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Watt’s Up With That: A Tale of Two Sigmoids

There are dozens of different mathematical constructions that yield bell-shaped curves. The “Hubbert” or “Peak Oil” curve is actually a special case of a class of s-shaped functions called sigmoids. While most sigmoid functions begin and end at different values, Hubbert’s curve is constrained to begin and end at zero by the formula and boundary conditions imposed that represent a perfect mathematical translation of Hubbert’s worldview. The curve reflects a battle between two competing forces or trends – one for growth and one for contraction – where the balance shifts between the two along the way. […]

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