> As an analogy, this whole discussion of PLs in CS circles is like complaining about whether we should use `dot` notation or `d/d(t)` The fact that makes all

> As an analogy, this whole discussion of PLs in CS circles is like complaining about whether we should use `dot` notation or `d/d(t)` The fact that makes all the difference is that informal notations in math, science, linguistics and other fields are interpreted by human brains, human brains are flexible at filling the gaps and deriving most reasonable consequences from their incomplete descriptions. Symbolic notations outside of formal logic and programming are mostly an annotation DSL to augment humans communicating with each other. In contrast, a programming language imposes itself upon you in a way that those notations don't. You have to describe a lot of things in it. Underspecification leaves too much to the machine, overspecification tortures the poor brains reading after you. The optimal boundary differs depending on the thing being described, might not always exist and sometimes not always that satisfactory (still pisses off the humans or the machines in some parts or another of the program). Making different programs in different languages and making them somehow all cooperate to describe the same problem opens a whole new can of worms that's just as hard to solve as the original problem. It's nowhere near as hard to mix-and-match mathematical notations (e.g. Lagrangian formulation of classical mechanics where Newtonian dot notation is used to denote time derivatives and Leibnizian fraction notation is used to denote coordinate derivatives). If you're stuck, you can always invent a new notation or whip up a diagram, describe how they work on-the-fly in some shared meta-language, then use it right away anywhere and everywhere you want, including in conjunction with old notations. So it basically boils down to the capabilities of the underlying machine. The human brain is one hell of a machine, you have a lot of leeway. But programming languages are primarily ways to communicate with a very different type of machine, and as if that wasn't enough they _also_ still have to support wet brains, and as if that wasn't enough they are extremely rigid and heavyweight compared to human notations, i.e. much more difficult and time-consuming to design and implement and spread (when they are new) and de-spread (when they are obsolete and there are better alternatives).