Distance or time for example. I look at my watch and I can see how long 1 second takes. I can look at a ruler and see how long 1 centimeter is. But how do they make rulers and watches? How do you define what a centimeter or a second is without just saying “1/10 of a decimeter” or “1/60 of a minute” or just pointing at another ruler/watch?
I guess time is easier since you can just reference recurring events (like moon phases for example) and then go down in scale from there until you get hours, minutes, seconds. But distance just seems completely arbitrary.
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It used to be that units were defined based on some physical examples.
Somewhere in the city hall there would be an object that weighed a pound and a rod that was foot long etc and authorities would make copies that weighed as much or where exactly that long and would check what merchants were selling against that.
That led to every kingdom and sometimes every large town having their own units. If you traveled around Europe you would find people something called pound in many places but it would always be a different value and they would divide it differently into different subunits. since trade meant traveling that was bit of a problem.
When they created the metric system they tried to get rid of most of the trouble.
One system that was the same everywhere.
Instead of some pound having 16 ounces and other 12 and others again 15 ounces all smaller and bigger units were power of 10.
They were all 10,100, 1000 or 1000 to some power as large as or a fraction of the main unit and you would use the same prefixes for all units.
Next they tried to define units as much as possible by the main units. A Watt is just a kilogram times a square meter divided by a second cubed for example.
You could even define some helper units like a liter being a decimeter cubed and a hectare a square 100 to the side, if you didn’t want to use cubic and square meters for that
That however left a small number of core units that you couldn’t define by reference to something else.
They tried to define those by reference to the planet itself. a second is defined by the length of the solar day and a meter was defined by reference to the circumference of the planet.
A day has 24 hours and each hour has 60 minute and each minute 60 seconds. That seems easy enough if you can look at the sun.
A meter was defined by taking the distance from equator to pole and dividing it into 10,000,000 meters. You can figure out the circumference of earth quite accurately even with limited tech.
Kilogram and kelvin were defined by the mass and the melting and boiling point of water.
1 kg of water weighs 1 liter and we divide the difference between melting and boiling point of water in 100 degrees and count kelvin from absolute zero.
Ampere was also defined with reference to tother metric units of distance and force.
None of those were really very good.
The world turns out to be not quite as uniformly spherical as thought and initial measurements were of and the length of the day varies a bit more than you would think.
Later these original definitions were refined in reference to natural constants.
We can define and measure time extremely accurately and the speed fo light is fixed, so we can define a meter by the speed of light and the amount of time it needs to travel a meter.
The kilogram was the hardest to pin down with natural constants and we used a physical object until quite recently. It is now defined with reference to the speed of light and the Planck constant.
Someone who had gone to the travel of memorizing all the definitions and the numbers involved could by transported to a different planet and recreate the metric system exactly as it is from ground up.
Since all other system still in use are now defined in reference to the metric units you could recreate them too if you memorized the legally defined conversion numbers.
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