5 ms·

Frankly, while mathematically speaking 12 is a great base, people don't think in twelves - you can quickly perform arithmetic and our entire education system of

Frankly, while mathematically speaking 12 is a great base, people don't think in twelves - you can quickly perform arithmetic and our entire education system of math relies on base 10. Kind of hard to suddenly add two fingers to everyone. Additionally, base 12, would not act like 12 does in base 10, thus if base 12 is your key point of reference, a foot should be 10 in base 12 for inches.....

Just_Smith 8y ago
People don't really think in terms of 10s either - that's just societal conditioning based on the usage of fingers to count. If you can accurately picture 1/3 of set, but your number system cannot, it's not really that accommodating of a system. By the way, you can count base12 on your hands using the digits of your fingers. We just teach kids to use fingers because it's the norm.
- jodrellblank 8y ago
  Why are you so obsessed with thirds? If you care about short, clean fractions on a human scale, base 6 is overall better, see this table: https://youtu.be/qID2B4MK7Y0?t=992 https://youtu.be/qID2B4MK7Y0?t=992 Plus you get all the convenience of having five digits on a hand and 5 as the highest counting digit, so you can count to 55 on two hands, and all the rest of the benefits in that (totally serious) video.
- DareRight 8y ago
  A numbering system based on human fingers would be base6.
  - umanwizard 8y ago
    You've got it backwards. Counting to ten on your fingers predates the concept of our modern positional number system by hundreds of thousands of years. That's why base 10 was already the well-established natural choice when that system was invented. Thinking that you could represent the quantity IIIIIIIIIIIIIIIIIIIII by the string "21" because it's 2 * 10 + 1, or similarly as "three fingers on left hand, three fingers on right hand" seems obvious to us now, but is actually pretty recent technology relative to the whole timescale of human development
    - DareRight 8y ago
      I'm not sure what your point is. A numbering system based on five-fingered hands is still base6. It doesn't make mathematical sense to argue that we learn base10 today because our hands have 5 fingers. Even if you argue that we have 10 total fingers, that's base11. Does anybody advocate that? How did we come to such an arbitrary thing as base ten?
      - umanwizard 8y ago
        No, counting on the hands is not base anything, because positional number systems did not exist. Just like Roman numerals or tally marks aren't base anything. People counted on fingers like with tally marks - they could express the numbers one through ten. Thus ten became an important and familiar number to humans. Thus it would have seemed natural to use a base 10 number system many millennia later.
bnjms 8y ago
Additionally, base 12, would not act like 12 does in base 10, thus if base 12 is your key point of reference, a foot should be 10 in base 12 for inches..... I honestly cannot make any sense of this part of your argument. The symbols 10 would only look like ten they would still mean a dozen and the properties would remain the same. Furthermore people don’t think in twelves because we are not taught in a dozenal numbering system. And there is no need for twelve fingers it would be a simple thing to create two additional hand symbols to teach children to count to a dozen. Twelve is a great base. I would prefer it but it isn’t the sort of thing that can be changed.
- kiriakasis 8y ago
  He is saying that you need twelve digits to actually use base 12 and that in every base N with N>1 you write N as 10 (eg in hex 10 is A and 16 is 10)
  - bnjms 8y ago
    Understood, his mistake was this “base 12, would not act like 12 does in base 10". That statement is mistaken. A dozen would look like ‘10’ but it would still behave like a dozen.
thrower123 8y ago
Clearly, people do think in 12s, because it's been a common thread in mathematics and measurement and calendaring through many different cultures going back to the Sumerians.
- kiriakasis 8y ago
  Let me clear something: how do you count? Can you multiply 63895 by 12? By 6? By 3? By 10? This is an standard, there have been coltures where the base was 60 and they could multiply 63895 by 60 easily. But now the whole world counts in 10. I would be happy if that number was 12 but the simple fact that we write in base ten makes it not the case (also mathematically speaking 12 is divided by a square which causes weird things) There is nothing wrong with 12 but as long as you cannot do 63895*12 easily 10 is better

Just_Smith 8y ago

People don't really think in terms of 10s either - that's just societal conditioning based on the usage of fingers to count. If you can accurately picture 1/3 of set, but your number system cannot, it's not really that accommodating of a system. By the way, you can count base12 on your hands using the digits of your fingers. We just teach kids to use fingers because it's the norm.

jodrellblank 8y ago
Why are you so obsessed with thirds? If you care about short, clean fractions on a human scale, base 6 is overall better, see this table: https://youtu.be/qID2B4MK7Y0?t=992 https://youtu.be/qID2B4MK7Y0?t=992 Plus you get all the convenience of having five digits on a hand and 5 as the highest counting digit, so you can count to 55 on two hands, and all the rest of the benefits in that (totally serious) video.
DareRight 8y ago
A numbering system based on human fingers would be base6.
- umanwizard 8y ago
  You've got it backwards. Counting to ten on your fingers predates the concept of our modern positional number system by hundreds of thousands of years. That's why base 10 was already the well-established natural choice when that system was invented. Thinking that you could represent the quantity IIIIIIIIIIIIIIIIIIIII by the string "21" because it's 2 * 10 + 1, or similarly as "three fingers on left hand, three fingers on right hand" seems obvious to us now, but is actually pretty recent technology relative to the whole timescale of human development
  - DareRight 8y ago
    I'm not sure what your point is. A numbering system based on five-fingered hands is still base6. It doesn't make mathematical sense to argue that we learn base10 today because our hands have 5 fingers. Even if you argue that we have 10 total fingers, that's base11. Does anybody advocate that? How did we come to such an arbitrary thing as base ten?
    - umanwizard 8y ago
      No, counting on the hands is not base anything, because positional number systems did not exist. Just like Roman numerals or tally marks aren't base anything. People counted on fingers like with tally marks - they could express the numbers one through ten. Thus ten became an important and familiar number to humans. Thus it would have seemed natural to use a base 10 number system many millennia later.

bnjms 8y ago

Additionally, base 12, would not act like 12 does in base 10, thus if base 12 is your key point of reference, a foot should be 10 in base 12 for inches..... I honestly cannot make any sense of this part of your argument. The symbols 10 would only look like ten they would still mean a dozen and the properties would remain the same. Furthermore people don’t think in twelves because we are not taught in a dozenal numbering system. And there is no need for twelve fingers it would be a simple thing to create two additional hand symbols to teach children to count to a dozen. Twelve is a great base. I would prefer it but it isn’t the sort of thing that can be changed.

kiriakasis 8y ago
He is saying that you need twelve digits to actually use base 12 and that in every base N with N>1 you write N as 10 (eg in hex 10 is A and 16 is 10)
- bnjms 8y ago
  Understood, his mistake was this “base 12, would not act like 12 does in base 10". That statement is mistaken. A dozen would look like ‘10’ but it would still behave like a dozen.

thrower123 8y ago

Clearly, people do think in 12s, because it's been a common thread in mathematics and measurement and calendaring through many different cultures going back to the Sumerians.

kiriakasis 8y ago
Let me clear something: how do you count? Can you multiply 63895 by 12? By 6? By 3? By 10? This is an standard, there have been coltures where the base was 60 and they could multiply 63895 by 60 easily. But now the whole world counts in 10. I would be happy if that number was 12 but the simple fact that we write in base ten makes it not the case (also mathematically speaking 12 is divided by a square which causes weird things) There is nothing wrong with 12 but as long as you cannot do 63895*12 easily 10 is better