Why do such parts exist? Often, because formal systems grow organically. Programming languages evolve from practical needs, accruing edge cases and legacy behaviors. Mathematics expands by generalization, sometimes producing results that contradict earlier intuitions (e.g., the Banach-Tarski paradox). Human cognition itself is a patchwork of evolutionary shortcuts, leading to systematic biases. The weird parts are not bugs in the universe—they are features of systems that were never designed from scratch with perfect foresight. Perhaps no field offers a richer collection of weird parts than software engineering. Consider JavaScript’s type coercion: [] + [] evaluates to an empty string, [] + {} becomes "[object Object]" , but {} + [] is 0 . The explanation involves the language’s implicit type conversion rules, the distinction between statement and expression contexts, and the + operator’s overloaded behavior. At first glance, this seems arbitrary. But after studying the specification—how the ToPrimitive abstract operation works, how valueOf and toString are called—the weirdness becomes understandable. It is still surprising, but no longer mysterious.

Write code that explicitly tests weird behaviors. Derive mathematical paradoxes step by step. Try to construct sentences that break your native language’s grammar rules. Weird parts become familiar only through exposure. But not passive exposure—active experimentation. Change one variable, see what happens. Ask “what if” questions.

Weirdness is often the result of simplified mental models. The beginner’s model of arithmetic (addition as repeated counting) fails for negative numbers because it is a special case. The expert’s model (addition as group operation on the integer ring) handles all cases uniformly. Reading the ECMAScript specification, the Python data model documentation, or Euclid’s axioms transformed by modern set theory is the work of moving from folk understanding to formal understanding.

Fractal geometry offers another kind of weirdness: objects with non-integer dimension, infinite perimeter enclosing finite area (the Koch snowflake), or curves that fill space entirely. These defy Euclidean intuition, but they model coastlines, clouds, and biological growth more accurately than idealized shapes. The weird parts here become useful tools once we accept that dimension is not a simple whole number but a measure of complexity. The weirdest parts of all may be within our own minds. Cognitive biases like the conjunction fallacy (Linda the bank teller problem) show that human probability judgments violate the basic axioms of probability theory. We think that “Linda is a bank teller and a feminist” is more likely than “Linda is a bank teller,” even though the conjunction cannot be more probable than its constituent. This is weird because our brains evolved for heuristic reasoning about social and survival scenarios, not for abstract logical consistency.