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How high can you count on your fingers?

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It seems like a question [br]with an obvious answer.

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After all, most of us have ten fingers,

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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[br]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[br]we use in our modern numbering system

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are called digits as well.

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But that's not the only way to count.

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

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How?

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Well, each finger is divided [br]into three sections,

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

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That gives us an easy to way to count[br]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[br]keep track of each time we get to twelve,

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up to five groups of twelve, or 60.

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Better yet, let's use the sections[br]on the second hand

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to count twelve groups of twelve,[br]up to 144.

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That's a pretty big improvement,

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but we can go higher by finding more[br]countable parts on each hand.

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For example, each finger [br]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[br]groups of 24

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gets us all the way to 576.

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Can we go any higher?

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It looks like we've reached the limit[br]of how many different finger parts

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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 [br]mathematical inventions

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is the system of positional notation,

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where the placement of symbols allows[br]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[br]three times,

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each position indicates a different[br]order of magnitude.

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

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Let's forget about finger sections[br]for a moment

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and look at the simplest case of having[br]just two options per finger,

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up and down.

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

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but it's perfect for the counting system[br]that uses powers of two,

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otherwise known as binary.

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

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so we can assign [br]our fingers values of one,

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two,

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four,

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eight,

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all the way up to 512.

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And any positive integer,[br]up to a certain limit,

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can be expressed [br]as a sum of these numbers.

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

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so we can represent it by having[br]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?

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That would be the number with all ten[br]fingers raised, or 1,023.

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Is it possible to go even higher?

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It depends on how dexterous you feel.

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If you can bend each finger just halfway,[br]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 [br]a base-three positional system,

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up to 59,048.

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And if you can bend your fingers[br]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,[br]and your own flexibility and ingenuity.

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Even with our fingers in just two[br]possible states,

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we're already working pretty efficiently.

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

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Each microchip consists of tiny[br]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[br]they represent numbers.

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

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computers can perform billions [br]of operations

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