Hard Problem of Formal Sciences

The paradox that formal systems like mathematics and logic, which are human creations of pure thought and symbol manipulation, describe and predict the physical universe with uncanny, often inexplicable accuracy. These sciences deal with abstract, necessary truths (2+2=4 is true in any possible universe). The hard problem is why these mind-born rule-sets, which require no empirical input, are so deeply "baked into" the fabric of our contingent, empirical reality. It's the question of whether we invent mathematics or discover it, and if we discover it, why is the universe inherently mathematical? The success of the formal sciences suggests a pre-established harmony between human reason and cosmic structure that borders on the mystical.

Example: A mathematician, working purely from axioms and logic, derives a strange, non-intuitive structure called a "Lie group." Decades later, a physicist finds that this exact mathematical structure perfectly describes the behavior of fundamental particles and forces in the Standard Model. The hard problem: How did a game of intellectual symbols, played out on notebooks, anticipate the operational code of the cosmos? It's as if the universe runs on software written in a programming language that the human brain, by sheer coincidence, independently invented for fun. This "unreasonable effectiveness" is the foundational shock of the formal sciences. Hard Problem of Formal Sciences.

by Enkigal January 24, 2026

Formal Social Sciences

The attempt to apply the methods of formal sciences—mathematics, logic, abstract modeling—to the study of human society, with predictably mixed results. Game theory explains why people cooperate (sometimes), social network analysis maps who talks to whom (approximately), and formal models of political behavior predict elections (except when they don't). The challenge is that humans are not logical symbols; we are messy, contradictory, and prone to doing things just because. Formal social sciences are what happen when mathematicians discover that people refuse to follow the rules.

Example: "A formal social sciences study used game theory to prove that rational actors would never start a war, as the costs always outweigh the benefits. The researchers then looked at human history, which is basically a list of wars, and concluded that humans are either irrational or playing a different game. Probably both."

by Abzugal February 14, 2026

Formal Sciences

The branch of knowledge that studies abstract structures and symbolic systems, unconcerned with whether they correspond to anything in the real world. Mathematics, logic, and theoretical computer science live here, in a pristine realm where 2+2 always equals 4 and arguments are either valid or invalid, not just "like, your opinion, man." Formal sciences are beautiful, consistent, and utterly indifferent to the messy reality of human existence, which is why mathematicians are so calm and everyone else is so confused.

Example: "He loved the formal sciences because in mathematics, unlike in relationships, things either worked or they didn't, and when they didn't, you could prove why. His girlfriend pointed out that this attitude might be why he had so much time for mathematics."

by Abzugal February 14, 2026