Mesoamerican chronology divides the history of pre-Columbian Mesoamerica into several periods: the Paleo-Indian (first human habitation–3500 BCE), the Archaic (3500–2000 BCE), the Preclassic or Formative (2000 BCE–200 CE), the Classic (200 CE–1000CE), and the Postclassic (1000 CE–1697 CE).
 Some of the period divisions are taken from the history of the Maya: The Preclassic-Classic boundary marks the first Maya "collapse", the Classic-Postclassic boundary marks the second, and the end date of 1697 marks the conquest of the last independent Maya city-state, Tayasal.
 However, this chronology applies to other pre-Columbian Mesoamerican civilizations as well.
Pedro Armillas Garcia (9 September 1914 – 11 April 1984) was Spanish academic anthropologist, archaeologist, and an influential pre-Columbian Mesoamerica scholar of the mid-20th century.
 As an archaeologist he was known both for his fieldwork and excavations at numerous sites in central and northern Mexico, and his contributions in archaeological theory.
 His study of how Mesoamerican agriculture and subsistence modes of production influenced the development of Mesoamerican cultures was a pioneering one, and he was one of the earliest to investigate pre-Columbian irrigation and hydraulic systems.
Obsidian is a naturally formed volcanic glass that was an important part of the material culture of Pre-Columbian Mesoamerica.
 Obsidian was a highly integrated part of daily and ritual life, and its widespread and varied use may be a significant contributor to Mesoamerica's lack of metallurgy.
 Lithic and contextual analysis of obsidian, including source studies, are important components of archaeological studies of past Mesoamerican cultures and inform scholars on economy, technological organization, long-distance trade, ritual organization, and socio-cultural structure.
The Maya calendar is a system of calendars used in pre-Columbian Mesoamerica and in many modern communities in the Guatemalan highlands, Veracruz, Oaxaca and Chiapas, Mexico.
David Humiston Kelley (April 1, 1924 in Albany, New York – May 19, 2011) was a Canadian American archaeologist and epigrapher, most noted for his work on the phonetic analysis and major contributions toward the decipherment of the writing system used by the Maya civilization of pre-Columbian Mesoamerica, the Maya script.
Talgua Cave, (“The Cave of the Glowing Skulls”; “Cueva del Rio Talgua”), is a cave located in the Olancho Valley in the municipality of Catacamas in northeastern Honduras.
 The misnomer “The Cave of the Glowing Skulls” was given to the cave because of the way that light reflects off of the calcite deposits found on the skeletal remains found there.
 The site has gained the interest of archaeologists studying cave burials of Central America and of Mesoamerica as one of the most extensive Early to Middle Pre-Classic (~1000-900 BC in this case) ossuary cave sites currently known to have been in contact with the Maya societies of nearby Mesoamerica.
 It provides many valuable clues to how the inhabitants of the Talgua Cave may have been an important link between Pre-Columbian Mesoamerica and parts further south and east in Central America and extending into those societies in northern South America, a region known as the Isthmo-Colombian Area.
John Major Jenkins (1964-2017) was an American author and independent researcher, best known for his works that theorize certain astronomical and esoteric connections of the calendar systems used by the Maya civilization of pre-Columbian Mesoamerica.
 His writings are particularly associated with 2012 millenarianism and the development of Mayanism in contemporary and popular culture, as an outgrowth from the New Age milieu.
 He is one of the principal people who have promoted the idea that the ancient Maya calendar ends on 21 December 2012 and this portended major changes for the Earth .
 He has self-published a number of books through his Four Ahau Press.
Joachim Rittstieg (born February 23, 1937 in Berlin, died May 27, 2014 in Rendsburg) was a secondary school mathematics teacher who had travelled in Mexico, Guatemala, Belize, Honduras and El Salvador, and had studied the Mayan calendar system as a 40-year hobby.
Talud-tablero is an architectural style most commonly used in platforms, temples, and pyramids in Pre-Columbian Mesoamerica, becoming popular in the Early Classic Period of Teotihuacan.
 "Talud-tablero" consists of an inward-sloping surface or panel called the "talud", with a panel or structure perpendicular to the ground sitting upon the slope called the "tablero".
 This may also be referred to as the slope-and-panel style.
Maya cave sites are caves used by and associated with the Maya civilization of pre-Columbian Mesoamerica.
 Certain beliefs and observances connected with cave sites are also maintained among some contemporary Maya communities.
 These cave sites are understood to have served religious purposes rather than utilitarian ones.
 Accordingly, archaeological artifacts found within caves can inform interpretations of religious ritual and cave studies combined with epigraphic, iconographic, and ethnographic studies can further inform Maya religion and society.

Question: How long and in what capacity did Joachim Rittstieg study a system of calenders used in pre-Columbian Mesoamerica?
Answer: 40-year hobby