Fallacy of extrapolation
The fallacy of extrapolation occurs when a phenomenon responsible for a number of trivial local effects is read into the great global phenomena. For example, Darwin's theory of evolution makes use of a fantastic extrapolation in which the mechanisms of random variation and natural selection are declared to account for the development of such complex structures as the mammalian eye or the immuno-defense system. When attempting for an interpretation of research results, the scientist must be leery of extrapolating beyond the range of the data and conscious of the underlying assumptions to avoid drawing invalid conclusions.
Based on evidence from unsuccessful manual searches of relatively few numbers, Euler predicted that there were no whole number solutions to the following equation, similar to one pertaining to famous Fermat's Last Theorem:
- x4 + y4 + z4 = w4
For two hundred years nobody could disprove this claim despite years of computer sifting. Lack of a counter-example was interpreted as strong evidence in favor of a theory until Naom Elkies of Harvard University discovered the solution in 1988. Despite all the evidence, Euler's conjecture turned out to be false at the end. Extrapolating a theory to cover an infinity of numbers based on insufficient and limited amount of evidence without absolute proof has shown to be an unacceptable gamble. The moral is that it is not possible to use evidence from first local set of million numbers to prove the theory or rather conjecture about global set of all numbers.
In 1980 the scientists at the Chicago conference were trying to address the question whether the mechanisms underlying microevolution can be extrapolated to explain the phenomena of macroevolution. Despite the risk of doing violence to the positions of some of the people at the meeting, the answer given was a clear "No".
- ↑ David Berlinski (2009). "Has Darwin met his match?", The Deniable Darwin. Seattle, USA: Discovery Institute Press (reprinted from Commentary February 1998 by permission), 307. ISBN 978-0-9790141-2-3.
- ↑ Riegelman R. (September 1979). The fallacy of free extrapolation 189-91, 194. Postgraduate medicine. Retrieved on October 31, 2013.
- ↑ David Searle (2009). The True Marvel of Numbers: And How Fermat Proved His Last Theorem!. AuthorHouse, 71. ISBN 978-1-4389-4530-9.
- ↑ Simon Singh (1997). Fermat's Last Theorem. Fourth Estate, 177-178. ISBN 1-85702-521-0.
- ↑ Evolutionary theory under fire: A historic conference in Chicago challenges the four-decade long dominance of the Modern Synthesis 883-887. Science (November 21, 1980). DOI:10.1126/science.610799. “The central question of the Chicago conference was whether the mechanisms underlying microevolution can be extrapolated to explain the phenomena of macroevolution. At the risk of doing violence to the positions of some of the people at the meeting, the answer can be given as a clear, No.”