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

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

#121

Post by such_a_casual » Mon, Jan 04, 2016, 10:46 PM UTC

threatofrain wrote: post #104

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…

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?

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

#122

Post by Terr_ » Mon, Jan 04, 2016, 10:47 PM UTC

Terr_ wrote: post #68

dnautics wrote: post #29

Earlier quoted context omitted.

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.

Why? No matter what radix you pick, there's always going to be some rational-value you cannot accurately encode. Moving to binary just gives you a different distribution of "un-encodeable values". (I'd say a larger/worse set, but I'm not yet sure how to prove it.) In the long run, trinary gives you the best radix-economy, being closest to e: https://en.wikipedia.org/wiki/Radix_economy

Making a self-reply here, I think I know how to show binary is "worse" when it comes to un-representable rational numbers. I'm not a math major, so this is probably some incredibly obvious textbook stuff to somebody else, but...

In base-N, you can accurately write any fraction of (1/y) provided that y can be expressed using the same prime-factors found in N.

For example, 10 has the prime factors of 2 and 5, leading to the requirement that y=(2^a × 5^b) .

This means base-10 can accurately represent (1/80), because 80 = (2^4 × 5^1). In base-2, you're limited to stuff in the form (2^a).

Finally, the, uh, infinity-of-integers that matches (2^a) is always going to be "smaller" than the infinity which can be matched by (2^a × 5^b), since the latter "contains" the former when b=0.

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

#123

Post by spike021 » Mon, Jan 04, 2016, 10:48 PM UTC

khedoros wrote: post #106

spike021 wrote: post #45

Earlier quoted context omitted.

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.

Yeah, my CS courses covered 2, 8, 10, and 16 as well. I think one class used some other bases for a project, but I wouldn't say it was a particular focus.

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

#124

Post by amelius » Mon, Jan 04, 2016, 10:50 PM UTC

Let's just switch to binary, and let them learn the 1-times table.

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

#125

Post by rezashirazian » Mon, Jan 04, 2016, 10:51 PM UTC

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…

I came here for this. I am disappointed it is only the third response. I suggest anyone reading this to also watch this video https://www.youtube.com/watch?v=U6xJfP7-HCc

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

#126

Post by TimJRobinson » Mon, Jan 04, 2016, 10:55 PM UTC

antod wrote: post #116

Scarblac wrote: post #103

Earlier quoted context omitted.

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.

Interestingly in Australia we learnt all the way to 12.

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

#127

Post by mark-r » Mon, Jan 04, 2016, 10:59 PM UTC

trgn wrote: post #53

SixSigma wrote: post #3

I recently worked with a person who had to do her three times table using her hands, starting from 3. She would still struggle at about 6 or 7 times. We worked behind the counter in a builder's merchant. She is no longer working for us.

Due to some airline delays, I was trying to schedule a new flight. I ended up showing a boarding pass to an attendant at the booth and asking something along the lines of "I'd like to make this connection". The ticket said departure "22.17". She asked me "What's that in `real` time?". Two more from the garden center: I was looking for a pump for an ornamental pond, and the pumps were advertised by the amount of gallo…

A long time ago, a coworker bought a surplus water tank and was curious how much it would weigh when filled. I asked him the dimensions, and as he was talking I converted everything to inches, multiplied by 2.5 to get approximate cm, rounded to the nearest power of 2 and added the exponents, and used 3 as the value of pi (it was a cylinder). Using 1 cm³ of water = 1 gram, I divided by 1000 (or was it 1024?) to get the weight in kg, and finally multiplied by 2.2. I was able to give him an answer by the time he was done.

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

#128

Post by golergka » Mon, Jan 04, 2016, 11:00 PM UTC

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…

Just imagine how strange today's world will look when people will switch to binary (and probably hex for writing).

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

#129

Post by contravariant » Mon, Jan 04, 2016, 11:05 PM UTC

As someone who never learned the 12 times table, and only uses metric, I'm not sure if it would have been better if I had learned the 12 times table, but for some reason I have actually memorized most multiples of 12 (without any conscious effort). They do seem to turn up a lot for various reasons.

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

#130

Post by such_a_casual » Mon, Jan 04, 2016, 11:05 PM UTC

dnautics wrote: post #29

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…

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.

Decimals do not cause any problems for computers. Computers are just a bunch of switches of states. The meaning of these states is completely up to us. For example, 4 switches creates 2^4 states (16 states). That means we could have those states represent the numbers 1-16. As far as I'm aware, the only reason we use base 2 numbers in computing (floats) is because there are mathematical shortcuts you can take when doing so. There is nothing forcing a computer to interpret those 16 states as x * 2^y instead of x * 10^y. That is a software choice.