I love the Numberphile. His videos are always great and they remind me of the wonder I get when I sat through some of the more esoteric mathematics courses in undergrad.

With regard to the base 12 system, I think that it makes sense why these people are pushing for it. I mean I never really thought about 12 as being prevalent, but I guess it is. I'd just be happy if the US adopted the metric system for things other than government and scientific work.

I mean come on, 1000 meters in a kilometer is so much easier than 5280 feet in a mile or 1760 yards or 63360 inches.

The conceptual leap required to effectively perform mathematics in this new system would require a re-write for most people's already fragile understanding of maths. My dad spends at least one minute every time he eats out to calculate 15% of the bill with a pen and paper. Plus, it's 20% nowadays, ya old dick.

Cool side note: The value of every single physical constant would change. Yes?

*>the sarcastic paragraph*
Of course, this minor adjustment into base 12 would pale in comparison to the sheer *inconvenience* of Americans performing simple metric conversions for a few months to a couple years (and for some Americans, never) until they can think in Standard International units.
*>it's over now*

There would be considerable costs associated with switching ongoing government/military, scientific, business, and civilian operations from base 10 to 12. We're certainly too entrenched in base 10 for that to be a smooth transition.

Whiny side note: I had a component that needed metric screws for fastening. Are M6 screws hard to find in a U.S. city of 1.5 million? Why, yes. Yes they are.

Horses for courses. Base 16 is a great representation when you want to visualise computer memory contents (see my other comment); but that doesn't mean people will ever use it for ordinary counting. Same for 12 - not gonna happen. No impetus to do so, no gain.

I was a little surprised by the behavior of the digits past the decimal point. For any number less than 10, the digits behave the same way: 1 base 10 is 1 base 12, 4 base 10 is 4 base 12, etc. But all bets are off as soon as you're past the decimal point. 0.6 is a half? 0.4 is a third?

It shouldn't have been surprising. Recalling the definition of decimals makes it obvious: 0.xyz in base b is x/b + y/(b^2) + z/(b^3). Abbreviated fractions. Base 12 0.6 is 6/12 just as base 10 0.5 is 5/10.

The general public is NEVER going to convert to this, though.

Reminds me a little of this piece, which I love :

I use base 16 almost every day - hexadecimal, or hex. It uses digits 0-9 and A-F.

The primary reason to use it is because, in hex, each "digit" represents a 4-bit pattern - and these patterns are position-independent (because 16 is a power of two). Converting *any part* of a hex number between hexadecimal and binary is a simple matter of replacing the hex digit with the 4-bit pattern which it represents. You can do this with any part of a large number, without having to worry about the values of the other parts. It's really just binary shorthand, once you've memorised the 16 bit-patterns for the digits.

Thus, if you have a memory location (say, holding 16 bits) in a computer which has the hex-number-value of "89AC", you can instantly tell (for example) that the highest bit is set, and the next three are not (because 8 is '1000'); the lowest two bits are not set (because C is '1100'); etc etc.

Sometimes in programming you just need to know which bits are on or off, and nobody wants to look at this (same value, in binary ) : 1000100110101100 or this (same value, in normal base-10) : 35244.

This. Although it wouldn't make everyday arithmetic easier. It's true that 16 has more factors than 10, but it still has fewer factors than 12, and, most importantly, it hasn't got three.

Personally, I'm sold, except for the fact that then I wouldn't be able to communicate numerically with the whole rest of the world. But I think I'll start practicing. I'd like to see the look on the professor's face when I turn in a set of homework in dozenal. It'd be utterly worth the F.