The Analytic Garden

Geological change usually takes thousands of years to happen but we are seeing the climate changing not just in our lifetimes but also year by year.  James Lovelock Part of the charm in solving a differential equation is in the feeling that we are getting something for nothing. So little information appears to go into the solution that there is a sense of surprise over the extensive results that are derived. George Robert Stibitz As James Lovelock points out when it comes to climate change timescale is everything. I am involved in a study of the Pleistocene epoch, a period from about 2.6 million years ago to about 12 thousand years ago. This was a period of cycles of advancing and retreating  glaciers and ice sheets, especially in the Northern Hemisphere. Obviously, there was extensive change in the global climate during this period. However, the geological record shows that the climate changes occurred over periods of thousands to tens of thousands of years rath...

The whole is simpler than its parts. J. W. Gibbs as quoted by Irving Fisher In certain versions you can hear a women's voice say "Reticulating Splines" Sim City What is a Spline Anyway? Consider this data, > head(women.height) height weight 1 58.04797 115.2637 2 58.52034 115.3882 3 58.67279 115.8949 4 58.86290 116.2369 5 58.90874 117.6327 6 59.09578 119.8376 The plot shows a series of women's weight vs. height. The data is made-up, but realistic. There's a definite relationship between increasing height and increasing weight. We could  build a linear model of this relationship. The red line is a linear model height ~ weight. That is \[height =\alpha +  \beta  * weight + \varepsilon (0,{\sigma ^2})\] where ${\alpha}$ and ${\beta}$ are constants and ${\varepsilon (0,{\sigma ^2})}$ is Gaussian noise with a mean of zero and some variance. The fit doesn't look all that satisfactory. It misses the curves in the plot. May...