Mental Nonlinearity

Human mental arithmetic simplicity limits popular support for dealing with pandemics and industrialized self-extinction.

Our everyday world is full of small numbers. Dozens of anything sizable seems like a lot. Hundreds are a plethora. Thousands are overwhelming. This idea of a million is abstract. Billions are beyond comprehension.

Psychologists William Wagenaar and Sabato Sagaria succinctly diagnose that people have “severe problems in dealing with quantitative data in an intuitive way.”

Earth seems a preternaturally large planet. Toward the end of the 15th century, Christopher Columbus and his backers figured he could reach India in 3 months by sailing west from Spain. Even now, that men have despoiled half of the land on Earth and extinguished a majority of its animals is hard to believe.

We underestimate multiplicative large numbers. 2 groups of study participants were asked to estimate in 5 seconds either the ascending sequence 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 or the descending sequence 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1. (Test yourself by quickly guesstimating either sequence.) The median answer for the ascending sequence was 512, while the average answer for the descending sequence was 2,250. The correct answer: 40,320.

Our minds are adapted to a world where transformations appear linear. The idea of exponential growth is alien. As with multiplication, we sorely underestimate nonlinear acceleration.

The problem is that both Nature and industrialization produce accelerating growth. Burgeoning human population is a classic issue – one which Thomas Malthus presciently fretted over at the end of the 18th century, but which his contemporaries dismissed as doomsaying. Material shortages of all sorts, hunger, poverty, crime, and other social problems often bloom in an accelerating way.

We can’t effectively deal with dynamics we cannot properly grasp the scope or rate of. Whence humanity has failed to comprehend the environmental damage wrought by exponential growth in polluting manufactures (e.g., plastic, pesticides) which are increasingly employed by continually surging numbers of people.

The failed response to covid-19 owes to a failure in fathoming the virus’ exponential potentiality. German psychologists Joris Lammers, Jan Crusius, and Anne Gast: “People have difficulty understanding exponential growth; erroneously interpreting it in linear terms instead. This exponential growth bias is remarkably robust.

“Making matters worse, people are overly confident in their ability to predict change. Those who have least knowledge about exponential growth and consistently apply linear thinking have particularly strong confidence in their erroneous forecasts.”

Indeed, stubborn ignorance characterizes the political response to covid-19 – both in thinking the spread is controllable and in failing to enact effective measures to limit the spread.

In a very real sense, humanity’s fate rests on coming up to snuff in recognizing and dealing with nonlinearity.


Ishi Nobu, The Echoes of the Mind, (2019).

Joris Lammers et al, “Correcting misperceptions of exponential coronavirus growth increases support for social distancing,” PNAS (24 June 2020).

Willem A. Wagenaar, Sabato D. Sagaria, “Misperception of exponential growth,” Perception & Psychophysics 18: 416–422 (1975).

Willem A. Wagenaar & Han Timmers, “The pond-and-duckweed problem: Three experiments on the misperception of exponential growth,” Perception & Psychophysics 43: 239–251 (1979).