lines and relationships

Nineteenth-century mathematicians discovered to their discomfort that as the conceptual machinery of mathematics became more precise, it became more difficult.
—David Berlinski, The Advent of the Algorithm

I suspect that same will be said of our industry.

One such precision tool is relationships. At the base of any good domain expertise pyramid is a whole mess of relationships between two or more variables. What is the relationship between compensation and performance? How are budgets spent across the development and launch of a new project?

Here are some of my favorites generic relationships.

• The linear relationships.
• The bell curve.
• The s-curve.
• The asymptotic relationship.
• The price/demand relationship.

Or visually:

I suspect that increasingly, we will all have to be as comfortable with using these and other relationships to characterize knowledge as we currently are with bullets, headings, and fonts.

Taxes are always a great example: sales taxes are a fixed percentage of the cost of an item, whereas with a progressive income tax, the proportion of their income one has to pay increases as their income bracket rises.