6 ms·

Arabic notation / base ten seems to work really well with our brains. Having that many fingers probably helps. I couldn't imagine a modern world running on Roma

Arabic notation / base ten seems to work really well with our brains. Having that many fingers probably helps. I couldn't imagine a modern world running on Roman Numerals.

maliker 5y ago
The real killer application of arabic numerals is arithmetic. Doing even multiplication and division in roman numerals is very time consuming [1]. [1] https://scienceblogs.com/goodmath/2006/08/16/roman-numerals-and-arithmetic https://scienceblogs.com/goodmath/2006/08/16/roman-numerals-...
slver 5y ago
Most of us are programmers here, you are just as used to hex. Also technically we don't have that many fingers. We have one more finger. We don't have a number digit for ten right? They go zero to nine. But out fingers go zero to ten. If our numeric base matched our fingers, we should've used base eleven. Not many people think this through :) I think the real breakthrough is having "order of magnitude" in numbers. So indeed the Roman Numerals suck and probably wouldn't last regardless.
- the_monocle 5y ago
  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.
- nicetryguy 5y ago
  > you are just as used to hex. I do 6502 ASM with bit tricks and all and i can tell you straight up that hex is never as intuitive as decimal IMO. Base eleven sounds like the stuff of nightmares =)
  - tenebrisalietum 5y ago
    Where the hex is "intuitive" is showing what's "even" to the CPU. For example we think of 10, 100, 50 as nice round convenient quantities. CPUs see 16, 256, 2048 as convenient quantities--in hex that's visible: 0x10, 0x100, 0x800.
    - nicetryguy 5y ago
      Right. It lets you see the bits more easily: 0-F is a good representation of 4 bits. Say i were to name a random hex value like #$9C right now it would take me a few seconds to convert that to decimal in my head though... 156 took me a few seconds to sort out. I don't have to think about what 156 means in decimal because i just know what it is.
      - vangelis 5y ago
        The radix I've used since birth is easier than the one I haven't. Wild stuff.
        nicetryguy 5y ago
        Yes i do simplify my posts and try to write them in ways that normal people can understand. Your snide comment is a sign of success =)
      - sipos 5y ago
        Do you though? Why is 156 anymore familiar than 9C? I can't imagine 156 things any more than I can 9C things.
        5y ago
laurent92 5y ago
> Having 10 fingers probably helps. Yes, so we can count to 31 on one hand. Somehow, no civilization invented a base-32 notation.
- bobsmooth 5y ago
  A few civilizations have used base 60 https://en.wikipedia.org/wiki/Sexagesimal https://en.wikipedia.org/wiki/Sexagesimal
  - bee_rider 5y ago
    The idea of counting to 12 by pointing to knuckles is something I hadn't encountered before, and really neat. Kinda surprised base-12 didn't end up dominating. Having so many factors would have made division so much more convenient for mental math, and it is only 2 extra characters to remember.
- bee_rider 5y ago
  I don't think the choice of base is really dependent on finger encoding efficiency. Going 0-5 on a hand has the advantage that we only really care about the "last" finger. Anyway, if we really want to go crazy, the knuckle and first joint on (my, at least) fingers can be controlled somewhat independently, so I think we can fit in 4 states per finger: | _ | | __ _ |
- sipos 5y ago
  You might be able to. Personally I can't raise my ring finger without my little/pinkie finger also being raised. Also, some numbers in finger binary are liable to get you punched if shown the wrong way round.
- flo123456 5y ago
  Try using that to explain arithmetic to a child. In a base-10 system the explanation is as simple as holding up both hands and then holding up the number of fingers for each hand you want them to add. The kid can count and intuitively learn how to add up two numbers. It’s really simple and really efficient.
perl4ever 5y ago
It occurred to me once that the big/little endian issues people have are really due to the conflict between Arabic numbers going in the opposite direction from English letters. If both ran right to left, or left to right, then there would be no difference.

Arabic notation / base ten seems to work really well with our brains. Having that many fingers probably helps. I couldn't imagine a modern world running on Roman Numerals.

maliker 5y ago

The real killer application of arabic numerals is arithmetic. Doing even multiplication and division in roman numerals is very time consuming [1]. [1] https://scienceblogs.com/goodmath/2006/08/16/roman-numerals-and-arithmetic https://scienceblogs.com/goodmath/2006/08/16/roman-numerals-...

slver 5y ago

Most of us are programmers here, you are just as used to hex. Also technically we don't have that many fingers. We have one more finger. We don't have a number digit for ten right? They go zero to nine. But out fingers go zero to ten. If our numeric base matched our fingers, we should've used base eleven. Not many people think this through :) I think the real breakthrough is having "order of magnitude" in numbers. So indeed the Roman Numerals suck and probably wouldn't last regardless.

the_monocle 5y ago
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.
nicetryguy 5y ago
> you are just as used to hex. I do 6502 ASM with bit tricks and all and i can tell you straight up that hex is never as intuitive as decimal IMO. Base eleven sounds like the stuff of nightmares =)
- tenebrisalietum 5y ago
  Where the hex is "intuitive" is showing what's "even" to the CPU. For example we think of 10, 100, 50 as nice round convenient quantities. CPUs see 16, 256, 2048 as convenient quantities--in hex that's visible: 0x10, 0x100, 0x800.
  - nicetryguy 5y ago
    Right. It lets you see the bits more easily: 0-F is a good representation of 4 bits. Say i were to name a random hex value like #$9C right now it would take me a few seconds to convert that to decimal in my head though... 156 took me a few seconds to sort out. I don't have to think about what 156 means in decimal because i just know what it is.
    - vangelis 5y ago
      The radix I've used since birth is easier than the one I haven't. Wild stuff.
      - nicetryguy 5y ago
        Yes i do simplify my posts and try to write them in ways that normal people can understand. Your snide comment is a sign of success =)
    - sipos 5y ago
      Do you though? Why is 156 anymore familiar than 9C? I can't imagine 156 things any more than I can 9C things.
      - 5y ago

laurent92 5y ago

> Having 10 fingers probably helps. Yes, so we can count to 31 on one hand. Somehow, no civilization invented a base-32 notation.

bobsmooth 5y ago
A few civilizations have used base 60 https://en.wikipedia.org/wiki/Sexagesimal https://en.wikipedia.org/wiki/Sexagesimal
- bee_rider 5y ago
  The idea of counting to 12 by pointing to knuckles is something I hadn't encountered before, and really neat. Kinda surprised base-12 didn't end up dominating. Having so many factors would have made division so much more convenient for mental math, and it is only 2 extra characters to remember.
bee_rider 5y ago
I don't think the choice of base is really dependent on finger encoding efficiency. Going 0-5 on a hand has the advantage that we only really care about the "last" finger. Anyway, if we really want to go crazy, the knuckle and first joint on (my, at least) fingers can be controlled somewhat independently, so I think we can fit in 4 states per finger: | _ | | __ _ |
sipos 5y ago
You might be able to. Personally I can't raise my ring finger without my little/pinkie finger also being raised. Also, some numbers in finger binary are liable to get you punched if shown the wrong way round.
flo123456 5y ago
Try using that to explain arithmetic to a child. In a base-10 system the explanation is as simple as holding up both hands and then holding up the number of fingers for each hand you want them to add. The kid can count and intuitively learn how to add up two numbers. It’s really simple and really efficient.

perl4ever 5y ago

It occurred to me once that the big/little endian issues people have are really due to the conflict between Arabic numbers going in the opposite direction from English letters. If both ran right to left, or left to right, then there would be no difference.