tag:blogger.com,1999:blog-3829599.post651035566348307071..comments2019-03-25T04:36:39.066-07:00Comments on Agoraphilia: Anchor AgesGlen Whitmannoreply@blogger.comBlogger8125tag:blogger.com,1999:blog-3829599.post-88217067819239557162007-04-17T15:31:00.000-07:002007-04-17T15:31:00.000-07:00For an Economics student, I've taken surprisingly ...For an Economics student, I've taken surprisingly little statistics, so maybe this is overly simplistic:<BR/><BR/>Why are we assuming that apparent age advances less quickly than actual age? Couldn't someone, a smoker for example, start off looking younger than they are, but then age overly quickly?<BR/><BR/>This would solve the question of where perceived ages come from: they are the mean of appearances of people of that age. Presumably these form a normal distribution (the apparent age of a group of people of the same age form a bell curve centered on their actual age).<BR/><BR/>There is still the childhood problem, but maybe the model is more usefully focused only on grown adults?Evannoreply@blogger.comtag:blogger.com,1999:blog-3829599.post-76689461866557692302007-04-03T23:28:00.000-07:002007-04-03T23:28:00.000-07:00Ari, your model depends on the implausible assumpt...Ari, your model depends on the implausible assumptions that 1) no one can look younger than they are when they're born and 2) no one can look older than their age when they die. The former assumption is contradicted by Glen's premie example, and the latter could even be thought of as implying that no one can ever look older than their age, if we consider that anyone could die at any moment. Alter the model by allowing y (apparent age) to be less than 0 (actual age at birth) or greater than 1 (actual age at death) and the fixed point theorem no longer applies.<BR/><BR/>Something like the anchor age phenomenon might arise on occasion out of wishful thinking, since many people want to look (or to be) older than they are when they are young and younger than they are when they are old. But as a general rule it seems to be both implausible in the abstract and contradicted by experience.Blarhttps://www.blogger.com/profile/10365458357413212250noreply@blogger.comtag:blogger.com,1999:blog-3829599.post-57672642205590257792007-04-03T15:20:00.000-07:002007-04-03T15:20:00.000-07:00Ahh, finally a conversation where being a mathemat...Ahh, finally a conversation where being a mathematician is helpful. What you need is something called a <A HREF="http://en.wikipedia.org/wiki/Fixed_point_theorem" REL="nofollow">fixed point theorem</A>, and actually a pretty simple one (the most abstract ones are pretty mind bending).<BR/><BR/>Let x = actual age and y = apparent age. Instead of measuring in years, measure each of these variables on the scale [0,1], where 0 is newborn and 1 is dead. Then each person has an "apparent age function" f:[0,1]->[0,1], such that y = f(x).<BR/><BR/>If f is a continuous function, there always exists a "fixed point" where x = f(x) -- that is, where a person looks exactly their age. This point is not necessarily unique, though. For example, you could have someone who always looks exactly their age -- or someone who looks young up through early adulthood, is old-looking in middle age, but then ends up being a very well-preserved 90-year-old. (This could certainly happen for someone who goes bald at a young age, but never gets especially wrinkled or sickly.)<BR/><BR/>Now, one can argue over whether representing ages on a scale from [0,1] is reasonable, and whether f is continuous or not, but this is the relevant math.Arihttps://www.blogger.com/profile/00697016203754246440noreply@blogger.comtag:blogger.com,1999:blog-3829599.post-29660953449646479912007-04-02T00:02:00.000-07:002007-04-02T00:02:00.000-07:00This seems somehow related.<A HREF="http://dilbertblog.typepad.com/the_dilbert_blog/2007/03/whats_your_perm.html" REL="nofollow">This</A> seems somehow related.My anchor age is 20noreply@blogger.comtag:blogger.com,1999:blog-3829599.post-85270845521342219082007-03-31T20:48:00.000-07:002007-03-31T20:48:00.000-07:00Half-baked at most, I'd say. Note that premies ar...Half-baked at most, I'd say. Note that premies are actually contrary to the theory, since they begin below the y=x line, although you could get around that by counting from conception rather than birth. But I find it highly implausible to claim that no one has ever looked younger than they were from the beginning. I have known several people who looked young for their age ever since early childhood, although I admit that my memories do not go all the way back to day 0 (especially if we place the origin where I suggested). August, did you ever look old for your age when you were younger? If not, then you are actually one of these counterexamples to Glen's theory.Blarhttps://www.blogger.com/profile/10365458357413212250noreply@blogger.comtag:blogger.com,1999:blog-3829599.post-89308120806564122252007-03-31T14:15:00.000-07:002007-03-31T14:15:00.000-07:00Jeffrey -- yes, that's true, if we assume everyone...Jeffrey -- yes, that's true, if we assume everyone looks zero when they are zero. However, I don't think that non-linearity is sufficient to save my theory. I'll still have a "next-to-the-endpoint" problem, epsilon distance to the right of zero.<BR/><BR/>But hey, maybe some people don't look zero at zero. Premies, for instance.Glen Whitmanhttps://www.blogger.com/profile/01425907466575991113noreply@blogger.comtag:blogger.com,1999:blog-3829599.post-41549602667999049882007-03-31T05:43:00.000-07:002007-03-31T05:43:00.000-07:00Those apparent age functions probably go through t...Those apparent age functions probably go through the origin, so they've got to be nonlinear in order to cross the y=x axis again.Jeffreyhttps://www.blogger.com/profile/00708682858926029668noreply@blogger.comtag:blogger.com,1999:blog-3829599.post-67403027181959667612007-03-30T21:32:00.000-07:002007-03-30T21:32:00.000-07:00Well,I am 32, and people still ask me for I.D.when...Well,<BR/><BR/>I am 32, and people still ask me for I.D.<BR/>when I buy wine. Last year I had a teenaged girl burst out in surprise when she read my birthdate on my driver's license. <BR/>My experience seems to count in your theory's favor, but I've always thought it was genetics. My father has always looked young for his age.Augusthttps://www.blogger.com/profile/08758314961163692341noreply@blogger.com