Dec. 25th, 2016

cjwatson: (Default)
Happy Christmas and happy Hanukkah (they coincide this year)! This is not especially festive except that I was reminded of it at Midnight Mass while counting verses of a rather long litany.

When I was a teenager, I invented what as far as I know is an original method of finger-counting; at least I was unaware of having based it on anything else and I haven't seen it used anywhere since. No, please stop backing away slowly, I promise I'm not dangerous. I don't remember exactly why I bothered, but it may have had something to do with being a cellist and therefore occasionally having to count off long rests in a reasonably discreet way that was harder to lose track of than just counting in my head. I still sometimes use it in similar circumstances.

My method goes as follows:
  • Begin by counting off the three segments of each finger on your left hand by touching the palmward side of them with your left thumb: 1, 2, 3 for the tip, middle, base of your index finger, 4, 5, 6 for your middle finger, and so on. This takes you to 12.
  • Touch your left palm with your left thumb for 13.
  • Now return to your left fingers as before, but this time touch the backs of the segments: 14, 15, 16 for the tip, middle, base of your index finger, and so on. This takes you to 25 on a single hand.
  • If you need more, use your right hand in the same way as a 25s place. The upper limit is therefore 625.
I was certainly aware of binary and hexadecimal bases by that time and reasonably fluent in both, and I thought of finger binary independently, but converting between bases can take a bit of thought, and the point was to be easily usable in situations where I didn't have much spare brainpower available, for example when in the middle of an orchestral concert with lots of other stuff going on. I basically wanted to be able to delegate the job of counting to a simple motor task and be reasonably sure of getting it right.

This method has several nice properties:
  • 25 is very decimal-friendly, at least at smallish values. It's pretty rare to have to "manually" count higher than 100, and that's just 0 on the left hand and 4 on the right. Most numbers one is likely to need to count to come out easily. Wikipedia tells me that there are Asian systems that use finger segments in a similar way to reach 12 on each hand, but that's not as decimal-friendly.
  • Only involves small movements, mostly within the natural crook of your hand. You can quite easily count this way in a context where other methods would be awkward or gauche, and probably nobody will notice.
  • Reasonably useful upper limit with a single hand. (As a cellist I was usually holding a bow with my right hand, but during rests my left hand was free.)
It is, I suspect, not at all useful for communication: distinguishing between two different sides of a finger is quite easy by touch but probably not by sight.

Am I weird? Is anyone aware of a previous base-25 system like this? Feel free to only answer the second of those questions.

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