Technology
The number of degrees of freedom in a solution should match the number in the problem. If you have extra degrees of freedom, then you have to write extra code to keep them in sync. This opens the door for bugs. To count the degrees of freedom in a solution, count the mutable fields and the auto properties. These constructs introduce one degree of freedom for each instance of the object. Kurt Godel proved that first order predicate calculus is complete. Any true statement can be proven from axioms. However, he also proved that more complex systems are incomplete. No matter how many axioms you introduce, there will be true statements that you cannot prove. See how he did it, and how that eventually lead to the invention of the comupter. Many of the data structures that we use are directed graphs. Relational databases have foriegn keys, which are directional edges between two records. Build systems have dependencies, which are directional edges between projects. Some of these systems not only directed, but also acyclic. Find out which ones, and prepare to explore the advantages of directed acyclic graphs.