Or, you could have a very fine thermometer,

grading into a hundred degree segments from 0 to 100 degrees C.

And you've characterized the information by more bits.

So there's this direct relationship whether you're measuring sound or

light, or anything, position into bits of information.

Let me give you another example.

Suppose I asked you to think of a number between 1 and 1000, and

don't tell me what it is.

And I told you I could guess that number in only eight guesses,

you'd probably think that implausible.

Just by guessing numbers surely it would take me 500 guesses just to

have a 50% chance of getting it right.

But that's not true, that's not the most powerful use of information.

If instead my questions were, is the number above or below 500,

the answer is either yes or no, and I've localized it to half the number line.

If I then ask, is it above or below 250, I've localized it to another factor of 2.

And as you can see, following this logic, each question I ask,

each answer you give, one new bit of information divides the line in two,

in two, in two, and in two again.

And so, with only 8 bits of information, 2 to the power 8,

I can characterize the numbers from 1 to 1,000.

This is the power of information.

It's a very efficient way of packing information into questions asked about

the world.

We live in an amniotic fluid of information, in increasing volumes.

And we sort of take it for granted, the power of our computers,

the amount of information we're subjected to and

have available to us is increasing exponentially,

which means doubling essentially every year or every six months.

This is Moore's Law, it applies not only to the speed of computers, but

also the bandwidth of the internet and the amount of information available online.

Maybe you are not aware of it, but when you watch the silly cat video on YouTube,

you're watching a set of ones and zeroes, binary digits of information amounting to

some billions of them changing sometimes a second and

it's produced by this power of information technology.

It's the same process that leads to localization of that dot on a piece of

paper, by defining a region of space in smaller and smaller quantities.

What level of information are we talking about in modern culture

after several decades of the computer and internet revolution?

You probably know the amount of data you have access to.

Some gigabytes, I suspect.

The amount of information in the modern world is growing at a phenomenal rate.

It is indeed growing exponentially, doubling every year.

The amount of new information created last year was something like 50 exabytes,

which is close to one with 20 zeros after it number of bytes.

A simply unimaginable amount of information.

So it's not just scientists that have to deal with and parse information and

know how to characterize it, our everyday lives are a wash with information and

we do need to understand it at some level.

This power of information is so

efficient the packing of this information, that we can characterize large number of

items with a very small number of bits of information.

As we saw, it takes less than ten items, or decisions, or

questions to characterize a number line from 1 to 1,000.

Which means, a 1,000 items are characterized by 10 bits.