41–50 of 198 posts
They should probably learn HEX at age 9
Back in the 70's (UK) I remember doing non base 10 maths at about that age plus basic set theory much more useful than rote leaning your times table.
I think that's been dropped from most US elementary school curricula now, bit of a shame.
Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…
Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?) With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both…
1 2 3 4 5 6 7 8 9 a b
so 10 would be 12
Earlier quoted context omitted.
Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?) With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both…
decimals cause huge problems for computers. How do you represent 0.6 as a floating point? In the long run, the correct solution is for everything to be binary.
It is easier for the computer to adapt to us, rather than vice versa. And over time things get easier and easier for the computer, while staying the same for us. Which is why over time we wind up interacting with computers in ways that are more and more adapted to us rather than them.
We already have acceptably good algorithms to convert to/from different representations, and roundoff errors are generally acceptable. (If they weren't, we wouldn't default to using floating point for most things.) Where precision matters, we have reasonably efficient implementations of exact integer arithmetic and exact fraction arithmetic. The performance hit from using these is less than the hit from using a high level language like Python versus a low-level language like C.
The main challenge is getting programmers to use the right representation for the purpose that they are using it for. Which is mostly challenging exactly because floating point works so well in practice that it is easy not to learn what its limitations are.
They should probably learn HEX at age 9
Forget the stats and calculus. Think carpentry, measuring and cutting wood products. If you are building things in the US/UK/Canada then you are using feet and inches. 12 inches to a foot. It's a tiny thing to learn and will serve kids well in any number of professions. Now 11, that's a total mystery. Other than it being between 10 and 12, I see no reason to memorize 11s.
> in the US/UK/Canada And the other 94% of the world population…?
Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…
Easy divisibility is the reason why when we switched to metric, the one thing that didn't switch is time. Which means that, for example, converting from m/s to km/h is a mess. (You have to multiply by 3.6, can you easily do that in your head?) With a base 12 version of everything you would have 1/12 of a day being 2 hours, 1/144 of a day is 10 minutes, and 1/1728 of a day is 50 seconds. These units would give us both…
The only country to actually use the calendar was, of course, France for 16(!?) years until Napoleon repealed it during his imperial reign.
https://en.wikipedia.org/wiki/Metric_time
Anyone, feel free to correct me. I, literally, just read about this (fascinating) subject a couple nights ago. I haven't had time to independently follow up on the topic, but I plan to do so soon.
Amendum: A better link, https://en.wikipedia.org/wiki/Decimal_time#France
Twelve has more divisors than ten (1, 2, 3, 4, 6 & 12 vs 1, 2, 5 & 10). If we were really smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. One can very quickly count by twelves on the joints of one's fingers, using the thumb as an index (0-143 is a much larger range than 0-10, and it's easier to hold one's hands in the shape necessary). If we were really sm…
Forget the stats and calculus. Think carpentry, measuring and cutting wood products. If you are building things in the US/UK/Canada then you are using feet and inches. 12 inches to a foot. It's a tiny thing to learn and will serve kids well in any number of professions. Now 11, that's a total mystery. Other than it being between 10 and 12, I see no reason to memorize 11s.
I don't think that's been the case for a pretty long time in the UK - certainly DIY supplies are metric e.g. here is the Homebase site:
http://www.homebase.co.uk/en/homebaseuk/diy/timber/planed-ti...
Earlier quoted context omitted.
Back in the 70's (UK) I remember doing non base 10 maths at about that age plus basic set theory much more useful than rote leaning your times table.
Did that in the US in the mid 2000s, though spent hardly a week on either IIRC. Something like base 20 Mayans, base 60 Sumerians, and base 2 computers. Do math in each and convert them to/from base 10. I think that's been dropped from most US elementary school curricula now, bit of a shame.