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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Entropy and Information</title>
<meta name="description" content="Entropy and Information">
<meta name="author" content="Luis Ibanez">
<meta name="apple-mobile-web-app-capable" content="yes" />
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent" />
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no">
<link rel="stylesheet" href="revealjs/css/reveal.min.css">
<link rel="stylesheet" href="revealjs/css/theme/sky.css" id="theme">
<!-- For syntax highlighting -->
<link rel="stylesheet" href="revealjs/lib/css/zenburn.css">
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<script>
document.write( '<link rel="stylesheet" href="revealjs/css/print/' + ( window.location.search.match( /print-pdf/gi ) ? 'pdf' : 'paper' ) + '.css" type="text/css" media="print">' );
</script>
</head>
<body>
<div class="reveal">
<!-- Any section element inside of this container is displayed as a slide -->
<div class="slides">
<section>
<h1>Entropy &</h1>
<h1>Information</h1>
<p>
<small>Created by <a href="https://opensource.com/users/luis-ibanez">Luis Ibanez</a></small>
</p>
</section>
<section>
<span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/InteractiveResource" property="dct:title" rel="dct:type">Entropy and Information</span>
<br>
by
<span xmlns:cc="http://creativecommons.org/ns#" property="cc:attributionName">Luis Ibanez</span>
<br>
is licensed under a
<br>
<a rel="license" href="http://creativecommons.org/licenses/by/3.0/deed.en_US">
<img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by/3.0/88x31.png" />
</a>
<br>
<a rel="license" href="http://creativecommons.org/licenses/by/4.0/deed.en_US">Creative Commons by Attribution 4.0 License</a>
<br>
<a rel="license" href="http://www.apache.org/licenses/LICENSE-2.0">
<img alt="Apache 2.0 License" style="border-width:0" src="http://www.apache.org/images/feather-small.gif" />
</a>
<br>
<a rel="license" href="http://www.apache.org/licenses/LICENSE-2.0">Apache 2.0 License</a>
</section>
<section>
<h1>Information</h1>
</section>
<section>
<h1>A Question...</h1>
</section>
<section>
<h2>Something that you</h2>
<h1>know</h1>
</section>
<section>
<h2>Something that you</h2>
<h1>don't know</h1>
</section>
<section>
<h2>Something that you</h2>
<h1>can guess</h1>
</section>
<section>
<h2>How</h2>
<h1>Likely ?</h1>
</section>
<section>
<h1>Why ask?</h1>
<h2>if you can guess...</h2>
</section>
<section>
<h1>The Cost</h1>
<h2>of asking...</h2>
</section>
<section>
<h1>The Reward</h1>
<h2>of getting</h2>
<h2>an answer</h2>
</section>
<section>
<h1>The Value</h1>
<h2>of an answer</h2>
</section>
<section>
<h1>Let's Try...</h1>
</section>
<section>
<h2>Is it Cold<h2>
<h2>in Albany<h2>
<h2>on January ?<h2>
</section>
<section>
<h2>Is it Cold<h2>
<h2>on January ?<h2>
</section>
<section>
<h2>Is it Cold ?<h2>
</section>
<section>
<h2>Would you<h2>
<h2>Eat a Monkey ?</h2>
</section>
<section>
<h1>Probabilities<h1>
</section>
<section>
<p>If you pick</p>
<h3>at random</h3>
<p>a day in the calendar...</p>
</section>
<section>
<p>What are the chances</p>
<p>that it will be a</p>
<h3>Tuesday ?</h3>
</section>
<section>
<h1>1</h1>
<h1>----</h1>
<h1>7</h1>
</section>
<section>
<p>What are the chances</p>
<p>that it will be</p>
<h3>the first day</h3>
<h3>of the month?</h3>
</section>
<section>
<h1>12</h1>
<h1>----</h1>
<h1>365</h1>
</section>
<section>
<p>If you pick</p>
<h3>at random</h3>
<p>a card from a deck...</p>
</section>
<section>
<p>What are the chances</p>
<p>that it will be</p>
<h3>an Ace ?</h3>
</section>
<section>
<h1>4</h1>
<h1>----</h1>
<h1>52</h1>
</section>
<section>
<p>What are the chances</p>
<p>that it will be</p>
