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Fallacy of extrapolation

59 bytes added, 12:35, October 2, 2017
/* Typical examples */ intlinks
:<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 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>
===[[Microevolution]] and [[Macroevolution]]===
In the 1980 [[University of Chicago ]] conference entitled "Evolution", scientists 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".<ref>{{cite web |title=Evolutionary theory under fire: A historic conference in Chicago challenges the four-decade long dominance of the Modern Synthesis|author= |publisher=Science |date=November 21, 1980
|volume=210 |number=4472 |pages=883–887 |url=http://www.sciencemag.org/content/210/4472/883.extract |doi= 10.1126/science.610799|quote=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.}}</ref>
|accessdate=2012-10-14
|url=http://www.youtube.com/watch?v=jWaOyy3WfWk
|quote=He also discovered that the universe is expanding. ... Some people think that Hubble is famous because here was a bunch of coffee stains at piece of graph paper and he was able to draw a straight line through it.}}</ref> Although Hubble hastily concluded, based on only 20 [[galaxy|galaxies]], that the [[redshift ]] of the galaxies appears to be a [[linear function ]] of their [[distance]], there is also a disturbing evidence that this linear relationship does not describe the facts entirely. Several authors made a point that Hubble's [[Scientific observation|observations ]] suggested a quadratic rather than linear relation. After research of [[quasar]]s, it has been discovered that if one trends apparent brightness against the redshifts as for galaxies, the result is unexpected diagram with scattered points instead of smooth curve as it is the case of galaxies. This seems to indicate that the quasars do not follow the Hubble Law as do the most other objects. According to other authors including Capria, the value of [[Hubble constant ]] depends on the cosmological model, and [[John Hartnett|J.Hartnett]] claims that the Hubble constant is not truly constant but it has shown up that there is an inherent scale dependence to its value. Consequently, new theories emerged such as [[Moshe Carmeli|M.Carmeli]]'s theory of [[Cosmological special relativity]] where the Hubble law is rewritten in a new invariant way.
== See also ==
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