how high can you count with your fingers and thumbs?

Troudeloup
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i can count only to 31 with 11111     of  an open right hand, and I want to save counting in binary with both of my hands for jail, so



how high can you count with your fingers and thumbs?
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Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
with all 10 fingers, you can count up to 2^10 -1 which is 1023

Author

Commented:
why minus one?
Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
because you start counting with 0.
with 10 digits, you have 2^10 values you can count.
starting with 0, you can count from 0 to 1023.
if you start at 1 (all fingers down), you can go of course from 1 to 1024
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Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
note that you had found 31 with 5 fingers.
guess, what is the result of 2^5  -1

Author

Commented:
what's about this thread is:


how can you count even higher?

Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
you could go higher by leaving the binary system, by giving more positions to the fingers, hence you replace 2^x by 3^x.
but you said you don't want to leave the binary system...

you could go higher by adding the position of the wrist/hand...

Author

Commented:
oh god.

don't break law.

Author

Commented:
oh he didn't get the joke.
Top Expert 2007

Commented:
Even though the author requested one hand, the Q did say thumbs(notice the S) this does imply perhaps a two handed approach as a way to go.
AngelIII is correct with 1023 and I thought this little applet would be helpful
Just click on the "applet" link or the hands at the right.
http://www.intuitor.com/counting/
Watch out for number 4 it may be disconcerting to some.

Author

Commented:
very popular
assuming you have at least one finger and at least one thumb (you have not suffered from a horrible table saw injury) you can count infinitely high with your fingers and thumbs. you said nothing about counting on your fingers just counting with them; with them attached to your body. I suppose even if you did have a horrible table saw accident, as long as you are in possession of your fingers you technically are with your fingers and could still count to infinity with your fingers.
correction: you need at least two thumbs. a thumb is a finger so you would also have two fingers. and meet the requirements of this question. (with fingers [plural] and thumbs [plural])

Author

Commented:
how do i count to infinities?
Top Expert 2007

Commented:
I believe you need to use your InfiniTOES

Author

Commented:
LOL


even then by using binary alone the capacity is only 20 bit


is there another system?
Top Expert 2007

Commented:
My mistake, I guess if you count all the fingers and toes only 20 nails can accurately be BIT and 20 bit certainly isn't infinity.

Author

Commented:
it's been suggested that maybe curling fingers differently can provide more capacity, but I figure that's still under the same system.

The question is really, so far, is there anyway other than binary to do it?
Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
>The question is really, so far, is there anyway other than binary to do it?
well, I mentioned that already, no?
the binary system is limited, to exactly the number of digits you can use.
to represent (count) to infinity, you need also an infinite number of digits (fingers).
changing to decimal, hexal or other system does not change this "limitation".

Author

Commented:
ok, how about less then infinity, but substantially increasing the capacity?
Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
I thought it should have been clear.

to count, you use a certain base [b] (binary system) and the exponent [f] (like you suggested, 10 fingers):
ie the formula:
xmax = [b] ^ [f]
xmax is the maximum amount of distinct numbers you can identify with your system.

so increase xmax, you have to increase either [b] or/and [f].
no other way
Top Expert 2007

Commented:
If you cross your eyes you will double the amount of fingers but you won't be able to differentiate between the real ones and the holographic as each set will duplicate the finger movements and you will make no progress.
I guess the old prison method of scratching  lines on the wall may have to suffice.

But I digress, If you think about it you can count to infinity with each number counted as there is an infinite number of fractions between each number. So if you could only fracture your finger enough times when you start at zero, counting each fracture as a fraction, you will never get to the number one, or play the violin again!
                                                                         
Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
>So if you could only fracture your finger enough times
which should not be a big problem in prison anyway ...
LOL
As mentioned earlier, you can increase the number of states (I mean plural of status) somehow. Help them with cans of colours. Say, you have 4 cans and you can put your finger into some colour. Then you can express 10 states with one colour -- combinations of finger up/down [sorry for my English] and uncoloured or one of 4 colours. However, the approach is rather destructive if the colour is difficult to remove from your hands (counter deterioration ;). You can add the 5th color. Assuming that the colours are not transparent, you can quickly recolor any finger.

