Posted by
Nick Thompson on
May 03, 2010; 7:03am
URL: http://friam.383.s1.nabble.com/Schroedinger-redux-tp4996555.html
Dear Friammers,
If anyone is curious about where I ended up on Schroedinger's glass of water, it's pasted in below.
I don't necessarily recommend it.
Thanks for your collective patience.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
As penance for my blunder last week re Schroedinger, please consider the following.
Imagine a perfectly rectangular and homogenous State, call it North Blandia, which is composed of ten counties, each of which contains ten thousand people. Thus there are a thousand times as many people in each county as there are counties in the State. Now imagine that there is a great depression in North Blandia and all the people scatter all over the State looking for work, such that the people of my County, Blather County, (as it happens, whose county seat is, Blatherville, by the way) are randomly distributed amongst all the ten counties of the State. I am one of those people, and I end up finding a job at the opposite end of the State (in Verbose County, as it happens, whose county seat is Verbose City). I am homesick and lonely. I decide to form a Verbose Blather County Club made up of other émigrés from Blather County who are living in Verbose County. How many potential members can I expect to find in my new County.
The chance of any former resident of Blather County ending up in any one of the counties, including my present one, is one in ten. And there were ten thousand people who could have done so. So I can hope to have at least a thousand members in my new club.
In general, the expectation is just the ratio between the number of elements in the smaller entity
county, glass of water, whatever
and the number of smaller entities in the larger, in this case, ten thousand to ten, in Schroedingers case 8x10^24/8x10^21.
As Schroedingers text makes evident, the reason for my intuitive failure is my inability to grasp both the fact and the implications of the fact that there are many more molecules in a glass of water than glasses of water in the ocean.
The only puzzle left is why Schroedinger came up with a hundred molecules, whereas I (and others of you) came up with a thousand. I can only assume that he used a smaller glass (or a bigger ocean).
Thank you for your patience,
Nick
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