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Topic: Counting (Read 457 times) |
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slaverstudent
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What is the largest number that you can count up to using only the fingers on both hands?
Hint: The answer is not 10.
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| « Last Edit: Jan 27th, 2010, 2:54am by slaverstudent » |
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towr
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Re: Counting
« Reply #1 on: Jan 27th, 2010, 3:05am » |
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Using the fingers as bits, you can get up to at least 1023. But you can also use them as ..err.. trits(?), and get up to 59048; although it can be difficult to move your fingers independently. And there are yet other schemes with which you may possibly count higher.
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slaverstudent
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Re: Counting
« Reply #2 on: Jan 27th, 2010, 4:45am » |
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on Jan 27th, 2010, 3:05am, towr wrote:| Using the fingers as bits, you can get up to at least 1023. But you can also use them as ..err.. trits(?), and get up to 59048; although it can be difficult to move your fingers independently. And there are yet other schemes with which you may possibly count higher. |
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Very fast answer! Only 14 minutes after posting. 
I think the binary system is the only practical solution as most people wouldn't have the dexterity to implement the ternary system (especially with the thumbs).
So IMO 1023 is the practical limit.
When considering the number of joints in thumbs and fingers, I think the theoretical limit is 589,823. (combination of base4 for fingers and base3 for thumbs. 
ie. (31 x 44)2 - 1
on Jan 27th, 2010, 3:05am, towr wrote:| But you can also use them as ..err.. trits(?) |
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If Binary ==> "bits", then I guess the appropriate Ternary terminology is "tits".
(Hang-on though, that's actually slightly in-appropriate.  )
It would be interesting to see if anyone can come up with a practical system to exceed 1023.
- one way would be to make the orientation of the hands significant as well. (palm facing towards or away).
This would give a practical limit of 4095.
ie. ( 26)2 - 1
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| « Last Edit: Jan 27th, 2010, 5:20am by slaverstudent » |
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towr
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Re: Counting
« Reply #3 on: Jan 27th, 2010, 5:18am » |
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One practical approach to exceed 1023, is to use the fingers on one hand to point at distinct spots on the other 5 fingers (if we can use the hand area also, we can get even further).
I can get at least 5 distinct areas on the thumb, 7 on the middle three fingers, and 6 on the pinky. So that's 10290 distinct values. It's not an easy number system, though. I suppose picking 5 spots on each finger might be simpler, but you only get up to 3125 values then. (Or double that if you switch hands.)
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SMQ
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Re: Counting
« Reply #4 on: Jan 27th, 2010, 5:20am » |
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I actually do this (count in binary on my fingers) with some regularity.
I've never needed to count over a thousand, but being able to count over 30 on one hand is very convenient sometimes. I've tried trinary/ternary, but I definitely lack the necessary dexterity.
Using position of the hand as an extra bit (or more) is an interesting idea. When I tried it just now, I found that when I turned my hand over I started to fumble the binary sequence that I can normally manage without thinking about it--how odd.
--SMQ
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towr
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Re: Counting
« Reply #5 on: Jan 27th, 2010, 5:30am » |
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Come to think of it, I wouldn't want to count over a thousand on my hands. That's 15 minutes better spent doing something else 
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slaverstudent
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Re: Counting
« Reply #6 on: Jan 27th, 2010, 5:30am » |
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on Jan 27th, 2010, 5:30am, towr wrote:| Come to think of it, I wouldn't want to count over a thousand on my hands. That's 15 minutes better spent doing something else |
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Come to think of it, neither would I, but it's an interesting mental exercise. 
I've corrected an error at the end of my last post, as I realized the palm orientation adds less powerful significant bits than I first calculated.
(ie. It adds 1 extra significant bit to each hand, giving 64 x 64 - 1 = 4095) not 1,048,575 as I first posted.
I think I've got it right now. 
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| « Last Edit: Jan 27th, 2010, 5:34am by slaverstudent » |
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slaverstudent
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Re: Counting
« Reply #7 on: Jan 27th, 2010, 5:37am » |
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on Jan 27th, 2010, 5:20am, SMQ wrote:Using position of the hand as an extra bit (or more) is an interesting idea. When I tried it just now, I found that when I turned my hand over I started to fumble the binary sequence that I can normally manage without thinking about it--how odd.
--SMQ |
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I imagine this will take some practice.
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SMQ
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Re: Counting
« Reply #8 on: Jan 27th, 2010, 5:48am » |
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on Jan 27th, 2010, 5:37am, slaverstudent wrote:| I imagine this will take some practice. |
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Indeed.
With practice, though, I could see getting at least two bits (four distinct hand positions) out of it: I think you can safely raise your practical limit to 16Ki. Plus that would put the one-hand count over 100, which just sounds more impressive: "I can count over 100 on one hand."
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slaverstudent
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Re: Counting
« Reply #9 on: Jan 27th, 2010, 5:49am » |
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BTW.
One of the most useful numbers in this counting system is the number 4. (Think about it. )
Hint: Useful in traffic.
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| « Last Edit: Jan 27th, 2010, 6:12am by slaverstudent » |
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Random Lack of Squiggily Lines
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Re: Counting
« Reply #10 on: Jan 27th, 2010, 7:14am » |
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You can also cross your arms, for 3? more bits(uncrossed, left arm over, right arm over), but is this restricted to hands.
Oh, and one can rotate their hands to different orientations.(palms facing each other, palms in same direction, palms in opistite directions) etc, all at 90 degree rotations. thats 4*4? or 16 more bits there.
Edit: wth was i thinking, thats not right
Oh, and i guess we should restrict it to hands then.
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| « Last Edit: Jan 28th, 2010, 8:26am by Random Lack of Squiggily Lines » |
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slaverstudent
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Re: Counting
« Reply #11 on: Jan 27th, 2010, 7:26am » |
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I think we'd better restrict it to hands, otherwise where does it end? ... Mouth open/closed, wink left/right eye, stand on left foot, right foot, both feet, etc ....etc .....etc ...
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Grimbal
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Re: Counting
« Reply #12 on: Jan 27th, 2010, 12:59pm » |
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132 is worse. But I don't think I ever counted so far.
Anyway, I usually count not by raising the fingers, but by touching some surface, as if playing piano. So It is not a problem if I have to stop at 132 a while.
If you care about what you look, when adding bits by turning the palms up or down, you better don't make these the least significant bits. Or you would look funny when counting.
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