Closed-Form Solutions

Day 334 Week 49 Q4  Wednesday, November 30, 2022

When a problem can be analytically solved through a finite number of well-known functions, it can be said to have a closed-form solution.  This does happen in mathematics and some of the time in engineering but not as much in real-life situations involving people, who tend toward the nonlinear, infinite and not-so-well-known. Still, the rational among us habitually strive for closed-form solutions while at some level know not to expect them to come about. 

The good news is most of the world does not even know they exist so they do not mind when we do not achieve them, unless of course we talk about them and try to gain converts to our approaches before they fall short, which is embarrassing.

The lesson here is if you are expecting rational linear clear finite solutions, you may not want to talk about it too much, for what will come out is likely to be something different. Another similar concept I call artificial accuracy or exaggerated precision; this is what happens when you divide ten by three and say the answer is 3.333333333, depending upon how many significant digits you think you really have or are required.  This sort of thing shows up in business 0pans written by MBA students while they are still in school or shortly after they graduate. Just because you know how to use a spreadsheet does not mean most of these numbers after the decimal point mean anything.

If you are a mathematician, engineer or physicist, you get to use a lot of significant digits, but if you are in the business world, and you hardly ever get more than one. Most of us live in a base ten world, meaning we deal with 0 to 9 and then roll over to the next column.  As early computer users we sometimes used binary and hexadecimal systems, but that is mostly hidden these days. Getting back to how many significant digits do you get in business, I would say most of the time, only one, especially in a startup. You are doing well if your projections are within ten percent of reality. For example, we will break even in 19 months. Yeah, right, sure you will. Nineteen months plus or minus 10% would still be pretty good. But when your business plan says 19.35 months, it is laughable. And in psychology, I am not sure there are any significant digits at all. No therapist would ever say you will be transformed in 67 days, and it may not even be 6 or 7 months.

I am not saying this to slam business people, psychologists or psychotherapists but to point out that the ability to wrangle spreadsheets does not make life more predictable or accurate except in the rearview mirror. You can certainly examine what-ifs, but just do not count on them being exactly right. Closed-form solutions are less for the living than for the mechanical. And when people are that predictable, you do not want to hang out with them. At least creative outliers do not have this problem. They are not very governed by linear artificial precision. If they were, they would never go for it, Whatever they are going for because the odds are too poor to get excited about.