from certainty to unknowable!

The inquiry into the nature of knowledge—what can be known, how it is known, and the limits of that knowing—has traditionally been the province of philosophers. However, in the digital age, these questions have migrated into the domain of computer science, cryptography, and information theory. The user’s query posits a spectrum of knowledge that spans two distinct poles: the binary decision, characterized by absolute logical entailment, and the SHA-256 cryptographic hash, characterized by a computationally irreducible opacity. The argument suggests that a binary system represents "perfect information" because the negation of one state () necessitates the affirmation of the other (). Conversely, it posits that a SHA-256 hash represents a "perfect lack of information" because the output offers no deductive path back to the input, leaving the observer with nothing but a probabilistic guess among almost infinite possibilities.

​This report undertakes an exhaustive, multi-disciplinary examination of this argument. It explores the validity of the proposed spectrum by dissecting the fundamental mechanics of certainty and uncertainty in digital systems. To do so, we must traverse the landscape of classical logic, where the Law of Non-Contradiction rules supreme , and descend into the chaotic machinery of the SHA-256 algorithm, where the Avalanche Effect shatters causal linearity. We will rigorously compare the concept of "perfect information" in Game Theory against its counterpart in Information Theory , and contrast the computational unpredictability of hashing with the information-theoretic secrecy of the One-Time Pad.