Saturday, November 7, 2015

Limitations of Central Planning

Quickly now, what is:

8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 ?

Too tough?  Ok, an alternate problem:

1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 ?

Write down your estimate.

Factorials


Factorials are calculations regarding the number of way a group can be arranged.  Suppose you had a single person (A).  There is only one order they could be standing in the lunch line.  Now suppose there are two people, (A)(B) or it could be (B)(A).  Three people could be ABC, BAC, BCA,  ACB, CBA, CAB.

Or, for a group with a count of "n", the number of ways it can be ordered are N!, 1 x 2 x 3 x...x n.

One reason given for the acceleration of technology is that it behaves in a factorial fashion.  Digital cameras and GPS and accelerometers and such can be incorporated into smart phones.  Inventions and devices and software can be stacked.

So?


The basic premise of central planning is that somebody else can more effectively optimize complex systems than those people who are actually living it.

Central planners have a gift for underestimating the magnitude of tasks.

Let's look at something as simple as ordering a lunch line.

1! =1
2! =2
3! =6
4! =24
Not a big deal, right?
5! =120
6! = 720
7! = 5040
8! = 40320 (the answer to the pop quiz at the start of this post)
9! = 362,880
10! = 3,628,800
11! = 39,916,800
12! = 479,000,000
13! = 6,230,000,000
14! = 87,200,000,000
15! = 1,310,000,000,000

So a very rivial task, the ordering a small classroom of fifteen students to go to lunch, offers 1.3 trillion options.  Ordering 52 students on a school bus offers 8e+67 options.

That is the Pandora's box that is opened when central planners 600 miles away start dictating "micro" details like what students can use which bathrooms.  Are they really sure that they are up to the task?




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