Explain any topic with three levels of analogy

**Key points** - The fiscal multiplier measures how much total output changes per unit of government spending. A multiplier above 1 means the spending sets off further rounds of activity beyond the initial injection. - The mechanism is circular: government spending becomes someone's income, that person spends part of it, which becomes someone else's income, and so on in shrinking rounds. - The size of the multiplier depends on how much of each round leaks out of the circular flow. Saving, taxat

*(Abridged — Steps 1, 2 and 6 shown.)* **Step 1 — Skill tree** ``` Foundations (must come first) ├─ Vectors: notation, addition, scaling, dot product [low] ├─ Matrices as data vs. matrices as transformations [low] └─ Matrix multiplication, transpose, inverse [medium] Core ├─ Linear independence, span, basis, rank (needs: vectors, matmul) [medium] ├─ Orthogonality and projection (needs: dot product) [medium] └─ Solving Ax = b; l

**LAYER 1 — Explain Like I'm 5** Imagine you have a favourite toy car. You love it exactly as it is, but you want it to sparkle. So you put it inside a clear box covered in glitter. The car hasn't changed at all — it's the same car — but now every time someone looks at it, they see glitter too. A decorator is that glitter box: it wraps something up without changing what's inside. --- **LAYER 2 — The Real Explanation** *What it is:* a decorator is a function that takes another function as inp

**Explanation** Every cell is wrapped in a thin boundary called the cell membrane. It is not a solid wall — it is more like a flexible skin with tiny gaps and doorways in it. Some things slip through those gaps on their own, and other things are too big or the wrong shape and have to be let in deliberately. That difference is the whole idea: the membrane decides what gets in and out, which is how a cell stays different on the inside from the water around it. Diffusion is the name for the "slip

Hi! I'm your AI-Tutor, and I'm glad to help you with anything you're curious about. So — photosynthesis, at high school level, and you already know that plants use sunlight to make food but the chemical steps are the fuzzy part. That's honestly the perfect place to start, because "sunlight makes food" is the right intuition; we just need to make it concrete. Let me set up one idea before I ask you anything. Think of photosynthesis as a recipe. Sunlight is the oven — it supplies the energy. But