9 ms·

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' (rea

by zeveb 11y ago

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 smart, we'd switch from base 10 to base 12: many more 'decimals' (really duodecimals) would be non-repeating. And then there are measures like a gross (144) and a great gross (1,728). Part of the reason for these traditional measures is that they are more flexible than base-10 measures: an eighth-gross or a third-gross are both integer quantities, unlike an eighth-hundred or third-hundred.

panglott 11y ago
Base-60 math is even superior.
- noobermin 11y ago
  The Sumerians had it right?
  - deleted 11y ago
    [deleted]
Retric 11y ago
The first 3 prime numbers are 2, 3, 5. Base 10 and base 12 both use two of them. (12/4=3 yay, but 10/4 = 2.5 so meh) The same is true of base 6 or base 15. Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5. PS: Several ancient systems use base 60 which uses 2, 3, and 5 and may have been created by joining a base 6 system with a base 10 system. However, base 30 also works well for this and is thus a clear step up from base 10 or 12 while being simpler than base 60.
- zeveb 11y ago
  > Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5. It's highly probable that in duodecimal one would divide by 2, 3, 4, 6, 8 & 9 as often as one divides by 5 in decimal, and avoid 5 as much as one avoids 3 & 7 in decimal.
  - Retric 11y ago
    You can divide by 2, 4 or 8 just fine in base 10. 3 and 9 are also fast though you get either a remainder or a repeating number. So, really the advantage is 6 vs 5.
dnautics 11y ago
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
- kobayashi 11y ago
  Any chance you'd be willing to explain that in laymen's terms?
btilly 11y ago
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 easy divisibility and are close enough to existing time units to make sense. This change would mean we have to memorize a 12 times table rather than a 10 times table. But in base 10 a 10 times table has easy patterns for 1, 2, 5, 9 and 10. A 12 times table has repeating patterns for 1, 2, 3, 4, 6, 8, 9, 11 and 12. The result is that a 12 times table in base 12 is actually less work to memorize than a 10 times table in base 10. In the long run this transition would be a clear win. But it isn't enough of one compared to the transition to ever make sense to initiate.
- dnautics 11y ago
  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.
  - btilly 11y ago
    This one I'm entirely unconvinced of. It is easier for the computer to adapt to us, rather than vice versa. And over time things get easier and easier for the computer, while staying the same for us. Which is why over time we wind up interacting with computers in ways that are more and more adapted to us rather than them. We already have acceptably good algorithms to convert to/from different representations, and roundoff errors are generally acceptable. (If they weren't, we wouldn't default to using floating point for most things.) Where precision matters, we have reasonably efficient implementations of exact integer arithmetic and exact fraction arithmetic. The performance hit from using these is less than the hit from using a high level language like Python versus a low-level language like C. The main challenge is getting programmers to use the right representation for the purpose that they are using it for. Which is mostly challenging exactly because floating point works so well in practice that it is easy not to learn what its limitations are.
nwatson 11y ago
One of my uncles was an engineer at Boeing and said he felt the Imperial system was a competitive advantage (30 years ago) when competing with BAE and other non-US companies. He claimed the standard thicknesses of rolled sheet metal in the U.S. provided better graduations between thicknesses and led to lighter engines.
martin-adams 11y ago
>> 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.
- zeveb 11y ago
  > But I only have 10 fingers! That's why I mentioned counting on the finger-joints :-) > On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 Already been done, over a hundred years ago, and they're even in Unicode already[1]! [1] https://en.wikipedia.org/wiki/Duodecimal https://en.wikipedia.org/wiki/Duodecimal
  - slavik81 11y ago
    Very cool. There are a few notations, but it seems the most popular one uses rotated digits (like 6 and 9). 10 is a rotated 2 (ᘔ) 11 is a rotated 3 (Ɛ)
- scoates 11y ago
  You have 12 finger segments per hand. "Finger-counting systems in use in many regions of Asia allow the counting to 12 by using a single hand."[0] [0] https://en.wikipedia.org/wiki/Finger-counting https://en.wikipedia.org/wiki/Finger-counting (Edit: silly me and trying to use Markdown)
- epimetheus 11y ago
  10 fingers, and two hands, so you could count raising your hand up to count as one, then 5 fingers, then the other hand, and 5 more fingers. I agree about the symbols, though.
- rglovejoy 11y ago
  There was an episode of "Schoolhouse Rock" that was about just this ("Little Twelvetoes"). After the number nine, they suggested two new numbers, "dek" and "ell", and for "10", call it "doe".
jameshart 11y ago
But that's not really an argument for learning your twelve times table. In fact it's an argument that basically it's trivial to learn your twelves if you already know your threes and fours - the twelves are the numbers that appear in both lists. Or you can just skipcount your four times table. Overall, seems to argue against having to learn it.
- lukeschlather 11y ago
  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.
  - lmm 11y ago
    > 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.
    - lukeschlather 11y ago
      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.
      - lmm 11y ago
        I don't think the times tables are for estimation.
rezashirazian 11y ago
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 https://www.youtube.com/watch?v=U6xJfP7-HCc
- such_a_casual 11y ago
  lol is he writing on bathroom paper towels?

