Is there any point to the 12 times table? • Hacker News Board

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

#171

Post by deadowl » Tue, Jan 05, 2016, 3:37 AM UTC

beachstartup wrote: post #105

deadowl wrote: post #87

Earlier quoted context omitted.

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.

Probably should have included that.

Meanwhile, reviewing my post it reminded me of my US History teacher in middle school telling me that the Conquistadors in the Americas were after the 5 Gs: Gold, Gold, Gold, God, and Glory. I listed five things: Time, Time, Time, Degrees and Factors. I'd be thrilled if someone could say the same thing but with all of the words starting with the same letter.

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

#172

Post by lukeschlather » Tue, Jan 05, 2016, 3:37 AM UTC

lmm wrote: post #91

lukeschlather wrote: post #76

Earlier quoted context omitted.

Maybe. But the thing is if it's easier to memorize the composites, why not skip primes entirely over 5? Just memorize 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 . I'd have to run the numbers. It would be interesting to consider different subsets. I also think adding in 15 would probably worth the extra number for real-world datasets.

> Maybe. But the thing is if it's easier to memorize the composites, why not skip primes entirely over 5? Just memorize 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 . Isn't that backwards? 7 is the hardest, so you spend more time on it, not less.

That's why I'm suggesting you not bother memorizing 7 since there are higher numbers that provide similar utility for estimation but are much easier to memorize.

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

#173

Post by nitrogen » Tue, Jan 05, 2016, 3:45 AM UTC

pklausler wrote: post #141

yes_or_gnome wrote: post #47

Earlier quoted context omitted.

I am in the process of reading 'The Story of French' by Nadeau and Barlow. There's a chapter on how France was able to push their influence, during the renaissance, to get the world to switch to the metric system. Prior to developing the metric system, France had no standard for the pound; unlike England. This was the height of enlightenment in France, so the reformers wanted to replace the Gregorian Calendar with a…

Vernor Vinge's novel, "A Deepness in the Sky", involves an spacefaring civilization that uses metric time (Ksec, Msec) after discarding Earth-based units. A feature of the book: the author never gives a footnote explaining how to convert these units to familiar ones, so you have to work it out yourself. Which means that you'll never forget it once you've done the homework. (Also, there's the old rule-of-thumb from Gr…

In my copy there's a timescale legend inside the front cover, and I've mostly forgotten the conversions.

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

#174

Post by threatofrain » Tue, Jan 05, 2016, 4:44 AM UTC

such_a_casual wrote: post #121

threatofrain wrote: post #104

Earlier quoted context omitted.

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…

Seeing as time is a universally applicable measurement (more so than distance, volume, or mass). I hardly see that as a "minor use case". Is there a field which doesn't use time? Quantum computing?

If you're talking about time in the science and engineering domains, you're supposed to represent your quantity using a tasteful unit of your choosing.

* Scientists and engineers culturally select tasteful units of their choice to represent time, like 1300 milliseconds or 134 hours... and everything else as well: $1.34 billion or $1.34 dollars, not $1 billion and 340 million or $1 dollar and 34 cents.

* When the number representation get too big, people just do X * 10^n where n is a tasteful choice.

* In business, days and hours are distinct concepts and should not be mixed together or confused. A person who worked for 5 days did not work 120 hours.

* Mathematicians could care less.

* Many culturally common units of time are bigger than 12 * 12.

* Calculations that are big are working-memory bound. This is the biggest point. Working memory is probably the strongest factor to large and fast calculation of any kind.

* The bigger the calculation, the more people tend to 10^n multiplicands with the distributive property, rather than 12^n, since most people work in base 10. Some engineers use 2^n or 3^n (I offer that 3^n is efficient without further explanation).

I propose the hypothesis that children who memorized up to 10 * 10 are no more likely to join or do well in the STEM fields than those who memorized up to 12 * 12.

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

#175

Post by threatofrain » Tue, Jan 05, 2016, 5:15 AM UTC

michaelbuddy wrote: post #168

threatofrain wrote: post #104

Earlier quoted context omitted.

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…

carpentry isn't a closed domain. It is a wide range of skills. If you're in a country using inches and feet you would benefit from knowing the 12 times tables, more than you need 8x or 7x actually you'll have practical benefits from 12x. having comfort in fractions of a fourths, eighths and 16ths is also nice for applying measurements. It's for everyone to put things to use in their life.

You're arguing for the hypothesis that memorizing up to 10 * 10 is going to make a difference versus memorizing up to 12 * 12.

In business? In the STEM fields?

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

#176

Post by stonogo » Tue, Jan 05, 2016, 5:26 AM UTC

duaneb wrote: post #162

deadowl wrote: post #87

Earlier quoted context omitted.

