Understanding the Exponential Growth of Technology

Technology is growing exponentially, doubling every fifteen years. To understand this growth, we can take the growth rate at one year and project a time line if this growth was constant or unchanging. I pick the year 1855 because it’s about the last date you could reasonable call a starting point, where some of the things that makes our modern world have come into being, such as the telegraph (electronic communications), railroad and steamboats (mechanized transportation), and the emergence of modern medicine. This was also the time when America was well into the industrial revolution, which was a major component in sparking the American Civil War. Level of technology has doubled every fifteen years, but since our minds cannot grasp this fifteen year doubling of technology, let’s do some simple calculations. Starting with the level of 1855 as 1 unit of technology, we calculate the levels of technology for every fifteen years by doubling that number as seen in the second column “Level of Technology”. How do these technology levels compare to linear growth? If the technology of 1855 grows at a constant continues rate, every 15 years, we would add 1 to the level in the “Linear Technology” column:

Year         Level of Technology         Linear Technology             Linear Year

1855                         1                                    1                                  1855

1870                         2                                    2                                  1870

1885                         4                                    3                                  1900

1900                         8                                    4                                  1960

1915                        16                                   5                                  2080

1930                        32                                   6                                  2320

1945                        64                                   7                                  2800

1960                       128                                  8                                  3760

1975                       256                                  9                                  5680

1990                       512                                 10                                 9520

2005                      1024                                11                               17200

2020                      2048                                12                               32560

In just five years from now, the level of technology will by over 2,000 times that of 1855, and the 1855 technology is a higher level of technology than many Americans today have reached. But let’s do some more calculations to try and bring these numbers into perspective. A level of 2048 as compared to 12 is quite a little difference, isn’t it? Now we might ask, “Well, how long would it take to get to the year of 2020 (2048 units of technology) if the growth was linear? As you might expect, we can write an equation that will give us that answer.

Linear Year = 1855 + (15 × (2 ((Year - 1855)/15) - 1))

Where the “Linear Year” (right most column) is the year that the technology level occurs if the growth is constant. So, using a calculator, we calculate the year where the linear growth would reach the level of technology for 2020, that is, the year that the level of technology is 2048 times the level of 1855 which is: