Science and physics
Half-life
A quantity that loses a fixed fraction per period has a half-life, and after a few of them most of it is gone, whether it is carbon-14 or a fact.
Radioactive decay physics; applied to medical knowledge by Thierry Poynard and colleagues (2002, 2010) and popularised by Samuel Arbesman, The Half-Life of Facts (2012).
A radioactive nucleus has a fixed chance of decaying in any given second, and that chance does not depend on how long it has already lasted. For a large sample this gives exponential decay: the time for half the atoms to go is the same whether you start with a kilogram or a gram. That time is the half-life. Carbon-14's is 5,730 years, which is why radiocarbon dating works on things that died within the last 50,000 years or so. The arithmetic is the useful part. After one half-life 50 percent remains; after two, 25 percent; after three (17,190 years for carbon-14) 12.5 percent. Ten half-lives leave about a thousandth, since one half to the tenth power is 1/1,024.
The transfer is to anything that loses a roughly constant fraction per period. Poynard and colleagues took the conclusions of 474 papers on cirrhosis and hepatitis published between 1945 and 1999 and had them re-examined in 2009: 60 percent still held, 19 percent were obsolete, 21 percent were false, and the fitted half-life of a conclusion was 45 years. Arbesman built his 2012 book on results like these: facts do not die at random, they turn over at measurable rates that differ by field. Memory decays with a similar shape, which is what the Ebbinghaus forgetting curve describes; that model gets its own entry later in this library. The move is the same each time: find the rate, then stop treating what you learned a decade ago as current.
Where it breaks. Exponential decay needs the per-period rate to be constant and independent of history, which is true of nuclei and rarely true of ideas. Some facts (the boiling point of water at sea level) have an effectively infinite half-life, while a web framework's conventions can be obsolete in two years, so one 'half-life of knowledge' for a field hides the spread. Poynard's figure also measures what later experts judged false, and those judgements have their own error rate. And decay is not the only process: new results arrive as old ones die, so the amount you need to know does not shrink. Use the model to decide what to recheck, not as a licence to ignore the old.
Example
In 2010 Thierry Poynard and colleagues published a follow-up to their 2002 'truth survival' study in PLOS ONE. They took 474 conclusions, one from each of 474 articles on cirrhosis and hepatitis published between 1945 and 1999, and had them reassessed in 2009. 284 (60 percent) were still considered true, 90 (19 percent) obsolete and 100 (21 percent) false. The survival rate of a conclusion was 85 percent at 20 years and 52 percent at 40 years, and the fitted half-life of truth was 45 years, the same figure as in the 2002 study.
Where it applies
List what you believe about your field and mark when you learned each item; anything older than one half-life gets rechecked. In machine learning, benchmarks and 'best practice' have half-lives of a few years, so a pipeline copied from a 2019 blog post is a decision to re-make, not a default. Cache entries, API versions and model weights decay the same way.
Think about it
What do you still teach or repeat that you learned more than ten years ago and have not checked since?
Applied it to something real? Log it.
Test yourselfA sample has been through three half-lives. How much is left, and how long is that for carbon-14?
12.5 percent, which is one half cubed. For carbon-14, with a half-life of 5,730 years, three half-lives is 17,190 years.
Related models
- The Lindy effectFor things that do not wear out, such as ideas, books and technologies, every year they survive raises how long they can be expected to last.
- CompoundingReturns earned on past returns: a steady rate applied to a growing base turns small repeated gains into large ones, mostly at the end.
- Exponential versus linear growthLinear growth adds the same amount each step; exponential growth multiplies by the same factor, and the two look alike only at the start.
- EntropyLeft alone, an isolated system drifts into its most probable, least ordered state, so keeping anything ordered costs continual work.
- The forgetting curveMemory for new material drops fast in the first hours and then slowly; what is left after a day is most of what will be left after a month.