# How high can you count on 10 fingers?

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Posted (edited)

So I watched the first episode of Chernobyl the other night and was pretty wound up, so I tried to think about something boring to help me fall asleep.

I though about binary numbers, and I wondered if I could count binary numbers on my fingers. Turns out you can! Using one hand, you can count up to 31, each finger has a value, which corresponds to a power of 2. The sum of any combination of finger positions will be a value between 0 and 31.

Example:

(Demonstrated with my favorite graphical software, Excel)

So what? Counting to 31 isn't that hard, I don't need my fingers...

Well if you get your left hand involved you use the power of 2s to count (almost*) up to 1024 with all 10 fingers! (really its 1023 with all 10 fingers up).

OK, cool party trick what's it good for?

Well I actually had the chance to use it today at work. I'm observing a construction project and trying to count things that have been installed, while navigating a hazardous construction site (train mounted drill rigs, cement augers, deep tunnel muck, etc), so it is hard to keep track and inconvenient to keep pulling out my notebook to keep a tally, so a fancy finger count was just the thing.

How else could this be useful?

Edited by Nightside

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What if you could bend each knuckle independently?

I can manage about 4 distinguishable states per finger (fully retracted, fully extended, one knuckle extended, half extended). 410 = 1048576.

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I do binary as well, it's much more efficient than unary and easy to learn every combination of up and down.

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All of the above.

Except the digits thing. You crazy.

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17 minutes ago, HebaruSan said:

What if you could bend each knuckle independently?

I can manage about 4 distinguishable states per finger (fully retracted, fully extended, one knuckle extended, half extended). 4101048576.

If we had tentacles, we could do integrals...

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Posted (edited)

using my 10 fingers, i take my smartphone, write a small app with a button and a counter that goes up every time i hit that button(30 min max developing time).

Now i can count almost abitrarily high with only one hand! :-P

Addendum: using a long to store the count i could count to 9,223,372,036,854,775,807 ...everything after that requires some thinking/google.

Edited by hms_warrior

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Posted (edited)
13 minutes ago, hms_warrior said:

using my 10 fingers, i take my smartphone, write a small app with a button and a counter that goes up every time i hit that button(30 min max developing time).

Now i can count almost abitrarily high with only one hand! :-P ﻿

Typing with one finger I open the system calculator.

***

Upd.

(Presuming that the counter has default numbers of fingers and phalanges:)

As "one knuckle extended" and "half extended" look not distinguishable quite easily, let's follow the historical duodecimal practice with the thumb pointer.

4 fingers x 3 phalanges each + 1 thumb.

1. Let's divide the long fingers in two groups: Index + Middle (MINDEX) and Ring + Pinky (RINKY).

2. Let's use the thumb as a pointer for the RINKY group. It will point at a particular phalanx of either Ring or Pinky.

3. In the MINDEX group let's use each finger as a pointer to its counterpart's phalanges. Only one of them at once.
I.e. either point with the Index to one of three Middle's phalanges, or vice versa.

4. Let's take the MINDEX and the RINKY numbers separatedly. They don't know about each other.

RINKY

1. Ring is straight, Thumb is pointing at Pinky.
Thumb points at the 1/2/3 phalanx of Pinky = +3 states.
So, +3 states.

2. Ring is bended, Thumb is pointing at Pinky.
The same states of Thumb and Pinky.
So, +3 states.

3. Pinky is straight, Thumb is pointing at Ring.
Thumb points at the 1/2/3 phalanx of Ring = +3 states.
So, +3 states.

4. Pinky is bended, Thumb is pointing at Ring.
The same states of Thumb and Ring.
So, +3 states.

5. Thumb isn't pointing.
Ring is bended/straight, Pinky is bended/straight
So, +4 states.

RINKY total: 16 states.

MINDEX

1. Middle is straight, Index is pointing at its phalanges.
So, +3 states.

2. Index is straight, Middle is pointing at its phalanges.
So, +3 states.

3. Both are bended/straight.
So, + 2 states.

MINDEX total: 8 states.

