It has been said “Problems are either trivial or intractable”. Several points can be made about this:
- This is experienced by the undergraduate when he or she experiences the something of a leap when going from the first two years of their degree to the last two years.
- The reason why problems are either trivial or intractable is a matter of combinatorics. As you add variables to a problem, the number of ways that these variables can be combined scales factorially
- This implies that there is a lack of middle ground problems.
- The fact that the vast majority of people who complete an undergraduate education do not complete a graduate education is, in part, a result of this jump discontinuity in problem complexity
- The task of the researcher is to make intractable problems tractable (trivial)
- In some since, research is an exercise in complexity management