Solving for X

There is a sense in which our usual math education misrepresents how math is done in the real world of science and engineering. In high school algebra in particular we 'solve for x', and the one-and-only correct answer can be found in the back of the book. In math, "solving for X" like this is called "a closed form solution" — that is, by moving symbols around in the correct manner we can arrive at The Solution.

However, among equations that arise naturally in science and engineering, almost none of them can be solved in 'closed form'. Instead, of necessity, mathematicians have devised methods of coming up with approximate solutions, where with additional [computer] time you can derive a solution as accurate as you need, but never exact out to the infinite decimal place.

Generally these are iterative (repeating some process) and involve these steps:

  1. An initial guess
  2. A method of improving that guess.
  3. Feed that improved guess back into your method, and continually improve that guess by repeating until it's good enough.

(Iterative mathematical approaches have a long and venerable history going back to Archimedes (287 — 212 BCE) — if not earlier still! And the great physicist/mathematician Isaac Newton (1642-1726) pioneered another approach, known as "Newton's Method", that is a still a mainstay in science and engineering. By the way, Newton did much of his ground breaking work during the Great Plague of London.)

Portrait of man in black with shoulder-length, wavy brown hair, a large sharp nose, and a distracted gaze

Isaac Newton

Right about now we're all facing a Giant Unknown. Heck, we've always been facing the Giant Unknown, but at the moment that Giant has become absolutely Gargantuan. I think I'm speaking for most of us when I state the obvious: that right about now I'm not finding an answer in the back of the book for what to do next. I have no idea whatsoever how to solve for a nice 'X solution' for what to do now.

So I remind myself that a lack of a nice and tidy 'closed form' answer is the norm, even in science and engineering. So time to apply Newton's Method to my own life: what can I do today to make a baby step improvement in my situation?

  • What can I do to make it a little less likely that I'll get Covid-19? Or inadvertently give it to someone else? (I've started wearing a mask at the grocery store — it can't hurt!)
  • What can I do to reduce my expenses even a little?
  • What can I do to help my community even a little? Courtesy and a smile in the grocery store line, for example.
  • What can I do to maintain my inner calm — because that's contagious too. (So is panic.)

I'm just not seeing a 'solution for X' that is going to make this all go away, either for me personally or for all of us collectively. (And if such a solution presents itself, fabulous!) But the lack of such a solution at the moment need not paralyze us: there is no lack of small things we can do, all of us, that repeated over and over will move us steadily towards Life Beyond the Virus. The continuous application of 'baby steps' in the right direction is how most things get solved — in science and engineering, and Life in general.