## Counting with Fingers

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Feddlefew
Posts: 258
Joined: Wed Jun 17, 2009 1:47 pm UTC

### Counting with Fingers

What is the highest number a human can count to with their fingers?

Conditions:
-You must count in integers. (+1 for each configuration)
-Both hands may be used.
-All human hands are assumed to have ten fingers.
-No repeating exact hand/finger configurations.
-Finger configurations must be human-friendly; no bending joints backwards.

The highest number I've gotten so far is:

Spoiler:
4099
Last edited by Feddlefew on Tue Sep 27, 2011 9:08 pm UTC, edited 3 times in total.
My spelling is abysmal. Just saying.

skullturf
Posts: 556
Joined: Thu Dec 07, 2006 8:37 pm UTC
Location: Chicago
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### Re: Counting with Fingers

Feddlefew wrote:-All human hands are assumed to have ten fingers.

Those are some big hands.

Krealr
Posts: 159
Joined: Wed Sep 09, 2009 8:22 pm UTC

### Re: Counting with Fingers

I can count to 10 billion without breaking a sweat.

1 billion (1 finger), 2 billion (2 finger), 3 billion ....

I'm thinking you meant for a few more conditions. Something along the lines of: Must start at 0 (or 1) and every integer after that must have a unique finger configuration.

imyourfoot
Posts: 24
Joined: Tue Dec 19, 2006 6:21 am UTC

### Re: Counting with Fingers

If we assume all finger joints can be operated sufficiently independently (including the ones at the base of each finger) then that gives us (3 joints per normal finger)*(8 normal fingers) + (2 joints per thumb)*(2 thumbs) = 28 joints. Each joint has 2 possible states for 2^28=268,435,456 possibilities, so that minus one would be the highest number given those assumptions.

Feddlefew
Posts: 258
Joined: Wed Jun 17, 2009 1:47 pm UTC

### Re: Counting with Fingers

imyourfoot wrote:If we assume all finger joints can be operated sufficiently independently (including the ones at the base of each finger) then that gives us (3 joints per normal finger)*(8 normal fingers) + (2 joints per thumb)*(2 thumbs) = 28 joints. Each joint has 2 possible states for 2^28=268,435,456 possibilities, so that minus one would be the highest number given those assumptions.

Okay, can anyone actually do that? I'm trying but my tendons won't let me.

Also, fixed the rules list. I forgot the integer rule....
My spelling is abysmal. Just saying.

imyourfoot
Posts: 24
Joined: Tue Dec 19, 2006 6:21 am UTC

### Re: Counting with Fingers

Feddlefew wrote:
imyourfoot wrote:If we assume all finger joints can be operated sufficiently independently (including the ones at the base of each finger) then that gives us (3 joints per normal finger)*(8 normal fingers) + (2 joints per thumb)*(2 thumbs) = 28 joints. Each joint has 2 possible states for 2^28=268,435,456 possibilities, so that minus one would be the highest number given those assumptions.

Okay, can anyone actually do that? I'm trying but my tendons won't let me.

Also, fixed the rules list. I forgot the integer rule....

I can't do them completely independently, and I wouldn't be surprised if nobody could. On the other hand, I can bend them separately enough that I could count arbitrary combinations if I was careful.

If you want to be more realistic/tolerant of error, it probably varies from person to person. When I bend my pinkie my ring finger bends to a lesser extent, and similar effects would occur to some greater or lesser degree for different people.

Qaanol
The Cheshirest Catamount
Posts: 3069
Joined: Sat May 09, 2009 11:55 pm UTC

### Re: Counting with Fingers

Assuming I have perfect control over the direction that my finger points, and perfect ability to determine that direction at a glance, then there is no limit. I can count arbitrarily high with just one finger. Just say the slope of the angle my finger makes relative to the reference direction of my choice.

In practice, I’m content with counting to 1023 on my fingers. I’m rather partial to the number 132 in that system.
wee free kings

Posts: 1267
Joined: Thu Jun 16, 2011 6:36 pm UTC

### Re: Counting with Fingers

As I understand the problem, you are just wondering how many distinct signs humans can make with their fingers, not actually wanting to assign numbers to the signs. There's a ton of things you can do to get many more distinct signs than a few thousand. I mean, just learn sign language and spell out numbers. That will get you as high as we have words for numbers.

Other things that aren't disallowed in the rules:

You can add several different motions to your signs to make them distinct.

You can make more than just a few distinct, easy finger positions (not many people can independently change each of their 3 joints on every finger). Easy ones would be up, down, completely curled, finger pointing down, horizontal, straight 3/4 up, straight 3/4 down, curled but with the first joint straight (first knuckle pointed up), etc.

You can use the interaction between hands and body - i.e. pointing at a particular place on your body.

You can hold fingers together, apart, or slightly apart.

You can just make several different signs in a row. I hold up 1 finger, then 3 fingers, then 9 fingers, then clench my fist, then quickly loosen my fingers before clenching my fist again, and I've just counted to 13,900.

rigwarl
Posts: 759
Joined: Wed Dec 09, 2009 9:36 pm UTC

### Re: Counting with Fingers

Qaanol wrote:I’m rather partial to the number 132 in that system.

redrogue
Posts: 116
Joined: Tue Dec 15, 2009 9:17 pm UTC

### Re: Counting with Fingers

Perfect control over finger joints, eh? I don't have perfect control over my last joints, but I thought I could get three states per finger. That failed. To see what I mean, extend your ring finger, then try to put your middle finger all the way down vs. half way down.

I can get 16,384 with relative ease, though. 2^10 for binary finger positions, times 4^2 for four obvious positions of your hand itself: thumb down, palm down, thumb up, palm up.

mfb
Posts: 950
Joined: Thu Jan 08, 2009 7:48 pm UTC

### Re: Counting with Fingers

Your 4 hand positions all use the same direction of the hand itself - but you can use more different directions for that.
3 different states with the thumb are easy with "on the palm", "parallel" and "stretched away".

Counting will get a bit tricky with ((2^4*3)*(2^2)*6)^2 different states.

Turtlewing
Posts: 236
Joined: Tue Nov 03, 2009 5:22 pm UTC

### Re: Counting with Fingers

Pint of pedantry:

you really need to specify a starting point or else I can count arbitrarily high with only 1 unique finger position by choosing an arbitrarily high integer as my starting point.

You probably should come up with a firm statment about the number of degrees of freedom per finger as the difference between 3 DoF and 4 DoF determines whether the "Vulcan live long and prosper sign", is distinct from the "high five" sign.