What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."
posted by escabeche
on Sep 18, 2012 -
61 comments
That is the structure of scientific revolutions: normal science with a paradigm and a dedication to solving puzzles; followed by serious anomalies, which lead to a crisis; and finally resolution of the crisis by a new paradigm. Another famous word does not occur in the section titles: incommensurability
. This is the idea that, in the course of a revolution and paradigm shift, the new ideas and assertions cannot be strictly compared to the old ones. Even if the same words are in use, their very meaning has changed. That in turn led to the idea that a new theory was not chosen to replace an old one, because it was true but more because of a change in world view.
The book ends with the disconcerting thought that progress in science is not a simple line leading to the
truth. It is more progress away from
less adequate conceptions of, and interactions with, the world. via 3quarksdaily
posted by cgc373
on Jun 20, 2012 -
37 comments
Hellenica is an encyclopedia of Greek culture, from classical Hellas, through the Byzantine Empire until the modern day, though its focus is on antiquity and especially the
science and technology of Ancient Greece. Featuring technical diagrams and explications, there's no better site if you seek information on
gigantic galleys,
now obscure great Greek mathematicians,
the last still working Ancient lighthouse and
gears and how they were used by Archimedes and other ancients. This is not to denigrate other sections of the site, such as the page on the
Olympics (including a
Google Map of the site of the games), biographies of
ancient,
Byzantine and
modern Greeks, the
warring and
healing of the Byzantines or the overview of Greek literature, taking in
antiquity,
the medieval era and
modern times. That said, Hellenica is at its finest when treating science and technology.
posted by Kattullus
on Jul 18, 2008 -
8 comments
