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To complete talking about how science works, let's talk for

Â a while about information.

Â What I really want to do since we live in the information age is to

Â connect information with knowledge, which is what science is all about.

Â Let me use a very simple example.

Â Suppose you put a dot on a piece of paper, and

Â you want it to be able to describe where that was in increasing levels of accuracy.

Â How would you do that?

Â You'd say the dot is on the piece of a paper.

Â That doesn't localize it or describe it in any detail.

Â However, you could fold the piece of paper in half and

Â say the dot is above the line or below the line.

Â You've localized the dot to within a factor of 2.

Â If you then folded the piece of paper the other way,

Â you do divided it into quarters, and the dot would be in one of the quarters.

Â So you'd localize it to 1 part in 4, 25%.

Â And you can follow this logic and see that each time you fold the paper in half and

Â then half again, the dot will clearly lie in one of the small rectangles.

Â And you will have localized it with increasing accuracy.

Â 1:42

We could extent this into three dimensions and imagine a room where there

Â was a particular molecule that happened to be in one place in the room.

Â Could divide the room in half and half again.

Â Both along its length and its width and its height.

Â And gradually, we would localize that particular molecule.

Â Each question asked, is it in this side or

Â that side, is a bit of information, one or zero, yes or no.

Â And so that's a direct connection between a bit, a binary digit,

Â which is how computers work and knowledge, or increasing knowledge.

Â 2:45

Or, you could have a very fine thermometer,

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

Â And you've characterized the information by more bits.

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

Â light, or anything, position into bits of information.

Â Let me give you another example.

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

Â don't tell me what it is.

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

Â you'd probably think that implausible.

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

Â have a 50% chance of getting it right.

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

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

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

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

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

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

Â in two, in two, and in two again.

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

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

Â This is the power of information.

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

Â the world.

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

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

Â the amount of information we're subjected to and

Â have available to us is increasing exponentially,

Â which means doubling essentially every year or every six months.

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

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

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

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

Â some billions of them changing sometimes a second and

Â it's produced by this power of information technology.

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

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

Â What level of information are we talking about in modern culture

Â after several decades of the computer and internet revolution?

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

Â Some gigabytes, I suspect.

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

Â It is indeed growing exponentially, doubling every year.

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

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

Â A simply unimaginable amount of information.

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

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

Â we do need to understand it at some level.

Â This power of information is so

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

Â items with a very small number of bits of information.

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

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

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

Â 6:22

30 bits would be enough to characterize 1 billion items and so on.

Â If we extrapolate this, it means that only about 80 bits of information will be

Â needed to characterize the position of any atom in the universe to within the size of

Â an atom, which is an extraordinary concept.

Â James Watson, co-discoverer of the mechanism of DNA,

Â said in the mid-1950s life is digital information.

Â Quite an extraordinary statement from someone before the era of

Â their personal computer.

Â What he meant was that the base pair sequence of biological material is

Â coding information of the genome, of the functioning of every organism.

Â If we run with this metaphor and

Â look at the history of information in this world over the last mil,

Â billion of years since the Earth formed, we can characterize different phases.

Â Life codifies information in biological molecules, and

Â as life has grown more complex, the information content has increased.

Â The human genome contains about 3 billion base pairs that characterize all

Â the information about a human being.

Â That's the biological rate of information growth on this planet.

Â When human culture started, and especially with the invention of the printing press

Â by Gutenberg, we elevated our rate of information gathering, retrieval, and

Â storage with books.

Â That corresponds to the uptick in this graph with the rate of

Â information growth started growing billions of times faster than it

Â had by simple biological evolution.

Â And then in the final phase of this progression,

Â at an even more rapid exponential rate, starting only a few decades ago, computers

Â allowed us to increase information storage, transmittal, and retrieval

Â by another factor of a million, to a phenomenal rate, the one I just mentioned.

Â So in terms of the age of information, we're in an unparalleled situation

Â compared to biological evolution, which may occur elsewhere in the universe.

Â 8:22

But let me finish talking about science not with bits and

Â bytes, but with the imagination that's at the heart of scientific progress.

Â We can imagine that our brains are able to encounter the things of the universe and

Â our observations.

Â But are really we able to imagine everything that happens in the universe?

Â Just imagine the universe divides into things that are and

Â things that aren't, things that do happen and things that don't.

Â I think our imaginations are good enough to imagine most of

Â the things that actually happen in the universe, but perhaps not all.

Â We're eternally surprised in cosmology and

Â astronomy with things that we never anticipated.

Â However the power of our brains,

Â of course, is that we can imagine lots of things that don't happen.

Â That's the basis of science fiction of poetry and art.

Â So while I think we can imagine most of the things that actually happen in

Â the universe, there are perhaps things in the universe that do happen that

Â we're not smart enough, clever enough or imaginative enough to conceive of.

Â However, our brains are supple and

Â we do imagine things that don't happen in the universe.

Â The power of imagination puts all of of this within the landscape of our head.

Â