Over the next 400 million years or so, invertebrate diversity showed little overall trend and vertebrate diversity shows an overall exponential trend.
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Kurzweil admits the exponential trend in increased computing power will hit a limit eventually, but he calculates that limit to be trillions of times beyond what is necessary for the Singularity.
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The other reason, often related, is when the values being plotted high an exponential trend-plotting such a trend logarithmically results in a straight line, which is easy to recognise.
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Kurzweil says " the knee in the curve " is the time when the exponential trend is going to explode, while Modis claims if the process is logistic when you hit the " knee " the quantity you are measuring is only going to increase by a factor of 100 more.
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