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Gödel, Artificial Intelligence, and Confusion

Sentient software is the hot topic as of late. Speculative news about Artificial Intelligence (AI) systems such as Watson, Alexa, and even autonomous vehicles are dominating social media. It’s feasible that this impression is nothing more than Baader-Meinhof phenomenon (AKA frequency illusion). However, it seems that the populace has genuine interest in AI. Questions abound. Are there limits? Is it possible to create a factitious soul? Gödel’s incompleteness theorem is at the core of these questions; however, the conclusions are cryptic and often misunderstood.

Gödel’s incompleteness theorem is frequently adduced as proof of antithetical concepts. For instance, Roger Penrose’s book Shadows of the Mind claims that the theorem disproves the possibility of sentient machines (Penrose, 1994, p. 65). Douglas Hofstadter asserts the opposite in his book, I Am Strange Loop (Hofstadter, 2007). This article aims to provide a cursory view of the theorem in laymen’s terms and elucidate its practical implications on AI.

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Diagonalization?

The goal of this article is to provide laymen with a conceptual understanding of diagonalization. Those interested in a deep dive full of mathematical jargon will be sorely disappointed. However, this piece is the perfect resource for a general understanding of the topic devoid of the more arcane details. Unlike the majority of my writing, this is not directly applicable to the daily responsibilities of software professionals. It is purely an endeavor to satisfy intellectual curiosity.

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Just Enough Set Theory - When Sets Collide (Part 3 of 3)

Welcome to the final installment of this three-part series on set theory. The first piece, Set Theory Defined, detailed requisite foundational knowledge. The second article, Set Operations, outlined some beneficial set algorithms. This post develops the concepts laid out in the first two; therefore, it is highly recommended that readers begin there.

Individual sets have many useful properties; however, preforming operations on multiple sets provides even greater utility. This piece outlines four such operations. Each operation provides a concise means for addressing common programming problems that virtually all software professionals encounter. There is a brief description of each from a mathematical perspective followed by JavaScript (ES6) code excerpts demonstrating how to apply theory to real world scenarios.

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Just Enough Set Theory - Set Operations (Part 2 of 3)

Welcome to the second installment of this three-part series on set theory. The first piece, Set Theory Defined (recently updated with code samples), detailed requisite foundational knowledge. It is highly recommended that readers begin there if they haven’t already.

The first piece in this series introduced sets and exhibited how ES6 arrays are analogous to them. It also depicted how to transform, or map, a set into a related set. This post expands on set theory by probing into set operations.

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