One must have been living under a rock not to have noticed the bombardment of media celebrating the 250th Anniversary of the United States declaring independence from what the colonies believed to be insufferable tyranny. And in typical fashion, our modern media is incapable of doing anything other than sowing discord in order to attract eyes, sell seats, and invite clicks. What gets lost in the various attitudes – let’s make a buck, let’s show how great the country is, let’s show bad the country is, etc. – is that objectively every person living in the United States is blessed beyond the imaginings of most of the people who have ever lived or are living today. By any objective (there’s that word again) standard, even the poorest amongst us are rich compared to all those who came before or who live elsewhere now. But instead of taking a moment to place the United States, with all it’s successes and failures, into perspective we have decided that envy and not charity should be the default. We would rather be unhappy because our blessings aren’t as large as some other guy’s rather than be objectively happy with those we have. This peddling of envy for profit flies in the face of the very reasons we broke away from England – life, liberty, and the pursuit of individual happiness. We would all do well to remember that this Fourth of July.
Now onto the columns.
After a very large slog through the inner workings of SymPy this month’s Aristotle2Digital finally arrives at the first of the rewrite rules for Fourier Transforms. The process combines and exploits all the numerous pieces covered over the preceding posts and uses an iterative sweep through the expression tree to achieve the various transformations. Along the way, it is worth noting just how much work it takes to do what people do without much thought.
The previous two posts laid down the groundwork concerning the statistical underpinnings of portfolio diversification and showed how a simple parametric scan could be used to balance return and risk. This month’s CommonCents tackles a full, nonlinear portfolio optimization the real way – with a computer. The result is a portfolio of 5 stocks that meets nearly the maximum return while lowering the risk far below what would result from depending on one stock alone.
Since the Lagrange points of the Circular Restricted Three Body Problem are dynamic equilibria a particle placed at rest on one of them will reside there forever in the absence of any uncertainty and/or noise. It is natural to ask, if there is uncertainty and/or noise (i.e. the real world) will the particle stay nearby or will it escape with abandon. This month’s Aristotle2Digital answers that question by analyzing the dynamic structure of nearby motion; it finds (perhaps paradoxically for those who follow JWST) that the colinear points are unconditionally unstable.
Enjoy!