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</o:shapelayout></xml><![endif]--></head><body bgcolor=white 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";color:windowtext'>On Behalf Of </span></b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif";color:windowtext'>Anders Sandberg<br><b>Subject:</b> Re: [ExI] Fashion<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><div><p class=MsoNormal>On 2013-05-09 15:41, Stefano Vaj wrote:<o:p></o:p></p></div><blockquote style='margin-top:5.0pt;margin-bottom:5.0pt'><div><div><div><p class=MsoNormal><span style='color:#1F497D'>…</span><o:p></o:p></p><div><p class=MsoNormal><o:p> </o:p></p></div><div><p class=MsoNormal><span style='color:#1F497D'>>>…</span>Hey, I spend more than a little time every day deciding what to wear, how to put things together in original ways, what else I may need and how much I do not care about the embarrassment of being unconventionally overdressed for the occasion. :-)<o:p></o:p></p></div></div></div></div></blockquote><p class=MsoNormal><br><span style='color:#1F497D'>>…</span>Yes, but you do live in Milano and you do have great taste. And a mutual friend mentioned an amazing shirt collection...<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><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'>EXCELLENT Anders me lad! Finally! Someone writes about fashion in a language I can understand! This is ground-breaking work sir. If fashion magazines would have articles with this kind of material, I might actually read them, and perhaps put together some spreadsheets. If the models work right, I could lose my geek status, by becoming a snappy dresser! Of course it would be done by formula rather than by the traditional means, so that might actually strengthen my status. It isn’t clear how it would work. <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><p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D'>Anders posted the following fascinating analysis:</span><br><br><span style='color:#1F497D'>>…</span>A mathematical model of dressing: suppose you have probability p of selecting something that looks good, and probability q of noticing when you have a bad combination. So after the first try you have a nice combination with probability p, leave with something ugly with probability (1-p)(1-q), and do a new try with probability (1-p)q. Then the total probability of ending up with something nice will be P = p + (1-p)q( p + (1-p)q ( p + ... )))). The series S=1+x(1+x(1+...)))) must fulfill S=1+x(S), or S=1/(1-x) (it is a geometric series after all), so P = p/(1-q(1-p)).<br><br>For example, if p=0.5 and q=0.25, P=0.5/(1-.125)=0.57. If you have a sharper eye, q=0.5, and now P=0.66. <br><br>But, how long does it take? The number of steps is distributed as a geometric random variable with parameter (1-p)q. So you should expect to do 1/(1-(1-p)q) trials before you finish. In the above p=q=0.5 case you would hence on average try 1.33 times. <br><br>What is the most efficient level of critical scrutiny? We could model the utility as the probability of dressing nicely divided by the number of steps it takes: <br>U=p[ (1+(1-p)q) / (1-q(1-p)) ] <br>Obviously the utility goes up as p increases. It is a bit less harder to see, but the bracketed expression is also monotonically increasing: higher q means better utility. Hence one should be as critical as one can.<br><br>Another utility model says that nice appearance has value N and sloppy appearance has zero value, and lost time has value -1 per step. In that case the total utility will be U=N(p/(1-q(1-p))) - 1/(1-q(1-p)) = (Np - 1)/(1-q(1-p))<br>So the utility goes up for higher q if N>1/p. If the value of looking neat across the day is better than losing a few minutes in the morning (how many minutes lost depends on your sense of style p) you should hence be a critical dresser. If if isn't, just throw on anything that fits and is clean enough.<br><br>However, the wisdom of XKCD strikes again: by thinking through these considerations now, you can optimize your dressing for the foreseeable future. And you can save a lot of time by increasing p, especially if it is really low (it is both likely easy to increase, and it reduces the time spent iterating). <br><br>But rationally, in situations where variation doesn't matter, it might be best to use memoization: just spend enough time to find a really perfect combination (or a set of combinations) and store them for later. That way dressing can be solved in O(1) time for everyday use.<br><br><br>(Currently going for a spring look with a tan suit and slate-blue shirt that I think complements my cryonics necklace nicely.)<span style='color:#1F497D'> Anders</span><o:p></o:p></p></div></body></html>