The Saecular world is characterized by rapid changes in culture, and occasionally of technology. At the time of the novel Anathem, the Saecular world is a consumer society, with constant distractions from advertisements and jeejahs, with the food containing Allswell.
The majority of the Saecular population are slines, who are aliterate or illiterate, with information coming from speelys. The style of clothes worn by slines changes rapidly, responding to corporate advertising. The family of Fraa Erasmas are slines.
The novel Anathem does not contain a great deal of history of the Saecular world. The most serious interactions between the Saecular and Mathic worlds came during the Reconstitution and during the three great Sacks.
During the time of the novel (A.R. 3689 - A.R. 3691) the political situation in the Saecular world is not described in great detail, although a number of clues are given. Arbre has a world government, a Federation of large political units. These "national" units are likely known as Tetrarchies (although there are eight of them). Also mentioned is The Plenary Council of Recovered Satrapies, which may be some type of legislative body, and Prefectures.
The world government is able to coordinate a Convox of Avout from all over the world following the discovery of the space craft in orbit around Arbre, but there remain "national" distinctions. Identity documents are required for passing from one continent to the other, although numerous smugglers exist to bypass this on the route over the north pole. There also remains a significant military presence, including the active mobile ballistic missiles which are used near the end of the novel to send the members of Cell 317 into space. These missiles are said to date from "the last major war."
It is possible that the political division of Arbre follows the nomenclature of the real-life later Roman Empire. The terms "Tetrarchy" and "Prefecture" were used by the Roman Emperor Diocletian (244 - 311 A.D.) to divide the Roman Empire into political units more suitable for defense against barbarian incursions, with the regions under each of the four Imperial rulers (Tetrarchs) were divided into a number of Prefectures.
Ignetha Foral has the title "Madame Secretary." Her exact position in the Saecular government is unknown, and there are hints that she no longer holds a high position during the latter portions of the novel. It is possible that this title is meant to be correspond with the U.N. Secretary General, which would imply that she was the head of the world federation.
The presence of mobile ballistic missiles (for a real world example, see SS-27) used to launch the individuals into space at the end of the novel suggests that warfare among "nation" state on Arbre has been fairly recent. The technology does not appear to be significantly more advanced than in real-life and even with their solid rocket motors they cannot be mothballed or left unattended for decades. This suggests that the missiles are active and tensions between different nations on Arbre remain. The world government was able to coordinate a launch of 200 missiles simultaneously, although this was during a time when the all of Arbre was threatened.