Summary
One standard hand can easily distinguish at least 128 regular states = 27.
Two standard hands - 214.
By crossing them when counting you can add 1 bit more = 215.
By, say, sticking out the tongue, you become a 16-bit memory cell with 65536 states.

Edited by kerbiloid

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Posted (edited)
20 minutes ago, hms_warrior said:

Addendum: using a long to store the count i could count to 9,223,372,036,854,775,807 ...everything after that requires some thinking/google.

Yeah but if you get carried away and punch the increment button a few too many times, suddenly your next order for the cookie dough is short and everybody goes hungry.

World food shortage level hungry, just because you didn't use unsigned for counting physical objects.

OP, get yourself a mechanical clicky counter. They are ~\$1 shipped. Much more comfortable to use than walking around a construction site having one of your hands in an awkward metal hand sign.

Edited by Shpaget

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(Types with one finger in the HTML editor:
for (var i = 0; ; ++i);

Presses F5.)

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40 minutes ago, Shpaget said:

Yeah but if you get carried away and punch the increment button a few too many times, suddenly your next order for the cookie dough is short and everybody goes hungry.

World food shortage level hungry, just because you didn't use unsigned for counting physical objects.

OP, get yourself a mechanical clicky counter. They are ~\$1 shipped. Much more comfortable to use than walking around a construction site having one of your hands in an awkward metal hand sign.

I also might get myself in trouble if anyone is around when I get to four.

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Four is not the only dangerous number. Depending on your location and coworkers you can be perceived as universally vulgar.

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Posted (edited)

1024?

I should have read the OP, lol.

Binary was my immediate thought.

Edited by tater

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Posted (edited)

I used to use binary and ternary to count laps in swimming. Other people cycled through 7 kickboards or whatnot repeatedly or mentally remembered the 35 or so laps in a mile, but I would rotate the kickboards in such a way that I only needed like 4 of them. Bonus was that it was totally unintelligible to everyone else that my kickboards were being used as ternary digits so nobody could actually read it but me.

It wouldn't be a great counting system but you could somewhat increase the total possible counts beyond 1024 if you add meaning for crossing fingers (both first above and first below) or positioning your thumb between any given fingers. Not easy to devise a system where these are counted through in a methodical, understandable way though.

Edited by Pds314

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if you need to count high but dont need accuracy, you can consider each finger equal to the previous finger times a power of 10. you can count all the way up to 11111 if you add the fingers or 10 billion if you do it multiplicatively.  you can use the other hand to store a mantissa to do fp math.

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1 hour ago, Nuke said:

if you need to count high but dont need accuracy, you can consider each finger equal to the previous finger times a power of 10. you can count all the way up to 11111 if you add the fingers or 10 billion if you do it multiplicatively.  you can use the other hand to store a mantissa to do fp math.

Please speculate a situation where this would be useful.

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We could get even more permutations by crossing or splitting fingers (live long and prosper!).

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7 minutes ago, Cunjo Carl said:

We could get even more permutations by crossing or splitting fingers (live long and prosper!).

Also rotating/reorienting the hand.

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9 hours ago, Nightside said:

Please speculate a situation where this would be useful.

impressing nerds on the ksp science forum.

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1 hour ago, Nuke said:
11 hours ago, Nightside said:

Please speculate a situation where this would be useful.

impressing nerds on the ksp science forum.

Long ago, in my school, there were no personal computers around, and even programming calculators were rare.
So I was playing lunar flights with an engineering calculator and simple formulas in my head.

Doing it with fingers would be much, much more tough...

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When doing hand binary, though, which finger is the LSB?

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There's a great extended discussion of this in Digits and Dastards by Fred Pohl.

He makes up a syllabic system based on Morse code for being able to quickly communicate numbers in binary.

The two relevant stories are: “How to Count on your Fingers" & "On Binary Digits and Human Habits"

*pass*/*check*

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