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Monday, September 1, 2014

Exponential Hockey Stick


In boom times promoters talk about 'when the market (for their product) takes off' and how everyone is going to get rich because because when the market does hit, growth is going to go off the chart.

Reading about the pyramids and I came across the idea that people today aren't any smarter than they were five or ten thousand years ago. We may have exposure to some sophisticated ideas, and we may have more knowledge readily available to us now, but we aren't really any smarter.

Then there was the idea that when the Egyptians were building pyramids, they weren't just just piling up rocks, plenty of thought and planning went into them. And once they had a successful design, they didn't just stick with it. Their next design improved on the last one, adding new features and used new construction techniques. Admittedly their progress was not rapid. Building one pyramid was a life's work, but this civilization persisted for thousands of years, and over time it did change.

You look back to the formation of the earth several billion years ago. Current theory seems to be certain chemical elements can self-assemble into long chains. Mix them into a stew and incubate for a billion years and you might get some single cell organisms. Let that percolate for another billion years and you might get some creepy-crawlies. You get the idea.

Anyway the upshot of all this is that whenever you look at an exponential growth chart, it always looks like a hockey stick. No matter what your time scale is, if you expand the vertical scale so that the end point is distinguishable from the rest, the rest of it looks like a flat line.

The graph above doesn't look like a hockey stick because it uses a logarithmic scale for the vertical axis, which we developed to help us cope with things like this, which are basically incomprehensible. A cubic meter of water contains a million cc's. That is moderately comprehensible. But a million cubic meters? What the hell is that? Dump that much water on your house all at once and it would likely be squashed flat. No wonder the ancients built their houses out of stone.

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