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We begin with a problem.

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[WIND BLOWING]

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Alice and Bob live in tree forts,

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which are far apart,

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with no line of sight between them.

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And they need to communicate.

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So they decide to run a wire

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between the two houses.

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They pull the wire tight,

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and attach a tin can to each end –

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allowing them to send their voices

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faintly along the wire.

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[BOB - MUFFLED] "Hello?"

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[ALICE - MUFFLED] Hello? I can't hear you.

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[BOB - MUFFLED] I can hear you, but just barely.

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[ALICE - MUFFLED] 1. 2. 3. 4. 5.

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However, there is a problem:

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'noise.'

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Whenever there is a high wind,

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it becomes impossible to hear

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the signal over the noise.

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So they need a way to increase

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the energy level of the signal,

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to separate it from the noise.

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This gives Bob an idea.

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They can simply pluck the wire,

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which is much easier to detect over the noise.

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But this leads to a new problem.

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How do they encode their messages as plucks?

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Well, since they want to play

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board games across a distance,

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they tackle the most common messages first –

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the outcome of two dice rolls.

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In this case, the messages they are sending

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can be thought of as a selection

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from a finite number of 'symbols' –

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in this case, the eleven possible numbers,

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which we call a 'discrete source.'

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At first, they decide to use the simplest method.

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They send the result as the number of plucks.

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So, to send a '3,' they send three plucks.

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'9' is nine plucks.

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And '12' is twelve plucks.

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However, they soon realize that this takes

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much longer than it needs to.

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From practice, they find that their maximum pluck speed

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is two plucks per second.

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Any faster, and they will get confused.

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So two plucks per second can be thought of as the 'rate' –

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or 'capacity' – for sending information in this way.

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[SOUND OF PLUCKING]

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And it turns out that

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the most common roll is a 7 –

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so it takes 3.5 seconds to send the number 7.

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[THE SOUND OF 7 PLUCKS]

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Alice then realizes they can do much better

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if they change their coding strategy.

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She realizes that the odds of each number being sent

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[follow] a simple pattern.

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There is one way to roll a 2.

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[There are] two ways to roll a 3.

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Three ways to roll a 4.

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Four ways to roll a 5.

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Five ways to roll a 6.

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And six ways to roll a 7 –

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the most common [result].

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And five ways to roll an 8.

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Four ways for a 9 –

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and so on, back to one way for a 12.

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This is a graph showing

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the number of ways each result can occur.

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And the pattern is obvious.

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So now, let's change the graph to

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'number of plucks versus each symbol.'

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She proceeds by mapping

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the most common number –

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7 – to the shortest signal – one pluck.

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[SOUND OF ONE PLUCK]

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She then proceeds to the next most probable number.

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And if there is a tie, she picks one at random.

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In this case, she selects 6 to be two plucks,

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and then 8 to be three plucks,

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and then back to 5 to be four plucks,

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and 9 is five plucks,

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and back and forth, until we reach 12,

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which is assigned to 11 plucks.

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Now, the most common number, 7,

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can be sent in less than a second –

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a huge improvement.

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This simple change allows them to send

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more information in the same amount of time, on average.

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In fact, this coding strategy is optimal

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for this simple example –

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in that it's impossible for you

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to come up with a shorter method

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of sending two dice rolls – using identical plucks.

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However, after playing with the wire for some time,

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Bob hits on a new idea.

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[PLUCKING SOUNDS BEING PLAYED BACKWARDS]

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[PLUCKS SHOWN IN SLOW MOTION – NO SOUND]