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.