<h3>a Red card ?</h3>
</section>
<section>
<h1>26</h1>
<h1>----</h1>
<h1>52</h1>
</section>
<section>
<h1>Amount</h1>
<h1>of</h1>
<h1>Information</h1>
</section>
<section>
<p>Of an event</p>
<p>with probability</p>
<h3>p</h3>
</section>
<section>
<h3>-log(p)</h3>
<h3>-----------</h3>
<h3>log(2)</h3>
</section>
<section>
<h2>Tossing</h2>
<h2>a coin...</h2>
</section>
<section>
<h3>probability</h3>
<h3>of head ?</h3>
</section>
<section>
<h1>1</h1>
<h1>--</h1>
<h1>2</h1>
</section>
<section>
<h3>amount of</h3>
<h3>information?</h3>
</section>
<section>
<h3>-log(1/2)</h3>
<h3>-----------</h3>
<h3>log(2)</h3>
</section>
<section>
<h1>= 1</h1>
</section>
<section>
<h1>Units ?</h1>
</section>
<section>
<h1>= Bits</h1>
</section>
<section>
<p>The answer to a</p>
<p>YES / NO</p>
<p>question</p>
</section>
<section>
<p>Where</p>
<p>YES and NO</p>
<p>are equally likely</p>
</section>
<section>
<p>Carries</p>
<p>an amount of</p>
<p>Information</p>
</section>
<section>
<h1>= 1 bit</h1>
</section>
<section>
<h1>STOP !</h1>
</section>
<section>
<h1>Reflect</h1>
</section>
<section>
<h3>consider the</h3>
<h3>question...</h3>
</section>
<section>
<h3>Is the card</h3>
<h3>an Ace ?</h3>
</section>
<section>
<p>The YES answer</p>
<p>has probability</p>
<h3>p = 4 / 52</h3>
</section>
<section>
<p>Its amount of</p>
<p>information is...</p>
</section>
<section>
<h3>-log(4/52)</h3>
<h3>-----------</h3>
<h3>log(2)</h3>
</section>
<section>
<h1>= 3.7 bits</h1>
</section>
<section>
<p>The NO answer</p>
<p>has probability</p>
<h3>p = 48 / 52</h3>
</section>
<section>
<p>Its amount of</p>
<p>information is...</p>
</section>
<section>
<h3>-log(48/52)</h3>
<h3>-----------</h3>
<h3>log(2)</h3>
</section>
<section>
<h1>= 0.115 bits</h1>
</section>
<section>
<h3>Why is it that</h3>
<h3>the most likely</h3>
<h3>answer...</h3>
</section>
<section>
<h3>Carries</h3>
<h3>less</h3>
<h3>Information?</h3>
</section>
<section>
<h2>Is the sky blue ?</h2>
</section>
<section>
<h2>How good</h2>
<h2>is the question ?</h2>
</section>
<section>
<h2>Back</h2>
<h2>to the cards</h2>
</section>
<section>
<h3>Is the card</h3>
<h3>an Ace ?</h3>
</section>
<section>
<p>p(Y) = 4/52</h3>
<p>p(N) = 48/52</h3>
</section>
<section>
<p>I(Y) = 3.700 bits</h3>
<p>I(N) = 0.115 bits</h3>
</section>
<section>
<h2>If we ask</h2>
<h2>many times...</h2>
</section>
<section>
<h2>In average...</h2>
</section>
<section>
<p>We will get a YES</p>
<p>4 out of 52 times</p>
</section>
<section>
<p>We will get a NO</p>
<p>48 out of 52 times</p>
</section>
<section>
<h2>So...</h2>
</section>
<section>
<p>4 out of 52 times</p>
<p>We get 3.7 bits</p>
</section>
<section>
<p>48 out of 52 times</p>
<p>We get 0.115 bits</p>
</section>
<section>
<h2>In average</h2>
<h2>We get</h2>
</section>
<section>
<p>( 4 x 3.7 bits + 48 x 0.115 bits)</p>
<p>------------------------------------------</p>
<p>52</p>
</section>
<section>
<h2>= 0.39 bits</h2>
</section>
<section>
<h3>The Moment</h3>
<h3>of Zen</h3>
</section>
<section>
<h3>The best</h3>
<h3>YES / NO</h3>
<h3>question</h3>
</section>
<section>
<h3>that we can</h3>
<h3>possibly ask</h3>
</section>
<section>
<h3>Is the one</h3>
</section>
<section>
<p>where</p>
<p>YES and NO</p>
<p>are equally likely</p>
</section>
<section>
<h3>That question...</h3>
</section>
<section>
<h3>Will carry...</h3>
</section>
<section>
<h3>an expected</h3>
<h3>amount of</h3>
<h3>information...</h3>
</section>
<section>
<h3>equal to...</h3>
</section>
<section>
<p>( 1 x 1 bits + 1 x 1 bits)</p>
<p>-------------------------------</p>
<p>2</p>
</section>
<section>
<h2>= 1.0 bits</h2>
</section>
<section>
<h1>Breath !</h1>
</section>
<section>
<h1>Smile !</h1>
</section>
</div>
</div>
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