Those arithmetic stories are clever and all, but what are they about?

I spend some of my time trying to persuade people. I want to persuade effectively, so I spend even more of my time thinking about how persuasion works, and how communication works, and sadly, how they don't work.

Arithmetic metaphor #1 is a warm-up, I suppose. It expresses my frustration at how much time and energy we can expend arguing about disconnected idealogies.

The second is about systems thinking -- understanding parts within the context of the whole. It's about remembering the bigger picture. When we understand the system of arithmetic we know it's absurd to reject one little part of it. Or we ought to know that. But how often do we reject one truth among many because it's just a little too unpleasant, a little too inconvenient, or little too scary? Does that make it go away?

I think not.

Finally, the third allegory is about how we demonstrate understanding...or not. During a conversation via blog comments elsewhere I asked participants how we might demonstrate to each other that we really understand each other's views. “Repeat the other person's argument back to him or her”, was the only reply I received.

That reply left me frustrated and dissatisfied, although it took me a long time to figure out why. For one thing, I was trying to carry on a conversation, not an argument. And the reply felt like a lecture. I know the basics of active listening. Most of us do. Repeating statements is fine; it's useful; it helps to confirm accuracy. But that's all it signifies.

That's not what I really want. Mere acknowledgement isn't very satisfying. I'd rather see an indication of understanding. And to me that means demonstrating that we have incorporated new information into our own thinking.

If I hand someone a message written on a puzzle piece, I hope to see that piece added to the puzzle. Could we at least try, before declaring it doesn't fit or simply ignoring it? Saying “thanks for the blue puzzle piece” while stuffing it into one's pocket, never to be considered again, that's not a demonstration of understanding. That's not why I deliver messages like puzzle pieces. Puzzle pieces belong in a puzzle, assembled, not in the linty darkness of a pocket.

Parroting words back and forth is a social ritual. It has value, but it's transient, fleeting. Demonstrating that we really understand the messages we exchange, that we can fit new pieces into our puzzle, that has lasting value. That's how we establish shared meaning. That's how we begin to make progress. That's how we create the world we want.