What be a heuristic? That is in terms of academics, instructing and learning.
If, one knows not. He should first consult at least one quality reference. And, it would be very wise. If, he reviews a number of different sources. When, he forms an “well-rounded understanding” of the term based upon the context of its usage. Such also is true. Whenever, one is addressing any question given as part of a course assessment. Whether, it be a regular homework assignment, quiz, or examination. One should be certain of the meaning of each term used within each problem statement. If, he is not; he most probably will “miss the mark”. When, he offers an answer for the given question. And of this, one might be sure. A top-notch instructor will require that his students be well-versed in course objectives “long passed” as well as those found among the current course curriculum, especially in courses which require cumulative knowledge. Take a second and study the definition and history of heuristics?
They have taken on a “new” and “erroneous” meaning within the realm of modern computing. Why? Most computer scientists, including those with doctorates, were “statistically normal” students. And, slothfulness, academic dishonesty, and ignorance are the “norm” among most educational-institutions in developed nations. And, few, if any, “normal” computer scientist students spend much time reading a dictionary or thesaurus. They might be “whirlwind-whizzes of sorts” when working with, configuring, or programming computational devices; however, most have a “grossly limited” capacity for creative communication. When, they are compared with the typical humanities major.
In short, a “heuristic”, based upon one of its definitions, is an educational tool. It is a “rule of thumb” for solving a given class of problems.
Yet, that is a secondary definition. Which arises and is drawn from its primary definition, “a very challenging problem that requires students using empirical methods and discerning new problem-solving approaches in the solution of the problem that might require leaning upon lessons learnt during previous academic courses.” And, it is the solution of such problems that produce the common “rules of thumb”, such as Russian peasant multiplication, used by mathematicians. For instance, freshman- or sophomore-level philosophy or computer science students might be presented the classic CNF-SAT problem. Which might be given in the form of a MIN-SAT problem. This would be shortly after “mastering” the fundamentals of predicate calculus and the basic rules of formal logic. The vast majority of these students would not have been taught discrete solution-strategies, such as covering or coloring. However, in the solution of such, they might uncover such.
Such is the nature of the class NP. It is necessarily a proper subset of P. Which truly is an artifice. That was constructed and proposed by a mathematician during decades passed. So, we might discuss and examine why certain forms of concern partitioning and organization is unfruitful when solving various classes of problems with specific structural characteristics. Especially, those that have been cast under the ultra-violet light of “non-determinism”.
If, that seems implausible; if not, laughable. Would it seem moreso? If, it were presented in the form of a DNF-SAT. Is one’s intuitive-senses peaked, yet? Next, place it under the “lucid logical light of solvability” by applying De Morgan’s rule. Then, get out the large Crayola and have fun finding a solution with the application of a coloring-algorithm.
One of the most “befuddling of social phenomena” on college campuses is this, “When, an authority figure, such as an instructor, professor, or dean tells a student in his late teens or early that he cannot consume beer and haphazardly fornicate on campus; because, it might result in self-harmful. He will disregard the caution and does so boldly and openly. Whenever, he chooses. Yet if, the same authority figure says that a problem rests in the realm of the “unsolvable” for that same student. And, the solution of the problem might produce many great opportunities for success. His “intellectual laziness” will never dare let him test that boundary of accomplishment.” As such, only the rare few modern computer science students have attempted the solution of this set of computationally-related problems. And only, a very small minority of that few have solved them without outside assistance.
And, the “original intent” of these problems classed NP was the “examination of why and how” many solution sets see a combinatoric-explosion. When, mathematicians use certain naïve “brute force” problem-solution strategies. And, its long-term goal was the identification of a set of “rules of thumb” for the solution of certain canonical classes of problem, much like balancing equations and elementary algebraic problems.
“It was by mere chance or a secondary design, that this classification of problems, known as NP, was recast as a means of slowing and retarding the “advance of mankind” in terms of computational-reasoning.”
- Forrest Gump, DSc Computational Theory