If understand you correctly, you are saying that most people are not knowledgeable enough about the different domains in question to make any (or judge any) cross-domain connections. This seems plausible.
I can think however of another argument that confirms this but also clarifies why on Less Wrong we think that people actively compartmentalize instead of failing to make the connection and that is selection bias. Most people on this site are scientists, programmers or other technical professions. It seems that most are also consequentialists. Not surprisingly, both these facts points to people who enjoy following a chain of logic all way to the end.
So, we tend to learn a field until we know it’s basic principles. For example, if you learn about gravity, you can learn just enough so you can calculate the falling speed of an object in gravitational field or you can learn about the bending of space-time by mass. It seems rather obvious to me that the second method encourages cross-domain connections. If you don’t know the basic underlying principles of the domains you can’t make connections.
I also see this all the time when I teach someone how to use computers. Some people build an internal model of how a computer & programs conceptually work and are then able to use most basic programs. Others learn by memorizing each step and are looking at each program as a domain on it’s own instead of generalizing across all programs.
One of the reasons I’m in favor of axiomatization in mathematics is that it prevents compartmentalization and maintains a language (set-theory) for cross-domain connections. It doesn’t have to be about completeness.
So yeah, thumbs up for foundations-encourage-connections… they are connections :)
If understand you correctly, you are saying that most people are not knowledgeable enough about the different domains in question to make any (or judge any) cross-domain connections. This seems plausible.
I can think however of another argument that confirms this but also clarifies why on Less Wrong we think that people actively compartmentalize instead of failing to make the connection and that is selection bias. Most people on this site are scientists, programmers or other technical professions. It seems that most are also consequentialists. Not surprisingly, both these facts points to people who enjoy following a chain of logic all way to the end.
So, we tend to learn a field until we know it’s basic principles. For example, if you learn about gravity, you can learn just enough so you can calculate the falling speed of an object in gravitational field or you can learn about the bending of space-time by mass. It seems rather obvious to me that the second method encourages cross-domain connections. If you don’t know the basic underlying principles of the domains you can’t make connections.
I also see this all the time when I teach someone how to use computers. Some people build an internal model of how a computer & programs conceptually work and are then able to use most basic programs. Others learn by memorizing each step and are looking at each program as a domain on it’s own instead of generalizing across all programs.
One of the reasons I’m in favor of axiomatization in mathematics is that it prevents compartmentalization and maintains a language (set-theory) for cross-domain connections. It doesn’t have to be about completeness.
So yeah, thumbs up for foundations-encourage-connections… they are connections :)
I basically agree, but I’d advocate category theory as a much better base language than set theory.