
British mathematician Christopher Zeeman FRS (1925-2016), in a photo taken at the University of Warwick Mathematics Institute in 2009. In 2007, he was interviewed by Justin Mullins of New Scientist. In the interview he speaks of his experience giving the Christmas lectures for children at the Royal Institution in 1978, in which he proved 20 mathematics theorems rigorously. He cites as an example Euclid's theorem that there are an infinite number of prime numbers. (Primes are integers that are divisible only by themselves and 1.) He gives the proof this way: assume that "there is a finite number of primes. Multiply them all together and add one. Call this new number n. Now n is not divisible by any of the primes you started with so it's another prime. The original assumption of a finite number of primes must be wrong."
Confirmation of one of your conjectures sometimes becomes possible only if you're willing to assume for the moment that it is false.
Photo (cc) Nicholas Jackson courtesy Wikipedia.
In Part I of this series, we suggested that deep thought about difficult subject matter can sometimes cause blindness to related and important ideas — a kind of looking, but not seeing. And when we have preconceptions or we think we know what's happening, we sometimes don't even look.
Let's continue exploring ways of missing the obvious.
- Not knowing your own patterns
- If you don't know your own patterns, repetitions are likely. Recall situations in which you or your team missed the obvious. Whatever caused those oversights might still be in place, waiting to trip you once again.
- Track the patterns you tend to repeat. Data on repetitions is valuable.
- Seeking confirmation but not counterexamples
- When we have hunches or conjectures about something, we tend to search for confirmation rather than disconfirmation. It's satisfying to prove guesses correct — especially if they're our own guesses. And it's risky to prove guesses incorrect, especially if they're someone else's guesses.
- Falsifying conjectures can generate new insight. Examine past efforts. An imbalance in favor of seeking confirmation, rather than disconfirmation, could indicate this bias.
Sometimes entire groups or teams miss the obvious. Here are two common patterns.
- Media distortion
- The medium a team uses for meetings or other communication can strongly affect outcomes. It can even prevent effective communication, especially when virtual teams rarely or never meet face-to-face. It can conceal the fact that someone is withholding information. It can so distract people in meetings that they forget to mention something important. And the audio quality can be so poor that people miss subtle points — or even the main point — of the discussion.
- If your team or group depends on a virtual workspace, distribute notes and meeting summaries regularly to clarify issues and decisions. It's a poor substitute for co-located meetings, but it does help.
- Information siloing
- Groups If your team or group depends
on a virtual workspace, distribute
notes and meeting summaries to
clarify issues and decisionsconvened to resolve issues or solve problems usually include representatives of all functions that have relevant skills, information, or assets. Typically, they assume that everyone shares whatever they know. But when some keep information within their individual delegations, declining to share it, the knowledge that is shared acquires a bias, which can lead to poor decisions and missing the obvious. - This comes about, in part, because of a cognitive bias known as shared information bias, which causes group members to discuss what all group members know already. They're less inclined to discuss what only a few group members know. The effect is more marked when there's a sense of urgency, or when group members are uncomfortable with ambiguity or lack of consensus. The effect is less marked when the group, as a whole, is concerned with decision quality. Sharing knowledge about the shared information bias is one way of mitigating its effects.
The human mind is endlessly inventive. Of the many more ways to miss the obvious, I'm sure I've missed some that are obvious. First issue in this series
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