Reply: We humans are digital animals. We evolved that way, from our DNA code on up, because digital decision-making is more effective than analog operations. As a result, we deal with analog existence but only by first digitizing it. The problem is that there are always many ways to digitize any analog information, so we are constantly looking for better ways to digitize existence.

Reply: A significant discovery during the last century is that set theory can be developed as a rigorously logical axiomatic system and can explain the foundations of mathematics—but numbers or functions cannot explain sets. Computers work with sets of bits and treat numbers as just another data type. Historically, however, working with numbers goes back thousands of years, while sets were not defined logically until 1874. With computers doing the detail work, set theory now provides a solidly logical foundation for mathematics and much else.

Reply: It’s confusing for many people, but it’s what gives us freedom in forming human groups. For example, there are two ways a group may try to regulate the physical actions of its members—authoritarianism and legalism. In authoritarianism the regulation comes from human behavior, such as the commands of a boss or dictator. In legalism, it comes from laws written in general, abstract terms. It helps us understand group organizations by asking whether a group is run by commands or rules, although many groups use both.