# Is the IoT growing linearly or exponentially?

## Understand exponential growth

Most people underestimate exponential developments - also with Corona. Depending on how they are presented, one can more or less easily imagine rapid developments. Correct communication helps in a pandemic to increase acceptance of the measures.

The outbreak of the corona pandemic was also a crash course in statistics for many. Terms like doubling time, logarithmic axes, R-factor, rolling averages and excess mortality are now on everyone's lips. But knowing mathematical functions does not mean that one can imagine the processes described with them in reality and to their full extent.

People are struggling with exponential growth. In ancient India, people told the story of the emperor who was fooled by a courtier. He said to him: “I want nothing more, noble master, than that you fill the chessboard with rice. Place a grain of rice on the first space, and then always double the number of grains on each additional space. "

It is not known how much rice the emperor expected when he entered into the trade. But it is very likely that he underestimated the exponential increase on the 64 squares of the chessboard. Because in the end he owed the courtier no less than 18 trillion, 446 quadrillion, 744 trillion, 73 billion, 709 million, 551 thousand and 615 grains of rice, which is about 11 billion railroad cars full of rice.

Systematically underestimating exponential growth can have devastating effects in a pandemic. Because if people fail to recognize the speed of expansion, they perceive containment measures such as wearing masks, distance rules or the closing of bars as exaggerated and pay less attention to them.

This is where research comes in that was carried out at the Center for Law and Economics at ETH Zurich and at the Lucerne University of Applied Sciences and Arts (HSLU) and published in the science journal “Plos One”. Martin Schonger, lecturer and course director at HSLU and Research Fellow at ETH, and Daniela Sele, doctoral student at ETH, wanted to know whether the way in which the exponential spread of a virus is represented influences systematic underestimation.

They already knew from other experiments that people underestimate exponential growth even when they know that people have this problem. It is therefore of little use to educate people about their "exponential growth bias", as science today calls the Indian emperor's chessboard problem. Those informed are just as wrong with their estimates as the others.

### Time easier to understand than growth rate

In an experiment with over 400 participants, the research team always worked with the same scenario: One country currently has 1,000 Covid infections. The number of cases is growing by 26 percent every day. The number of infections increases exponentially to 1 million within 30 days. However, there is the possibility of reducing the growth rate from 26 percent to 9 percent through containment measures.

The researchers queried this fact from different perspectives (“frames”): How many infections can the measures prevent? How much time could the measures save before the 1 million case mark is reached? How many infections will there be after 30 days if they only double every 8 days and not every three days? The latter, incidentally, corresponds to a reduction in the growth rate from 26 to 9 percent, something that few people recognize intuitively.

“We were surprised at the clarity and consistency of the results of our experiment,” say the two researchers. Your first finding: growth rates are not very suitable for communicating such a pandemic development. Over 90 percent of the participants were far too low when they had to estimate an exponential development of the infections over 30 days. They were able to estimate the number of cases much more accurately if they could start from the doubling time.

### Imagine how measures work

A second finding: people can hardly imagine how many infections can be prevented with containment measures. In the above example (1000 cases, growth rate of 9 instead of 26 percent over 30 days) the participants were far wrong: The typical participant (median) believed that 8,600 cases could be avoided. In fact, it's almost 1 million.

If, on the other hand, the question is asked about the number of days that can be gained through these measures (e.g. until the hospitals are overloaded or until a vaccination is available), the estimates are significantly better.

In the experiment, the best results were ultimately provided by a “frame” in which, on the one hand, questions were asked about the time gained and, on the other hand, about the effects if the time span in which the number of infections doubles becomes longer. An example of this is the statement: “Thanks to the preventive measures taken today, we can assume that the number of cases will no longer double every 3 days, but only every eight days. This gives us 50 days before the 1 million infection mark is reached, and we can take further measures to combat the pandemic. "

### The influence of communication

Communication with the authorities and media coverage were not the subject of the investigation that was carried out during the lockdown in spring 2020. Daniela Sele and Martin Schonger carefully followed how the drastic measures were communicated at the time and compared the observations with their research results.

In the opinion of the authors, the Federal Office of Public Health and the scientific task force often specify doubling times and do not mention growth rates, which made it easier to understand in the experiment. However, there is hardly any talk of the time gained, although the messages are better received with it.

The researchers suspect, however, that the direct influence of communication with the authorities is limited. The media are of greater importance, but they almost always report on cases and hardly ever on time saved.

For Martin Schonger and Daniela Sele, the Covid measures are just one application of the “framing” theory for the perception of exponential growth. You can imagine similar phenomena in the financial sector, in legal or environmental decisions.