## Slope fields and community alignment

My girlfriend shared today’s HBR Tip of the Day and it reminded me of an idea I haven’t shared previously.

The tip was about motivating your team by showing them what motivates you.

Motivation has to start with why. But motivation by itself has no direction. One could want to do X with no earthly idea how.

Motivation requires direction to achieve an outcome. In other words, a vector, a quantity containing both magnitude and direction. So when we think about an individual person’s productivity, one can imagine it described through these terms – the outcomes one attains are the function of magnitude (motivation) and direction.

And in fact, this mathematical metaphor scales to the organization. Another concept worth understanding is the slope field, or vector field. Vector fields plot these doublets of magnitude & direction across space, typically illustrated as vectors on a cartesian plot.

One can consider an organization’s total productivity as the aggregate of a vector field over time. That is to say, if we consider this graph as representing each individual’s motivation and direction at a given moment in time, adding these slices over some period should reflect the outcomes of that organization over the same period.

This illustration of vector addition should demonstrate the downside of organizational misalignment. It is so easy for two hard working people to totally nullify each other’s impact on the organization, or end up with some other unexpected impact once the outcomes are synthesized.

This is the same idea as “rowing in the same direction” but expanded to reflect the multi-function setup of a modern corporation, whose considerations are slightly more complex than your average eight-person shell.

Amazing things can happen when an organization or a community shares motivation and direction across its constituents; serendipitous things can happen when there are certain controlled divergence across vector direction; but dangerous be the group where vectors oppose or intersect perpendicularly.

That’s all I got for now. Enjoy your day!