CARBON DATING
t = t½·log₂(N₀/N) — a quarter left is 11,460 years, exactly, and the round trip is bitwise.
Use the simulation above to change the variables and play through the guided stages. The explanation below describes the default starting values; the simulation updates its explanation as you experiment.
Setup
While a thing lives, the atmosphere keeps its carbon-14 topped up; death stops the refill and the half-life module’s counter starts running down. Measure what remains and invert. The constant-atmosphere assumption is the model — stated on the canvas, corrected in real labs by calibration curves this module names and does not fake.
The date
The date is t-half times log-two of N₀ over N — the decay law solved for time. A quarter remaining means exactly two half-lives means exactly 11,460 years. The arithmetic is the archaeology.
The round trip
Run the answer forward again through the decay law and the input comes back — at the default it comes back bitwise. Two float roads to the date agree to four parts in ten to the sixteen. And left of the shaded wall the curve goes vertical: below about half a percent remaining, measurement noise owns the answer.
Riding the curve down
The sweep runs the sample from ninety percent down to a fifth of one percent. Watch the amber band: the same plus-or-minus in measurement buys an ever-wider window of years. Ötzi dates crisply; Lascaux still solid; at the wall, four millennia of doubt.
Audit
Audited: the round trip returns the input bitwise at the default and within a part in ten to the fifteen everywhere; t of twenty-five percent is 11,460 exactly; Ötzi’s ratio dates to 5310.94 years and Lascaux’s to 16,993.9 — published ratios, disclosed; and the ceiling is priced: the same half-a-per-mille of noise costs 33 years on a young sample and 4,223 on one at the wall — a 128-fold penalty for asking the method one question too old.