by zeveb 11y ago

panglott 11y ago

Base-60 math is even superior.

noobermin 11y ago
The Sumerians had it right?
- deleted 11y ago
  [deleted]

Retric 11y ago

The first 3 prime numbers are 2, 3, 5. Base 10 and base 12 both use two of them. (12/4=3 yay, but 10/4 = 2.5 so meh) The same is true of base 6 or base 15. Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5. PS: Several ancient systems use base 60 which uses 2, 3, and 5 and may have been created by joining a base 6 system with a base 10 system. However, base 30 also works well for this and is thus a clear step up from base 10 or 12 while being simpler than base 60.

zeveb 11y ago
> Every other prime number repeats so switching is pointless, unless you divide by 3 vastly more often than by 5. It's highly probable that in duodecimal one would divide by 2, 3, 4, 6, 8 & 9 as often as one divides by 5 in decimal, and avoid 5 as much as one avoids 3 & 7 in decimal.
- Retric 11y ago
  You can divide by 2, 4 or 8 just fine in base 10. 3 and 9 are also fast though you get either a remainder or a repeating number. So, really the advantage is 6 vs 5.

dnautics 11y ago

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

kobayashi 11y ago
Any chance you'd be willing to explain that in laymen's terms?

btilly 11y ago

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 easy divisibility and are close enough to existing time units to make sense. This change would mean we have to memorize a 12 times table rather than a 10 times table. But in base 10 a 10 times table has easy patterns for 1, 2, 5, 9 and 10. A 12 times table has repeating patterns for 1, 2, 3, 4, 6, 8, 9, 11 and 12. The result is that a 12 times table in base 12 is actually less work to memorize than a 10 times table in base 10. In the long run this transition would be a clear win. But it isn't enough of one compared to the transition to ever make sense to initiate.

dnautics 11y ago
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.
- btilly 11y ago
  This one I'm entirely unconvinced of. It is easier for the computer to adapt to us, rather than vice versa. And over time things get easier and easier for the computer, while staying the same for us. Which is why over time we wind up interacting with computers in ways that are more and more adapted to us rather than them. We already have acceptably good algorithms to convert to/from different representations, and roundoff errors are generally acceptable. (If they weren't, we wouldn't default to using floating point for most things.) Where precision matters, we have reasonably efficient implementations of exact integer arithmetic and exact fraction arithmetic. The performance hit from using these is less than the hit from using a high level language like Python versus a low-level language like C. The main challenge is getting programmers to use the right representation for the purpose that they are using it for. Which is mostly challenging exactly because floating point works so well in practice that it is easy not to learn what its limitations are.

nwatson 11y ago

One of my uncles was an engineer at Boeing and said he felt the Imperial system was a competitive advantage (30 years ago) when competing with BAE and other non-US companies. He claimed the standard thicknesses of rolled sheet metal in the U.S. provided better graduations between thicknesses and led to lighter engines.

martin-adams 11y ago

>> 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.

zeveb 11y ago
> But I only have 10 fingers! That's why I mentioned counting on the finger-joints :-) > On a practical note, wouldn't that mean inventing 2 new symbols to represent 10 and 11 Already been done, over a hundred years ago, and they're even in Unicode already[1]! [1] https://en.wikipedia.org/wiki/Duodecimal https://en.wikipedia.org/wiki/Duodecimal
- slavik81 11y ago
  Very cool. There are a few notations, but it seems the most popular one uses rotated digits (like 6 and 9). 10 is a rotated 2 (ᘔ) 11 is a rotated 3 (Ɛ)
scoates 11y ago
You have 12 finger segments per hand. "Finger-counting systems in use in many regions of Asia allow the counting to 12 by using a single hand."[0] [0] https://en.wikipedia.org/wiki/Finger-counting https://en.wikipedia.org/wiki/Finger-counting (Edit: silly me and trying to use Markdown)
epimetheus 11y ago
10 fingers, and two hands, so you could count raising your hand up to count as one, then 5 fingers, then the other hand, and 5 more fingers. I agree about the symbols, though.
rglovejoy 11y ago
There was an episode of "Schoolhouse Rock" that was about just this ("Little Twelvetoes"). After the number nine, they suggested two new numbers, "dek" and "ell", and for "10", call it "doe".

jameshart 11y ago

But that's not really an argument for learning your twelve times table. In fact it's an argument that basically it's trivial to learn your twelves if you already know your threes and fours - the twelves are the numbers that appear in both lists. Or you can just skipcount your four times table. Overall, seems to argue against having to learn it.

lukeschlather 11y ago
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.
- lmm 11y ago
  > 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.
  - lukeschlather 11y ago
    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.
    - lmm 11y ago
      I don't think the times tables are for estimation.

rezashirazian 11y ago

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 https://www.youtube.com/watch?v=U6xJfP7-HCc

such_a_casual 11y ago
lol is he writing on bathroom paper towels?