There is this popular statement that the technological progress is accelerating. People certainly disagree whether this is a good thing or a bad thing, but the claim itself is rarely disputed.

The argument usually goes like this: By definition, technological progress is the change rate of technological knowledge. And technological progress is proportional to technological knowledge. A quantity whose change rate is proportional to the quantity itself grows, by definition, exponentially and so does its derivative. Therefore, technological progress must be growing exponentially.

However, looking at human history in Europe, technological progress doesn’t seem to have been exponential. Even more, there have been severe setbacks to the technological abilities of civilizations. The Romans with their advanced city building technology were followed by the Dark Ages with feces running down the streets of capitals.

It is true that since the end Middle Ages, we have seen uninterrupted technological progress in the western world. But has it been growing exponentially?

Certainly, without a way of measuring technological knowledge in an objective way, we should not claim an absolute conclusion. But nevertheless, it can be fun to follow a few thoughts.

Consider the following scenario: In 1835, a young man at the age of 20 is studying law in Tübingen in the south of Germany when his mother, living in the northern city of Flensburg turns ill with an inflammation of her appendix.

The message reaches him via the post system of Thurn and Taxis, several days after her diagnosis. To see his mother, he has to embark on an expensive and dangerous five day journey using the same post routes. More than a week after day zero, he reaches his home, likely finding his Mother dead.

25 years, later, the student is now 45 years old and still living in Tubingen. One day, his brother who is living in Flensburg in the house where his mother lived, falls severely ill.

This time, our former law student receives the message as a telegram, just hours after his brother is sent to the doctor. Because Germany now has an extensive railway network, the journey home takes him no more than two days. It is also significantly cheaper than it would have been just two decades ago. And hopefully the advances of medicine will save his brother.

To me, it seems that the changes that technological progress brought to the lives of people from 1825 to 1860 are certainly comparable to the changes that it brought between 1990 and today.

The claim that technology is advancing exponentially seems misguided. There must be a mistake in the argument that I outlined above.

In fact, I believe that the premise is wrong: Technological progress is simply not proportional to technological knowledge. Of course, better technology also helps in making technological progress. But progress gets harder the further it advances. This effect is so strong that it not only cancels out the acceleration that better technology brings to research, it often brings progress to a grinding stop.

Technology isn’t advancing ever faster. It is not even always advancing. But sometimes it does. So let’s keep pushing forward.