Cultural Norm Phase Transitions

Phase transitions are very normal in our everyday experience, so perhaps we don’t realize how “surprised” we should be. Watching ice freeze into water at 0ºC seems like a commonplace occurrence, but if you think about it, something dramatic just happens very suddenly. Cooling room temperature water just gives you colder and colder water until suddenly – boom – the molecules that were happy flowing around each other snap into place to form an ice crystal. This occurs at a very specific temperature (that depends on the pressure and presence of impurities). Physics teaches us that phase transitions require some interactions between the molecules. That is, there is a certain temperature below which the potential energy gains from being organized win out over the entropy gains from the random motion of being free. Sometimes, however, you can get into a situtation of super-cooled water, in which the water is below the normal freezing point, but remains liquid since there is no “seed” crystal of nucleate the formation of ice. However, a sharp knock to the container can cause the whole thing to freeze very quickly.

I think there is an analogy with stores opening on Thanksgiving. I’m used to be a fan of old-school Black Friday Shopping – waiting for stores to open at 4 am or Midnight on the day after Thanksgiving to scoop up the deal stores offer to inaugurate the holiday shopping season. Stores were restrained from opening earlier by the cultural norm against tainting the spirit of a day in which we should give thanks for what we have with the acquisitive spirit of competitive shopping. Thus, in that cultural environment, the system was resistant to individual stores trying to gain an advantage by being the only ones to buck the trend. However, once a few stores were willing to go against tradition, others would quickly follow, since they wouldn’t be the only ones, and in fact, didn’t want to be left behind. This year, I think we are on the other side of the norm phase transition:

http://www.bostonglobe.com/business/2013/11/27/for-holiday-retailers-make-dueling-open-and-shut-cases/X9oL11BSECZiUWX7okBhSJ/story.html

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Damn Lies and Statistics

What never ceases to amaze me is how incredibly good the human mind is at some tasks (like divining the state of other human minds – a kind of “social superpower“) and yet so bad at others – like probability and statistics. It’s not just that our intuition is sometimes unable to answer questions about risk and chance; often, our intuition is indignantly screaming the wrong answer. Examples are plentiful: The Monte Hall Problem, Simpson’s ParadoxBertrand’s Box, The Shared Birthday Problem, Wason’s Selection Task, among many others. In each case, the most common reaction must be corrected with lengthy logical explanations to the contrary – see Daniel Kahneman’s system one and system two. Since thinking is costly, the mind gets by on heuristics, which are quick and dirty, and often mislead.

A recent post had a great example of one of the problems that can be caused by selection bias, in which the sample is not truly random, since their is some “unobserved variable” wreaking havoc. That is, if you only look at a subset of a population that was selected because of some combination of two variables, it will look like there is a negative correlation between the variables, even if in reality they are totally independent. This is sometimes called Berkson’s paradox.

See here for one graph that explains everything:

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This data was generated so that looks and smarts are totally independent. To be selected as an actor, however, the sum of looks and smarts must exceed a certain minimum threshold. Since it is much less likely to have both superstar looks and genius level intelligence simultaneously than to have one or the other, if you only look at the subset of employed actors and ignore the overall population they were selected from, you would erroneously conclude that there is some negative correlation between smarts and looks.