My friend asked me what I am doing so I made the material shown on this page. His native language is not English and I wanted to say to him what I have been saying to myself since roughly September 2008: The economic experts seem befuddled. I did not know if he knew that English word, so I looked it up online and wrote down most of the entry, which is shown in the next two pictures immediately below.

And it occurs to me to add:

I explained the exponential function with the drawing and text shown in the next two images.

The natural logarithm and exponential functions are inverses of one another.

The number e is the exponential function at 1: **Exp[1]**. It is irrational like Pi, but the first 15 digits are easy to remember because after 2.7 we have 1828 twice followed by 45, 90, and 45.

The next two **Table**s show how rapidly the exponential function increases.

The calculations below REALLY show how fast the exponential function increases. The unit on the plot is one inch, and the distances to the values of the exponential function at 10, 20, 50, and 100 are converted to feet, miles, light years, and known universe diameters. Astronomers seem to think that the universe is 156 billion light years across.

All rolled over growth can be shown on a single plot of the exponential function. At each growth rate we get a sequence of points. We must avoid requiring as a precondition for success those growth rates which produce amounts which are clearly impossible because they could not fit in the known universe. We also need to avoid requiring as a precondition for success those lesser growth rates which are not so obviously impossible, but which also may bust the economy.

Finaly, let me end with an answer to the anti-antiGrowth objection of Moore's Law, in which it is pointed out that computer power has doubled every 18 months from 1958 to 2013. However, to reach that seemingly impossible "100" point on the exponential function plot with Moore's Law requires approximately 216.4 years. Then, given that we are talking here about the atomic phenomena in semiconductors, it is not surprising that the law has held for as long as it has. But its perpetual holding seems highly unlikely.

Converted by