Math Fact of the Day and The Fatal Conceit
Q: If you shuffle a deck of 52 cards, what do you think the chances are that the resulting arrangement of cards has happened sometime before in history?
A: As hard as it seems to imagine, the answer is almost zero.
If you thoroughly shuffle a deck of 52 cards, chances are practically 100% that the resulting arrangement of cards has never before existed at any time in history!
Mathematically, the number of different ways to arrange any 52 items is 8.07 X 1067, which is a number so enormous (8 with 67 zeros after it) that no human can comprehend it.
By way of comparison, the number of ways to arrange a mere 20 items is 2,432,902,008,176,640,000 (2.43 x 1018)-- a number larger than the number of seconds that elapse in the course of 10 billion years. And this number for 20 items is microscopic compared to 8.07 X 1067 (for 52 items).
The information above is from George Mason economist Don Boudreaux's most recent column, who uses the math facts above to argue that "central planning won't ever work, because no human mind, or group of minds, (no matter how intelligent) can even list -- much less rank -- the gigantagazillion different possible arrangements of resources."
Like Sowell points out below, there are thousands of pieces of information about tastes, preferences, production, prices, costs, resources, inputs, etc. dispersed throughout the economy, and there an infinitely large number of combinations and arrangements possible to organize production to satisfy the ever-changing demands of consumers. Central planning can never work effectively because the central planners are powerless and helpless - they will never have access to enough information to organize a complex economic system efficiently.
Hayek called this the "fatal conceit" - the disastrous, often fatal consequences that result from conceited central planners' attempts to organize an economy that cannot be controlled from the top down.