A partial index of discussion notes is in
For example, anyone stopping a car who keeps the brake pedal on hard until the car comes to a stop will get a violent lurch at the end from the sudden release of pressure on compressed springs. Most drivers (but not all) seem to learn that braking should be continuously reduced until the car stops, to avoid this.
Suddenly turning a steering wheel to change direction can cause a serious skid and crash that can be avoided by changing gradually.
All sorts of well-designed machinery that can run at different speeds will be controlled using continuously changing pressures, voltages, flow rates, turn angles, rates of climb or descent, electrical resistances, etc.
But when governments try to control an economy they tend to divide things into bands with discrete changes between bands, e.g. for inheritance tax, stamp duty on houses, income tax, various entitlements, and others.
One of many undesirable consequences is that for those who are just above such a threshold it can be a useful investment to tke steps to move just below it, whereas if tax rates varied using a continuous formula it would not be so easy to avoid significant amounts of tax at so little cost.
Other consequences of discrete changes are unfortunate effects on house buyers or sellers, on entitlements to benefits, and most recently threats to elderly people who need long term care if they happen to own property above a certain value.
Isn't it time governments employed well educated, highly intelligent control engineers to help them devise policies that make far more use of differential equations and other mathematical structures instead of sticking with simple threshold-based mechanisms that were developed before the age of computers?
Will any radio/tv commentator make this point when interviewing politicians?