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Exponential
Phil Bowermaster has an interesting post on what the future may hold in terms of information storage and processing.
Posted by Rand Simberg at October 27, 2004 05:58 AM
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What I find weird about exponential growth and decay laws is that so many folks are impressed by the their existence. I mean, isn't it widely known that exponential growth and decay tend to pop out of the simplest and most ubiquitous equation of motion for dynamical variables A, namely dA/dt = f(A) ("A in the near future is solely determined by what's up with A right now")?
Most non-exponential growth and decay trends are some hideously complex combination of simpler, underlying exponential processes. That is, it's the non-exponential process that should bemuse.
Also worth emphasizing is that exponential growth implies a parallel exponential decay process. If per capita wealth has been growing exponentially, this fact implies it is perfectly capable of shrinking exponentially as well (cf. Russia in the last ten years). Indeed, what would be tricky would be to get it to balance on the exact cusp between growth and decay, so that it burbled along roughly constant as the population grew.
This should be a warning sign. Do not assume because things (e.g. national wealth, public opinion) are going exponentially in your favor that the trend is so robust you can mess with it as you please (e.g. dick with taxes and policies). It's perfectly possible for minor parameter shifts to suddenly get your trend going exponentially against you.
Posted by Carl Pham at October 27, 2004 04:09 PM
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