The above way, you can use your 10 fingers for counting in decimal system from zero to 10^10-1 (i.e. 9999999999). Anyway, one of your little fingers will be worn-out soon (working too hard and repainted too often). Finally, you will not be able to bow it, and you will need at least one more can with the paint thinner. Unless you use ecological paints/thinner, your brain can be (after counting to the maximum) damaged by chemical agents.

You can decrease the brain deterioration by combining the colours with wisdom. Or you can add half-bow of your fingers, or you can use more colours for coloring one finger -- like put it fully to blue and then half to red thus having blue+red combination + up/down. Notice that red+blue can be considered a different combination than blue+red. The number of states that can be expressed using one finger dramatically increases.

Further elaboration on using only 2 colours but more stripes. This way you can use binary system for coding the status of one finger. If you are able to work with 3 stripes, than you can express one hexadecimal digit using a single finger (+ up/down). Then you can count up to 16^10-1 which can also be expressed as 2^40-1 which is quite a big number.

I know all of this may be quite time and brain consuming, but the time in prison will be well spent ;)

Author

Commented:
this makes me wonder -

how is compression done?


is it possible given the hardware?


Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
????

Author

Commented:
like, how stuff is compress?

into zip

for intsance
Guy Hengel [angelIII / a3]Billing Engineer
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Top Expert 2009

Commented:
I am very sorry, but you are either in the wrong question, or in the wrong state of sanity...
the question is about counting with fingers, so I don't see what "hardware" to "zip compression" are to be about here...

Author

Commented:
yeah , i am saying if you compress the data

1111111111  could very well be something else!

Guy Hengel [angelIII / a3]Billing Engineer
Most Valuable Expert 2014
Top Expert 2009

Commented:
you cannot compress a single value.
Top Expert 2007

Commented:
Well you could bite your fingernails (Hardware)and add them in a pile (lets call it a cache) that makes your fingers that much smaller(Compression),and when ever you need to uncompress you buy those paste on fingernails.
Some use the hammer method but found that during compression the hardware actually expanded.

Is it just me or did we all  get transported to the lounge on this Q??

Commented:
The addition of a simple pen should allow you to mark your fingers with digits - the finer the tip, the more capacity your fingers would have.
And also, you can glue some memory chips on your nails. Then the number of bits on your fingers increases enourmously. Only some details should be solved like which finger will have also processor and even if each finger will have one or more, and how everything is to be powered and interconnected. This way the simple finger counting moves towards theory of parallel computation and things starts to be really interesting ;)

(Yes, that's it! The more experts, the more inventions! We are closer to solving the problems of the World now ;) My personal prover also is: "The more heads, the more cabbage." I do not know if it sounds well in the English language :)

Commented:
"And also, you can glue some memory chips on your nails"

Or, we could use the DNA in cells as storeage. There's bound to be sections that are redundant, and which could be used to represent digits.

Yes, this is called the evolution. From counting on fingers to DNA computers :)
Had you the time (forever), you'd be able to continue counting to infinity, right?

Commented:
So you start cutting little pieces of your fingers off. Say, bits of your nails. They grow back and you simply count the number of pieces that you have. Based on the average growth rate and actuary tables, and an expected size of finger nails, you might be able to guess how many pieces you could accumulate.
Hang about:

The mention of jail in the question reminds me of finger-prints:-

The answer is infinity.  You just need a black ink-pad and a rather large white wall...  Oh and a step-ladder if it is a very large wall
You don't need a wall or ink. Just keep counting your fingers and toes to infinity.
I personally like the "bit slicing technique" -- cutting the pieces of nails as pitonyak suggested. You could do it with your teeth (i.e. "bite nails technique"). The bite (as word) also resembles byte when pronounced. ;)
N MConsultant

