Daily GUIDE-ance:

Saturday, February 15, 2014


I think that if we all had 12 fingers instead of ten, we’d be better off. I think we’d all be smarter, and possibly a little more patient and kind, more enlightened, more generous, and less gullible, more skeptical in the face of stupidity, and less close-minded, less hardhearted in the face of truth. I think we’d all be better able to relate to the world, and definitely better at math.

Ok so some of that was an exaggeration, maybe.

But go with me for a second on this.
Thought experiment time. Suppose for a minute that you woke up in a world with nothing but left handed gear. Left handed scissors, were all that existed. Mouse on the other side of the computer, gear shift on the other side of the drivers seat. (if you happen to be left handed, just pretend that the world is as it is, but everyone is lefthanded.) And pretend with me that handedness matters more than it does. Like pretend that everything-pencils, cups, jugs, doorknobs, toilet paper, light switches, forks- are all designed subtly wrong. Everything works, technically but awkwardly, and awkward in ways that you can never quite put your finger on. And also pretend with me that there is some moronic force out there preventing anyone from ever inventing a right handed version of anything.

How would that world be different than ours? It’d be a clumsier, less efficient world for sure. Would it also be a grouchier world? A less creative world? I think so. If every time a person with the seed of a great idea has to write it down on backwards paper, while looking in the mirror, with a backwards pencil… How many awesome innovations are going to die before they can get started, or at least seriously slowed down? More interesting- what about that awesome synergy that happens when multiple great ideas begin sparking each other into life? How much less often will that occur? And how often will bad, short sided ideas thrive and spread just because they are easier (in the short term) than the better solution that takes a bit more energy to think through- energy that most people are wasting trying to do everything with the wrong hand? Will this be a world with a crappy attention span? Will people waste hours arguing about meaningless things while real problems go ignored because they are fundamentally frustrated at a level they don’t understand…

Wait- did I just describe Facebook? Did I just describe real world economics? Did I just describe our actual world?
Is there actually something fundamental screwy, (like everything being made for the other hand) about the way we see and interact with the world?

What if, in that imaginary world, every so often, someone got fed up enough to actually invent something right handed, but then somehow it always got screwed up? So that many of your house hold appliances came standard with adaptors that made them left handed, but that actually worked better if you went to the trouble of unscrewing the adaptors and chucking them.

Think about that, and then consider this.
Here’s a really odd statement that I heard recently:

“There are lots of ways of measuring time, but a really bizarre base 60 system is nearly universal.”

How the heck did that happen?!!!

12 hours on the clock. 60 minutes to the hour. 60 seconds to the minute. 12 months to the year. Why has no one suggested a metric system for measuring time yet? Better question, why did we ever start dividing the days hours minutes, years etc, up that way? Why not into tenths? I mean, clearly, base 10 math is universal in human culture for the obvious reason that we all happen to have ten fingers. (One might argue that base 10 is so deeply inherent that its not just a human trait, but it’s a primate trait, or a mammalian or a vertebrate trait because, except of course that snakes don’t do math) So why 12 hours?

I think I know why.

Suppose you are a guy (or girl) living in a preliterate society, where the only math that is ever done is the useful, practical kind of math that goes into, problems like "I have 8 fish, how does that divide among 11 people" or "I have 6 rocks, how many more do I need to fill in this hole?" Suppose you and a friend in this society are building a wall, or a house, or going on a trip or something like that, and need to talk about how long it is going to take. It won't take all day maybe, you agree, but roughly-and you start reaching, naturally, for fractions- half a day. Or maybe it's less than that: a third of a day, or a fourth of a day. You are going to use 1/2, 1/3 and 1/4 alot: the first three fractions, the most useful, most common, and easiest to visualize of the fractions. 

Now this journey or job or whatever it is, is a repetitive task and you talk about it during the course of your work every single day of your lives. Its not hard to understand that before long you are going to invent words for these fractions.

It happens that 12 is the first number that conveniently divides by 2, 3 and 4. You wind up cutting the daytime into 12 sections, quite naturally, because you tend to think in these fractions and 12 is a very fraction friendly number. 10 isn’t. 10 divides cleanly by 2, but is not very good for understanding thirds or fourths. It allows for fifths which 12 does not, but 12 does allow for sixths which is just as good.

You also wind up with 12 inches in a foot for the same simple reasons. Also 12 pence to a shilling. We chop up the year into months similarly. Think of all the things we naturally count out in dozens- eggs, doughnuts, you name it. Someone even invented the word 'dozen' to describe this uniquely useful number. Notice that English doesn’t have any friendly nickname for the word ten. Or for seven, or nine, or six, or any other number besides twelve. Well, there's a 'score' I guess, for twenty, and a 'gross' which is twelve dozen- but the point is made.

