What is a half-life?

A half-life is the time it takes for half of something to disappear. It only applies to things that vanish at a pace set by how much is left: radioactive material, medicine in your blood, and not much else. After one half-life you have half. After two you have a quarter. The amount never reaches zero, it just gets too small to matter.

Carbon-14 has a half-life of 5,730 years. A bone holding 100 units of it holds 50 after 5,730 years. After another 5,730 it holds 25. The fraction lost is always half. The amount lost shrinks every time, because each period starts from less than the one before. Atoms break down at random, with no sense of how long they have already sat there. Why not just say how long the material lasts? Because halving never reaches zero, so a material with a 30 year half-life still holds a thousandth of itself after three centuries. That property is what makes carbon dating work, since there is always a trace left to measure. Medicine behaves the same way, as your liver clears a fixed share of what is in your blood each hour. A chair has no half-life, because nothing about it disappears at a rate tied to how much chair is left.

A hot coffee cools the same way. What halves is the gap between the coffee and the room, not the temperature. In a 20 degree room, a 90 degree coffee sits 70 degrees above it. One halving takes it to 55. The next takes it to 37.5. Each step takes the same time as the one before, and each removes less heat. That is why a coffee goes lukewarm quickly and then sits there.