The U.S. national debt (red) compared to U.S. GDP (blue) from 1940 to 2016 (estimated from 2011 to 2016) – top chart with a linear scale, bottom chart with a logarithmic one.

Nicolas Bissantz:

Since the selected 75-year time frame is impressively long, we should take some time to examine this wealth of information more closely. Take a good look at the chart with the linear scale, then the chart with the logarithmic one, and see for yourself:

1. You can’t get much information on the first 25 years from the linear scale. The large values at the end of the series dominate the small values at the beginning. You think you are seeing the development of the data when in reality you aren’t. Your look at the historical data does not achieve the desired result, and collecting the data was a waste of time. And worst of all, you have a completely wrong impression.
2. The logarithmic scale shows that the sharpest rise in debt in the past took place in the 1940s. From 1944 through 1948, the debt was larger than the GDP. From 1948 on, GDP growth was always clearly larger than that of the national debt.
3. If you look at the linear scale between 1965 and 1983, you think you are seeing the “good old days”. GDP growth was apparently much faster than that of the national debt. The logarithmic scale, however, straightens out the story. It shows a development that is almost parallel and, in fact, it is. The GDP and national debt grew by 400 and 326 percent respectively in this period.
4. The period from 1983 to 1993 is also deceptive but in the opposite way. Although the gap between the data actually decreased, the linear scale shows a seemingly parallel development. While the GDP rose by 90 %, the overall debt on the other hand tripled in this period. This is the reality – and this is what the logarithmic scale shows.

We wanted to prove that you don’t have to know logarithms in order to understand logarithmic data. However, you need to know the pitfalls of linear scales if you don’t want to misinterpret linear data. In our example, you would have to see the pattern of the logarithmic scale in the linear chart to still be a skeptic regarding logarithms. You would have to be able to identify and interpret all the distortions of the linear chart just by looking at it. My eyes couldn’t do that – could yours?