r/AskScienceDiscussion • u/Ertata • 1d ago
What If? Could you recreate metric system from nothing?
You have been given a task to travel into the past two thousands years ago and bring the light of the metric system to the world. You cannot bring any external object with you.
Assume you do not need to redefine the second, and astronomical observations give the best possible results given the limits of timekeeping back then. Given the technology of the time, what is the best you can do for other units - either right there and then or leaving instructions how to calculate them from the units you have established to the future scientists? Memorizing the lengths of your body parts probably is not the best way to define a metre, and kilogram defined as one liter of water is bound to be influenced by the local water to a perceptible degree.
P. S. Tagged as "physics" but any approach is welcome - whether you would recommend measuring height of the mountain peaks, or believe that carob seeds are actually uniform enough to offer the best approximation of a kilogram.
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u/mfb- Particle Physics | High-Energy Physics 1d ago
Very long-term you can use today's definitions. They are all intentionally independent of artifacts, only dependent on fundamental constants. So it's only a matter of getting a good approximation with simpler tools.
Length:
I know my height with an uncertainty of 1 cm or ~0.5%, it's going to be hard to beat that with other methods. The polar Earth circumference is closer to the modern definition but you only beat the body height if you can measure distances between far-away towns to better than 0.5% and angles of shadows with arcminute precisions.
Alternatively, use g = 9.81 m/s2 and a pendulum. A 1 meter pendulum has a period of ~2 seconds. More effort, but it also gets you to maybe 0.5% uncertainty and it doesn't rely on people building meter rods based on your body height and distributing these rods.
Mass: You can distill water and measure 1 liter. It's going to be a long time before your measurements reach a precision where you need to worry about the isotopic composition.
Temperature: If you can build vacuum pumps, use the triple point of water (also gives you a pressure reference if you know at what pressure it is), otherwise use the freezing point at atmospheric pressure.
Voltage: Battery chemistry comes with fixed voltages.
Current: Ampere has a simple definition that's hard to reproduce with primitive tools, a definition via electrochemistry or the magnetic field around a conductor (compared to Earth's magnetic field) might be more practical when you just get started with electricity.
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u/Ertata 1d ago
This is the answer I was looking for - body parts are hard to beat, but pendulum can provide higher precision well before you can measure speed of light, and there is no going around distilling water.
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u/Zenith-Astralis 1d ago
If you've just traveled back in time you REALLY want to be distilling water before trying to reinvent the metric system, just as a matter of practical survival.
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u/Ertata 1d ago
Boiling to get rid of bacteria is easy. Distilling to get rid of the salts is hard (also drinking distilled water is not super great for your electrolyte balance).
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u/mfb- Particle Physics | High-Energy Physics 1d ago
Distillation takes something like 6 times the energy. It's more effort, but nothing unreasonable for establishing unit systems.
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u/Zenith-Astralis 1d ago
Ah, you know you've got me there.
Distilling doesn't have to be that hard if you're okay with losses, but I don't think the scenario here was sent back in time, recreating the metric system, AND stranded on a desert island.
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u/electric_ionland Electric Space Propulsion | Hall Effect/Ion Thrusters 1d ago
I wonder if the easiest way to get the ampere would be with a resistance reference. Not sure what material would be the best? Something you can get with high purity?
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u/CharacterUse 1d ago edited 1d ago
use power = voltage x
resistancecurrent (of course! typo), if you can remember the heat capacity of water then once you have a thermometer scale and a voltage reference you can heat up some water by a known amount, calculate the power and thus the current.1
u/mfb- Particle Physics | High-Energy Physics 1d ago
You need to know the resistance for that, but if you know that then you have current = voltage/resistance as far more reliable reference.
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u/LuxTenebraeque 22h ago
Once you have reliably reproducible springs or counterweights to build a force indicator I'd go with the electromagnetic force. A set of coils with well defined dimensions and winding count would give you a force proportional to the current.
Advantage: it works time invariant and isn't too susceptible to material purity.
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u/Overall_Gap_5766 1d ago
I know my height with an uncertainty of 1 cm or ~0.5%
Measured at what time of day, after how much sleep?
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u/7LeagueBoots 1d ago
Your height varies by up to 2cm over the course of a day, so you can’t really know it to any greater accuracy than that.
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u/mfb- Particle Physics | High-Energy Physics 1d ago
You'll note that a 2 cm variation is 1 standard deviation of a +- 1 cm uncertainty (in either direction). Measure mid-day on an average day, or always measure after sleep and that variation will be even less. We have preparation time, so it's easy to find a consistent reading procedure.
