March 31st, 2013
According to this article, historians of science have demonstrated that science is a process of cultural acquisition:
A well-documented example of cumulative cultural evolution is seen in the growth of scientific knowledge. Historians of science have detailed how scientific knowledge has gradually accumulated over successive generations of scientists, with each new generation building on the advances of previous generations. To paraphrase Isaac Newton, each new generation of scientists can only see further by “standing on the shoulders of giants”. Mathematics, to which Newton himself contributed, is an illustrative example of how scientific knowledge slowly accumulates over successive generations and thousands of years. Only after Babylonian scholars invented numerical notation and basic arithmetic in around 2000 BC could Greek and Arab scholars subsequently develop geometry and algebra respectively, which then allowed Newton, Liebniz and other Europeans to invent calculus and mechanics in the 17th century, through to present-day mathematics.
The author relies heavily on Derek de Solla Price’s Little Science, Big Science (New York, 1963) for this and subsequent claims about the “exponential increase in scientific knowledge over time.”
For the author, mathematics is the paradigm for cumulative scientific knowledge and for the acquisition of that knowledge. A cultural version of Haekel’s phylogeny recapitulates ontogeny undergirds the article:
…individual learning recapitulates history, in other words, that people learn during their lifetimes a sequence of concepts or skills that have previously been accumulated historically. While this assumption may not apply to all cultural domains, certain domains of scientific knowledge do appear to show this recapitulation. While this assumption may not apply to all cultural domains, certain domains of scientific knowledge do appear to show this recapitulation. Figure 2A shows how present-day mathematics education during a single lifetime recapitulates the order in which concepts were discovered in human history ….
Here is Figure 2A, with its wonderfully convincing linear fit:
A few difficulties spring to mind:
- Empirically, many sciences don’t seem to show a cumulative evolution in the way described. Humans did not have to perfect Ptolemaic astronomy before developing Copernican astronomy, which was not necessary for Tychonic.
- Typically, science curriculum does not reflect the recapitulation theory. As a necessary step in their science curriculum few students, for example, have to learn alchemical reaction theories before learning stoichiometry; in biology, understand earlier theories of transformationism before learning modern theories of evolution; in physics, master Aristotelian physics before learning Newtonian physics.
- Finally, historians of science as well as philosophers of science have detailed the difficulties in the older “scientific knowledge has gradually accumulated over successive generations of scientists, with each new generation building on the advances of previous generations” model. Way back in 1962 even Thomas Kuhn tried to distance himself from that overly simplistic, cumulative model of scientific progress.
Oh well, the numbers, equations, and graphs in the article more than compensate for any empirical or conceptual worries I might have.