Pythagoras' hammers and the harmony trap

There is a story that the ancient Greek mathematician Pythagoras (of Theorem fame) walked past a smithy one day and was struck by the delightful musical sound of their hammering. To cut a long story short, he investigated this phenomenon and eventually discovered that the weight of the hammers changed their note, and that a hammer twice as heavy as another would be an octave lower and so sound pleasantly in tune. Other hammers that formed perfect fourths, fifths and so on also had weights proportional to their frequencies. Pythagoras was delighted that harmonious notes were so simply and mathematically related.

Legend has it that four hammers sounded well together, but a fifth was discordant, so Pythagoras just rejected this. In strange way, we are still throwing away a fifth hammer. When we try to understand things, we often select pieces evidence that work well together and reject that which is unhelpful. Even scientists, desperate to prove a theory may quietly ignore unhelpful experimental results.

Why do we do this? Because we believe there are simple patterns that explain most things, so we look carefully for them. Unfortunately, the world is a messy place and many things are less predictable them we might hope. Yet faced with a choice between confusion and false understanding, we very often go for the latter. And it may yet have value, as partial understanding may well be better than none. The trap, however, is ignoring non-compliant data rather than holding it nearby, perhaps as 'unexplained', even though this may weaken your thesis.

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