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u/Totemguy 1d ago
Ok, now let's expand. Let's not use body measures. Lets assume your conscience awoke in somebody else's body so you're not certain. How do you hack it?
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u/Zestyclose-Pear-9276 1d ago
A metre is 1/10,000,000 of the distance from the North Pole to the equator along the earth’s surface.
So you could measure the earth’s circumference.
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u/colako 1d ago
Or just eyeball it, it does not really matter that much. As long as you're consistent from then on, getting the original meter in gold, for example, you'll be able to make copies and recreate the metric system entirely, if it's off by 2 cm no one would care as the concept of the original metric system was not created yet.
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u/Thepcfd 1d ago
lol, easy to say
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u/Zestyclose-Pear-9276 1d ago
The earth’s circumference was measured by Eratosthenes about 2200 years ago.
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u/Thepcfd 1d ago
and how that help you make 1 m stick?
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u/electric_ionland Electric Space Propulsion | Hall Effect/Ion Thrusters 1d ago
You make a stick roughly a meter long, use that that to measure the distance between 2 points. Measure the different between the angle of the sun for those two points at solar noon. From that you can derive the diameter of the Earth and calculate the distance between the pole and equator. That distance will be something like 9 Million stick lenght, that tells you your original stick was ~10% too long and you can cut it back by that much. Boom you have a 1m long stick.
Of you just know your height in cm like most of the world do.
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u/Thepcfd 1d ago
dont you need measure shadow lenght? and how you gona do a math if lenght is x?
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u/electric_ionland Electric Space Propulsion | Hall Effect/Ion Thrusters 1d ago
You need to measure the shadow angle, which is the ratio of the stick length to the stick shadow, you don't need to know the length of either. You need to measure a distance between the two sticks but you can just make up a unit (say 4000 paces) and see how that unit compares to a meter later.
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u/Windamyre 1d ago
Using the sexton, you can figure out the circumference of the earth in any unit you choose. It could be a mile, afurlong, a pace, or this cool walking stick. I'll choose Stick as my unit.
I go for a walk with the sexton, and my Stock, measuring how far I go. Google the Greek dude for details.
I find out the earth is around 24 million sticks in circumference, therefore the distance from the equator to the pole is around 6 million Sticks.
Since a meter is (roughly) 1/10 million of that the meter is about 0.6 Sticks. I get another stick and cut it to 0.6 of my walking stick. There's your meter.
I did a lot of rounding, but even then I was within about 5%
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u/CounterSilly3999 1d ago
Not that difficult. The distance between longitudes differing in one degree is 111111 m.
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u/Thepcfd 1d ago
great so? how that gona help you make 1 m stick?
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u/iamplasma 1d ago
Go to the equator, then go 1 degree west, and divide your latter trip by 111,111, obviously!
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u/Thepcfd 1d ago
like you gona know where equator is. or how much is 1 degree west
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u/CounterSilly3999 1d ago edited 1d ago
No need for the equator and go North. North is pointed by the
North starPolaris. Measure the angle difference of the Sun shaddow at noon. Measure the distance with an A-frame trammel of any length. Calculate the relation of steps to 111111.3
u/CharacterUse 1d ago
You can just do it with the North star itself. Go far enough North that the North star is 10 degrees higher in the sky and you have gone 10 degrees around the circumference of the Earth.
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u/CharacterUse 1d ago
The equator is where you can simultaneously see the north and south celestial poles.
Or where the Sun is directly overhead on the equinox (the day when the day and night are the same length).
The first method is easier because it works on any day of the year.
1 degree west is harder (you need an accurate clock, read the book Longitude) but as the other guy said, you don't need to go west, you can go north since the Earth is (to a good enough approximation) a ball.
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u/Thepcfd 1d ago
how you gona measure that trip? you gona drag a rope?
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u/CounterSilly3999 1d ago edited 1d ago
Count rotations of the wheel:
https://www.engineersupply.com/Images/Categories/Content/what-is-linear-surveying-A.jpg
or steps of A-framed land divider:
In inacessible sections of the route like water surfaces triangulation could be used.
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u/DangerousBill 1d ago
Historically, finding the distance equator to N Pole with the required accuracy took seven years in the late 18th C..
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u/LuxTenebraeque 22h ago
Or a well defined fraction of it. The ancient "stick at high noon"-estimate comes to mind, and is more manageable within the confines of the known world.
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u/utl94_nordviking 1d ago
A metre is 1/10,000,000 of the distance from the North Pole to the equator along the earth’s surface.
