“One cannot really argue with a mathematical theorem.”
Stephen Hawking
I’ve been working at one company with the same group of people long enough now that our meetings have fallen into a comfortable pattern. There’s a lot of mutual trust and respect around the table, and we have settled into a lovely process. Everyone knows their area of responsibility, there’s lots of good listening and even better, lots of good humor. We laugh a lot during a staff meeting! There was this one time though where I got weird and killed the bonhomie to make a point about being too relaxed.
Here’s what usually happens at the end of our weekly staff meetings: one of our members, I’ll call him Krishna, almost always resorts to going to the whiteboard to write an equation or sketch out a graph that supports one of our conclusions. The group knows we’re coming to the end of the meeting because Krishna is about to buttress the group’s conclusion with math. Concluding in this manner wasn’t something we did on purpose, it evolved that way.
At this particular staff meeting, Krishna rises to the whiteboard, a purple dry erase marker in hand. As Krishna stands up to help us all find closure I guess I am not ready to be closed; we are being too easy on ourselves. We have done all the rituals all in the proper order. Our notebooks are closed and aligned neatly on top of our laptops. We have even unplugged the HDMI cable, so there are no powerpoint slides left to scroll through. Perhaps your meetings have a different liturgy of ending, but this is the way we do ours. Except when my need for discomfort strikes, so I said: “Hang on a minute, this time can we end on a theorem, and not a lemma?” I don’t know where this stuff comes from; I am confident in stating that I have not uttered the word “lemma” since high school. I am capable of much worse, I assure you.
If you don’t remember your mathematical terminology, a lemma is a result used as a support for a theorem. Lemmas are smaller “proofs” that support the big conclusion of a theorem. What I was inarticulately saying was that our staff had had fallen into a process of delivering little conclusions rigorously and feeling good about that outcome. However, we shouldn’t have felt good about that; lots of little conclusions do not necessarily add up to a proof of anything. As you know from your own experience, many conflicting conclusions are possible with such a process. If you were to end up with two different ones the term would be “dilemma” or two (di), lemmas. Satisfaction with multiple answers might be a process that cannot deliver THE answer.
Conclusions have a way of doing that. Sometimes we can fool ourselves that lots of little repetitive findings are a conclusion; that however is tautology masquerading as proof. Our staff meeting had fallen into a trap of adhering to the form of a proof, without the function of actually proving anything. A lemma, even a significant one cited many times, is still a lemma—the theorem is harder to get to, and sometimes you need to stick with it, unplugged HDMI be damned. It is worth considering that many meetings are lemma oriented. That’s not a bad thing if the lemma is the thing you’re after, but what happens if you need an unarguable proof? Here is perhaps an even more interesting question I have been asking myself: which one, the lemma or the theorem, represents how I operate in the world? Am I living my life as a string of loosley-connected lemmas or would I rather it be a single unarguable proof of something else? There’s a dilemma worth thinking about.