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We're already hearing that the 2012 election is going to be the most important election ever.  Before that, the 2010 election was the most important election ever.  Of course, the 2008 election was clearly the most important election ever, and I'm pretty sure I remember the 2004 and 2006 elections being described as the most important too.

How can this be?  How can every election be the most important ever?

We can answer this question with math.  At Daily Kos we often mention the Republicans "doubling down on crazy," but we rarely consider the mathematical consequences when this phenomenon is allowed to continue over time.  Expressed as a time function, "doubling down on crazy" becomes exponential crazy growth. The basic mathematics of exponential growth, when applied to crazy, can explain so much that is baffling about modern politics.

In contrast to political systems, the importance of exponential growth in biological systems is generally understood.  Exponential growth models can be used for all types of organisms, but bacteria fit particularly well because they reproduce by binary fission, in other words one bacterium becomes two identical bacteria.  Thus, in ideal conditions bacteria will divide at regular intervals to produce new generations each twice as large as its parent generation.

The simple math rapidly produces astronomical results:

Generation Number of progeny
1 1
2 2
3 4
4 8
5 16
6 32
7 64
8 128
9 256
10 512
11 1,024
12 2,048
13 4,096
14 8,192
15 16,384
16 32,768
17 65,536
18 131,072
19 262,144
20 524,288
21 1,048,576
Notice that each number in the table is one greater than the total of all the numbers above it.

Any type of exponential growth can be expressed in terms of doubling times.  The "rule of 70" used for compound interest lets us skip some of the math here.  If your credit card bill grows at 20% interest, we can divide (70% / 20% per year) and see that your debt doubles every 3.5 years.  If your savings account is returning 1% interest, you can expect your balance to double about (70% / 1% per year) = 70 years from now.

So if we take the expression "doubling down" literally rather than figuratively, it means that the candidate or party has put twice as much crazy on the table as the previous wager.  If the "doubling down" continues, then each new bet contains more crazy than had been gambled in all previous bets since the doubling down began.

House rules usually limit the quantity of crazy chips played on a single hand.  Or, at least, they used to.  Today, "no limits" Texas Hold-'em is the most popular game of poker and apparently we're all playing "no limits" politics as well.  

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What has allowed this to happen?  If crazy is normally kept under control, what is now allowing it to grow out of control? Have Republicans lost an internal governor that self-regulates their internal crazy levels?  Or has the political environment changed in such a way that it no longer exerts any negative feedback against excessive crazy?  

How long have we been in exponential crazy growth?

What is the doubling time of crazy in our political system?

What happens when crazy is allowed to grow out of control?

If every doubling time contains more crazy than all previous doubling periods combined, can we doubt that every election is more important than every previous election?

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