Occam's Razor vis-a-vis Theory of Algorithms

This is a brilliant, compelling short film on Occam's Razor.  We may witness something or hear something, and immediately our imagination and fears run amok, and we think the worst of it.  It's the stuff of conspiracy theories.  So, in my reading of Occam's Razor, it's about turning to the simplest, perhaps most common explanation for something.  I love the fact that art - film, in this case - helps us grasp a scientific and philosophical concept.

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The origins of what has come to be known as Occam's Razor are traceable to the works of earlier philosophers such as John Duns Scotus (1265–1308), Robert Grosseteste (1175-1253), Maimonides (Moses ben-Maimon, 1138–1204), and even Aristotle (384–322 BC).  Aristotle writes in his Posterior Analytics, "we may assume the superiority ceteris paribus [all things being equal] of the demonstration which derives from fewer postulates or hypotheses."  Ptolemy (c. AD 90 – c. AD 168) stated, "We consider it a good principle to explain the phenomena by the simplest hypothesis possible."

Phrases such as "It is vain to do with more what can be done with fewer" and "A plurality is not to be posited without necessity" were commonplace in 13th-century scholastic writing.  Robert Grosseteste, in Commentary on [Aristotle's] the Posterior Analytics Books (Commentarius in Posteriorum Analyticorum Libros) (c. 1217–1220), declares: "That is better and more valuable which requires fewer, other circumstances being equal... For if one thing were demonstrated from many and another thing from fewer equally known premises, clearly that is better which is from fewer because it makes us know quickly, just as a universal demonstration is better than particular because it produces knowledge from fewer premises. Similarly in natural science, in moral science, and in metaphysics the best is that which needs no premises and the better that which needs the fewer, other circumstances being equal."

Reference: Occam's Razor.

In Theory of Algorithms, I have posited that we encounter difficulties, when we attempt to solve a complex problem with a simple solution and when we attempt to solve a simple problem with a complex solution. This particular algorithm speaks to the importance of matching the level complexity (or simplicity) between problem and solution.

So is Theory of Algorithms antithetical to Occam's Razor?

Not necessarily.  In fact, Theory of Algorithms abides by Occam's Razor to a large extent.  It's about finding the algorithm, that is, the most parsimonious explanation or rule, to account for something, someone, or some situation.  For example, when estimating how long it will take to travel somewhere, finish a task, or complete a project, I use the simple algorithm of multiplying that time by two or three.  For the much of my purpose, I don't need to arrive at more specific or precise figure.  Rather, this simple algorithm has improved my time estimation drastically.

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My cautionary note is this: We must not misinterpret or misapply Occam's Razor?  What Herr Professor says above is crucial.  Finding the simplest solution to a complex problem does not mean we ought to arrive at simplistic or simpler solution.  In other words, an explanation derived from Occam's Razor may be rather complex, but it's the most economical or parsimonious one to help us grasp a particular phenomenon.  In this respect, Theory of Algorithms and Occam's Razor very much resonate with one another.