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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>>…</span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'> <b>On Behalf Of </b>Anders Sandberg<br><b>Subject:</b> Re: [ExI] Anders on io9<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal><span style='color:#1F497D'>>…</span>Currently I am making a math paper (besides the things I *should* work on, of course) about the statistics of mistyping numbers. Here is a hint: if you randomly change a digit in a number, does it become larger, smaller or stay roughly the same?<o:p></o:p></p><div><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal>Anders Sandberg<span style='color:#1F497D'>…</span><o:p></o:p></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Anders it depends on how you interpret the question. I wrote a sim based on the way you worded the hint, rather than the way your original question implies. My sim takes random numbers between 0 and 999 inclusive, replaces exactly one of the digits with a random number. I ran the sim 6 299 370 times with the following results: <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>The number was unchanged 629 887 times or 9.9992 percent of the time, so I might need to throw those out (you meant to mistype a digit but accidentally type it correctly about 10% of the time)<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>The number went down 2487 times more often than it went up. Went up 2833498 times, went down 2835985 times, the rest stayed the same<o:p></o:p></span></p><p class=MsoListParagraph style='text-indent:-.25in;mso-list:l0 level1 lfo1'><![if !supportLists]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><span style='mso-list:Ignore'>-<span style='font:7.0pt "Times New Roman"'> </span></span></span><![endif]><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Stated in percentages, up 49.978%, down 50.028%, ignoring the 10% no changes, which is a no-change<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>The intent of the question (not the hint but the original question) seems to imply a reference to the elevated occurrence of striking adjacent keys, assuming you use the top row above the qwerty rather than the 10 key. If you do that, the number will go down more often. Reasoning: the above sim, based on the hint, would suggest a no-net-change, but with the adjacent keys assumption, about 10% of the time you lose a digit by replacing a 1 with ` about 5% of the time and a 0 with - about 5% of the time. <o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Losing a digit divides the number by 10 if the trailing zero goes to - and drops the number by half if the leading 1 goes to ` . (Follow me?) By intuition, your number goes to 10% of its value about 10% of the time, and goes to half its value 5% of the time. So your expected value goes to about 93% with the assumptions implied by the original question (see how I got 93%? (Thank you Thomas Bayes, may your hallowed memory live forever in Geekdom Hall.))<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>My code is available on request, but it is pretty simple-minded stuff. You must agree to refrain from ridiculing my humble coding skills, and to avoid holding me in excessive disdain for my egregious persistence in using excel macros for everything, oy vey.<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>spike<o:p></o:p></span></p><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'><o:p> </o:p></span></p></div></div></div></body></html>