4 ms·

In base 8 (if we'd had 8 fingers), an "order of magnitude" would have been defined as "times 8" instead of "times 10", so it would also be adding another 0. Sa

In base 8 (if we'd had 8 fingers), an "order of magnitude" would have been defined as "times 8" instead of "times 10", so it would also be adding another 0. Same with base 12. Base 16 would have the further advantage that we could easily halve, quarter, eighth, or 16th any number ending in 0 to a whole integer (in base 10, we can only halve, fifth, or tenth).

FabHK 7y ago
There's an argument against intelligent design right there (4 or 6 fingers per hand are obviously better).
- Retra 7y ago
  Sure, if you assume the only purpose of fingers is for counting.
- alexanderdmitri 7y ago
  Eh, evolution is a pretty nifty mix of oo class extensions, recursion, brute-force and bias weightings. I'd wager Gawsh made the best system S/He could given product constraints (completely unfocused if you ask me [which I know no one did]) and the real need to deliver (take it easy over there Leibniz, the world is still crap as evidenced everywhere). Anyway, can't knock it 'til you've built it. This is an interesting article: https://www.scientificamerican.com/article/why-do-most-species-have/ https://www.scientificamerican.com/article/why-do-most-speci...
  - FabHK 7y ago
    Well, my comment was partly in jest (though I do think it's by no means clear that 5 is a local optimum, thus it's quite possible that 4 or 6 would be better, and twice either would give us a better base for counting), but I'm amazed that there's actual scientific discussion of the issue. I wish to quote the most pertinent part of the article though: > Is there really any good evidence that five, rather than, say, four or six, digits was biomechanically preferable for the common ancestor of modern tetrapods? The answer has to be "No,"
wallace_f 7y ago
Yea you are obviously right now that I think about it, and I still have such a strong willingness to think there is something special about the number 10.
- crdrost 7y ago
  Meanwhile, there is something special about base-12, namely that the log base 2 of 3 has a really good rational approximation as 17/12, the log base 2 of 5 has a pretty good approximation as 7/3 (you can do better with 28ths). This is the basis for the 12-tone equal temperament scale in music, and it only works if you use base-12. So if we used base-12 for our numbers then someone would have the bright idea to name all of our musical notes with numbers and we could just do a key change (or chord formation) by addition.
nullc 7y ago
> In base 8 (if we'd had 8 fingers) Seven fingers. Base 11 is the natural base for a ten fingered person: Base 11 has a distinct symbol for ten, base 10 does not. [A prime base has quite a few practical disadvantages... and their advantages are fairly esoteric...]
- crdrost 7y ago
  I mean it's not so bad. If we meet aliens there is a decent chance that they will have a base-9 counting system in balanced ternary: so their digits would be -4, -3, -2, -1, 0, 1, 2, 3, 4. Rather than prefixing negatives with a minute sign, maybe negation would flip a number top-to-bottom.

FabHK 7y ago

There's an argument against intelligent design right there (4 or 6 fingers per hand are obviously better).

Retra 7y ago
Sure, if you assume the only purpose of fingers is for counting.
alexanderdmitri 7y ago
Eh, evolution is a pretty nifty mix of oo class extensions, recursion, brute-force and bias weightings. I'd wager Gawsh made the best system S/He could given product constraints (completely unfocused if you ask me [which I know no one did]) and the real need to deliver (take it easy over there Leibniz, the world is still crap as evidenced everywhere). Anyway, can't knock it 'til you've built it. This is an interesting article: https://www.scientificamerican.com/article/why-do-most-species-have/ https://www.scientificamerican.com/article/why-do-most-speci...
- FabHK 7y ago
  Well, my comment was partly in jest (though I do think it's by no means clear that 5 is a local optimum, thus it's quite possible that 4 or 6 would be better, and twice either would give us a better base for counting), but I'm amazed that there's actual scientific discussion of the issue. I wish to quote the most pertinent part of the article though: > Is there really any good evidence that five, rather than, say, four or six, digits was biomechanically preferable for the common ancestor of modern tetrapods? The answer has to be "No,"

wallace_f 7y ago

Yea you are obviously right now that I think about it, and I still have such a strong willingness to think there is something special about the number 10.

crdrost 7y ago
Meanwhile, there is something special about base-12, namely that the log base 2 of 3 has a really good rational approximation as 17/12, the log base 2 of 5 has a pretty good approximation as 7/3 (you can do better with 28ths). This is the basis for the 12-tone equal temperament scale in music, and it only works if you use base-12. So if we used base-12 for our numbers then someone would have the bright idea to name all of our musical notes with numbers and we could just do a key change (or chord formation) by addition.

nullc 7y ago

> In base 8 (if we'd had 8 fingers) Seven fingers. Base 11 is the natural base for a ten fingered person: Base 11 has a distinct symbol for ten, base 10 does not. [A prime base has quite a few practical disadvantages... and their advantages are fairly esoteric...]

crdrost 7y ago
I mean it's not so bad. If we meet aliens there is a decent chance that they will have a base-9 counting system in balanced ternary: so their digits would be -4, -3, -2, -1, 0, 1, 2, 3, 4. Rather than prefixing negatives with a minute sign, maybe negation would flip a number top-to-bottom.