* Henry Baker <hbaker1@pipeline.com> [Aug 15. 2015 07:49]:
If I hear another TV pundit talk about "exponential" increase in something, when the vast majority of these examples are *polynomial* (usually only quadratic), I'm going to scream.
Today, I heard the following nonsequitur: "Do the math. This {whatever] is increasing exponentially ...".
Well, I did the math, and it was increasing quadratically, at best.
Can we hook an electrode to some lower extremity of each news person/politician to Pavlov them into understanding the true meaning of "exponential" ?
[...]
Note that one use of "quadratic" (convergence) actually means "faster than exponential". For example, the rate of convergence of the arithmetic-geometric mean (number of correct digits is doubled at each step) is said to be "quadratic" in about every text about it. This unfortunate terminology leaves no gap(*) for the rate of convergence of, say, Theta series (e.g., sum(k>=0, q^(k^2) ) ). (*)The non-gap is between "linear" (e.g., power series) and "superlinear" (e.g., AGM as above, or the Newton iteration). The source of this confusion is the drastic difference between moving along the square function and _iterating_ it.