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How high can you count on your fingers?

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It seems like a question 
with an obvious answer.

3
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After all, most of us have ten fingers,

4
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or to be more precise,

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eight fingers and two thumbs.

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This gives us a total of ten digits
on our two hands,

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which we use to count to ten.

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It's no coincidence that the ten symbols
we use in our modern numbering system

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are called digits as well.

10
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But that's not the only way to count.

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In some places, it's customary to
go up to twelve on just one hand.

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How?

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Well, each finger is divided 
into three sections,

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and we have a natural pointer
to indicate each one, the thumb.

15
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That gives us an easy to way to count
to twelve on one hand.

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And if we want to count higher,

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we can use the digits on our other hand to
keep track of each time we get to twelve,

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up to five groups of twelve, or 60.

19
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Better yet, let's use the sections
on the second hand

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to count twelve groups of twelve,
up to 144.

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That's a pretty big improvement,

22
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but we can go higher by finding more
countable parts on each hand.

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For example, each finger 
has three sections and three creases

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for a total of six things to count.

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Now we're up to 24 on each hand,

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and using our other hand to mark
groups of 24

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gets us all the way to 576.

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Can we go any higher?

29
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It looks like we've reached the limit
of how many different finger parts

30
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we can count with any precision.

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So let's think of something different.

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One of our greatest 
mathematical inventions

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is the system of positional notation,

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where the placement of symbols allows
for different magnitudes of value,

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as in the number 999.

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Even though the same symbol is used
three times,

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each position indicates a different
order of magnitude.

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So we can use positional value on
our fingers to beat our previous record.

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Let's forget about finger sections
for a moment

40
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and look at the simplest case of having
just two options per finger,

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up and down.

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This won't allow us to represent 
powers of ten,

43
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but it's perfect for the counting system
that uses powers of two,

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otherwise known as binary.

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In binary, each position has double
the value of the previous one,

46
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so we can assign 
our fingers values of one,

47
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two,

48
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four,

49
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eight,

50
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all the way up to 512.

51
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And any positive integer,
up to a certain limit,

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can be expressed 
as a sum of these numbers.

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For example, the number seven
is 4+2+1.

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so we can represent it by having
just these three fingers raised.

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Meanwhile, 250 is 128+64+32+16+8+2.

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How high an we go now?

57
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That would be the number with all ten
fingers raised, or 1,023.

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Is it possible to go even higher?

59
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It depends on how dexterous you feel.

60
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If you can bend each finger just halfway,
that gives us three different states -

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down,

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half bent,

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and raised.

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Now, we can count using 
a base-three positional system,

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up to 59,048.

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And if you can bend your fingers
into four different states or more,

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you can get even higher.

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That limit is up to you,
and your own flexibility and ingenuity.

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Even with our fingers in just two
possible states,

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we're already working pretty efficiently.

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In fact, our computers are based
on the same principle.

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Each microchip consists of tiny
electrical switches

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that can be either on or off,

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meaning that base-two is the default way
they represent numbers.

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And just as we can use this system to
count past 1,000 using only our fingers,

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computers can perform billions 
of operations

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just by counting off 1's and 0's.