Fantastic Measurement Systems: Some Notes

Copied and pasted from the G+ comment thread on this trope-a-day, as I deem it worth repeating for other interested parties:

Jasper Janssen:

I assume there is lots of vocal arguing about why don’t you simply adopt a straight duodecimal system, get with the program man, it isn’t 5145 any more!

Actually… no, not really.

This all ties back to one of the fundamental psychological differences between Homo sapiens and Eldrae alathis . Namely, that our brains are literally hard-wired to generate error signals when we see other human-shaped things disagreeing with us. We’re programmed right down at the meat level to tell other people that They’re Doing It Wrong, or to suffer mental stress when other people Tell Us That We’re Doing It Wrong.

The eldrae don’t have that innately, and while they have a scientific understanding that some minds can be wired that way, they don’t really grok the urge.

The powers-of-12 system was invented by the Fellowship of Natural Philosophy (the largest and oldest of the scientific branches) because it was useful for the sort of things they do. But it never occurred to them that they ought to go out and tell everyone else that they were doing it wrong. Sure, they published it for anyone who wanted to use it to use, but that’s about as far as it went.

And even if they had , the Edifacient Sodality of Bakers and Pastrywrights (say), would just have come back to them with, “Okay, so, show me how this will lead to better pie?” As far as they’re concerned, they’ve got a perfectly cromulent system of units already, optimized over literally hundreds if not thousands of years for the purpose of helping them turn assorted ingredients into delicious pastry. They’re smart, rational people; they’ll listen to practical arguments for adopting it, but they don’t feel any urge to change just for the sake of it, because they’re Doing It Wrong, or because there’s a One Right Way to do it, and were you to make that argument to them, they’d still be waiting for your point after you were done.

(As a not unrelated psychological quirk, they find the parallel existence of multiple ways of doing things natural in a way that we don’t. Even the most rabid individualist running on human hardware has to silence or otherwise deal with that little nagging inner voice that wants to conform with the group. We define ourselves, as humans, largely by reference to other people.

They… really don’t. The dominant inner voices an eldrae is listening to concern themselves with devotion to ideals – which they call estxijir – and to their brilliant, shining, unattainably perfect Platonic ideal of themselves – and that one’s valxijir. Notions, on the other hand, like conformity or relative status games don’t form part of their psychology, and even social identity per se barely gets a look in. Those are concepts both alien and, for that matter, deeply creepifying.

All of which alien minds are alien foo is background to say that the competitive-standards, This Is The Way Of Progress, All Right-Thinking People silent arguments for, say, metrication bounce right off people who see measurement systems only as tools to be used to help them immanentize their awesome, when relevant and best for the task at hand, and not as signifiers of anything at all.)

So, practical arguments (“Makes better pastry! For Great Excellence!”) work. (And, indeed, there are branches which advocate various systems for various things on those grounds.)

Coordination / specific consistency arguments work – everyone understands why the Spaceflight Initiative declares that everyone contracted onto one of their projects will compute trajectories, etc., in the powers-of-12 system and otherwise use Lorith-Llyn Engineering Units.

And some de facto standards exist – when Llyn Standard Manufacturing, ICC, declares that they’re calibrating all their components in Lorith-Llyn Engineering Units, the majority follows suit because it’s just common sense to be compatible with the 800-pound gorilla in the field.

But absent something like that, no traction is there to be had.

Jasper Janssen:

I did say duodecimal, not decimal — nothing wrong with factors of twelve per se. What bothers me about the outlined system is the spurious factor of 2 you introduce by using a 24 there. That makes calculations needlessly difficult when they have to cross that boundary, which is particularly annoying if you have a (monetary) system that goes from macro to micro with all nice and regular duodecimal factors and that one factor of 2 in there.

And conceptually, it also makes it not a power of twelve system, which itches my brain.

Oh, just the money , right. I thought you were talking about weights and measures systems in general (which, aside from the strict powers-of-12 system used for scientific purposes, includes all manner of irregular factors around the same base units).

Well, that started out that way for much the same reason that many non-decimal currencies here did – when setting up the esteyn way, way, way, way, way back in history, it turned out that 1/144th of it was an inconveniently large penny-equivalent unit. 1/288th, on the other hand, was just right , and in practice, since most people just had to worry about the selenis being 1/24th of a lumenis most of the time (an esteyn being a big chunk’o’money), that’s why the difference is where it is.

(There’s also a factor of 6 further up – 6 esteyn = 1 arien – but an arien is almost purely money-of-account used under certain specialized circumstances, like guineas, so.)

Why didn’t they duodecimalize it later?  Well, three reasons:

(a) The size factor of the penny-equivalent unit still applied. Es. 1/144 was too large. Es 1/1728 was way too small. And just as in the weights-and-measures systems that are focused on non-scientific functions, people want to use units scaled to be optimal for their common usage.

It’s not optimal from the point of view of centralizing standardization, etc., or mathematical purism, but – since the people who run the monetary system are the people who have money-focused estxijir and they think it’s optimal from the point of view of how people actually use their cashy money – fitness for purpose kicks both of those in the face and does it its way;

(b) I’m actually pretty sure the “easy calculation” aspect never came up in their context, simply because their society – for a variety of reasons too lengthy to go into in this comment: genetic, demographic, economic, religious – achieved widespread literacy and numeracy both somewhere around the early Bronze Age – so by the time people might have been mooting the idea of duodecimalization, it simply wouldn’t have occurred to anyone that handling these irregular factors wasn’t already about as don’t-consciously-think-about-it mathematically trivial as it could get;

and (c), it being a free society and all, anyone who found it useful (some accountants, the Guild of Numbers, difference engine Stannic cogitator programmers, etc.) was perfectly at liberty to write currency amounts as a single number of esteyn with a duodecimal point in it if they wanted to. And thus, they did.

And as per (b) above, people generally considered it intuitively obvious that something priced as four-and-ten cost Es. 0.46.

Trope-a-Day: Fantastic Measurement System

Fantastic Measurement System: Well, yes.  Both for money (the esteyn, to match base-12 Imperial mathematics, uses the 288-system: 12 selenis to the lumenis, 24 lumenis to the esteyn, and also goes down so far as to include special units for micropayments and up so far as to include units convenient for major bank transfers – particularly important since there’s not a standardized international clearing mechanism, making correspondent banks, letters of credit and currency transfers matters of some importance);

And for everything else.  The time measurement system has already been mentioned (see Alternative Calendar), but of course, there’s also the Imperial System (sic) of general measurement, notable for basing its core units on the Planck units, and permitting them to be scaled up and down using the equivalent of SI prefixes, or their base-12 equivalents, for scientific purposes, but also including traditional units (after the fashion of the traditional US or Imperial systems) based off the same core units for convenience in non-scientific situations, including a variety of craft- or task-based units which bake sensible basic assumptions, safety margins, etc. right into the measurement system.

If this sounds complicated, it is; their point of view on that amounts to, essentially, “cope”.