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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?

#141

Post by pklausler »

yes_or_gnome wrote: post #47
btilly wrote: post #28

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…

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 Grace Murray Hopper that "pi seconds equals a nanocentury".)

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

#142

Post by gknoy »

mserdarsanli wrote: post #71

> Take as an example 7,203 x 6,892. If I want to know that exactly, then I reach for Mathematica They are always trying so hard to sell Mathematica in these blog posts, but this is the lowest I've seen.

I don't know that it's meant to shill the product -- rather, that's the tool that he has handy. I work all the time with Python, and frequently open an IPython shell to do some quick math ("what's the average of 4d6 pick 3?" "what is X% of my paycheck?" "how much do I need to contribute to max out my $FOO?"), simply because it's easier than a calculator.

I mean, sure, it's advertising Mathmatica, but it doesn't seem to be unecessarily doing so. It's more that it's ${programing-language-of-choice} for the author.

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

#143

Post by the-dude »

pc86 wrote: post #24
BillTheCat wrote: post #17

Earlier quoted context omitted.

A simple trick: For 11 x a 2-digit number you can simply take the first digit of the 2-digit number then the 2 digits of the number added together then the last digit of the 2-digit number. Ex: 11 * 12 = 132 or 1, 1+2, 2. 11 * 45 = 495 or 4, 4+5, 5. For numbers which sum to more than 10 add the carry to the first number ex: 11 * 59 = 649 or 5, 5+9 = 14 so add 1 to the initial 5 and keep the 4, 9.

I'm 29 and never heard this before. Neat!

This is golden: I am just over 40 and I now know that I knew nothing at 29!

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

#144

Post by jdonaldson »

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…

There are 12 semitones on a musical scale

There are 12+ loaves in a baker's dozen (the exception that proves the rule)

The point on #5 is critical. Before we had a solid currency system or notion of debt, we commonly had to divide things up from a group. 12 gives a lot of flexibility in that regard. In fact, selling 12 units of something became so common that certain industries added an extra unit just to be sure that the number 12 was given (baker's dozen).

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

#145

Post by kijin »

legulere wrote: post #107

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 lear…

Actually, it's only ~32% more combinations to learn, because nobody really needs to memorize the 10's and 11's (except 11 x 11).

You memorize all the combinations up to 9 x 9, compute the 10's and 11's on the fly, and memorize the 12's.

Edit: Corrected the number. This is how you get 32%:

The 9 x 9 multiplication table contains 8 x 8 = 64 combinations to memorize. The 1's don't count.

The 12 x 12 multiplication table contains an additional 20 combinations to memorize, namely:

- 10 combinations from 12 x 2 to 12 x 12, not counting 12 x 10

- 9 combinations from 2 x 12 to 11 x 12, not counting 10 x 12

- 11 x 11 = 121

So the total is 84 combinations, which is ~32% more than 64.

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

#146

Post by kuschku »

mjevans wrote: post #135
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…

In addition to the upward counting of time, memorizing the 12s column (I agree that the /human/ difficulty of learning 10s and 11s is mostly simple tricks to calculate those numbers on the fly) gives users the ability to work backwards and forwards with fractions of time based on 12s. Thanks to the seconds and minutes counting in 60s and hours and months (somewhat) counting in 12s knowing base 2, 3, 4, 6 and 12 is ex…

> Many baking items are also sold in units of 12 (E.G. eggs, 144 being that packet size that businesses buy in).

We’ve solved that in Europe, too – they’re sold in packages of 10, and businesses buy in packages of 100.

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

#147

Post by mserdarsanli »

gknoy wrote: post #142
mserdarsanli wrote: post #71

> Take as an example 7,203 x 6,892. If I want to know that exactly, then I reach for Mathematica They are always trying so hard to sell Mathematica in these blog posts, but this is the lowest I've seen.

I don't know that it's meant to shill the product -- rather, that's the tool that he has handy. I work all the time with Python, and frequently open an IPython shell to do some quick math ("what's the average of 4d6 pick 3?" "what is X% of my paycheck?" "how much do I need to contribute to max out my $FOO?"), simply because it's easier than a calculator. I mean, sure, it's advertising Mathmatica, but it doesn't seem…

I don't work with Python, but when I want to multiply some numbers, I type `python` into terminal and use it as a calculator, as it allows me to do such operations quickly.

It sounds weird that someone opens an IDE and waits ten seconds looking at a splash screen to do a simple multiplication.

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

#148

Post by dahart »

The reasons given for learning multiplication tables all focus on multiplication, but one of the best reasons is for division. Doing division on paper or in your head is made so much easier if you have your single digit multiplication table memorized.

But why 12 instead of 10? I think:

- There are loads of common everyday uses that overflow 10 by just a little.

- Clocks

- Eggs

- 11 is almost as trivial as 10, it would be a shame to stop at 10 when 11 is free.

- 12 is really super easy, and combined with the above reasons has a good case.

- 13s are significantly harder to remember and work with than 11 or 12, nothing comes in 13s, its the perfect place to stop. :) (edit: course, as soon as I wrote that I remembered the baker's dozen, which was super common to hear when I was a kid, not so much anymore for me. But I think the point still stands, because with a baker's dozen you only pay for 12, you never had to multiply by 13.)

* edited for formatting

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

#149

Post by kuschku »

btilly wrote: post #86
hasenj wrote: post #42

Earlier quoted context omitted.

I'd assume if we used base 12 for everything we'd also use it for writing numbers too. 1 2 3 4 5 6 7 8 9 a b so 10 would be 12

You have to be clear on the difference between the number and its representation. In English we represent numbers in base 10 unless otherwise specified. Hence you say things like, The base 12 number 10 is 12. I did not otherwise specify, so I represented my numbers in base 10 everywhere even though I was talking about base 12.

In math, we prefer to use either (101010)_2 or (101010)2 or 101010_2 – which represents (42)_10

(With TeX formatting implied)

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