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387 lines
13 KiB
HTML
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HTML
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<h1 class="center">Random Words</h1>
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<div class="center"><i>Probability and English ... what a mix!</i>
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</div>
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<h2>Random Letters</h2>
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<p>You would think it was easy to create random words ... just pick letters randomly and put them together, and voila! a random word.</p>
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<p>Well, here are 20 words made that way:</p>
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;"><font face="Courier New, Courier, mono"><b>tldkl oewkx dmwol vuptg hvwjk naqid avypr zwtip zgnzs bvdhd<br>
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muyfd ighgd xhlng oyecn vjnsl ssjrx gxald tukxj rvfoq yxzxq</b></font></td>
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</tr>
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</tbody></table>
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<p>It turns out that the words are not only nonsense, but quite hard to pronounce!</p>
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<p>(Try saying "<font face="Courier New, Courier, mono"><b>tldkl</b></font>" or "<font face="Courier New, Courier, mono"><b>oewkx</b></font>")</p>
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<p>You see, the <a href="../probability_line.html">probability</a> is <i><b>very unlikely</b></i> ... you would have to try lots of random combinations before getting lucky.</p>
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<p>Why? Well, English has around 200,000 words <i>(228,000 in the Oxford English Dictionary including many words no longer used)</i> ... but how many different words can be made with just 5 letters?</p>
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<p class="center larger">26 × 26 × 26 × 26 × 26 = <b>11,881,376</b> possible 5 letter words!</p>
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<p>And that is just the 5 letter words ...</p>
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<p>Let us guess that there are 40,000 words in English that have 5 letters. So the probability of making a real word just <b>randomly</b> would be:</p>
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<p class="center">40,000 / <b>11,881,376</b> = 0.003, or about 0.3% chance</p>
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<p>So <i><b>real words are rare</b></i>. And we can see that putting random letters together is very unlikely to produce a real word.</p>
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<h2>Vowels</h2>
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<p>We can improve our success by insisting that a word have at least one vowel, since nearly every word in English has one (except <i>fly</i>, <i>by</i> and a few others). Like this:</p>
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;"><font face="Courier New, Courier, mono"><b>ectot gjaqv kuifg vzicu zspsu pdidb wqdis uerrs ucgej okimw<br>
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fnevz ewxko ljgew aglgo jpfoq dcytu uwkcj dzioy wekdx xuybk</b></font></td>
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</tr>
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</tbody></table>
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<p>This is a great improvement. More words can be pronounced.</p>
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<p>But there are still lots of strange words like "<font face="Courier New, Courier, mono"><b>zspsu</b></font>" and "<font face="Courier New, Courier, mono"><b>xuybk</b></font>"</p>
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<h2>Letter Frequency</h2>
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<p>So, our next improvement is to use <i>less</i> of the letters like j, x, z and q and <i>more</i> of the letters like e, t and s.</p>
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<p>In fact the <b>frequency of letters</b> in the English Language is well known. Here is how many times you would <i><b>expect</b></i> to see a letter in every 1,000 letters:</p>
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<div class="full">
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<table style="margin:auto;" border="1">
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<tbody>
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<tr style="text-align:center;">
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<td>a </td>
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<td>b </td>
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<td>c </td>
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<td>d </td>
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<td>e </td>
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<td>f </td>
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<td>g </td>
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<td>h </td>
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<td>i </td>
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<td>j </td>
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<td>k </td>
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<td>l </td>
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<td>m </td>
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<td>n </td>
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<td>o </td>
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<td>p </td>
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<td>q </td>
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<td>r </td>
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<td>s </td>
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<td>t </td>
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<td>u </td>
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<td>v </td>
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<td>w </td>
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<td>x </td>
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<td>y </td>
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<td>z </td>
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</tr>
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<tr style="text-align:center;">
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<td>82</td>
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<td>15</td>
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<td>28</td>
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<td>42</td>
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<td>127</td>
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<td>22</td>
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<td>20</td>
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<td>61</td>
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<td>70</td>
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<td>2</td>
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<td>8</td>
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<td>40</td>
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<td>24</td>
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<td>67</td>
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<td>75</td>
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<td>19</td>
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<td>1</td>
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<td>60</td>
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<td>63</td>
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<td>90</td>
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<td>27</td>
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<td>10</td>
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<td>24</td>
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<td>2</td>
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<td>20</td>
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<td>1</td>
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</tr>
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</tbody></table>
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</div>
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<p>Can you see that "e" is common, but "z" is rare?</p>
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<ul>
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<li>"e" is lkely to occur 127 times in every 1,000, or as a ratio 127/1000 = .127 (=12.7%)</li>
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<li>"z" is lkely to occur only 1 time in every 1,000, or as a ratio 1/1000 = .001 (=0.1%)</li>
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</ul>
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<p>So, by selecting letters based on that frequency (a bit like rolling a 1,000 sided <a href="../geometry/fair-dice.html">die (dice)</a>, where each die has 82 <b>a</b>'s, 15 <b>b</b>'s ... and only one <b>z</b>), we can get output like this:</p>
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;"><font face="Courier New, Courier, mono"><b>elnao etgov segty laast aessn siuon oenha eaoas ncoot ctwka<br>
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dmswo dpuoh eewis ebdni laarm syucs idvos lhina igahh soyie</b></font></td>
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</tr>
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</tbody></table>
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<p>Still no real words, but some are close. And most of them can be pronounced. (Great names if you are writing a science fiction novel!)</p>
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<h2>Try For Yourself!</h2>
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<p>You can try all three methods here ... see if you can get lucky and find a real word:</p>
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<iframe src="irandwords.html" scrolling="no" style="width:452px; height:252px; overflow:hidden; margin:auto; display:block; border: none;"></iframe>
