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From: eder@hsvaic.hv.boeing.com (Dani Eder)

Newsgroups: sci.nanotech

Subject: Re: The Singularity

brauchfu@fnugget.intel.com (Brian D. Rauchfuss) writes:

>eder@hsvaic.hv.boeing.com (Dani Eder) writes:

>>...

>>is simple projection from human population trends. Human population

>>over the past 10,000 years has been following a hyperbolic growth
trend.

>

>This does not jive with my information, which is that human population

>increases 2-3% per year, an exponential, not hyperbolic growth pattern.

My sources are (1) World Almanac and Book of Facts, 1992 edition and (2) Statistical Abstract of the United States, 1988 edition. I can't plot a graph in ASCII, but here's the data:

Year (A.D.) |
Population (Billions) |
Inverse (1/Billions) |
Change in Inverse/year |
Growth Rate (%/year) |

1 |
0.200 |
5.000 |
-0.0019 |
0.06 |

1650 |
0.550 |
1.818 |
-0.0044 |
0.28 |

1750 |
0.725 |
1.379 |
-0.0053 |
0.48 |

1850 |
1.175 |
0.851 |
-0.0045 |
0.62 |

1900 |
1.600 |
0.625 |
-0.0042 |
0.75 |

1930 |
2.000 |
0.500 |
-0.0055 |
1.25 |

1950 |
2.565 |
0.390 |
-0.0056 |
1.87 |

1980 |
4.477 |
0.223 |
-0.0036 |
1.77 |

1990 |
5.333 |
0.187 |
- | - |

As can be seen by inspection of the fourth and fifth columns, the data since 1650 is much closer to a hyperbolic than an exponential. The inverse of a hyperbolic is a line of constant slope, and the slope varies by +10% to -25% of its average value of -0.0048 over the period 1650-1990 A.D. An exponential has a constant percentage growth rate. Here the growth rate varies from -60% to +175% of its average value of 0.67% per year over the same time period.

Extrapolating the average change in the inverse gives 39 years from 1990, or 2029 A.D. An eyeballed line fit to the graphed data indicates 2035 A.D.