Infinity: Sizes Beyond Counting
Infinity is not a single vast number but a hierarchy of sizes, some larger than others. The counting numbers and...
Year: 2026
Gödel: Truths a System Cannot Prove
Within any sufficiently rich system of mathematics there are true statements it cannot prove. Consistency and completeness cannot both be...
The Unreasonable Effectiveness of Mathematics
Mathematics, invented by contemplating abstractions, turns out to describe the physical world with uncanny precision. Concepts pursued for their own...
The Holographic Principle
A startling idea suggests that everything within a region of space can be described by information on its boundary. The...
Wave-Particle Duality
Light and matter behave sometimes as waves, spreading and interfering, and sometimes as particles, arriving in discrete lumps. Neither picture...
The Uncertainty Principle: Limits of Simultaneous Knowledge
Certain pairs of properties cannot both be known sharply at once. The more precisely one fixes a particle's position, the...
Decoherence: Why the Quantum World Looks Classical
If matter is quantum, why does the everyday world appear solid and definite, never blurred across possibilities? Part of the...
Reversibility and Its Limits
At the microscopic level, physics runs equally well forward and backward; the film of colliding particles looks lawful in reverse....
Landauer’s Principle: The Energy Cost of Forgetting
Erasing a bit of information is not free. To discard what a system knows, one must pay a minimum amount...
The Second Law: Why Time Has a Direction
Among physical laws one stands apart for caring about direction. The second law declares that the entropy of an isolated...