What about minutes and seconds? Since you are not an idiot, you have already noticed that 12 is a factor of 60. 60 fits smoothly into base 12 reckoning, but notice also how many 12’s it takes to make 60. It's 5. The one simple fractions that 12 doesn’t divide easily into. Just as 12 is the first number that divides nicely by 2, 3 and 4, so 60 is the first number that divides nice by 2,3,4 AND 5.

So, when you want to talk about time more precisely than12 hours to a day, you get 60 minutes to an hour and then 60 seconds to a minute. 60 is also nice cause it fits clean(ish)ly into base ten.
For a similar reason you wind up with 360 degrees in a circle. '360?!?' one might ask 'Who was smoking what when they picked that arbitrary number?' It becomes a lot less arbitrary when you open your mathematical eyes and see that 360 divides crisply by 2,3,4,5,6,8,9,10,12,15,18 and 20.

While the humans are fitted with the ten fingers and are more or less doomed to think in base ten math, it seems that math itself would be more elegantly and cleanly described in base 12.

Groove on this for a minute:
The ten in Base 10 simply means (for those of you who don’t know) the number of symbols you use when counting. We use 10 symbols (0, 1,2,3,4,5,6,7,8,9) then, to describe the next number, we have to add a digit (10). It’s a bit of a 'jump-over-your-shadow' to realize that there is nothing particularly special about TEN, as a numbe,r at all.  You could do math just as well with only four symbols (like DNA) or two (like a computer or morse code), or 26 (like the alphabet) or with11, or 9 or 12 or whatever. Tens, twenties, hundreds, millions, and no more or less useful to round up or down too than any other number, once you get past the notation and into the actual numbers behind it.

What would we use for the 11th and 12th symbols if we decided to switch to base 12?
I like U for ten and J for 11 because: 1 they would both fit on existing digital led read outs, and 2: because J starts my name out and I think I deserve some of the credit and blame for the idea. So we'd count like so: 0,1,2,3,4,5,6,7,8,9,U,J. Twelve, of course, we would write out like this: 10. It’d be pronounced twelve. U would be pronouced 'ten' and J would be pronounced 'eleven'. The number 11 would be pronounced 'twelvety-one' (or maybe 'a dozen-one'- rolls off the tongue better, I think) and would mean thirteen.

Now this brings up a very very interesting point indeed.

Why do we have the word ‘eleven’? Shouldn't a base ten society pronounce 11 as‘one teen’ and this number (12) as ‘two-teen’ (or twain-teen or something like that)? Why do we have unique, non-derivative words for eleven and twelve but not for thirteen, fourteen and all the rest? 

Can you see that part of us desperately wants to work in base 12?! I had to invent the symbols U and J. But I didn’t need to invent names for them! We already HAVE the NAMES! It’s as if we took a base 12 verbal system and force mapped it on to a base 10 number system. Doesn’t that strike you as CRAZY? As in, literally, a bit mad? It’s just as weird as a world of right handed gadgets for right handed people, all with left handed adaptors tacked on.

Is it possible that the reason so many people dread math the way that others dread the dentist is because we are all left handed folk trying to get along in a right handed world!? Or rather that we are all base 12 people stuck in base 10 bodies?! Is it possible that we would all understand math a lot better if we were using a system in which 1/3 wasn’t a weird decimal that went on forever but was just 0 .4? Would gambling and credit card debit be more obviously a fools game if we all had better tools with which to think about math? Would we all be smarter shoppers if every division problem (5 lbs of meat at $12, is how much per pound) was easy to do in your head? Would the global economy shape up,  would people save for retirement, and budget etc; would fewer people go hungry if we could just do the freaking math?

What’s the take away from all this? I dunno that there is one. Do I think we should start a massive public campaign to change everything over to base 12? No. I think the change could happen and that with in a generation, base 10 would seem as weird and goofy as base 12 does now. But it’d be a lot of work, (although it’d be hilarious to throw a third system of measure into the mix with the English and metric systems, and I will get rich investing in a socket wrench company. Every poor sap of a mechanic will have to buy yet another set!) and all the benefits I have described are just a Saturday morning thought experiment. Someday, who knows, maybe we really will all convert over to base 12, but that sounds like long term scifi to me.

But maybe, next time you see 12 inches in a foot, you might do well to not pompously boast of the theoretical merits of the metric system, and your own personal superiority for preferring it, and instead spend some time understanding the practicality, reasoning and mathematics that went into the evolved, inherited units of measurement. And when the Earth is overthrown by a race of superior alien engineers, mathematicians, scientists and philosophers, and they all have six fingers on each hand (or three on each of their four tentacles?) remember that I told you so.