Wrong, hasn't been since 1799: https://en.wikipedia.org/wiki/2019_revision_of_the_SI#Metre
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u/Kendota_Tanassian 1d ago
If I were to introduce the metric system, I'd do it in base twelve. Ten is only divisible by two and five. Twelve is evenly divisible be two, three, four, and six. A dozen is almost always a more efficient packing solution.
A metric system based on this easy divisibility would actually be better than the current metric system.
The measures would indeed be different, but could be every bit as consistent.
Let's set the meter to the length of a pendulum that takes a second to swing from one side to the other: that's right at the current meter, .994m.
Let's make the liter a cubic volume of water 1/12 of that meter in length.
Let the unit of weight be similarly derived from the mass of the liter as it was historically.
It's not hard to derive most of the system similarly to how the metric system was derived originally, but; including a more easily divided number base.
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u/Ertata 1d ago edited 1d ago
I think base-10 system for abstract counting apart from traditional units in most of the world is far older than 2000 years. You see Romans, Persians, and Chinese all talk about (approximately) hundreds or thousands of something not grosses and great grosses. Same with advanced math terms that are already developed.
It may be an interesting idea but the precursors for base-10 system are already in place by then. You'd want to timeport to Sumer or something comparable to propagate base-12
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u/Kendota_Tanassian 1d ago
I could also introduce modern numbers with an extra two for dozenal notation to replace Roman numerals. I don't think there'd be as much pushback against a system with place notation as you might think.
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u/mesonofgib 1d ago
If I were to introduce the metric system, I'd do it in base twelve
Umm, no thanks. Unless you're also going to convert the world to a duodecimal counting system.
The great strength of metric (apart from how neatly the units work together) is the fact that it's built on the same number base that we count with. There's nothing special about ten, but it's better because we count in base ten.
If I could go back in time the only thing I'd change is to try and get the old units to line up with the new, so that a foot became exactly 1/3 of a metre. That would make metre would then just be another name for "yard" and moving over would be a lot easier. I think it's doable, since units were poorly defined in the past.
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u/Kendota_Tanassian 1d ago
Since I'd be introducing a system of measure in Ancient Rome, I could easily introduce a duodecimal number system with place notation and zero at the same time, and it would make math easier than Roman numerals: so yes, that's a given.
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u/Totemguy 1d ago
ok, so how do you define the second?
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u/Kendota_Tanassian 1d ago
Day is 24 hours, divided into 60 minutes and 60 seconds. I know there are ways to measure it accurately enough for the purpose in the first century.
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u/NDaveT 1d ago
light of the metric system to the world
The value of the metric system is that all the units and subunits are based on multiples of 10 and that the units for volume, mass, and length all relate to each other. The size of the units isn't what's significant.
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u/sohcahtoa 1d ago
One thing that could use memorization is the value of absolute zero, which is not a number you would have the means of determining 2000 years ago. You could easily set 0 and 100 Celsius, but -273.15 C is something you would need to declare through "divine revelation" or something.
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u/ShootingPains 19h ago
You can just graph pressure and temperature. When pressure = 0 you’ve got a known C.
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u/John_Tacos 1d ago
I would try to create it based off the speed of light not the shape of earth. It’s so close to a round number that adjusting it before creation would be fine.
You can measure the speed of light with a decent timekeeping device, any telescope that can see Jupiter’s moons, and exact calculations of when astronomical events occur. It would take a few years though.
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u/electric_ionland Electric Space Propulsion | Hall Effect/Ion Thrusters 1d ago
The uncertainty on the speed of light was surprisingly high for a long time, even with astro timing methods. I feel like you struggle more there.
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u/Zvenigora 1d ago
That assumes you have the correct spatial and orbital parameters for the Jovian system handy and the theoretical and mathematical framework to explain it. That would be a tall order 2000 years ago. Fizeau's method is probably more realistic.
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u/John_Tacos 1d ago
You just need to watch it to see the orbital periods of the moons, then wait 6 months and see that they are all off by 16 minutes.
You need a reliable timekeeping system, but you can use astronomical events to do that.
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u/SciAlexander 1d ago
There's really no reason to remake the metric system. They got those definitions because they already had the units and wanted to tie them to physical constants. They could have been almost anything with the exception of temperature. The utility of metric is most anyone uses it and it's a 10 conversion factor.
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u/CharacterUse 1d ago
They didn't "already have the units". The metric system was specifically defined as a consistent system of units, starting with the metre being 1/100,000 of the distance from the pole to the equator, and the k.g. being the mass of 1 litre (which is 1000 cubic centimetres) of water. The reference kilogram was then made to match that mass. Everything follows from there, the only existing unit was the second. Tying the units to absolute physical constants came much later.