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…

What is the advantage of using degrees (e.g. "30 degrees") versus radians (π/6)? Regardless, your observations seem to come down to "12 is highly composite and we use highly composite numbers for time"—valid, but interesting?

> What is the advantage of using degrees (e.g. "30 degrees") versus radians (π/6)?

Integer math.

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

#177

Post by such_a_casual » Tue, Jan 05, 2016, 5:59 AM UTC

threatofrain wrote: post #174

such_a_casual wrote: post #121

Earlier quoted context omitted.

Seeing as time is a universally applicable measurement (more so than distance, volume, or mass). I hardly see that as a "minor use case". Is there a field which doesn't use time? Quantum computing?

If you're talking about time in the science and engineering domains, you're supposed to represent your quantity using a tasteful unit of your choosing. * Scientists and engineers culturally select tasteful units of their choice to represent time, like 1300 milliseconds or 134 hours... and everything else as well: $1.34 billion or $1.34 dollars, not $1 billion and 340 million or $1 dollar and 34 cents. * When the numb…

You're misinterpreting the point entirely. The memorization of a 12 x 12 multiplication table has nothing to do with mathematics passed the multiplication of 12 x 12. It is an everyday use case. Most people use time every single day of their lives. Being able to multiply something by the amount of months in the year or the amount of hours in a day without having to bust out a calculator is something that comes in handy for everyone, even scientists, engineers, and mathematicians.

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

#178

Post by threatofrain » Tue, Jan 05, 2016, 6:15 AM UTC

such_a_casual wrote: post #177

threatofrain wrote: post #174

Earlier quoted context omitted.

If you're talking about time in the science and engineering domains, you're supposed to represent your quantity using a tasteful unit of your choosing. * Scientists and engineers culturally select tasteful units of their choice to represent time, like 1300 milliseconds or 134 hours... and everything else as well: $1.34 billion or $1.34 dollars, not $1 billion and 340 million or $1 dollar and 34 cents. * When the numb…

You're misinterpreting the point entirely. The memorization of a 12 x 12 multiplication table has nothing to do with mathematics passed the multiplication of 12 x 12. It is an everyday use case. Most people use time every single day of their lives. Being able to multiply something by the amount of months in the year or the amount of hours in a day without having to bust out a calculator is something that comes in han…

Actually I did respond to you -- and more. I argue against its usefulness in business and the STEM fields. I'm shrinking the sphere in which your argument is useful.

I argue that calculations are working-memory bound, and that common uses of time go beyond 12 x 12.

For time, we often go by units of 5, 10, 15, 30, 45, 60, of these only 60 can find 12 as a divisor. You don't get to claim usefulness for all time. For the rest of these units, it's working memory doing arbitrary integer computation for us.

If we're talking about months in a year -- what's the use case for fast mental calculation? Is this the little sphere where we say 12 * n is useful?

We're talking about a policy for education for all children here. Your use cases sound really limited, if it at all impacts later cognitive performance outcomes.

It's working memory that's going to be the differentiating line between "fast mental math" and "busting out calculator" or "punching in numbers into SAS or SPSS". It's difficult to believe that Taiwanese children are going to have trouble versus American children in time based operations, if that at all continues to be a practice under the common core.

I can't imagine asking some Taiwanese business man, "Quick, what's 6 * 12 in a business context", and he goes, "Let me quickly grab a calculator."

Can you do 15 * 14? I think you can. Why can we do it? Is it because we learned 12 * 12? No. It's working-memory bound. We're doing capricious calculations with distributive property via 10^n multiplicands.

How about 24 * 17? I think you can do that too. Why can we do it? Working memory. Not because we learned 12 * 12 when we were little.

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

#179

Post by lmm » Tue, Jan 05, 2016, 7:24 AM UTC

lukeschlather wrote: post #172

lmm wrote: post #91

Earlier quoted context omitted.

> Maybe. But the thing is if it's easier to memorize the composites, why not skip primes entirely over 5? Just memorize 1, 2, 3, 4, 5, 6, 8, 9, 10, 12 . Isn't that backwards? 7 is the hardest, so you spend more time on it, not less.

That's why I'm suggesting you not bother memorizing 7 since there are higher numbers that provide similar utility for estimation but are much easier to memorize.

I don't think the times tables are for estimation.

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

#180

Post by kobayashi » Tue, Jan 05, 2016, 7:33 AM UTC

dnautics wrote: post #27

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…

divisors are bad. Here's why: If you have a prime (or p^n) base, you can assess how much computation you have to do based on the non-zero digits on the left. say in hex you have a number 0x56aF900000, you know that your divisors can have no more than 5 non-zero (hex) digits. This is not so for decimal numbers; 32 * 125 = 4000

Any chance you'd be willing to explain that in laymen's terms?