5 ms·

0 to 9 are exactly 10 digits.

can_count 5y ago
0 fingers to 10 fingers is exactly 11 numbers.
depaya 5y ago
I think their point is that we use our 10 fingers to count to a value of 10. We can use our 10 fingers to represent 0 (no fingers) through 10 (all 10 fingers). This is essentially base 11 if you try to assign a specific digit to each finger. While I agree with that viewpoint I think it's missing the point. As humans with 10 fingers it's easy for us to group things into increments of 10, so base 10 comes naturally. Think about how you count a quantity over 10: once you run out of fingers you mark down (or remember) that you've already counted one quantity of 10, now you're counting the next quantity of 10, etc... It's more like a shifted base 10 where we represent digits 1-10 instead of 0-9.
- slver 5y ago
  Everyone is thinking about a "shifted" base 10, yes. But every base starts with 0, there's no such thing as "shifted base" because then you literally can't represent 0. Also "zero fingers" is still a thing that exists in this shifted base 10. So it remains base 11. This is like the classic "0-based indexing" vs. "1-based indexing" dilemma. The "first" thing is represented by 1, we think. But the "first" year of our life, we're zero years old. The "first" hour after midnight is 0 o'clock. Building your "first" million as a business is the period before you have 1 million. And so on.
  - dylanh 5y ago
    A base 10 with symbols only for 1 through 10, where zero is represented with an empty set is a Bijective Base 10 numeration. The columns in excel are bijective base 26. https://en.wikipedia.org/wiki/Bijective_numeration https://en.wikipedia.org/wiki/Bijective_numeration
    - deleted 5y ago
      [deleted]
    - slver 5y ago
      The number of sets we can represent with fingers is 11, including the empty set. As for bijective base 10, it's interesting, but it's still not the base 10 we're using, so we can't quite blame this on our fingers.

0 fingers to 10 fingers is exactly 11 numbers.

I think their point is that we use our 10 fingers to count to a value of 10. We can use our 10 fingers to represent 0 (no fingers) through 10 (all 10 fingers). This is essentially base 11 if you try to assign a specific digit to each finger. While I agree with that viewpoint I think it's missing the point. As humans with 10 fingers it's easy for us to group things into increments of 10, so base 10 comes naturally. Think about how you count a quantity over 10: once you run out of fingers you mark down (or remember) that you've already counted one quantity of 10, now you're counting the next quantity of 10, etc... It's more like a shifted base 10 where we represent digits 1-10 instead of 0-9.

slver 5y ago
Everyone is thinking about a "shifted" base 10, yes. But every base starts with 0, there's no such thing as "shifted base" because then you literally can't represent 0. Also "zero fingers" is still a thing that exists in this shifted base 10. So it remains base 11. This is like the classic "0-based indexing" vs. "1-based indexing" dilemma. The "first" thing is represented by 1, we think. But the "first" year of our life, we're zero years old. The "first" hour after midnight is 0 o'clock. Building your "first" million as a business is the period before you have 1 million. And so on.
- dylanh 5y ago
  A base 10 with symbols only for 1 through 10, where zero is represented with an empty set is a Bijective Base 10 numeration. The columns in excel are bijective base 26. https://en.wikipedia.org/wiki/Bijective_numeration https://en.wikipedia.org/wiki/Bijective_numeration
  - deleted 5y ago
    [deleted]
  - slver 5y ago
    The number of sets we can represent with fingers is 11, including the empty set. As for bijective base 10, it's interesting, but it's still not the base 10 we're using, so we can't quite blame this on our fingers.