Unfortunately, they get off to a shaky start.
Millenarianism is the belief that an impending change will dramatically change society; millenialism expects such transformations to happen every thousand years; chiliasm (from the Greek chilia, "a thousand") is the specifically Christian form of these beliefs, rooted in the biblical Book of Revelation; the destructive, end-of-world (or eschatological) manifestation of this transformation is often called the Apocalypse ... They are all, significantly, rooted in Western -- not Mayan -- languages [3-4].I'm slightly awed by the authors' ability to cram so much misinformation into a brief paragraph. (And they are, they report in the Introduction, going to be teaching a course on this material at Penn State in the fall of 2012.) But then they don't claim to be experts in the Bible, or even in "Western" history.
Like chiliasm, millenarianism and millennialism both come from words meaning "a thousand," or rather "a thousand years." They're associated with the claim in the biblical Revelation that Christ and the saints will, after defeating the forces of Evil, rule on earth for a thousand years. The belief that the Second Coming would occur in a year divisible by 1000 is a spin-off from this, which has been elaborated into a variety of beliefs over time, but it's not biblical. The New Testament consistently promises that Jesus will return within the lifetime of some of his first followers. The belief that the end of this wicked age and the coming of God's kingdom on Earth is imminent runs through almost all of the New Testament, but it's "rooted" in the Book of Daniel, in the Hebrew Bible (aka "The Old Testament"), and in some other ancient but non-biblical books like the Book of Enoch. The belief in a cataclysmic intervention by Yahweh that would change the world occurs in various forms in several of the Hebrew prophets. As such it turns up several times, in Noah's flood and the Exodus for example; but also in Isaiah 63's imagery of Yahweh treading the winepress of the nations and soaking his garment in their blood. (This passage is the basis for "The Battle Hymn of the Republic," Julia Ward Howe's celebration of Lincoln's Civil War bloodbath.)
Eschatology refers not to "the destructive, end-of-world ... manifestation" but to any doctrine related to the end of the world. However, "end" here doesn't mean end as in terminus; it means the goal, or aim, toward which history is headed. (Think of the everyday distinction between "means" and "ends.") [CORRECTION: Of course the term I didn't look up was the one I got wrong: eschatology means "the study of the last things," and can deal not only with the Last Judgment but with death, Heaven and Hell. Which still means that Restall and Solari have it wrong.] Ironically, biblical scholars tend to split off eschatology as the respectable older brother of apocalyptic, with its low-class tendency to specify an exact date for the Second Coming and its trashy sensational imagery. Apocalypse, though, means "revelation": the biblical Book of Revelation is also known as the Apocalypse of Saint John. Over time, as with millennial, the word "apocalypse" spread out from its original meaning and came to be associated with the kinds of cataclysmic events the book describes -- the four horsemen, plagues, natural disasters, and blood in the streets to the height of the horses' bridles -- to the point that it can be used to refer to almost any major disaster and its aftermath. So Restall and Solari have reversed the associations of eschatology and apocalypse here.
It's also worth pointing out that Christianity, Judaism, and apocalyptic literature are not really "Western" phenomena: they originated in the Middle East and Asia Minor. While Patmos, where John the seer had his revelation, is a Greek island, most scholars agree that he was a refugee from the Asian mainland. Christianity became a "Western" religion by historical accident. And according to Wikipedia, "Millenarianism is a concept or theme that exists in many cultures and religions. Millennialism is a specific type of millenarianism as it applies to Christianity" -- that is, beliefs about thousand year ages and cycles are not specifically Western. I admit that the fascination with the Mayan calendar and the year 2012 are related to contemporary American forms of "apocalyptic" belief, and it's worth stressing that against hucksters who claim to be drawing on Native American wisdom.
Like I said, that's a lot of misinformation for one brief paragraph. It doesn't even seem that the authors even consulted a dictionary as they defined their terms; apparently they just winged it. I hope they're more careful in their handling of Maya history, language, and culture.
