tag:blogger.com,1999:blog-2811189992135134605.post3604048259308780213..comments2024-01-24T09:55:51.044-06:00Comments on Elvis Sightings: What Is Happening in Her Head?JoyMamahttp://www.blogger.com/profile/15073328328434957851noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2811189992135134605.post-11074446778925839812008-07-20T11:14:00.000-05:002008-07-20T11:14:00.000-05:00Schnirelmann - I'm not sure that there's much I ca...Schnirelmann - I'm not sure that there's much I can add to that, except:<BR/><BR/><A HREF="http://en.wikipedia.org/wiki/Answer_to_Life%2C_the_Universe%2C_and_Everything" REL="nofollow">42</A>.JoyMamahttps://www.blogger.com/profile/15073328328434957851noreply@blogger.comtag:blogger.com,1999:blog-2811189992135134605.post-33935195873875345942008-07-20T09:40:00.000-05:002008-07-20T09:40:00.000-05:00Oops, I pulled the trigger too quickly in my previ...Oops, I pulled the trigger too quickly in my previous reply. Three levels of severity doesn't allow me to cube the number of diagnoses; the increase in the number of diagnoses is proportional to the number of symptoms. If there are twelve symptoms, there are 3^12 ways to allocate severity, whereas if there are eleven symptoms, there are only 3^11 ways, etc.<BR/><BR/>Thus the actual number should be 1*3^12 + 12*3^11 + 66*3^10 + 216*3^9 + 460*3^8 + 656*3^7 + 616*3^6 = 15,707,763 different diagnoses.<BR/><BR/>However, the exact number is not so important as the reassurance that comes from knowing that all of life's important questions can be answered mathematically.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2811189992135134605.post-18108282680727217622008-07-19T15:36:00.000-05:002008-07-19T15:36:00.000-05:00Oh, but if quantize the symptoms into categories, ...Oh, but if quantize the symptoms into categories, say mild, moderate, and severe, then each can take on three values for a total of 2027^3 = 8,328,393,683 kinds of autism.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2811189992135134605.post-72689434584624205622008-07-19T14:37:00.000-05:002008-07-19T14:37:00.000-05:00Schnirelmann -- Whew... looks good to me! Thanks ...Schnirelmann -- Whew... looks good to me! Thanks so much. (And if you've missed anything, I'm sure someone else will be along to pile on eventually...)<BR/><BR/>The extra dimension on top of the calculated combinations, of course, is that each symptom can range from relatively mild to quite extreme. But since there aren't fixed points identifying the severity of each symptom, that dimension will have to remain uncalculated.JoyMamahttps://www.blogger.com/profile/15073328328434957851noreply@blogger.comtag:blogger.com,1999:blog-2811189992135134605.post-673415875928890562008-07-19T12:50:00.000-05:002008-07-19T12:50:00.000-05:00We can calculate the number of different autism di...We can calculate the number of different autism diagnoses by breaking into cases on the number of symptoms.<BR/><BR/>There is one way to have all twelve symptoms.<BR/><BR/>There are twelve ways to have eleven symptoms, one for each that is missing.<BR/><BR/>With ten symptoms, there are twelve ways to choose the first missing one, and eleven ways to choose the second missing one, for 132 possibilies, but we have to divide by two since they could have been chosen in either order, for only sixty-six different diagnoses.<BR/><BR/>With nine symptoms, there are (12*11*10) ways to choose missing symptoms divided by (1*2*3) different orders of choosing, but we have to remember to throw out four of these corresponding to the four cases where only one social symptom is present. That leaves 216 diagnoses with nine symptoms.<BR/><BR/>There are (12*11*10*9)/(1*2*3*4) ways to choose eight symptoms, but of these one has no communication symptom, one has no behavior symptom, and one has no social symptom. Also there are four ways to have exactly one social symptom times eight ways for one other symptoms to be absent, so thirty two more cases must be subtracted, leaving 460 eight-symptom diagnoses.<BR/><BR/>Seven symptoms can be chosen in 12!/(7!*5!) ways. For each category of symptoms, there is one way for it to be empty times eight distributions of the other symptoms, so we subtract these twenty-four cases. The social category can have exactly one symptom in four ways, times 8*7/2 ways for two of the other symptoms not to be chosen, thus another 112 combinations are not autism, leaving 656 diagnoses with seven symptoms.<BR/><BR/>Six symptoms (hang on, we're alomst there) can be chosen in 12!(6!*6!) ways. For each category of symptoms, there is one way for it to be empty times 8*7/2 ways for two of the other symptoms not to be chosen, ergo eighty-four non-daignoses. Also the social category can have exactly one symptom in four ways, times 8!/(5!*3!) ways to choose the other five symptoms, for another 224 almost-but-not-quite autism cases. That leaves 616 possible diagnoses with six symptoms.<BR/><BR/>In total there are 1 + 12 + 66 + 216 + 460 + 656 + 616 = 2027 different kinds of autism, or as we mathematicians like to say, "a lot".Anonymousnoreply@blogger.com