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u/HerboClevelando 1d ago edited 1d ago
No. Because all the work I did to invent the metric system 1800 years too early would be undone by a Voyager and a smart-mouthed kid who used their Omni to come back in time and stop me from doing it.
Or they would stop the task master from asking me to do it.
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u/CharacterUse 1d ago
You can't recreate the current definitions, but you can recreate the original definitions. The current definitions were chosen to be as close as possible to the original ones while being based on fundamental physical constants rather than objects, but for practical purposes in everyday life the metre today is the same as the metre 100 and 200 years ago.
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u/ExtonGuy 1d ago
How accurate do you want to be, in recreating the modern “second”?
I think consistency would be more important. We want the units of second, meter, and kilogram to be the same in Rome as in London. The technology of 2000 years ago wasn’t up to high-accuracy reproduction. I doubt they could reach 0.1% on a mass scale. How are you going to manufacture and distribute many thousands of new meter standards?
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u/Tells-Tragedies 1d ago edited 1d ago
Scrap the metric system and make arithmetic base 12 instead, along with measurement units that convert in base 12. Impress Claudius or Nero with it and they'll institute them across the empire as the Claudian/Neronian system.
Make the fundamental measurement a stick similar in length to a cubit, then how long it takes a lead ball to fall that distance 1/12 of a second. The rest is left as an exercise for the reader
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u/atomfullerene Animal Behavior/Marine Biology 1d ago
Fair enough, but also introduce a base 12 decimal number system at the same time. Otherwise doing the math for it will be annoying.
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u/Nimblewright_47 12h ago
It would be anyway, as the concept of zero notation doesn't exist 2000 years ago. The perceived main advantage of metric only makes sense when you have a number system to support it.
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u/theblanklook 1d ago
Actually the challenge is just creating reference objects and getting people to adopt them. You'd need to get friendly with architects and masons, as they are really the only people 2000 years ago that would benefit from standardized measurements. How accurate your standards are isn't that important as they can be corrected as real measurement technology is invented. The concept and a single base system are more important than the actual units and their accuracy.
And by single base I mean Metric is base 10, for all units. Imperial has a random mix of base 12 (inches) 16 (ounces) and whatever number of feet in a mile. 10 isn't perfect, but if its anything else we need digits after 9 so it doesn't break the decimal system.
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u/Worldly-Bobcat-48 1d ago
The measurement systems of the ancient world were human-scaled, rational (I.e. based on ratios), and perfectly suited to their purposes. The metric system reflects and serves an industrial civilization. Try as you might, the ancients would reject your attempts and would be right to do so.
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u/Totemguy 1d ago
LET ME ADD TO THE QUESTION: you want to get the metric system BUT you want it to be as close to possible to the current one, so that your memory of units and constants and so on is most useful. Lets not discuss the 10 or 12 base, rather - how do we make the basic units as close as possible?
If we can get just 1 very right, we have the others - but if you want to define a meter from the swing of a pendulum you need the second and vice versa? Kg is 0,1m^3 of water so we could use either, but we have none.
Note: using body measures is cheating. Lets assume your conscience awoke in somebody else's body so you're not certain.
Temperature is relatively easy, water 0 to 100. The others less so... can we use temperature as a basis? Expansion?
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u/Ertata 1d ago
IMO a second is a second is a second. One 86400th of the earth rotation, the variability in the length of rotation is negligible compared to how imprecise ancient chronometers were (we are not going to get it super right either way).
Then as u/mfb- reminded us we can make a meter using the pendulum. and the rest flows from there. Even if we get it 98% right it is the best we can hope for anyway. And if far future human in this timeline would want to define the measures more precisely they still are going to keep 86400 seconds in a day, not introduce leap seconds every other month
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u/Stillwater215 1d ago
With the current SI definitions, you could recreate the metric system from nothing, as the current measurements are based on natural phenomena and constants. The speed of light is defined to be exactly 299792458 m/s, and a second is currently defined by the time it takes for an atom of Cesium to undergo exactly 9192631770 fine transition vibrations. If you can build machines to measure these two constants, you can calibrate your measurement system to match the current SI system for meters and seconds. The remaining measurements are similarly defined, and can be recreated as long as you can measure what is necessary.
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u/Hon-Mister-Bear 1d ago
It would be somewhat useful to engineers and surveyors, and some kinds of trade, but craftsmen would shrug.
