1
00:00:10,049 --> 00:00:20,484
So anything that has two states corresponds
to one bit.
2
00:00:21,634 --> 00:00:25,303
Heads or tails, as well as true or false, zero
or one.
3
00:00:25,303 --> 00:00:35,338
If you have four states, that corresponds
to two bits.
4
00:00:35,606 --> 00:00:39,151
But now what corresponds to three bits?
5
00:00:39,151 --> 00:00:41,457
Would it be six states?
6
00:00:41,457 --> 00:00:45,925
No, actually what happens is that you have
eight states.
7
00:00:47,065 --> 00:00:51,362
That corresponds to three bits.
8
00:00:51,362 --> 00:00:53,582
So why is this so?
9
00:00:53,582 --> 00:01:02,839
So if I look at three bits, I can have zero
zero zero, zero zero one, zero one zero,
10
00:01:02,839 --> 00:01:11,429
zero one one, one zero zero, one zero one,
one one zero and one one one.
11
00:01:11,429 --> 00:01:19,692
Three bits, eight states.
12
00:01:21,976 --> 00:01:26,625
All I'm doing is just counting out and here
you see me counting in binary notation.
13
00:01:26,729 --> 00:01:33,990
These are just the numbers zero, one, zero
one zero is two in binary notation, zero one
14
00:01:34,246 --> 00:01:43,949
one is three, one zero zero is four, one zero one
is five, one one zero is six, one one one is seven,
15
00:01:43,949 --> 00:01:50,862
which shows the rationale behind the old joke,
which is that there are ten different kinds of
16
00:01:51,144 --> 00:01:57,861
people in the universe. Those who understand
binary notation and those who don't.
17
00:02:01,479 --> 00:02:10,138
If I go to more bits, so if I have n bits, where
n is equal to one, two, three, et cetera,
18
00:02:10,138 --> 00:02:17,524
what it means is that I have two to the n
different possibilities.
19
00:02:22,572 --> 00:02:25,619
Or sometimes called states.
20
00:02:25,619 --> 00:02:38,016
So I can have 00....0, 00....1, 00....10, 00....11,
you can tell, there's a heck of a lot of possibilities
21
00:02:38,016 --> 00:02:44,059
here, and end up going 11111....1.
22
00:02:44,059 --> 00:02:52,358
So this is zero, this is one, this is two,
this is three and this is two to the n minus one,
23
00:02:52,358 --> 00:02:59,522
because two to the n would be 1000.....0,
which is two to the n.
24
00:02:59,959 --> 00:03:06,894
So when you are counting in binary, when
you have bits, you have for a relatively small
25
00:03:06,894 --> 00:03:13,971
number of bits, you can have a very very very
large number of possible states, possible things
26
00:03:13,971 --> 00:03:17,111
that you could label with these bits.
27
00:03:17,111 --> 00:03:23,639
In fact, it's an interesting question to ask
how many bits are there in the universe?
28
00:03:25,258 --> 00:03:34,122
How many bits in the universe?
29
00:03:34,122 --> 00:03:36,637
Well, this seems kind of a crazy question,
you would think.
30
00:03:36,637 --> 00:03:40,263
There's an infinite number of bits in the
universe.
31
00:03:40,263 --> 00:03:46,412
But actually this is not so, if you look at
it in our universe, which is the part that
32
00:03:46,412 --> 00:04:05,675
we have access to since the Big Bang, which
was, last time I read, 13 * 10^9 years ago.
33
00:04:05,949 --> 00:04:12,814
So the part of the universe that could be
within 13 billion light years in any direction,
34
00:04:12,814 --> 00:04:15,177
this amount is actually finite.
35
00:04:15,177 --> 00:04:19,782
This is a rather surprising result that the
amount of information in the universe is finite.
36
00:04:20,516 --> 00:04:24,950
It comes from the laws of quantum mechanics,
but it turns out that within the universe,
37
00:04:24,950 --> 00:04:34,855
there are 10^90 particles, most of these are
microwave photons from the black body,
38
00:04:34,855 --> 00:04:37,567
radiation that is left over from the Big Bang.
39
00:04:37,567 --> 00:04:39,945
They are all over the place, they are around us
right now.
40
00:04:40,155 --> 00:04:43,872
There are particles of light, wavelength is
roughly about that size.
41
00:04:44,830 --> 00:04:56,266
There are 10^90 of them, so this is a one
followed by 90 zeros, in ordinary digital notation,
42
00:04:56,266 --> 00:05:01,285
and each of these particles carries a few bits
of information with it.
43
00:05:02,681 --> 00:05:09,561
And in fact, if you go to the absolute limits
that are allowed by the Laws of Physics,
44
00:05:09,561 --> 00:05:14,821
the total number of bits that could be
allowed would be 10^120,
45
00:05:14,821 --> 00:05:20,839
which is a one followed by 120 zeros.
46
00:05:21,436 --> 00:05:26,925
These are large numbers of bits, but they're
not infinite.
47
00:05:26,925 --> 00:05:30,245
They're big numbers, but I could think of much
bigger numbers.
48
00:05:30,245 --> 00:05:35,717
For instance, 10 to the 120 plus one is bigger
than 10 to the 120.
49
00:05:35,717 --> 00:05:39,614
Or 10 to the 220, or 10 to the 240.
50
00:05:39,614 --> 00:05:47,631
There are large numbers, but there's a finite
number of bits, and a large number of bits but
51
00:05:47,631 --> 00:05:49,188
it's finite.
52
00:05:49,590 --> 00:05:51,398
Now what does this mean?