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:

32,560 AD

It would take a little over 30,000 years to get to the level of technology of 2020 AD. That’s 300 centuries to do what actually took less than 165 years to do. And that’s the real technology gap that American’s are facing today . . . in their personal daily lives, and more important, in their jobs. Today, the bulk of Americans are closer to the stone age than the modern age they struggle to live in. And that’s what obsolescence is all about!

Below is a graphic illustration of the above linearization of the growth of technology, with the actual year when a technology in your world first appeared, shown on the vertical left axis. The horizontal axis shows the year that technology would have appeared if technology had grown linearly. For instance, space flight for man stated around 1960, but with linear growth, we wouldn’t have seen space flight until the year 3,760 AD. Note that the Twentieth Century would have been 12,071 years long while the Twenty-First Century will take 1,226,362 years. Also note that the stone age is just 6,000 years in the opposite direction, and indication of just how far behind many Americans are.

For more detail and clarity, click here for PDF Download copy of Linear Growth of Technology.