Difference between revisions of "Fallacy of extrapolation"
(→Euler's conjecture: fix typos for now, I will neeed to take a hatchet to this later (as it's not really the fallacy of extrapolation but rather someone finding cexample to long-open conj)) |
(→Euler's conjecture: adding source for Elkies 1988 solution) |
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==Typical examples== | ==Typical examples== | ||
===Euler's conjecture=== | ===Euler's conjecture=== | ||
| − | Based on evidence from unsuccessful manual searches of relatively few numbers, Euler | + | 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]]: |
:<math>x^4 + y^4 + z^4 = w^4</math> | :<math>x^4 + y^4 + z^4 = w^4</math> | ||
| − | 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 | + | 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.<ref>{{cite book |title=The True Marvel of Numbers: And How Fermat Proved His Last Theorem! |author=David Searle |publisher=AuthorHouse |year=2009 |pages=71 |url=http://books.google.sk/books?id=PQC8AQiFCSsC&pg=PA71&lpg=PA71&dq=Naom+Elkies+of+Harvard+University+1988&source=bl&ots=vtJbAgMJdI&sig=rGHNn8o_kiBJ9Vx9o5XpP41Ep2k&hl=en&sa=X&ei=8OBzUuPcLKi24ATAjYGwCw&ved=0CFYQ6AEwBQ#v=onepage&q=Naom%20Elkies%20of%20Harvard%20University%201988&f=false |isbn=978-1-4389-4530-9}}</ref> 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 [[scientific evidence|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.<ref>{{cite book |title=Fermat's Last Theorem |author=Simon Singh |publisher=Fourth Estate |place=London |year=1997 |pages= 177-178|url=http://books.google.no/books?id=Ncrnn9hCn_kC&dq=simon+singh&hl=en&sa=X&ei=29NyUrXWEIGv4ASqzIDoAQ&redir_esc=y |isbn=1-85702-521-0}}</ref> |
== See Also == | == See Also == | ||
Revision as of 17:23, November 1, 2013
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.[1] 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.[2]
Typical examples
Euler's conjecture
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:
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.[3] 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.[4]
See Also
References
- ↑ 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.
