The Limits of Formal Systems
We build systems of axioms and rules hoping to capture a domain completely and mechanically. Yet such systems run into...
Year: 2026
Information and the Black Hole Paradox
Throw something into a black hole and it seems to vanish, and when the hole slowly evaporates, its information appears...
Superposition: Being in Many States at Once
A quantum system need not be in one state or another but can be in a blend of both, in...
The Measurement Problem
Between measurements, a quantum system evolves smoothly through many possibilities at once. Yet every measurement finds it in just one...
Maxwell’s Demon: Information and the Second Law
Imagine a tiny being that sorts fast molecules from slow, seeming to create order for free and defy the second...
Least Action: Nature’s Economy
Of all the paths a system might take between two moments, it follows the one that makes a certain quantity...
Small-World Networks
In a huge web of connections, any two nodes may be surprisingly close. A few long-range links collapse the distances,...
The Church-Turing Thesis: What Computation Means
What does it mean to compute? A remarkable claim holds that every intuitive notion of mechanical calculation amounts to the...
Tractability: Why Some Problems Resist
A problem solvable in principle may be unsolvable in practice. If the effort required grows explosively with size, even modest...
Undecidability
Not every well-formed question has a computable answer. Some problems are undecidable, admitting no algorithm that settles every instance. The...
