Algebra books seem to believe that base 12 is a good idea for humans to use. This is only in the case of that pianist in GATTACA that has 12 fingers. We have a base 10 system because we have 10 fingers. (This is why you’re allowed to count and do arithmetic on your hands.)

Regardless of the general uselessness of a base 12 system, working with it is a good exercise in patience, alternate thinking and puzzle solving.

Here’s how to “count” in base 12:

But what if you want to get higher than you can count? For instance, what if some algebra book asks, “What’s after EE0_{12}?”

Now check out how to switch a base 10 number (which is our way) into a base 12 number:

Want more? Check out how to add and multiply in the next post.

*Thanks to Kellie for the inspiration for this post.*

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This is a very healthy interest in base 12. If you are curious, there is an addition and multiplication table in bases 2-36 and lots of information on conversion between the bases.

Oh, Alexander! How cool is this: http://www.cut-the-knot.org/blue/SysTable.shtml

Thanks so much!

Why do you call the base 12 system generally useless. 12 hour clock, 60 min (5×12) per hour, 12 in per foot, 36 (3×12) per yard, 12 months per year, 12 musical notes, less infinite numbers, etc.

Thanks for your comment, Bill. Our time and some other units have 12 in them, but they aren’t true base 12.

A base 12 time system would have 12 (not 24) hours, and 144 minutes, etc.

But it is fun to play with!

It seems more practical to me in some aspects. They might not BE base 12, but they are multiples of 12 which makes things more logical to me. I don’t think we will be making any switch over to base 12 though haha. It is quite fun, and useful. Not only that but it encourages creative thinking. I would love to see a future generation that is comfortable using various bases from a young age, I think that would be phenomenal!

The rest of the world uses the metric system. A 10 base system. Only the US and the UK use the imperial system.

Thanks for stopping by, Ukiah.

The metric system and the imperial system both use numbers from a base 10 system. The metric system also structures all its units to be a power of ten more or less than each of the other units in a given “measurement category.” So yes, the metric system is often called a base ten system.

There’s no unique multiplier for the various units in the imperial system.

“Metric system” is radix based system not a base 10 system. The “system international” is the current agreed upon common unit system, it is base ten. “system international” was not the first under the “metric system” nor will it be the last.

You are an idiot detached from nature and even human nature if you think that base 10 is superior or even useful and that dozenal is not. Almost all native useful, non-currency, measures are dozenal is nature and easy for grouping, imagining, subitizing, and working with both in your mind and your fingers. you can quite easily count to 144 decimal on your fingers using a dozenal system.

I’m not sure if name-calling is appropriate, parjo, here or in any learning situation. Especially since “easy” is in the eye of the beholder.

Thanks for your thoughts, though, and I’m glad to know that you find base 12 natural and appealing.

ERROR IN POST: you can’t do base 10 math on one hand, you can only go up to base 5 if your counting only fingers, like you say (if you need it any more plainly: you only have five fingers on one hand). On the other hand you can go up to 1 dozen (base 12) on one hand, because you have 12 finger bones on your four fingers and use the thumb as a pointer.

don’t give people false information just because your ignorant.

Retraction: he says “hands” not “hand”, oh well. Still its incorrect that we can’t do math on our hands with other bases. Other cultures used other bases for the reason of “that’s how many we have on our hands”, not just base Ten.

It is indeed not confirmed that we do base 10 because of our fingers. But I challenge you to come up with a better answer.

It is generally agreed on that it IS because of the fingers: http://math.stackexchange.com/questions/8734/why-have-we-chosen-our-number-system-to-be-decimal-base-10 and http://ideonexus.com/2008/07/08/why-a-base-10-number-system/

“And (nearly) every civilization has used base-ten math probably for the simple reason that we have ten fingers.” from http://www.purplemath.com/modules/numbbase.htm

It should be noted that there is in no way a consensus at the math.stackexchange link. I think the better argument comes from one of the posters that suggested base 10 came from those with the biggest sticks.

Funny. Big sticks create power of all sorts. ðŸ™‚

I was very surprised to read your comment about the “general uselessness” of a base 12 numbering system.

My understanding is that a base 12 system is far MORE useful than the base 10 system we currently use. The number ten has only two factors, for example, – 5 and 2.

The number 12, on the other hand, can be divided by 2, 3, 4, and 6 making it much more useful for just about everything that humans do. Basically, you can easily work with halves, quarters, and thirds.

I’m not a mathematician, but I’ve always been interested in the idea of a base 12 numbering system, and every article I’ve ever read and every website I’ve ever visited on this topic (except this one) goes on at some length about all the many advantages of a base 12 system. My understanding is that we use a base 10 system simply as a quirk of history. It’s what we ended up with and are used to, but a base 12 system is superior in every way.

Any Google search will bring up dozens of articles about this, but here’s an interesting one:

http://io9.com/5977095/why-we-should-switch-to-a-base-12-counting-system

I assume that by “general uselessness”, you meant simply that nobody uses it. So even if you understood it, it wouldn’t be of much use to you in daily life. For better or worse, the world uses a base 10 system today. Using base 12 would be like speaking a language that nobody else speaks. Even if it were the greatest language ever, it wouldn’t be very useful if you are the only person that can speak it.

However, your phrasing comes across as if you are saying that base 12 is inferior and pointless, when it certainly isn’t. I think that’s why the base 12 supporters are leaving so many comments in this thread. ðŸ™‚

Doug

I don’t think we can close the book on the claim that we use a base ten number system since we have ten fingers. I know it’s the most popular hypothesis, but I believe the fact that the Babylonians used a base 60 number system should make us reconsider.

I also have to object to the idea that base 12 is useless. The fact that you can divide 10 into halves, thirds, and fourths in base 12 is pretty darn useful.

The question of the ‘best’ number system I think is a very interesting one. Fewer symbols means arithmetic is easier, so binary is a good choice in that regard. But anyone who spends anytime playing with binary numbers quickly realizes how cumbersome expressing large numbers can be. Larger bases allow us to express larger numbers more concisely, but at the cost of more symbols to memorize. So where’s the happy medium? I suspect most mathematicians would choose base-8 or base-12 if given the choice to switch over.

Good points, Michael.

I love your thinking on the “best” system. Balance is key for the feeble minds of the humans. Ah, if we could only be like Data of Star Trek TNG. #sigh ðŸ™‚