How to expect the unexpected: A guide to harnessing nonlinearity and randomness for better predictions

Author and mathematician Kit Yates explores the intriguing science behind our predictions in this talk.

Drawing from his book ‘How to Expect the Unexpected: The Science of Making Predictions―and the Art of Knowing When Not To’, he discusses how understanding nonlinearity, randomness, and cognitive biases can enhance decision-making processes across different areas.

Nonlinearity is a principle where an equal change in input does not result in a proportional change in output.

It’s prevalent but often overlooked due to our inherent bias towards linear relationships.

Instances include conversions between Fahrenheit and Celsius, running times over different distances, or drying times for multiple towels.

Pseudo-linearity questions are used by psychologists to reveal our bias towards linear thinking.

For instance, predicting sprinting time based on shorter distances falls short as it doesn’t account for factors like stamina.

Similarly, assuming that if three towels take three hours to dry, then nine would take nine hours, ignores variables like weather conditions and space on the line.

We are so familiar with linear relationships that we never, or we often don’t, stop to step back and think, what happens if the relationship between these two variables is not linear? – Kit Yates

The relationship between pizza prices and their sizes demonstrates how our understanding of area versus length can influence perceptions of value for money.

As pizza prices increase linearly with diameter while the quantity scales with area (a square function), larger pizzas offer better value due to this nonlinear relationship.

Positive feedback loops occur when an element increases its own quantity.

They’re seen in phenomena like stock market trends or global warming through ice albedo feedback loop.

Recognizing these loops is critical as they can instigate exponential changes that could potentially spiral out of control.

Exponential growth bias is a cognitive bias where people undervalue the speed of exponential growth compared to linear growth.

This can affect financial planning and response to pandemics, as individuals may underestimate the potential increase of savings or virus spread.

Our perception often misinterprets randomness.

Humans tend to identify patterns even in random sequences due to our evolutionary history.

This flawed understanding can lead us to find problems where none exist, such as questioning iPod shuffle’s randomization algorithm.

The fact that there’s this nonlinear relationship, that the area scales as the square of the diameter while the price scales linearly with the diameter, means you get better value for money with your larger pizzas. – Kit Yates

Middle bias refers to our tendency to opt for options that are in the middle when presented with a range.

This phenomenon is observed in various scenarios including online purchasing decisions and choosing toilet cubicles.

Understanding this bias can help us make more informed decisions.

The ‘Aaronson Oracle’ experiment tests our ability to act randomly by pressing two keys in a sequence and having a computer predict the next key press.

If we were truly able to act randomly, the computer’s accuracy should not exceed 50%, highlighting our struggle with true randomness.