How could SI units be derived from scratch without the use of modern technology?
How could SI units be derived from scratch without the use of modern technology?
Think "you wake up in the woods naked," Dr. Stone-style tech reset. How could humans acquire a 1-gram weight, a centimeter ruler, an HH:MM:SS timekeeping device, etc. starting with natural resources?
My best guess was something involving calibrating a mercury thermometer (after spending years developing glassblowing and finding mercury, lol) using boiling water at sea level to mark 100 ° C and then maybe Fahrenheit's dumb ice ammonium chloride brine to mark -17.7778 ° C, then figuring out how far apart they should be in millimeters on the thermometer (er, somehow). I can already think of several confounding variables with that though, most notably atmospheric pressure.
I feel like the most important thing to get would be a length measurement since you can then get a 1 gram mass from a cubic centimeter of distilled water.
That's as far as I got with this thought experiment before deciding to ask the internet. I actually asked on Reddit a while back but never got any responses.
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!
Thanks for a thought provoking question.
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.
The metre was originally defined in 1791 (...) as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's circumference is approximately 40000 km.
https://en.m.wikipedia.org/wiki/MetreThe kilogram was originally defined in 1795 during the French Revolution as the mass of one litre (1/1000 m³) of water.
https://en.m.wikipedia.org/wiki/Kilogram... and the last major SI unit is the second which of course you know is (originally was) 1/86400 day.
Please notice about the Celsius scale : the second reference point isn't a mixture of ice and salt but rather pure water freezing point.
Now how can we as naked humans develop technology to figure this out is something of historical proportion, that's a quite amazing story !
Your definition of the meter leaves out the most interesting part. Yes, it was 1,000, 000th the distance of the equator to the North Pole, but how far is that? That wasn't known accurately in the 18th Century. So, two Frenchmen, Delambre and Mechain conducted the longest meridian survey every attempted. They also did so while half of Europe was at war with one another. It was an amazingly dangerous endeavor. There is also significant evidence they totally flubbed and hand-waived their results. So, although their science ended up being questioned, the process and method was accepted and the Meter was defined.
Re Celsius 0 °: the reason I thought perhaps Fahrenheit's Weird Brine might be a more absolute thing to take de novo temperature from was because I don't actually know the answer to "how can you ensure water is exactly freezing temperature?" If it's solid ice it could be colder, if it's liquid it's probably warmer, and even if it's a bucket of cold distilled water with distilled water ice in it, isn't it still likely hotter than 0 ° C? I feel like there's probably something involving equilibrium between solid and liquid water that would be difficult to sus out
Not that Weird Brine is any better really 🤦♀️
if you have both liquid and solid water at equilibrium then you have zero degrees Celsius. Pressure has minimal effects ...at plus or minus 0.5 atmosphere. of course if you go to a hundred or a thousand atmosphere then there is an effect of pressure.
Small pieces of ice will equilibrate their temperature faster in water.
Surface tension has minimal effect on melting temperature unless you go to extremely small pieces of ice meaning less than one micron, ...which is not possible to achieve anyway because such small ice pellet with fuse rapidly to form larger ones.
Guess what? You get to reinvent modern metrology!
I'd start with making a surface plate using Whitworth's 3 plate method.
Next, make a perfectly square block, pick two opposing faces of that block, that's your unit of length. Use your surface plate to make more and measure things against it.
If you're really smart you would have made that block out of some sort of homogeneous material like steel and made it a perfect cube, not just perfectly square. That's going to be your prototype weight.
Temperature is the easy one, make a thermometer. Mark where the liquid is at based on two different repeatability phenomenons. Subdivide as desired. Someone will come up with a "better" way later.
Time is another easy one, just build a pendulum and start counting.
That sould get you through most of the neo-industrial revolution.
The rest of the base units will come later for now focus on building a lathe.
https://www.howtoinventeverything.com/
This book was interesting.
Are you asking about how you reinvent the exact same meter? Well that won't happen. Our units were arbitrary, useful, widely adopted, and then rigorously defined.
The book walks you through it all. You can don't need to redo civilization exactly the same (the author even suggests some very important things to invent differently, especially in better orders)
It's one of my favorite books of all time 😁 to the point where I own a hardback of it despite being staunchly pro-just-read-books-on-my-phone
IIRC they actually printed a centimeter ruler in the back of the book as an answer to this specific problem.
Start with your finger, 4 fingers to a palm, 4 palm to a bar. So 16 fingers. Give each finger a unique name and symbol.
Then make a perfect cube of that size, fill with alcohol and that weights 256 bwu, base weight unit.
1024 bars, or 2048 if you're one of those crazzy bastards from up north, is a mile now.
Skip a head a few century and niw wr entet the computer age with a hexdecimal counting system.
Skip a head a few century and niw wr entet the computer age with a hexdecimal counting system.
And a new language too!
I hate my phone keyboard
SI is great, but if you reset everything (and lose all tech and most of knowledge), just create a new system. Embrace what makes SI great (easy conversions and a the nature-based properties) and do it over.
For length, use Hydrogen line when you advance your society enough. It's more universal than using 🌎 as a 📏.
10 000 km from the pole to the equator?
I think it would be a huge amount of work to get something more accurate than my guess.
I don't know, if America sends us all back into the stone age with nukes I think I'll also agree to use the imperial system.
I've heard of this book which you may find interesting
ah, Freedom Units...
Added the book to my list :]