Saturday, 2 July 2016

The urn model of the history of science

The urn model of the common pool of knowledge
Suppose that scientists draw their ideas from a common pool of knowledge and that really new elements are rarely ever added to that pool. Most "new" ideas are new combinations of old elements from the pool of common knowledge rather than adding new elements of knowledge.

Suppose further that this pool of knowledge contains an urn with the elements called causes and another one with the elements called effects. If both urns contained only a black and a white ball, drawing one ball from each urn, the probability P to draw the combination white-white for cause and effect would be 1/4. If 100 people drew one cause and one effect from these urns, but each drawn ball would be replaced, so that each draw would be independent, then 25 of them should end up with the combination white-white.

Adding meaning to the colors, suppose the black ball in the urn for causes meant artificial (human) selection and the white one natural selection. Likewise, the black ball in the effects-urn meant that species were fixed, whereas white meant that species transform. These elements were in the pool of knowledge since ancient times (see Zirkle 1941, Wilkins 2009). Anyway, we can set modern dates for them, for example: species transmutability at least since 1750 (see Telliamed); natural selection at least since 1751 (see Maupertuis); artificial selection at least since 1664 (see Evelyn).

Between the middle of the 18th and that of the 19th century, then, scholars had drawn from those urns in the pool of knowledge for a full century. At the end of that period, however, only three (Matthew 1831; Wallace 1858 and Darwin 1858) had come up with the combination white-white meaning that natural selection transforms species. Here, the fact that three had independently drawn white-white from the urns is not a surprisingly high number that defeats all likelihood and suggests plagiarism among these three. It is instead a surprisingly low number telling us that the drawers must have been biased against this particular combination of elements and often refused it, when they have come up with it in their mind.

The historical record supports this. For example, Buffon discussed and dismissed the possibility (see here). The same is true for Maupertuis, Lyell, Blyth and many others who considered natural selection, if not by that name, by the concept.

Even if we allowed Lamarck's use-inheritance and the wide-spread belief in special creation as further causes into the causes-urn, which would then hold the black and white ball plus, say, a red and a green one, the probability of drawing white-white would be reduced to only 1/8 or 12.5%.

The creation from scratch model of knowledge
Certain plagiarism theorists do, instead, take an abridged and potted narrative as their point of departure, wherein the theory of species transformation through natural selection had to be thought up from scratch and no part of it had ever been heard of before. Based on this anti-historical assumption, they conclude that Darwin and Wallace must have plagiarized Matthew (1831. On Naval Timber and Arboriculture), because they fail to notice that all the parts were in the common-knowledge pool and think of three men independently drawing white-white as an astronomically unlikely event.