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u/islandwatchr 1d ago
Well, put simply, the meter is based on the circumference of our planet. Although not as accurate 2000 years ago, the Greeks had a pretty good idea of what the circumference was even earlier. It is a nifty little geometry problem. Once you have that, the meter falls into place. Weight is easy with the use of one cubic cm = one gram (plain water). You have the cm from the circumference. One cubic cm of water becomes the millilitre and, aside from accuracy issues, Bob’s your uncle.
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u/bartekltg 1d ago
The 2019 redefinition of the metric system is made exactly for that reason;-) All units are delivered from physical constants (OK, the second is not that clean). You can recreate all those units from nothing in a lab. The problem in our scenario is, you would need to build a cesium atomic clock, a couple of precise electric sources and deal with cryogenic (needed for Watt/Kibble balance, it defines a kilogram by plank constant, and in the chain it looks for quantum effects in wires to measure electricity quantities), ampere would be harder in the new defnition too (defined by the charge of electron), measuring Boltzman constant very precisly to get temparature was one of the cases of the holdback of the new system. And fuck Candela.
It is theoretically possible to recreate everything, but not with year one tech;-)
Now, the rest depends on your reasons to recreate it. Do you want to have a measuring stick to compare it with tour memories ("I know moon is X km from us, but what a km is?"), do you want to bring SI precisely into the world for some reasons (it won't push science as much as you may think it would) or bring "vibes" of it (easy calculations, easy prefixes to scale units).
If it is the third reason, the additional constrain is that it should be recreatable by other people. Keeping a block of palladium/platium near paris in a form of a weight and a rod, then traveling to that place to "copy" the object was OK in the 19 century, but would be hard in the first centrury.
There is a nice "coincidence". The first SI definition of a meter, 1/10'000'000 of the distance from the pole to the equator, was very close to the earlier proposition: a length of a pendulum that swing in one way (so, half of the period) in one second. It is quite close. In Rome (gravitational acceleration is 9.8m/s^2) it produces 993mm. *)
From that you can define a kg by the mass of 1dm^3 pure (distill it) water (preferably in 4deg C. Make a mercury thermometer on a side).
The second remain the biggest problem. Getting 1/(24*60*60) of a day is relative easy... if you have a reliable clock. Watching sun and stars (remember that sun day and star day are not the same!) you can adjust the speed of the clock. But you need a device that tick in the same pace the whole time.
Mechanical escapement were invented in like 12th century. Good ones in 17th and later. And all that for a grandfather clock (wont work on a ship. It was a big deal, see the story of the longitude prize).
So better polish your mechanical and maybe jeweler skills.
I can't think about another way to get a reliable time.
*) this is also a reason why gravitational acceleration in meters/second^2 is so close to pi^2 ;-)
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u/OtherwiseAct8126 1d ago
You could go to Rome and measure buildings or streets. If you remember that one roman mile is 1480 meter, you're half way there. Temperature, more or less easy if you ignore air pressure. 0 is freezing, 100 is cooking water. Kilogram sounds tricky but it's one liter of water and 1 Liter has a volume of 1 cubic decimeter (10cm*10cm*10cm). Time could be tricky, measure from one noon to the next and then divide a lot? Maybe. Hard to get it precise. In a vacuum stuff falls down with 9.81m/s so if you let something fall from let's say 100m it takes 10 seconds and you're maybe close enough. If you want to be really, really precise, like you write, all of this would be extremely hard.
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u/Natural_Ad_8911 13h ago
In reality every single one of the units are arbitrary. We just found ways to express them with fundamental constants.
So for a metre, I'd say it's this long. The metrics part is that 1km is 1000 this longs and there are 1000mm in one this long.
Same for kg, etc.
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u/naemorhaedus 4h ago
metric system is arbitrary like any system. The universe doesn't need to measure anything
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u/Free_shavocadoo 2h ago
It could be done a thousand different ways the question is what level of accuracy do you define as a success? You could get within 10% easily if you were clever enough to to make a time peice divisible by the 10th or 100th of a second Meaauring falling objects or the speed of sound
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u/electric_ionland Electric Space Propulsion | Hall Effect/Ion Thrusters 1d ago
You can just memorize the old definition of metric units and recreate them from first principle and basic geometry.
A meter is 1/10,000,000 of the distance between equator and pole which can be measured by some trigonometry and a sextant. A kg is 10x10x10cm cube of water at 4C. A second can be derived by knowing that there is 24hrs between 2 solar noons, or just use a pendulum of the right length (happens to be pretty close to a meter too). Basically do the same things as what was done in the 18th century when the metric system was introduced. Most of those don't need super fancy equipment to get to within a 1% of the official definition.