Uncertainty

Pebbles

He says Carl Jung once claimed that if you collected a sample of 1,000 pebbles, you could calculate the average weight of a pebble on the beach. And yet the chances of finding a single pebble that matches that weight is about a million to one: it basically can't be done. Waltz loves this analogy; he thinks it proves that everyone is a square peg in a round hole, as awkward and as thorny as he is. “You cannot reach a generality,” he says. “And you cannot reach an individual through generalities.”

Various statements and definitions

Daniel Kahneman popularized the idea of two systems of thinking – one is rapid and intuitive, and the other more considered and analytic. When it comes to dealing with uncertainty, he argues that the first, fast system tends towards over-confidence, neglects important background information, ignores the quality and the quantity of evidence, is unduly influenced by how the issue is posed, takes too much notice of rare but dramatic events, and suppresses doubt. These are not characteristics that should be encouraged.

We know, there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns – the ones we don’t know we don’t know.

Words like probability, chance and likelihood are often used interchangeably in everyday language, but I shall be a bit more pedantic.

Numbers expressing uncertainty, although when the probabilities can be generally agreed due to shared understanding of the underlying process, such as when flipping coins, I will refer to them as chances – I will also use chance as a more general term for unpredictability. Likelihood will generally be restricted to its technical meaning. Risk can mean almost anything you want it to, and in everyday language is often used to describe both a threat (‘that broken paving stone is a definite risk’), and the chance of an event (‘the risk of falling over is small’). Take its meaning from the context.

This is sometimes termed aleatory uncertainty, about the future we cannot know. But now the object is the current state of the coin, and the uncertainty is due to your lack of knowledge; this is called epistemic uncertainty, about what we currently do not know.

Where appropriate, an emotional response to the uncertainty, also known as the ‘affect’, which might be dread, excitement, anxiety, resignation, and so on, and can have physical manifestations of ‘butterflies in the stomach’, upset sleep, and so on.

Our responses can be broken down into those that are cognitive (how we think), emotional (how we feel), and behavioral (what we do).

Aggregation: they use multiple sources of information, have an openness to new knowledge and are happy to work in teams. Meta-cognition: they have an insight into their own thinking, and the biases we all have, such as looking for confirmation of pre-set ideas. Humility: they have a willingness to acknowledge uncertainty, admit errors and change their minds. Rather than saying what is going to happen, they are prepared to give only probabilities for future events, acknowledging both the known unknowns and the unknown unknowns.