A team of researchers in a company cooperate and produce a valuable commodity for a business. The item is very successful and generates huge income. The president of company wants to reward and give lots of bonus to those responsible for the commodity. But there is a problem. Which among the team is more or less responsible for the product? Who caused the product to be? Who invented it? Who developed it? Who tested it? Who deserves which reward?
The methods for determining responsibility, applies to determining causality. In humans, this is the phenomenon of Morality. Some people are responsible, and cause things to be, whereas others do not, or do much less so. There is a range of responsibility, causality, morality, etc.
So arguing over circles and sides, is very much the same process of determining correctness, cause, and responsibility.
Determining definition, and handing authority (reward) over to one individual instead of others, can be a very important occasion.
With circles and shapes, simple geometry, there ought not be too much to argue about, not much risk involved. But then you go further and apply these definitions, descriptions, and their accuracy to the real world. What then? Would you not prefer the better or best, most accurate, most aligned with reality, definitions? Wouldn’t you like to know the closest representation of “the cause” of what you seek?
Wouldn’t you, as the lead researcher, the inventor of the item, like the most reward? You certainly earned it, did you not, if you were responsible for inventing it?
But there are many intricacies, details, 1,000,000 straight sides, that people overlook. Maybe the reward goes to somebody else, for some other reason. Maybe the reward isn’t worthwhile in the first place.