Radiometric dating works because some atoms are unstable and decay into other atoms at a fixed, unchangeable rate. The key number is the half-life — the time for half of a radioactive "parent" isotope to convert into its stable "daughter." Decay follows an exponential curve, so by measuring the ratio of parent to daughter in a sample, you can read off how long the clock has been running.
Uranium is the gold-standard parent for deep time because it offers two clocks at once: uranium-238 decays to lead-206 with a half-life of about 4.47 billion years, while its faster sibling uranium-235 decays to lead-207 in roughly 710 million years. Two independent clocks ticking in the same grain must give the same answer — a built-in lie detector. For young material there's carbon-14, with a half-life of just 5,730 years, perfect for things like the Iceman but useless past about 50,000 years.
Zircon is the ideal host because it "begins as an empty box" — it accepts uranium into its lattice but excludes lead, and it has the highest blocking temperature of any common mineral, meaning it locks in its clock and resists being reset. Because different minerals seal at different temperatures, dating several of them in one rock can even reconstruct its heating-and-cooling history. This is the instrument every absolute date in the next seven parts ultimately rests on.