I have heard quotes from 2 to 14 years on how often knowledge doubles (it varies by field). The average seems to be 7. However are they talking about compound doubling or non-compund doubling? In 28 years will we know 5x as much or will we know 16x as much?
They are talking about compound doubling. The quotes are intended to emphasize the exponential growth of knowledge – the more we know, the more we are capable of learning.
With, as you note, so many informal estimates, it’s kind of difficult to know in general.
But in the case of one early and influential attempt to do this sort of thing, the doubling was non-compounding. In chapter 8 of his Science Since Babylon (1961; Yale 1975), Derek de Solla Price considered several measures for charting how “big” science has been over the years. New journals published, papers published, number of scientists, etc. In each instance the doubling time was on the order 10-20 years. However, these were explicitly non-compounding. Thus he was interested in the number of scientists active in 1950 vs. those in 1910, not the total number of scientists there’s ever been.
Price expanded on this sort of issue in Little Science, Big Science (1963).
Moores law is compounded, so i was wondering if this ‘law’ was compounded too. Since computers, available higher education to whoever wants it globally and advances in communication, travel and standard of living (which make labs cheaper) i figured it would be compounded as there would be better communication, more labs, more computers to process the data and more educated people every few years. But at the same time the idea that we will know 32x as much about ‘everything’ in 2039 seems implausible to me.
Obligatory links to the Technological Singularity:
The Original Paper
Vernor Vinge with more
The Techno-Rapture (references to more articles)