Murch then relates his work with Bode's Law, an exponential function that yields the relative sizes of the real orbits of the planets...more or less. The excitement that Murch describes as he uses ratios to satisfy his own curiosity is something math teachers try to foster but rarely achieve:

I came up with a formula that generated the same set of ratios, yet was different from the original – and that really made the hair on the back of my neck stand up!

I suspect that events such as this are what fueled Murch's success as a

*lifelong learner*, a concept much talked about but systemically discouraged .

What are the conditions necessary to encourage lifelong learning, what is the cost, and what is the value?

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