Wednesday, May 30, 2012

results of a much wider sample

There are several books on what the internet is doing to society.  Quite a few are clearly about negative aspects and I wouldn't be surprised if there are indeed many of them, some serious.  But the book I have been reading is "Too Big to Know" and it emphasizes the changes in attribution of authority: who we think knows what they are talking about and why we think that.  The basic effect examined is the broadening of conversations, assertions and arguments.  In more ways, more sorts of people can weigh in on a talk with their viewpoint, whether they know anything about the issue or not.

Well-known stat effect: the county champion may not be the state champion.

See my page "Sample Size and Extremes"  This page shows a table of numbers.  It displays the most extreme score to occur in random samples of size 5, 25 and 625 scores.  The comparison was run 10 times and once in all 30 of those results, the most extreme score in the set of 25 was more extreme than the most extreme in the set of 625.  That's equivalent to the best team in the county managing to become the state champion.

I thought C.S. Lewis said something along the same lines: not until he spoke around the country about Christianity, did he experience the breath of opinion and expression that actually existed.  Previously, he had kept his discussions to his campus colleagues, who tended to use the same language and recognize the same argument steps and manuevers that he did.  

The same thing happened to me when I taught statistics.  I taught large classes of a wide variety of students: graduates and undergraduates, elementary teachers and secondary, math specialists and mathphobes. As the years rolled by, I kept being surprised by a new way to complete the assignments and a new way to misunderstand that I had never seen before.  As experience accumulates, the most extreme example seen before gets surpassed by something still more extreme.

It is rather calming to me to find that maybe the society I know about is not getting nastier but wider.  Not turning more barbaric and impolite but simply mixing together more divergent types of minds and backgrounds that have had opportunities to get together before.  It is only when journalists or cameras or writing on the internet's comments sections are present, do I get a chance to see interactions and read statements.  As those observing tools get more widespread, I get a chance to see things I didn't know about before.

As Weinberger points out, for a discussion or a parliament to take place, a certain amount of agreement and respect is needed.  If I think you are pure evil, I probably won't listen to a word you say.  I will probably dismiss your arguments and statements immediately.  We need a common language and some agreement on the format of a discussion to ever be able to understand each other.

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