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Is there any point to the 12 times table?

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

#111

Post by arh68 »

martin-adams wrote: post #51
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…

>> 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.

What about X and E? (pronounced deck and ell) There are other symbols you could use instead of ASCII if you really wanted to distinguish them (like chi & epsilon).

You can count to 10 with 5 fingers with not much practice (look up Chisanbop); I think most kids could pick up counting to 12 on their finger joints pretty quickly.

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

#113

Post by antod »

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.

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

Seldom enough that I 'calculate it in my head' (as your comment suggests you do too) rather than memorise the 12x table.

But then again I grew up in metric country that only bothered with drilling kids up to the 10x table at school. Never had to worry about feet to inches conversions very often either.

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

#114

Post by yes_or_gnome »

vidarh wrote: post #75
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…

The renaissance is usually seen as being the 15th and 16th centuries. France didn't switch to metric until the end of the 18th century, after the French revolution. If anything, the way the French "pushed their influence" was by conquest: The first countries that adopted metric were forced to when they were conquered by Napoleon. Many of them reverted after Napoleon was beaten, but then gradually they started convert…

Thanks for the clarifications; You're right that I am mixing up eras and nomenclature. 'The Age of Enlightenment' would be the correct name, yes? This was all during the first french republic and ended by the end of Napoleon's reign.

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

#115

Post by Namrog84 »

cjensen wrote: post #112

I grew up in the Bay Area in California. We only memorized up to 9x9. Though 12 is used often in measurements, I can't say as that I've missed having rote knowledge of the multiples of 12.

Would you say then that you don't have any x10 memorized and just consider it trivially easy to compute any number?

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

#116

Post by antod »

Scarblac wrote: post #103
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.

Same in New Zealand. The only times I ever saw anything with 12x tables it had escaped from the US education market and had exercises involving nickels, dimes and quarters etc.

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

#117

Post by dnautics »

btilly wrote: post #101
dnautics wrote: post #56

Earlier quoted context omitted.

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 calculati…

depends. If you're running a simulation in physics, e.g. n-body problem, you can choose your parameters to be exact to start off with, and rescale your units to be exact. Moreover, even if you start with measurement error, the error moves in generally a predictable fashion, so it tends to be O(1). A floating point roundoff error is a martingale, with O(sqrt(N)) - unless you "always round up" or "always round down" which is O(N). In the initial domain, the measurement error dominates, but over time fp roundoff gets bigger.

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

#118

Post by beachstartup »

antod wrote: post #113
beachstartup wrote: post #105

Earlier quoted context omitted.

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.

> how many times do you calculate "X per year" in your head? i do it multiple times per day, and not just at work. Seldom enough that I 'calculate it in my head' (as your comment suggests you do too) rather than memorise the 12x table. But then again I grew up in metric country that only bothered with drilling kids up to the 10x table at school. Never had to worry about feet to inches conversions very often either.

i run a business so basically i'm calculating "X per year" all day long.

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

#119

Post by Bulkington »

We're overthinking. Think, instead, as a school marm with real chalk and a switch in hand, or even when kids used slate tablets: 10x is easy. 11x is easy up to 10x. 12x requires a little work and pulls all the multiples together, but 13x just screws with everything we've learned so far. So, stop at 12. Or is a calculator in hand the default these days? As one who was proud to finally get to 12 x 12 = 144, I say make 'em suffer.
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