# Which numeric base should I use for universal measurement unit prefixes? [closed]

I'm developing a story where Earth is obliterated by an asteroid and the small mars colony collapses into chaos shortly after. The last survivor enters a criogenic chamber for indefinite amount of time only to be awakened thousands of years later by alien archeologists from an intergalactic, multi-species, civilization.

I thought that i needed an universal measurement system and i thought about using SI anyway, with base measures that can derive all the other measures, but using Planck Units, being the smallest units possible, but it would result in unwieldly big numbers at the macro level.

And it's not as simple as determining prefixes for 10, 100, and 1000 units for example because it's not garanteed that every species will use base 10 numerical systems.

Humans stuck to base 10 probably because we have 10 fingers (even though some societies used other bases when it was advantageous, like base 60 for measuring angles because it could be divided into more whole numbers) and didn't want it to be an arbitrary decision but rather a logical one based on a constant natural quantity.

So I thought about using binary because it's the simplest number system, though it would result in unpractically big numbers nonetheless.

Do you have any better idea?

• Can you explain why you need a universal measurement system? Your survivor will need to learn the alien's language to live among them, and learning their measurement system is trivial compared to that. Commented Jul 12, 2022 at 17:49
• Our own current International System is perfectly universal. All fundamental units of measurement have absolute definitions which can be reproduced by anybody who needs to, be they Earthlings or extra-terrestrials. All the rest is simple unit conversion. I'm sure that any advanced civilization already has a working knowledge of multiplication. It is not more complicated than knowing that 2.5 inches is 6.35 centimeters. Commented Jul 12, 2022 at 18:08
• Without a criterion for the "best" answer, this is too open-ended and opinion-based. If I say you should use base 16 for the binary conversion and someone else says you should use base 12 because sometimes dividing by 3 is useful, how will you pick between them? Commented Jul 12, 2022 at 21:29
• Go full British Imperial and mix loads of different bases together. Why not? The intergalactic empire has thrived regardless. Hell, throw in some units that aren't even related to other units by integer quantities. Binary? Hell no, avoirdupois grains and bushels, hell yes.
– user86462
Commented Jul 12, 2022 at 23:06
• We use decimal because of the simplicity of only ten unique digits. An advanced civilization with a very large mental capacity could use, for instance, a 'centimal' system with base 100, and that uses 100 unique digits. centimal.org Commented Jul 13, 2022 at 3:12

## You have options

We prefer to measure things in meters rather than Planck lengths not because writing 1E35 or equivalent is so painful, it's because the meter is a familiar unit that is convenient because its size is meaningful in the everyday world. I can talk millimeters or kilometers and they still have everyday comprehension. Astronomers can the talk about A.U., light-years, parsecs and megaparsecs because its more convenient (due to tradition) for them and this does not cause a problem though none of these is a convenient factor of 10 worth of meters.

The problems with traditional Imperial units is that there are so many local variations of all various types of units and few of the are power of 10 based. When you start doing calculations and units have to be converted it makes the complication calculation - say you need to do some thermodynamic calculation involving heat and liquid fuels, so you need to plug in numbers of air density, fuel density, fuel energy density, enthalpy, etc. Now you have to mix units like BTUs, pounds per gallon, pounds per cubic foot, and it's just a mess (an engineer myself). As a student engineer in the US they made us do some problems in metric, some in Imperial units. We all hated the Imperial units problems because metric was just so much easier to work with.

Why memorize the acceleration of gravity as 32.174 ft/sec^2 instead of 9.806 m/sec^2 when you have to do a calculation involving miles you then have to memorize 5280 ft/mile (or look it up). In real engineering and scientific calculation there are at least a few, and often a dozen or more (sometimes many more) unit conversions needed. Just do the whole calculation in metric then convert the final answer to what unit is expected if the customer wants a different unit.

As another commented, a meter is roughly 10E35 Planck lengths.

You could define your base length unit (the Raposo) as exactly 1E36 Planck units, and then in everyday use you talk about Raposo, milliRaposo, kiloRaposo, etc.

Of course if decide to use base-16 then the Raposo would be defined as 16^30 Planck units instead (about 1.329E36) and everyone would be happy with this definition instead.

The original definition of the meter as 1/10000000 of the distance from equator to the pole is only a historical note today, yet we use the meter constantly. Had the standards committee have settled on the Raposo, we would happily use it today.

It should also be considered a non-issue, the aliens you talk to may well have their meter defined as 1/1000000 of the equatorial circumference of their planet so the fact that their basic length unit is equivalent to a different number of Planck lengths to the Raposo is not any barrier to communications. Or they will be using base 14, or whatever else makes a translation step required.

I'm sticking with meters for my engineering problems as long as it is the standard, and if I ever need the answer in terms of Planck lengths, I'll look up the conversion.

Why base 16 instead of base 2 - easier for humans to use - fewer digits to read/write. Much easier to read 17AC than 0001011110101111 even if you add formatting to the binary 0001 0111 1010 1111. Good luck converting world to hex.

So I thought about using binary because it's the simplest number system, though it would result in unpractically big numbers nonetheless.

Consider that if you are basing your unit system on Planck units (which is a reasonable thing for a galactic civilization to do), you need scientific notation anyway. For example, a meter is about 1e35 Planck lengths in base 10. That's already impractical to write out in full, so we use scientific notation, like I just did. In base 2, the exponent becomes a bit more than three times as large, so it's about 110. Still perfectly practical.

I'd say go with binary, using scientific notation. It's just unusual enough to look alien, while still being comprehensible, and is a logical choice.