Troubleshooting: don’t be too quick to zoom in

Now imagine a mathematician who stumbles on the curious fact that if you double a prime number and then halve the result, you get back the number you started with. It works for the prime number 2, for 3, for 5, for 7, for 11… What is it about primes, the mathematician wonders, that yields this pattern? He begins delving deeper into the properties of prime numbers…

…the mathematician is zooming in when he should be zooming out. The right question is not “Why do primes behave this way?” but “What other numbers behave this way?”. Once you notice that the answer is all numbers, you’ve got a good chance of figuring out why they behave this way. As long as you’re focused on the red herring of primeness, you’ve got no chance.

However, beyond awareness of this tendency, the real challenge is knowing when to zoom in and when to zoom out. There are no easy answers, which emphasises the importance of intuition, and that only comes with practice and knowledge.

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