While loading our dishwasher, I was reflecting on what a black box it is. My spouse has found we can use a half of a detergent brick, supposedly because of our naturally soft water. How does that work?
Our water is naturally soft because it contains few minerals. Metro Vancouver collects rain in reservoirs in the north shore mountains, which are granitic and don't dissolve much. Detergent packaging seems to be designed for the many places with harder water than us.
Soaps and detergents contain surfactants, which lower the surface tension of water. Surfactants have one end that grabs onto water and another end that grabs oils. They help loosen and emulsify dirty bits and hold them in suspension until they can be scrubbed away. Detergents are now much more common than soaps. They can be concocted to make more suds if you're washing dishes by hand so you think they are doing a better job. Or they can be made not to have suds like for automatic dishwashers where the suds would be nuisance. Unfortunately, many detergents contain ingredients that can mess up the biology of living things.
The Fall Out
In hard water, soaps react with the minerals to form insoluble scums, such as the bathtub ring in the Cat in the Hat Comes Back. Detergents react with minerals, but with water soluble results. So detergents work in both hard and soft water, although some of the detergent will get taken out of action, the more minerals present. So, you don't need as much detergent if the water is softer. Using only enough detergent to do the job is better for your dishes, pocketbook (if you still have one of those), and Mother Nature, who prefers just eating with her fingers anyway.