Sampling the offerings at the Edge site (“What Scientific Concept Would Improve Everybody’s Cognitive Toolkit?”), it seems that many of our deep thinkers are at a loss to come up with profundities on demand. I mean, come on, “positive sum games”? “The edge of a circle”? “The other”?
I feel the most appreciation for the prob/stat oriented answers (e.g. Diane Halpern, Clay Shirky), but I know that’s because of my own biases.
I offer a statistics-oriented answer that touches on several of these themes: “Distribution is Not the Same as Exchange”. By which I mean, if you take a pile of things and distribute them randomly among a bunch of people, you get a radically different distribution function than you do when those same people exchange those things.
Here’s the paradigm: take $100,000 and distribute it randomly among 1000 bank accounts. (Here “randomly” means a uniform distribution where each bank account is equally probable of being picked as the recipient of a dollar.) What does the probability distribution for wealth look like? It is a bell curve centered around $100, close to a normal distribution a with standard deviation of $10. The most likely value of wealth is $100.
Now pick two accounts at random, call them A and B. If A has any money in it, take a dollar and give it to B. Repeat with new randomly picked accounts. Repeat about 20 million times. What does the probability distribution for wealth look like now? It is strikingly different. In fact it resembles an exponential distribution: exp(-w/wbar) where wbar=$100. The most likely value of wealth is $0.
This simple example suggests why the socialist utopia, where everyone shares wealth equally, is unstable. I’ve had socialist friends who insisted that if we could just “reboot” the wealth distribution, erasing historical inequality, then everything would be peachy. But it’s just not so. As soon as people start to exchange money for goods, the wealth distribution starts to widen, and the Gini coefficient starts an inexorable march toward 0.500….
Sampling the offerings at the Edge site (“What Scientific Concept Would Improve Everybody’s Cognitive Toolkit?”), it seems that many of our deep thinkers are at a loss to come up with profundities on demand. I mean, come on, “positive sum games”? “The edge of a circle”? “The other”?
I feel the most appreciation for the prob/stat oriented answers (e.g. Diane Halpern, Clay Shirky), but I know that’s because of my own biases.
I offer a statistics-oriented answer that touches on several of these themes: “Distribution is Not the Same as Exchange”. By which I mean, if you take a pile of things and distribute them randomly among a bunch of people, you get a radically different distribution function than you do when those same people exchange those things.
Here’s the paradigm: take $100,000 and distribute it randomly among 1000 bank accounts. (Here “randomly” means a uniform distribution where each bank account is equally probable of being picked as the recipient of a dollar.) What does the probability distribution for wealth look like? It is a bell curve centered around $100, close to a normal distribution a with standard deviation of $10. The most likely value of wealth is $100.
Now pick two accounts at random, call them A and B. If A has any money in it, take a dollar and give it to B. Repeat with new randomly picked accounts. Repeat about 20 million times. What does the probability distribution for wealth look like now? It is strikingly different. In fact it resembles an exponential distribution: exp(-w/wbar) where wbar=$100. The most likely value of wealth is $0.
This simple example suggests why the socialist utopia, where everyone shares wealth equally, is unstable. I’ve had socialist friends who insisted that if we could just “reboot” the wealth distribution, erasing historical inequality, then everything would be peachy. But it’s just not so. As soon as people start to exchange money for goods, the wealth distribution starts to widen, and the Gini coefficient starts an inexorable march toward 0.500….