Feynman Finite Shadow Histories
A useful way to think about Feynman path integrals: Do not start with “sum over all possible paths.” Start with finite histories. Take a finite time grid.Take a finite set of allowed states.Enumerate the possible histories.Assign each history an action.Turn the action into a phase.Sum the phases.Check the result. Only after that should anyone talk […]
How Do You Know If a Collection of Claims Is Consistent?
Author: Jeremy H. CarrollDate: 2026-02-22Type: Blog post (technical audience, non-specialist) The problem everyone has You’re reading a report. It’s 200 pages. Each section was written by adifferent person, or generated by a different model, or pulled from a differentdatabase. Every section looks reasonable on its own. The question is: do they agree with each other? […]
What is a Triangle?
“The triangle is not three points in space. It is the minimal cycle in a simple graph — the atom of geometry and the seed of physics.” Scope. All geometric statements refer to generic planar Euclidean bar-and-joint frameworks modulo rigid motions ($E(2)$). Rigidity means infinitesimal rigidity under the Laman condition unless otherwise noted. The relational […]
Monty Hall, But Make It Physics – Part 3 of 4
A short series that builds intuition for quantum mechanics (without asking you to become a monk) Series map Part 3 — The Quantum Physicist You’re not dumb, the notation is just terrible If you look at the Wikipedia page for POVM (Positive Operator-Valued Measure) (https://en.wikipedia.org/wiki/POVM), you will see a bunch of squiggly integrals (integral = […]
Monty Hall, But Make It Physics – Part 2 of 4
A short series that builds intuition for quantum mechanics (without asking you to become a monk) Series map Part 2 — Claude Shannon and the Valve That Moves 2/3 of the Water Previously: In Part 1 we treated probability like a conserved fluid in a three-chamber system.You chose a door, which split the fluid into […]
Monty Hall, But Make It Physics – Part 1 of 4
A short series that builds intuition for quantum mechanics (without asking you to become a monk) The Monty Hall Problem – Series map: Post 1 — Geometry, Vectors, and the Death of “50/50” Monty — who knows where the car is — opens one of the other rooms and shows you a goat. Then he […]
Triangles and Shannon’s Information
How to understand the most important equation in information theory using nothing but a humble triangle The Goal We’re going to completely understand this equation: $$H = -\sum_{i} p_i \log_2 p_i$$ It looks scary. It has Greek letters. It has weird symbols. It has subscripts. By the end of this document, you’ll see it’s just […]
What the Bit — Claude Shannon?
“The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at other point.” — Claude Shannon, 1948 “Information is physical.” — Rolf Landauer, 1961 The Simplest Profound Idea In 1948, a 32-year-old mathematician at Bell Labs published a paper that created an entire field overnight. Claude […]
Треугольники, вероятность и квантовый опыт
«Вселенная не только страннее, чем мы предполагаем, но страннее, чем мы можем предположить.» — Дж. Б. С. Холдейн «Или, возможно… ровно настолько странная, насколько мы должны предположить, если серьёзно отнестись к различению.» Вопрос Каково это — ощущать себя в суперпозиции? Это не мистика. Это самый практичный вопрос в физике. Если мы собираемся строить квантовые компьютеры […]
Triangles, Probability, and the Quantum Experience
“The universe is not only queerer than we suppose, but queerer than we can suppose.” — J.B.S. Haldane “Or perhaps… exactly as queer as we must suppose, once we take distinction seriously.” The Question What does it feel like to be in superposition? This isn’t mysticism. It’s the most practical question in physics. If we’re […]