If only we could combine the two and get to 2^12… Sadly, this would require 12 thumbs.
Ooh, actually you can get to 2^8 without worrying about those pesky tendon issues by putting your fingertips against your thumb instead of trying to extend your fingers… Hmmm… Maybe we can even go to 2^10 this way by incorporating knuckles. Might lose some time today figuring out more hand counting systems. I wonder if anything higher than 2^10 is possible…
Some might say it’s giving finger counting too much thought, others might say it’s a tangent too serious for dad jokes, I say… the efficiency gains seem to come from a change in technique for how a count is stored.
Base-10 finger counting technique just accumulates, the number of fingers held up is the count.
Base-12 uses a pointer (your thumb) to point to a value (a knuckles or finger segment).
Base-2 uses a finger up or down to show a place value as one or zero.
You could tattoo numbers on your forearm so all five fingers from your other hand could point to a value for up to five more places to point.
Base 10 on your hands is really base 1. Every finger is either 0 or 1 and we just count them! Base 12 we do have 12 positions each representing a digit, and two potential digits from our hands.
Binary is so much more efficient because you have 10 digits, just like in base 1, but you use them more efficiently.
The next logical step is trinary, if we can incorporate enough fingers it would go higher than binary. Wikipedia suggests three positions of your fingers - up, down, and somewhere in between, or folded - but I’d be surprised if anyone can realistically do that with all their fingers. However, using four fingers on each hand and pointing them at different knuckles/the tip of your thumb gets you 8 digits of base 4 (including not pointing at the thumb at all as 0)… And actually doesn’t tangle your fingers up too bad.
If only we could combine the two and get to 2^12… Sadly, this would require 12 thumbs.
Ooh, actually you can get to 2^8 without worrying about those pesky tendon issues by putting your fingertips against your thumb instead of trying to extend your fingers… Hmmm… Maybe we can even go to 2^10 this way by incorporating knuckles. Might lose some time today figuring out more hand counting systems. I wonder if anything higher than 2^10 is possible…
Some might say it’s giving finger counting too much thought, others might say it’s a tangent too serious for dad jokes, I say… the efficiency gains seem to come from a change in technique for how a count is stored.
Base-10 finger counting technique just accumulates, the number of fingers held up is the count.
Base-12 uses a pointer (your thumb) to point to a value (a knuckles or finger segment).
Base-2 uses a finger up or down to show a place value as one or zero.
You could tattoo numbers on your forearm so all five fingers from your other hand could point to a value for up to five more places to point.
Base 10 on your hands is really base 1. Every finger is either 0 or 1 and we just count them! Base 12 we do have 12 positions each representing a digit, and two potential digits from our hands.
Binary is so much more efficient because you have 10 digits, just like in base 1, but you use them more efficiently.
The next logical step is trinary, if we can incorporate enough fingers it would go higher than binary. Wikipedia suggests three positions of your fingers - up, down, and somewhere in between, or folded - but I’d be surprised if anyone can realistically do that with all their fingers. However, using four fingers on each hand and pointing them at different knuckles/the tip of your thumb gets you 8 digits of base 4 (including not pointing at the thumb at all as 0)… And actually doesn’t tangle your fingers up too bad.
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