Commented:
Question: while using your fingers and thumbs, is it ok to use the mid-space as well? Peru indians used the mid-finger space to count (thus, counting to octal system).
1.   If your answer is no, do you need a finger to hold the remainder?
1.1 If your answer is no, the answer is infinity. If your answer is yes, the result is not 1023.
2.   If your answer is yes, you may still ask yourself if you need the mid-finger spaces. Personally, as if you were in jail, I would prefer to use them. This technique can give you 9 integers for each hand, plus some extra abilities. If you count as a stack (in a row) that means Number 1 is your left thumb, Number 2 is the space between your left thumb and left index, Number three is your left index etc. If you count as a heap, then No 1 is your left thumb, No 2 is your left index, etc, up to Number 6 the space between your left thumb and left index, No 7 the space between your left index and your left middle, etc.

The stack system show you immediately if a number is even or odd (in one hand, or odd or even at the other, assuming you keep the same order of fingers and spaces as you count). If a number falls on a finger is odd, otherwise is even. Now, you may think this is easy to know beforehand - and you're right. But, additionally, you may know if a division remainder of two numbers is even or odd. It is a trick of how yuou count and additionally placing one hand on top of the other, either palm down or up. I can explain more if you wish.

The heap system is quite useful as well because it can give you base 18. This means extremely large numbers can be count and written down. For example, from octodeciamal to binary you can count up to 18 digits and no remainder, meaning positive integer of 262143 (which is 18 aces in binary: 111111111111111111 or written in octodecimal as 28H19), not bad for a 10 fingers man. A 36-based number would exhaust the normal "numbers and letters" signing system (we use digits 0 to 9 and A to Z letters, which is 10 numbers and 26 letters, 36 signs for a position total).

If you accept to use remainders, which is a great plus, then your ability to count integers is being compromised, meaning you can count less numbers, but you will have the ability to calculate decimal numbers. This is the first step to wisdom, since you will be able to count fractions and thus, also be able to express measures in fractions of their own measure, calculate mass and rates (like percentages). I would suggest a two numbers remainder sacrifice. In that case you will be able to have one remainder for purpose of factions and one remainder for base, which means that you can be able to have signs (positive or negative numbers). If you choose this, then you will be able to calculate almost any physical numbers, including the real and imaginary part of complex numbers.

For a jail incident, I would suggest counting in one finger, together with mid-finger spaces, and have two finger remainders of your other hand. You would definitely need short distances AND fractions (for time measurement and percentages) and I dont think that you would found interesting the complex numbers (except if you would have to calculate falling in a substance that would be broken and change your falling rate, like falling into a thin tent and then into water and you would need to calculate penetration speed on your mass index).

If you just want to measure large integers, use all fingers and mid-spaces, including your feet toes. Using 20 toes and hexatrigesimal (trigesimal = 30, 6 = hexa) which would give you the ability to count up to 36 indexes, meaning 111111111111111111111111111111111111 which is a very large number (29 indexes is 536,870,911 imagine 36 indexes - each index works as a 10-multiplier to this decimal number).

If your quest is astronomical, you can use the mid-finger spaces (example: index has 3 bones, lower, middle and upper), which, together with mid-finger spaces and nails gives you an enormous 23 indexes (thumb counts for 2 bones and a nail) for each hand, meaning a 92-base system if you use your feet as well. You will need extra symbols apart from our usual 10 digits in numbers (0-9) and twenty-six letters. You could use a magnetic tile toy for this purpose (http://tinyurl.com/2vnzw9) but your question says toes only.

Just for the sake of argument, if indeed you would need to have such vast abilities in calculating things inside a confined environment, you could manufacture a small calculator (http://tinyurl.com/3b6nlj) like Curta (http://tinyurl.com/36zhhm). I did follow the plans, but it took me almost an entire summer to make it..

Provide specifications of finger counting method if you would like an exact number.


Nick


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