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<p> </p>
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<h3 align="center">but we can do better ...</h3>
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<h2>2-Letter Frequencies</h2>
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<p>We can take the idea of Letter Frequency one step further by asking</p>
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<p class="center"><b>"what is the frequency of letters that <i>follow</i> another letter"</b></p>
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<p>For example, if we already have a "t", the next letter is <b>very likely</b> to be an "h" (making "th").</p>
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<p>To illustrate this, I built up a <a href="two-letter-frequencies.html">Table of Two-Letter Frequencies</a> (from <i>Alice's Adventures in Wonderland</i>). Here is the line for "t":</p>
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<div class="full">
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<table style="margin:auto;" border="1">
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<tbody>
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<tr>
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<th>Freq</th>
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<th>a</th>
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<th>b</th>
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<th>c</th>
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<th>d</th>
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<th>e</th>
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<th>f</th>
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<th>g</th>
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<th>h</th>
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<th>i</th>
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<th>j</th>
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<th>k</th>
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<th>l</th>
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<th>m</th>
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<th>n</th>
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<th>o</th>
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<th>p</th>
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<th>q</th>
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<th>r</th>
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<th>s</th>
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<th>t</th>
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<th>u</th>
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<th>v</th>
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<th>w</th>
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<th>x</th>
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<th>y</th>
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<th>z</th>
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</tr>
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<tr>
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<th>t</th>
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<td>238</td>
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<td><br></td>
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<td>41</td>
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<td><br></td>
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<td>727</td>
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<td>11</td>
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<td><br></td>
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<td>3197</td>
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<td>459</td>
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<td><br></td>
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<td><br></td>
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<td>275</td>
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<td>18</td>
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<td>12</td>
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<td>990</td>
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<td><br></td>
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<td><br></td>
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<td>149</td>
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<td>153</td>
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<td>333</td>
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<td>125</td>
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<td><br></td>
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<td>65</td>
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<td><br></td>
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<td>54</td>
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<td><br></td>
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</tr>
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</tbody></table>
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</div>
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<p>So, "h" occured 3197 times after a "t" ("th") ... but "b" <b>never</b> followed a "t"</p>
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<p>OK, let us start with a "t", and let us say we choose an "h" to make "th", then next we would use the "h"-row to choose another letter (maybe an "e" to make "the"), and so on ... well, here is a sample:</p>
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;"><b><font face="Courier New, Courier, mono">the cur the bund hof arytowno d sheromasees asemedosouro f<br>
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soacthake d imon binofowat oaten d heng wa </font></b></td>
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</tr>
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</tbody></table>
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<p>The results are remarkable ... nonsense, but almost like some strange language.</p>
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<p>In fact we are not just making random words now, we are making random <b>sentences</b>!</p>
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<h2>Higher Letter Frequencies</h2>
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<p>Why stop there? We can make tables of three letter frequencies or more ...</p>
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<h3>3 Letter Frequencies</h3>
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<p>How do 3 Letter Frequencies work?</p>
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<p>Well, say I already have two letters (like "ei") ... we then:</p>
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<ul>
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<li>look through the sample text for every time "ei" appears,</li>
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<li>randomly choose one of those</li>
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<li>look for the letter following "ei" (possibly "t").</li>
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<li>then add the "t" to make "eit"</li>
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<li>and start again using "it" (... always the last two letters)</li>
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</ul>
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<p>Here is a sample:</p>
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;"><font face="Courier New, Courier, mono"><b>Either great into get very deep welled of it it, and<br>
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to wondere started into the book about hear!</b></font></td>
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</tr>
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</tbody></table>
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<p>Now, <b>that</b> looks good! By sampling from a real source we can get good results.</p>
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<h3>4 Letter Frequencies</h3>
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<p>Using the same method I used groups of 3 Letters to decide on the 4th letter and got:</p>
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;">
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<p><font face="Courier New, Courier, mono"><b>Either the sides or conversations in time to<br>
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</b></font><b><font face="Courier New, Courier, mono"> happen next. First, she look down mind</font></b></p>
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</td>
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</tr>
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</tbody></table>
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<h3>5 Letter Frequencies</h3>
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<p>And with 5 Letter frequencies:</p>
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<table align="center" width="80%" border="0">
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<tbody>
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<tr>
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<td style="text-align:center;"><font face="Courier New, Courier, mono"><b>There was just in time it all seemed quite natural);<br>
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but to take out of time as she had not like to do</b></font></td>
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</tr>
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</tbody></table>
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<h2>Try For Yourself!</h2>
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<p>Yes, I wrote something for you to play with. It has the first 6 paragraphs from <i>Alice's Adventures in Wonderland</i>), but <b>you can put you own source text in there</b>.</p>
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<p>Find something from Shakespeare, or a political speech and see what it comes up with ... you could even combine quotes from different authors to see what their children might write.</p>
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