How do we use bits?
We can count.
00000, 00001, 00010, 00011, et cetera.
So we can count, but we can also label things.
And a good example of this is the barcode
for things you buy in the supermarket.
The barcode is a series of lines,
the lines are a bunch of narrow lines,
and then there's some thicker lines in between.
And the idea is that each of these narrow
lines is zero and each of these thicker lines is a one
so this barcode that I actually drew for you right
here is in fact a barcode that says 000 11 000 1.
It's a number in binary but each item in the
supermarket has its own specific barcode,
that says, "Hey it's just a label that says this is
an apple, a gala apple from Washington State."
Or "This is a box of All-Bran Buds."
So we can use these bits as labels, and now
you see how the power of information comes in.
Because with a relatively small number of
bits, we can label a very very large number of things.
To get a sense for how many things we can
label with bits, let's note the following feature.
So two to the tenth, which is equal to two times
two times ... times two, ten times,
this is two raised to the power of 10
which is equal to 10000000000 in binary.
is actually equal to 1024 in digits.
That is to say two to the tenth is approximately
equal to ten to the third, a little more than a thousand
thousand plus change.
Actually in the old days with computers, when
you bought a computer and you would say,
"I bought a computer with a thousand bits of
memory."
That's how old computers have a very small
amount of memory.
It didn't mean a thousand, a kilobit, it meant
a thousand twenty-four bits.
A byte, by the way, is equal to eight bits.
A megabyte was a computer with not just a
million bits of memory, but an extra 2.4% for free.
Sadly, a few years ago, the computer companies
realized the error of their ways and they stopped
giving you this extra bonus.
It's terrible, you can call this progress, and
progress, you know, information processing
Microsoft Word 95 was significantly easier
to use than Microsoft Word today,
which shows you the perils of information processing.
So if we have these 10 to the 90 particles,
that's approximately equal to two to the 300
elementary particles in the universe
and because there are two to the 300 particles,
that means that a barcode for each particle.
If we wanted to make a barcode to label every
elementary particle in the universe, it's not
really quite clear where we would put this
barcode on the elementary particles,
but if you could put a barcode on elementary
particles, that means that 300 bits suffice
to label every elementary particle in the universe.
So say, well I want this microwave photon
over here, and they take this microwave photon
this got a 300 bit barcode, and they put it
on the scanner, "Yes here's your microwave
photon, sir. That will be 300 dollars."
Well, inflation is also taking its toll over
the last few decades.
So, you see information can be measured
independent of what it means.
We can count things, and because we can count
things, we can label them with digits or with bits.
And with a very small number of bits, we can
label a huge number of things.
Three hundred bits suffice to label every
elementary particle in the universe.
By contrast, if you look at DNA,
three billion base pairs of DNA,
and there are four possibilities for each
base pair
and that means two bits per pair, which means
that there are six billion bits in the human DNA.
This is way way way... more amount of information
than is required to label every single elementary
particle in the universe.
And what do these bits represent in DNA?
They represent possibility,
they represent the different possible genetic
combinations which could program what we do.
Now, of course, most of these bits, the vast
majority of these bits are programming just
elementary processes about chemical reactions
on ourselves, we share most of these bits with
yeast, and we share 99% of our bits with other
primates like chimpanzees
and 99.8% of our bits with other human beings
but that extra little tiny bit makes that
extra difference
the difference that makes a difference.