions is one second. But doing that is quite hard in a Lab (Curious Marc mad a wonderful Video explaining the Process) and even harder on an island.

1 metre: About the length of a long step... A bit more precise (as already mentioned in the comments): 1/10000000 of a meridian from aequator to pole (depending on the size of your island not as easy to do) Precise: get a Lab full of equipment to measure how far light travels in 1/299792458 of a second...

So creating any measurment unit is basically just like saying "I declare this, being a unit of that". Recreating the SI units is a huge task that took an army of scientists decades if not centuries to get to the stat we have today (and they are still looking for better ways).

So yes, recreating the SI units is possible but not alone on a remote island.

kruemi
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