NecessaryButNotSufficient

"Necessary but not sufficient." is a powerful distinction that occurs a lot in mathematics. I think the distinction has value in interpreting other things - it's another tool in the "What's going on?" toolbox.

"Necessary but not sufficient" shows up in math in proofs, where some particular factoid needs to be true for another factoid to be true. At the same time, the truth of the first factoid doesn't prove the second factoid by itself. The first factoid allows the second factoid to be true if some additional conditions are met.

Think about a dinner party. Having the ingredients for what you are going to serve is necessary for dinner to happen - without them, the eating part is a challenge. At the same time merely having the ingredients says nothing about whether you've got the skills to prepare them, somewhere to cook, or someone to eat dinner should dinner be produced. Any one of these conditions: ingredients, skills, kitchen, and guests is "necessary but not sufficient."

"Necessary but not sufficient" is itself both an interesting tool, and an hypothesys. If we keep buying ingredients but no dinner party happens, we suspect that ingredients are necessary, but not sufficient for dinner to happen. We have an hypothesis that there is something else we need for dinner. In math you don't always have to know what else is needed in order to prove that the thing you've got - ingredients - isn't enough by itself.

Of course actually naming the other thing is a convenient and relatively satisfying way to prove necessary, but not sufficient. But the powerful thing in non-math life is being able to have the hypothesys. If my one trick isn't working, maybe there's something more going on here. In life, at least for me, the most powerful insights come when I realize the trick I've got isn't making it, and can't name what else I need.

One example of where this is useful is in the discussion of the ProductionPracticesCheckList linked to this extended definition. Skills are necessary, but not sufficient in doing operations. So are human factors, and the human characteristics of the people doing operations. Having something worth doing is probably necessary but not sufficient for operations to last for any length of time as well.

Somehow in the systems field, we seem to like talking about the thing - the one, whole thing. More often we are presenting one thing of many. The one thing we are talking about - operations KPAs, for example - may be the one thing that we need most, in this business right now. Or it may be the one thing that I can think of that I think will help. Neither of those is a small gain. Lots of places would pay diamonds for knowing what they need most at the moment, or even to have an idea that might help.

This is an actual usefulness in math, I think - the training in identifying fine distinctions that make a difference, like necessary but not sufficient. The tools of mathematical inference really come down to one question: What do I actually, really know? Learning about asking that question is real useful in doing systems things, and even in real life, I think. But while it's necessary, that question by itself isn't sufficient.

- JimBullock, 2002.11.22

Jim, nice rant, but you don't need to keep SHOUTING the WikiWord. It gets a little highlighted when you're on the page, doesn't it. So perhaps a WikiWord is SufficientButNotNecessary - the other interesting tool.

--BobLee 2002-11-21

Good point, and nice addition. I took an edit pass at the rant - less caps. Also more pith & less words, I think. Thanks for the comment.

I have trouble editing for readability on the same day I first write something. Sleeping seems to help me forget enough to see what I've written afresh. Thanks (all) for the indulgence.

-- JimBullock, 2002.11.21

Updated: Friday, November 22, 2002