Constraints and impossibilities


Stretch a spring, and you can predict the force. There is another time-free constraint relationship. For one spring, all possibilities lie on a straight line. Change the spring: swap to a new set of possibilities.

You can also write this as:

force = spring stiffness × extension

The line of possibilities is set by the spring stiffness.

Impossibilities in circuits

Build an electric loop by choosing a battery, one or more resistors or bulbs and wiring them up. The resulting current in the loop is constrained by the choices you made.

You can write this as a mathematical relationship:

voltageresistance = current

You could also plot the possibilities like this.

Again, as a mathematical relationship

voltage = resistance × current

This is the same relationship, just rearranged. The graphs show the same possibilities and impossibilities, just from different points of view, depending on what you want to emphasise.

Impossibilities in changing motion

Force changes motion: there is an acceleration. But you cannot get any acceleration from any force. Force, mass and acceleration shrink and grow in lockstep. These three are constrained.

This relationship shows the same pattern as the three quantities in circuits.

forcemass = acceleration

You can plot this constraint relationship as a line of possibility.

Not always a straight line

Plotting constrained quantities may give possibility lines that are not straight. Move away from a planet, and gravitational force is smaller: there is a constraint pattern here.

This is the famous inverse square law.

gravity force = constant depending on the mass of the planetdistance from centre of planet2