4 ms·

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 ar

by deadowl 11y ago

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 multiple of 12.

threatofrain 11y ago
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.
- such_a_casual 11y ago
  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?
  - threatofrain 11y ago
    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.
    - such_a_casual 11y ago
      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.
      - threatofrain 11y ago
        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.
- michaelbuddy 11y ago
  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.
  - threatofrain 11y ago
    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?
beachstartup 11y ago
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.
- antod 11y ago
  > 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.
  - beachstartup 11y ago
    i run a business so basically i'm calculating "X per year" all day long.
- deadowl 11y ago
  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.
  - WorldMaker 11y ago
    Rate, Rate, Rate, Radian, and Ratio?
mjevans 11y ago
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 exactly what someone needs to work up and down. Many baking items are also sold in units of 12 (E.G. eggs, 144 being that packet size that businesses buy in). Finally there's the learning aspect. Learning the 12s is a lot like extending the factor tables beneath it in a way that makes sense to analog brains. It's actually not /that/ much more costly. 13 however is a whole new prime, which isn't that useful in daily life; all of the larger numbers are big enough to be handled as estimates or 'long math' precision numbers. PS: If I could magically force all humans to learn, know, and use a new base (and that's the only option I had) I'd probably pick Octal. Hex (for the above reasons) is useful, and great for computer addressing, but less great for actual human-analog computation.
- kuschku 11y ago
  > 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.
  - teh_klev 11y ago
    Six or twelve egg boxes are still prevalent in most shops and supermarkets in the UK. Bulk deliveries are usually on 30 egg or 40 egg trays.
jdonaldson 11y ago
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).
duaneb 11y ago
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?
- deadowl 11y ago
  Radians are superior IMO. Using degrees for measurement is archaic compared to radians, but I imagine whole arabic-numeral numbers are more familiar than PI symbols in the learning process at the point in life when most kids are first learning geometry something related to angles. Understanding PI symbols for the first time could possibly come alongside an algebra curriculum, but I'm not a K-12 educator so if I had an opinion, it wouldn't be worth any weight. Meanwhile, your response got me to look up whether there's a metric equivalent to degrees or radians. Apparently that exists and it's a measure called Gradians. There are 400 Gradians in a circle, and 400 is not divisible by 12. I guess that idea went the way of the French Republican Calendar.
  - thaumasiotes 11y ago
    grad is used to measure the incline of the earth; you might see a 45-degree slope described as "50% grad". And apparently, in what I have to assume is a related use: > In surveying, the gradian is the default unit of angles in many parts of the world. ( https://en.wikipedia.org/wiki/Gradian https://en.wikipedia.org/wiki/Gradian ) If you ever fooled around with your calculator in school, you probably noticed that it provided angle measurement conversion between degrees, radians, and gradians; the idea has certainly not gone the way of the French Republican Calendar.
- stonogo 11y ago
  > What is the advantage of using degrees (e.g. "30 degrees") versus radians (π/6)? Integer math.
Animats 11y ago
17 silver Sickles to a gold Galleon, 29 bronze Knuts to a Sickle.

by deadowl 11y ago

threatofrain 11y ago

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.

such_a_casual 11y ago
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?
- threatofrain 11y ago
  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.
  - such_a_casual 11y ago
    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.
    - threatofrain 11y ago
      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.
michaelbuddy 11y ago
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.
- threatofrain 11y ago
  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?

beachstartup 11y ago

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.

antod 11y ago
> 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.
- beachstartup 11y ago
  i run a business so basically i'm calculating "X per year" all day long.
deadowl 11y ago
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.
- WorldMaker 11y ago
  Rate, Rate, Rate, Radian, and Ratio?

mjevans 11y ago

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 exactly what someone needs to work up and down. Many baking items are also sold in units of 12 (E.G. eggs, 144 being that packet size that businesses buy in). Finally there's the learning aspect. Learning the 12s is a lot like extending the factor tables beneath it in a way that makes sense to analog brains. It's actually not /that/ much more costly. 13 however is a whole new prime, which isn't that useful in daily life; all of the larger numbers are big enough to be handled as estimates or 'long math' precision numbers. PS: If I could magically force all humans to learn, know, and use a new base (and that's the only option I had) I'd probably pick Octal. Hex (for the above reasons) is useful, and great for computer addressing, but less great for actual human-analog computation.

kuschku 11y ago
> 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.
- teh_klev 11y ago
  Six or twelve egg boxes are still prevalent in most shops and supermarkets in the UK. Bulk deliveries are usually on 30 egg or 40 egg trays.

jdonaldson 11y ago

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).

duaneb 11y ago

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?

deadowl 11y ago
Radians are superior IMO. Using degrees for measurement is archaic compared to radians, but I imagine whole arabic-numeral numbers are more familiar than PI symbols in the learning process at the point in life when most kids are first learning geometry something related to angles. Understanding PI symbols for the first time could possibly come alongside an algebra curriculum, but I'm not a K-12 educator so if I had an opinion, it wouldn't be worth any weight. Meanwhile, your response got me to look up whether there's a metric equivalent to degrees or radians. Apparently that exists and it's a measure called Gradians. There are 400 Gradians in a circle, and 400 is not divisible by 12. I guess that idea went the way of the French Republican Calendar.
- thaumasiotes 11y ago
  grad is used to measure the incline of the earth; you might see a 45-degree slope described as "50% grad". And apparently, in what I have to assume is a related use: > In surveying, the gradian is the default unit of angles in many parts of the world. ( https://en.wikipedia.org/wiki/Gradian https://en.wikipedia.org/wiki/Gradian ) If you ever fooled around with your calculator in school, you probably noticed that it provided angle measurement conversion between degrees, radians, and gradians; the idea has certainly not gone the way of the French Republican Calendar.
stonogo 11y ago
> What is the advantage of using degrees (e.g. "30 degrees") versus radians (π/6)? Integer math.

Animats 11y ago

17 silver Sickles to a gold Galleon, 29 bronze Knuts to a Sickle.