A few random thoughts on curve fitting: At a job some years ago in which I had to fit a curve to some data which showed how much hotter something got in response to how much radiant energy, I was criticized for first adding an additional data point representing no increase in temperature with no radiant energy. I added it because it was obviously true, and would help to make the curve more realistic. I was criticized because that experiment wasn't actually performed. When I first learned of Fourier transforms, I dreamed of getting rich by using them to project stock data ahead. I was disappointed when I discovered that all I got were the same sets of historic stock values repeated over and over again. Another learning experience. I had a similar experience after I learned that any N points can be fitted exactly onto an order N-1 polynomial. I was disappointed when I saw that the curve took absurd values, not just when extrapolated, but also when interpolated. One of the most astonishing (to me) calculus theorems is that any smooth curve (in the sense that all of its derivatives are continuous) can only be extended in one way. Any non-zero-length segment of such a curve, no matter how short, uniquely determines the rest of the curve. Also, if you know all the derivatives at any one point, then you know the value at every point. Since it seems plausible that my own motion is smooth, i.e. I never experience infinite anything (distance, velocity, acceleration, jerk, snap, crackle, or pop (yes, those are the official terms for successive derivatives of position)), that implies that all my past and future travels are predetermined. Eventually, especially after studying radio theory, I realized that that's just an instance of the many paradoxes that come from assuming an infinite signal-to-noise ratio. Or from assuming infinite anything. There's *always* noise in any physical signal, even if it's only from quantum fluctuations. A radio receiver is basically a device which fits a curve to a noisy signal in an attempt to reconstruct the intended signal. One of my projects for satisfying extreme skeptics is a way to construct a crude picture of the Earth from years of data on the brightness of the Earth-lit part of the crescent moon as seen from one's backyard. Of course the skeptic would have to trust my software, so there's little point in my writing such software unless I am the skeptic. Still, it's an interesting project. A much easier project is using a table of distances between cities to calculate the radius of the Earth. (Has anyone done that?) Any four cities will suffice, assuming a spherical Earth. With more cities you can tell more about Earth's shape. Or you can just try more subsets of four, and average all of the resulting values of radius to best approximate the correct radius of the spherical Earth. Should all sets of four cities be equally weighted? If not, what should determine their relative weightings, assuming all the distances between cities listed in the table are equally accurate and equally precise?