Everyone makes mistakes. Long before he shared the 2011 Nobel Prize for Physics for his role in demonstrating the accelerating expansion of the universe, Saul Perlmutter was a postdoc in a team of researchers who thought they had found the first evidence of an exoplanet. All their measurements pointed to a planet orbiting a pulsar – until they went back to the observatory the following year and realized that what they had measured was, in fact, background noise from another instrument in the building. They quickly retracted their original paper.

Perlmutter, now a researcher at the University of California, Berkeley, shares this anecdote in Third Millennium Thinking: Creating Sense in a World of Nonsense, which he co-wrote with the philosopher John Campbell, also at Berkeley, and psychologist Robert MacCoun, who is at Stanford University. The book describes the array of “thinking tools” that scientists use and encourages the reader to apply these in non-scientific contexts.

The authors emphasize that probabilistic thinking and other scientific thinking tools can be applied to many decisions in daily life

For example, one of the book’s five sections is devoted to the concept of probabilistic thinking: the way that scientists tend to be cautious about the statements they make because there is always a chance that they are incorrect. Perlmutter’s exoplanet-that-never-was is a case study of scientists getting it wrong and admitting their mistakes, but the authors emphasize that probabilistic thinking and other scientific thinking tools can be applied to many decisions in daily life. Throughout the book, they suggest ways in which you can evaluate facts to help you decide, say, which medical treatment to take or which local policies to support.

Many scientific standards and habits are covered, including correlation and causation; false positives and false negatives; and statistical and systematic uncertainty. Short examples apply these methods to day-to-day situations, from the mundane to the political. To illustrate statistical uncertainty, the authors use the example of a traveller weighing themselves every day in a different hotel. Each hotel’s bathroom scales will be a little bit off (statistical uncertainty), but the average will be their real weight.

The book also highlights biases that scientists and others may have and explains why it is important to validate statements. One example that illustrates this is the 1988 debunking of a French lab’s claim that water holds “memories” of molecules it has encountered before. John Maddox, the then editor of Nature, sent a team to the lab to rerun a double-anonymous experiment. The investigative team wasn’t able to repeat the findings and realized that the lab had ignored the many cases in which its experiments hadn’t worked. Part of the debunking team was magician James Randi, which also shows that you don’t have to be an expert in a field to see when someone has failed to account for bias and error.

Because there are many topics to cover, the examples are often short and some are never mentioned again after the narrative moves on to the next thinking tool. So while the book covers a broad range of ideas and applications, it can be difficult to stay focused. In the introduction, the authors say that you’re free to skim chapters about concepts that you already know, but where does that leave a reader for whom most of this is new?

Throughout Third Millennium Thinking, the authors say they want to give the reader the tools and confidence to ask the right questions and interpret claims. The book started as a successful course at Berkeley where Perlmutter, Campbell, MacCoun and others have been teaching students for the last decade how to apply scientific thinking to decisions about personal life or societal issues. But a reader may wonder how much of a difference they can make with these new ways of thinking.

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It’s not until the last few chapters that this all falls into place. Here, the authors step back and acknowledge that we are part of a larger discussion. In this part of the book, we learn how people in groups can either combine forces or lead each other astray. The authors recount an example from their course in which they asked their students to guess how many people in their electoral district voted for a particular candidate. The average guess was close to the correct answer, but if the students discussed their guesses with each other, their estimates became less accurate.

I would have liked to be more aware of this bigger picture earlier in the book. The way that the content is organized reminded me of an academic paper, with methods in the middle and the discussion left until the end. However, it was certainly a much more entertaining read than most papers. Third Millennium Thinking is a kind of self-help book for society, and it will appeal to anyone who loves to think about thinking.

• 2024 Hachette 320pp £22/$38.00hb