Beating a dead sigmoid
One of Polistra's favorite points ... In living nature and well-designed systems, you typically get 'sigmoid' responses like the one on the left. Inputs that attempt to go beyond a certain limit will be countered by negative feedback, and the molecule or neuron or critter or atmosphere will stabilize at a new value.
You can't get an exponential graph like the one on the right unless something goes wrong. Positive feedback (runaway response, increase potentiated by increase) is exceedingly rare
in nature. Think avalanche, eruption, fever. But you can do it on a graph or a computer model quite easily.
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Mostly valid generalization:
When you see a sigmoid response, you know you're looking at a living phenomenon, either natural or designed to be functional.
When you see an exponential, you're looking at an abstraction. A math model that either can't be applied to reality at all, or will cause explosive destruction when you try to force nature to follow along.
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As mentioned many times before, the fraudulence of "Global Warming" is revealed by this distinction. The real response of temperature to CO2 looks like the sigmoid.
When CO2 increases, temperature first goes up fast then gradually flattens out toward a top limit. [ In math talk, ΔT = 5.7 ln(CO2Proportion/388) ] And this is what we actually see in actual
temperature records. Even if you falsely assume that CO2 is an important influence on climate, we are already up on the plateau of the graph. Further increases of CO2 would have very little influence on temperature.
Needless to say, the Carbon Cult terrorists want to terrorize us into thinking the response is exponential, so they build computer models that go exponential, disregarding their own formulas.
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Also mentioned before: Living businesses follow a sigmoid pattern. Start a business or introduce a new product, and (if lucky) you'll get a rise in sales followed by a plateau of market saturation. If you see an exponential rise in "valuation", you're not looking at a living business. You're either dealing with an abstract derivative based on pure math, or a plain unvarnished fraud.
(One notable exception is compound interest. Most of the honest ways to earn compound interest have a time limit so the amounts won't approach infinity, but during the 10-year CD or the 30-year Treasury bond, your total does grow exponentially.)
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New thought: Well-designed cars have a sigmoid response. When you stomp on the gas, you get a fine pedestrian-squashing surge of acceleration at first, then the speed flattens out as the engine reaches the equilibrium of combustion volume versus friction and gravity. You can only get a runaway response, a sudden unexpected acceleration, when a computer model is in charge.
Labels: Natural law = Sharia law