Monty Hall with N doors
Move the door count and the number of doors the host opens. The model puts the advantage of switching at (N−1)/R — it tracks the reveals, not the door count.
0.667the model's switch win rate at three doors
Scale
Intuition is built for quantities that add. It handles quantities that multiply badly, and quantities that multiply over and over not at all. Everything in this section turns on that gap — a thickness that doubles, a distance light needs real minutes to cross, a signal that falls away by a factor rather than a subtraction.
The recurring device here is the axis. A doubling process on a linear axis looks like nothing happening, then a wall. The same process on a logarithmic axis is a straight line with no drama in it at all. Neither picture is wrong, and the disagreement between them is the whole point — when a headline says something grew tenfold, which axis you imagine decides whether that sounds alarming or ordinary.
Decibels are the same idea with a unit attached, which is why radio coverage belongs here rather than with the mechanics. At equal radiated power the model starts 5 GHz 7.07 dB below 2.4 GHz with no walls in the way at all, because that gap is fixed by the ratio of the two frequencies and nothing else. Walls do not change that offset; they change the rate at which it grows. Concrete widens it by about six decibels per wall, brick by under half a decibel. One of those effects survives the spread between published coefficients and the other does not, and the page says which.
The models are deliberately thin — a doubling is one multiplication, a light delay one division. Keeping the arithmetic trivial is what makes the result trustworthy, because there is nowhere for an error to hide, and it moves the interesting question from "is this calculated correctly" to "why does the correct answer feel wrong".
A question belongs here when the answer is a band rather than a number and the width of the band is the interesting part. A single figure quoted for an orbital distance or a signal margin is a figure taken at one setting; the model behind it will produce a very different one two clicks away, and saying which setting was used is most of the honesty in the answer. Each page names what it approximates — treating orbits as circular, holding a coefficient fixed — and what its formula has no term for at all.
Finished elsewhere on the site
The writing above is this section. Below are the tools running on the site today, from wherever they sit.