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In all likelihood, there is no forcing one society to adopt the other's system, instead, people would likely adopt a local market approach to measurements. Let's say you are on Earth building spaceship parts that will be used to make ships on Farawaynos, you manufacture to the other society's system of measurements. If they want to sell parts to Earth, they need to manufacture to the metric system of measurements. This is basically the same way that we do things now with the Metric and Imperial systems.

The only way you will probably see a standardisation is if one society is much more influential than the other. If Humans have 20 billion people across 5 planets and the Farawayans have 20 trillion people across thousands of planets, the humans would likely be strong-armed into accepting that the alien societies unit of measurement is more reasonable for standardisation. Or, if one society conquered the other, you'd likely see the loser's system be replaced.

Another option would be for the societies to agree on a new "interstellar" standard that is different than both nation's customary systems. If we use a base-10 metric derived from our own planetary motions and properties of water, and they use a base-6 metric derived from their planetary motions and properties of methane, we might agree that both systems have their flaws and adopt a new base-16 standard derived from the properties of our galaxy's central black hole and hydrogen. Chances are, both societies would be slow to adopt this as THE standard, but if all interplanetary trade becomes based on this, eventually, societies would shift to accept it as the more useful metric.

• The way the US is really metric. There are the scientific (and legal) units and then there are customary units which are defined in terms of the scientific units.


• The common scientific units are based on powers of two and naturally-occuring constants.

This isn't as hard as it might seem

It would be harder to work out the semiotics than the conversion and/or adoption. After that it's just software. Why?

Because a substantial amount of science involves relationships. For example, the value of 𝜋 is unitless (3.14159...) That relationship would be the same no matter what mathematical base was used, or what standard of length, or even what the alien's definition of base units like meters or "seconds" (base unit of time) are.

Consequently, once you've figured out how to represent 𝜋 in both languages (and every other unitless relationship number, like the proton-to-electron mass ratio or the Planck constant, (see more)), everything else is basically algebra.¹

As for whose version of the math/semiotics wins out, that has more to do with who's the bigger gorilla. If we have an empire of ten worlds and they have an empire of 100, the odds are very good that their systems will win out. In other words, we may use our systems internally, but anything that touches both species will also have their system.

Like o.m. said, it's like the U.S. being metric. We hate it, but every can of soda has both ounces and liters printed on the can. Eventually a generation will be born who wonders what an ounce is.... But not today. 😆

_{¹ Or calculus. It's either going to be high-school trivial or PhD hard ... but it'll still just be an issue of software.}

They might simply choose to use Planck units, which are all ratios of various physical constants of nature (like the speed of light and planck's constant), which implies that if you express the constants of physics in these units, they all have a numerical value of 1--for example, in these units the speed of light is 1 (planck length)/(planck time), and Planck's constant is 1 (planck mass)*(planck length^2)/(planck time).

The disadvantage of these units is that ordinary human-scale phenomena will have huge values, for example 10^35 planck lengths is about 1.6 meters and 10^44 planck times is about 5.4 seconds, but you could just invent special names for large multiples, for example 1 YGlengths could be defined as 10^33 plank lengths (where Y and G stand for yotta and giga) which would be about 1.6 centimeters, and 1 YZtimes (where Y and Z stand for yotta and zetta) could be defined as 10^45 planck times or about 54 seconds.

Humans have already solved this problem.

There are many useful universal numbers that can be used. mostly atomic phenomenon such as the mass of X atoms of a particular isotope or natural atomic oscillation. You may want to checkout the current definitions of all SI units. which are defined in such as way as to make them universal. That is they are based on universal constants like the transition states of cesium atoms.

Second: The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Meter: The distance travelled by light in vacuum in
1/299792458 second.

Kilogram: The kilogram is defined by setting the Planck constant h exactly to 6.62607015×10³⁴ J⋅s (J = kg⋅m²⋅s²), given the definitions of the metre and the second.

Mole:The amount of substance of exactly 6.02214076×10²³ elementary entities.

Kelvin: fixed numerical value of the Boltzmann constant k to 1.380649×10²³ J/K, (J = kg⋅m²/s²), given the definition of the kilogram, the metre and the second.

Ampere:The flow of 1/1.602176634×10¹⁹
times the elementary charge e per second.

Candela: The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×10¹⁴ hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

The individual numbers can be derived by any civilization you can communicate with. they might not have them but as long as you can communicate with them they can match them and use them as common unit of measure. Alternatively the two species can come up with a mutual set of units defined in similiar ways.