WEBVTT

00:00:06.646 --> 00:00:10.597
How high can you count on your fingers?

00:00:10.597 --> 00:00:13.176
It seems like a question 
with an obvious answer.

00:00:13.176 --> 00:00:15.786
After all, most of us have ten fingers,

00:00:15.786 --> 00:00:17.057
or to be more precise,

00:00:17.057 --> 00:00:19.397
eight fingers and two thumbs.

00:00:19.397 --> 00:00:22.796
This gives us a total of ten digits
on our two hands,

00:00:22.796 --> 00:00:24.676
which we use to count to ten.

00:00:24.676 --> 00:00:28.766
It's no coincidence that the ten symbols
we use in our modern numbering system

00:00:28.766 --> 00:00:30.957
are called digits as well.

00:00:30.957 --> 00:00:33.128
But that's not the only way to count.

00:00:33.128 --> 00:00:38.316
In some places, it's customary to
go up to twelve on just one hand.

00:00:38.316 --> 00:00:39.324
How?

00:00:39.324 --> 00:00:42.345
Well, each finger is divided 
into three sections,

00:00:42.345 --> 00:00:46.787
and we have a natural pointer
to indicate each one, the thumb.

00:00:46.787 --> 00:00:50.808
That gives us an easy to way to count
to twelve on one hand.

00:00:50.808 --> 00:00:52.337
And if we want to count higher,

00:00:52.337 --> 00:00:57.937
we can use the digits on our other hand to
keep track of each time we get to twelve,

00:00:57.937 --> 00:01:02.597
up to five groups of twelve, or 60.

00:01:02.597 --> 00:01:05.248
Better yet, let's use the sections
on the second hand

00:01:05.248 --> 00:01:10.968
to count twelve groups of twelve,
up to 144.

00:01:10.968 --> 00:01:12.788
That's a pretty big improvement,

00:01:12.788 --> 00:01:17.239
but we can go higher by finding more
countable parts on each hand.

00:01:17.239 --> 00:01:21.249
For example, each finger 
has three sections and three creases

00:01:21.249 --> 00:01:23.656
for a total of six things to count.

00:01:23.656 --> 00:01:25.988
Now we're up to 24 on each hand,

00:01:25.988 --> 00:01:28.518
and using our other hand to mark
groups of 24

00:01:28.518 --> 00:01:31.668
gets us all the way to 576.

00:01:31.668 --> 00:01:33.008
Can we go any higher?

00:01:33.008 --> 00:01:36.417
It looks like we've reached the limit
of how many different finger parts

00:01:36.417 --> 00:01:38.763
we can count with any precision.

00:01:38.763 --> 00:01:40.620
So let's think of something different.

00:01:40.620 --> 00:01:43.318
One of our greatest 
mathematical inventions

00:01:43.318 --> 00:01:46.689
is the system of positional notation,

00:01:46.689 --> 00:01:50.849
where the placement of symbols allows
for different magnitudes of value,

00:01:50.849 --> 00:01:53.218
as in the number 999.

00:01:53.218 --> 00:01:55.729
Even though the same symbol is used
three times,

00:01:55.729 --> 00:01:59.850
each position indicates a different
order of magnitude.

00:01:59.850 --> 00:02:05.539
So we can use positional value on
our fingers to beat our previous record.

00:02:05.539 --> 00:02:07.849
Let's forget about finger sections
for a moment

00:02:07.849 --> 00:02:12.163
and look at the simplest case of having
just two options per finger,

00:02:12.163 --> 00:02:13.939
up and down.

00:02:13.939 --> 00:02:16.329
This won't allow us to represent 
powers of ten,

00:02:16.329 --> 00:02:20.380
but it's perfect for the counting system
that uses powers of two,

00:02:20.380 --> 00:02:22.489
otherwise known as binary.

00:02:22.489 --> 00:02:26.279
In binary, each position has double
the value of the previous one,

00:02:26.279 --> 00:02:29.320
so we can assign 
our fingers values of one,

00:02:29.320 --> 00:02:30.190
two,

00:02:30.190 --> 00:02:30.940
four,

00:02:30.940 --> 00:02:31.738
eight,

00:02:31.738 --> 00:02:34.293
all the way up to 512.

00:02:34.293 --> 00:02:36.941
And any positive integer,
up to a certain limit,

00:02:36.941 --> 00:02:39.980
can be expressed 
as a sum of these numbers.

00:02:39.980 --> 00:02:43.771
For example, the number seven
is 4+2+1.

00:02:43.771 --> 00:02:47.640
so we can represent it by having
just these three fingers raised.

00:02:47.640 --> 00:02:56.290
Meanwhile, 250 is 128+64+32+16+8+2.

00:02:56.290 --> 00:02:58.260
How high an we go now?

00:02:58.260 --> 00:03:03.491
That would be the number with all ten
fingers raised, or 1,023.

00:03:03.491 --> 00:03:05.631
Is it possible to go even higher?

00:03:05.631 --> 00:03:07.730
It depends on how dexterous you feel.

00:03:07.730 --> 00:03:12.381
If you can bend each finger just halfway,
that gives us three different states -

00:03:12.381 --> 00:03:13.321
down,

00:03:13.321 --> 00:03:14.391
half bent,

00:03:14.391 --> 00:03:15.761
and raised.

00:03:15.761 --> 00:03:19.612
Now, we can count using 
a base-three positional system,

00:03:19.612 --> 00:03:24.980
up to 59,048.

00:03:24.980 --> 00:03:28.741
And if you can bend your fingers
into four different states or more,

00:03:28.741 --> 00:03:30.641
you can get even higher.

00:03:30.641 --> 00:03:36.202
That limit is up to you,
and your own flexibility and ingenuity.

00:03:36.202 --> 00:03:38.802
Even with our fingers in just two
possible states,

00:03:38.802 --> 00:03:41.301
we're already working pretty efficiently.

00:03:41.301 --> 00:03:45.332
In fact, our computers are based
on the same principle.

00:03:45.332 --> 00:03:48.492
Each microchip consists of tiny
electrical switches

00:03:48.492 --> 00:03:51.182
that can be either on or off,

00:03:51.182 --> 00:03:55.752
meaning that base-two is the default way
they represent numbers.

00:03:55.752 --> 00:04:00.192
And just as we can use this system to
count past 1,000 using only our fingers,

00:04:00.192 --> 00:04:03.199
computers can perform billions 
of operations

00:04:03.199 --> 00:04:07.373
just by counting off 1's and 0's.