The Half-Life of Facts
Excerpts
1. The Half-life of Facts
2. The Pace of Discovery
Derek de Solla Price lectured at Raffles College (now National University of Singapore). At that time, they were building a library. The library was giving out existing books to students and faculty to store while the library was being constructed. Price got a complete set of Philosophical Transactions of the Royal Society of London, dating back to 1665. He stacked them in his apartment and discovered that, over time, the volume got thicker and thicker. It turns out that the increase in volume was following an exponential curve.
He measured the same pattern in other fields and published it under the title “Quantitative measures of the development of science” in 1951.
This is reminiscent of the discovery of Benford’s law, where the physical book of logarithms gave out a hint.
He discovered many exponential growth in knowledge discovery, including number of universities, important discoveries, scientific journals, asteroids known, engineers, etc. See Little Science, Big Science.
Does basic science grow faster than derivative science?
Harriet Zuckerman‘s study on first authorship of Nobel laureates. They tend to move to non-first author positions more quickly than peers.
Eurekometrics: https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1002072 - discovery is getting exponentially more difficult.
P. 24 In fact, if you uttered the statement “Eighty percent of all the scientists who have ever lived are alive today” nearly anytime in the past three hundred years, you’d be right.
3. The Asymptote of Truth
Lazarus taxa: living things that had been presumed extinct but later discovered.
A study looked at cirrhosis and hepatitis literature to see how many studies are considered false or obsolete over time. (Truth survival in clinical research: an evidence-based requiem?) They showed that the half life is about 45 years.
“It takes 50 years to get a wrong idea out of medicine, and 100 years a right one into medicine” –John Hughlings Jackson
We can also look at citations to estimate the half-life. Papers in APS journals have ~5 years of half life. Rong Tang’s work shows that, for books, physics have ~13 years and other fields have shorter half life e.g., psychology ~7 years.
4. Moore’s law of everything
Heebyung Koh and Chris Magee looked at “information transformation” across history and found Moore’s law over a long period of time.
A potential explanation is that the exponential curve is the result of combining many logistic curves. New technologies slowly emerge, then follow an exponential growth and subsequent saturation. Because many technologies are happening at the same time, the combination can follow an exponential curve.
Technology changes facts. The magnetic permeability of iron has been changing because of the iron purifying technology.
One of the driving forces of these exponential growth is population growth. Michael Kremer wrote an article “Population growth and technological change: one million B.C. To 1990”, which argues that the technological change can be explained by the population growth.
David Bradley studied how far people move because he was interested in the nature of contagion over time. He found that he family has increased the range 10 times in each generation. (Exponential growth)
This has been confirmed by other studies. See Grübler “Technology and global change”
Cesare Marchetti argues that Berlin has been growing according the a simple rule: How far you can reach within 30 minutes or so? But then how about Los Angeles?
5. The spread of facts
Gutenberg’s printing press spread quite slowly. It required a combination of multiple innovation. Was it spread through “medium” strength ties, like JP’s study using cell phone network?
Homeoteleuton. A common scribal error where the scriber skips to the second occurrence of a particular phrase omitting everything in between. The same type of error happens in genetics and it’s called slipped-strand mispairing mutation. Other correspondences include dittography-insertions, metathesis-chromosomal transposition, and so on.
Simkin’s study. Kleinberg’s chain mail study.
6. Hidden knowledge
Don Swanson termed Undiscovered public knowledge. He actually systematically searched such unknown connections and discovered several.
BA model - price model - Herbert Simon - Gibrat’s law. ER random network was studied by Paul Flory in 1941. Stigler’s law, attributed to Robert Merton.
Joseph Lau studied how quickly we can learn by cumulative meta analysis. Compared with Swanson, their work is about combining knowledge from the same field.
CoPub discovery tool that automates Swanson’s process.
TheoryMine (theorem prover), Eureqa, …
The Book of Lost Books is about the books that are cited or mentioned but don’t exist anymore.
John Cisne used the population model to model how medieval manuscript went extinct. They can be copied or destroyed due to the space limit. He found that the half-life would be 4-9 centuries.
7. Fact phase transitions
Phase transition in a way that before and after a discovery we have a totally different understanding of things.
Often there is a slow, constant undercurrent that leads to logistic-like sudden phase transition. The example of extrapolating the fastest speed of projectiles that human achieved (roughly predicted the sputnik and moon landing) and the finding (by Sam & a colleague)of habitable planets by extrapolating the the largest habitability found so far.