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Is there any point to the 12 times table?

blog.wolfram.com

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Re: Is there any point to the 12 times table?

#101

Post by btilly »

dnautics wrote: post #56
btilly wrote: post #44

Earlier quoted context omitted.

This one I'm entirely unconvinced of. 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 rou…

you can't use exact fraction arithmetic to take a square root, which comes up, you know, just a little bit, in physics. Of course this is a problem for binary representations, too, but you might as well not start out with an input that is already imprecise.

Every representation has its limits. :-)

In physics it is uncommon to have exact measurements for much of anything except integers. In physics, measurement error is usually a bigger issue than roundoff errors from floating point, so the non-existence of an exact floating point representation of the stated measurement is a non-issue.

In the real world, most cases that I'm aware of where we need exact base 10 calculations have to do with dealing with money in a single currency. You would be amazed how often square roots don't come up in this context!

Fractions show up as soon as you start doing currency conversions. (In fact the Euclidean algorithm for finding the GCD is believed to have been first developed by merchants for exactly this problem.) They are easy to add to a programming language, but you'd only use them in contexts (like finance) where square roots make no sense.

If you want to go beyond fractions to add square roots and so on, you can do algebraic numbers. This is a fairly specialized mathematical need, but Mathematica has done it perfectly well for decades.

For arbitrary real numbers, we're sort of stuck. We can come up with representations that can cover any real number that we can talk about. But we can't take 2 arbitrary representations of a real number and in finite time decide whether or not they are actually the same number. That said, Mathematica again solves this problem "well enough" for most practical purposes. See http://mathworld.wolfram.com/Ferguson-ForcadeAlgorithm.html for more.

Re: Is there any point to the 12 times table?

#102

Post by nashashmi »

btilly wrote: post #28
zeveb wrote: post #11

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…

To add, multiplying 5'5" and 4'4" would become a whole lot easier. It would literally be 55 x 44 instead of 5.42 x 4.33.

Of course that would mean I would have to memorize the entire multiplication table again: because 55 in duodec would be 65 in dec. And 5x18 would be 84.

Re: Is there any point to the 12 times table?

#103

Post by Scarblac »

clarkmoody wrote: post #79

This type of post is perfect Hacker News material! 1) Challenge an existing assumption about something we all do 2) Hand-wave some first-order guesses as to why we do it 3) Get nerdy with code and graphs and come to your conclusion, along with helpful suggestions for bettering the reader With no prospect of the pre-decimal money system returning, I can only conclude that the logic behind this new priority is simply,…

But do we all learn tables up to 12? In the Netherlands it's only up to 10 for as far back as I know.

Re: Is there any point to the 12 times table?

#104

Post by threatofrain »

deadowl wrote: post #87
Animats wrote: post #21

Only in non-metric countries. Back in the British era of pounds, shillings, and pence, hardware had to be built to do arithmetic in that system. This resulted in one of the strangest, and most complex, purely mechanical computing devices ever built - the McClure Multiplying Punch [1], from Powers-Samas. This device came out in 1938. The comparable IBM machine was the IBM 602 Multiplying Punch, but IBM only did decima…

I disagree. 1. We have time. Days are 24 hours, a multiple of 12. 2. We still have time. Hours are 60 minutes, a multiple of 12. 3. Yet more time. Minutes are 60 seconds, a multiple of 12. 4. We have circles. There are 360 degrees in a circle, another multiple of 12. 5. The numbers 1, 2, 3, 4, 6 and 12 itself divide into 12 evenly. The next smallest number that has more factors than 12 is 24, which manages to be a mu…

Those seem like minor use cases for disagreement. I'm not sure there should be an education policy or tradition just because our current unit of time is divisible by 12, or just because circles can be represented with the arc degree, especially when a lot of students go on to use radians, even in non-metric countries.

And if there's some domain-specific application, like in carpentry, then let those people use their own units.

Re: Is there any point to the 12 times table?

#105

Post by beachstartup »

deadowl wrote: post #87
Animats wrote: post #21

Only in non-metric countries. Back in the British era of pounds, shillings, and pence, hardware had to be built to do arithmetic in that system. This resulted in one of the strangest, and most complex, purely mechanical computing devices ever built - the McClure Multiplying Punch [1], from Powers-Samas. This device came out in 1938. The comparable IBM machine was the IBM 602 Multiplying Punch, but IBM only did decima…

I disagree. 1. We have time. Days are 24 hours, a multiple of 12. 2. We still have time. Hours are 60 minutes, a multiple of 12. 3. Yet more time. Minutes are 60 seconds, a multiple of 12. 4. We have circles. There are 360 degrees in a circle, another multiple of 12. 5. The numbers 1, 2, 3, 4, 6 and 12 itself divide into 12 evenly. The next smallest number that has more factors than 12 is 24, which manages to be a mu…

you forgot the one i use the most often - there are 12 months in a year.

how many times do you calculate "X per year" in your head? i do it multiple times per day, and not just at work.

Re: Is there any point to the 12 times table?

#106

Post by khedoros »

spike021 wrote: post #45
ck2 wrote: post #5

They should probably learn HEX at age 9

The odd thing I've found in my experience is that hex is thought to be taught to everyone in grade school. None of the schools I attended from elementary to high school (in the US) taught hexadecimal. I learned that in my CS courses once I started college.

I remember doing some radix conversions before college, but with no particular emphasis on base-16. The same material in CS courses mainly focused on bases 2, 8, 10, and 16, of course.

Re: Is there any point to the 12 times table?

#107

Post by legulere »

In Germany you usually learn up to 10×10 in school and there are usually 10 eggs in a box (4, 6 and 25 are also common sizes though and there's also a big set that's 20×20 which you don't usually learn though)

> And when you want to raise standards in math, then who could argue with that?

The problem is that you can only spend so and so much time with children in class. Learning 12×12 is 80% more combinations to learn compared to 9×9. That's time you could teach them something else that might be more useful.

Re: Is there any point to the 12 times table?

#108

Post by jheriko »

politics is a component too... i wouldn't go looking for purely intelligent decision making from a government selected by popularity contest.

the perception that school is getting easier, a criticism of the government that is politically undesirable, can be addressed by a 'return to traditional methods' in superficial ways... even if there is not really a concrete problem to address.

politics isn't about doing or achieving anything in terms of education or quality of life for others - its about making other people happy.

Re: Is there any point to the 12 times table?

#109

Post by justinhj »

Whenever my son has a new math teacher, I taught him to ask if he can change the base when reciting the times tables. For example the 12 times table in base 12 is 10, 20, 30, 40 and so on. It usually gets a laugh or a tut before he has to do it the right way.

Re: Is there any point to the 12 times table?

#110

Post by slavik81 »

zeveb wrote: post #64
martin-adams wrote: post #51

Earlier quoted context omitted.

>> If we were really smart, we'd switch from base 10 to base 12 But I only have 10 fingers! On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 as single digits, otherwise I could see that getting very confusing. You could't really use A and B, as then some people would be unable to find the correct seat on an airplane.

> But I only have 10 fingers! That's why I mentioned counting on the finger-joints :-) > On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 Already been done, over a hundred years ago, and they're even in Unicode already[1]! [1] https://en.wikipedia.org/wiki/Duodecimal

Very cool. There are a few notations, but it seems the most popular one uses rotated digits (like 6 and 9).

10 is a rotated 2 (ᘔ)

11 is a rotated 3 (Ɛ)

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