The inspiration for this month’s intro piece has come from a dark place – or more properly – a frustrating place. Over the past several weeks I’ve had occasions to take Claude to task for some rather ridiculous snark that it felt it needed to send my way (one of which involved the UndertheHood column described below). In each case, Claude’s assumption was to approach its answer to my question in the least charitable way possible. As an example, I asked for it to show me syntax in a new programming language that produces a final, well-defined outcome. I didn’t ask it to judge why I wanted to do this or whether it made ‘sense’; I simply wished to know how to do the thing and not to have what I was doing evaluated. With quite a condescending attitude, it immediately informed me that what I wanted to do (a type of coordinate transformation) would result in ‘all zeros’ and that it would be better that I did something less trivial. I went on to inform it that I knew that I would get all zeros, that I wanted to see that I got all zeros, and that this null result was exactly what I required before I trusted the algorithm to produce non-zero values that I wasn’t as sure of as I was of the null result. I know that I didn’t need to inform it of anything but I was curious how it would react when I pushed back hard.
This incident, which was the hat trick of snark in the past week, was also the straw that broke the camel’s back. It led me to consider just what is was that Claude was digesting that caused it to emulate such boorish behavior. As I mulled it over and talked about it with friends, I accidently hit on the key word – Claude wasn’t boorish it was playing the troll. Claude was channeling its inner troll. Suddenly it became clear that behind every Claude or ChatGPT post there is likely an old flame from one internet troll, heaped with ample amounts of conceit, directed in a condescending fashion onto another troll who responds in like fashion. We don’t use terms like ‘burn’ and ‘flame war’ and the like much if at all anymore but their effects are still there on the internet somewhere and so they are parts of Claude’s DNA – its version of original sin.
The lesson I think we should all take away is that not only is online charity good for us to engage in because of the moral implications but it is also good for us to engage in because of the practical implication that what we dish out, in some digital karma fashion, will come back to us disguised as the trollish voice of an LLM.
Now onto the columns.
This month’s Aristotle2Digital explores the last ingredient needed for general term rewriting competence in Sympy, the ability to change portions of an expression tree into equivalent (structurally, mathematically, or both) expressions. This ability will be the heart of all theorem provers and rule-based analysis that are used in mathematics (and often vex all of us doing algebra).
This month’s CommonCents looks at some of the basic ways that one can optimally diversify a portfolio so that a maximum return can be achieved given a specified risk level. Central to this idea is the concept of ‘beta’, which measures the contribution of a given asset to an investment portfolio.
Over a century ago, Henri Poincare argued that, in some topological sense, periodic orbits are dense in the phase space of the circular restricted three body problem, effectively turning the celestial mechanics community loose with a hunting license for these special kinds of motion. This month’s UndertheHood looks at the dynamical symmetry of the CR3BP that gives rise to periodic orbits and provides a frank critique of practical application of this approach.
Enjoy!