Dream time is a commonly misunderstood term used to encapsulate Australian Aboriginal beliefs about time and space. The Aboriginal image of time is based on a perception of an individual’s place and role in their society that is different to modern Western thinking. Dream time is a view of reality that encompasses the beginning of life, the influence of ancestors, and of death, a view that transcends the time and space of ordinary experience. Aborigines think of it in terms of an ‘all-at-once’ image of reality rather than a ‘one-thing-after-another’ image of time that Western thinking holds to. Dream time can be experienced through altered states of consciousness induced by tribal mythology and rituals.

The Central Americans

The Maya

The Maya are famous for their sophisticated calendar and their system of recording time, a system still in use in parts of Central America. The Mayan system is based on mathematical relationships between a multitude of cycles of astronomical, religious, and cultural significance. These cycles were principally measured in days but some of the longer cycles ran to many thousands of years.

Mayan mathematics was vigesimal, that is, based on base 20, in contrast to our standard base 10. As we saw with the Babylonians above, the choice of base in any number system is an important factor in the flexibility and power of that system. Interleaving with their base 20 were some important factors outside of the Maya’s influence, such as the time the Earth takes to orbit the Sun. The solar year is approximately 365.25 days, which cannot be described exactly by any normal cycle. The Maya attempted to model the solar year approximately using integer- based cycles, forcing them to use some unusual prime numbers that in the long run gave rise to periods of extraordinary long duration.

Some of the cycles in their calendar are the following:

1. The Tzolkin cycle T lasted 260 days, which means we may write T = 2^{2} x 5 x 13.

2. The Haab cycle H was related to the solar year and lasted 360 days, so we may write H = 360 = 5 x 73. Clearly, H is a poor approximation to the solar year of 365.25 . . . days. Haab was defined as 18 Mayan ‘months’ of 20 days duration each, plus five ‘nameless days’, or Wayeb.

3. The Calendar Round cycle C consisted of 52 Haab cycles. This number is determined as the shortest time that contained an integral number a of Tzolkin cycles and an integral number b of Haab cycles. The calculation requires us to solve the Diophantine equation

which has an infinite number of solutions. The Calendar Round cycle involves the smallest non-trivial values, which are readily found to be a = 73 and b = 52.

We see here the (perhaps undue) dependency in the Mayan theory of time cycles on what is effectively a random number, that is the length of the solar year in days. The Haab cycle is very close to the solar year. Suppose that the solar year was precisely 367 days rather than 365.25 and that the Haab cycle was then taken to be 367. Keeping the Tzolkin value T = 260 then the modified Calendar Round cycle would require us to solve the diophantine equation

for integers c and d. However, 367 is a prime number, so we deduce that c must be a multiple of 367, leading to the conclusion that c = 367, d = 260 is the required solution. This means that the Calendar Round cycle jumps from lasting 52 ‘Old Haab’ cycles to lasting 260 ‘New Haab’ cycles, that is, just over five times longer.

4. The Venus cycle: as keen astronomers, the Maya were aware of the rising and setting of the planet Venus and associated a Venus cycle with it consisting of 584 days.

The Mayan calendar has been described as a ‘Long Count’, starting on a specific day, the date the Maya associated with the creation of the world and identified as 11 August, 3114 BCE in the proleptic Gregorian calendar and 6 September 3113 in the Julian calendar. Starting with the k’in, or one standard day, the Mayan calendar worked with a sequence of ever greater spans of time. After the k’in came the winal, which was the 20 day Mayan ‘month’, followed by the tun, a Long Count ‘year’ of 18 winal, and so on. At the other end came the Alautun, equivalent to a staggering 23,040,000,000 days, or 63,081,429 solar years.

A remarkable point about the Mayan’s scale of time is that the Alautan dwarfs Bishop Ussher’s scale of time (approximately 6,000 years) by a factor of about ten thousand.

The Aztecs

The Aztecs had a philosophy of time in which every day had a religious significance. For them, time went in cycles of repeated destruction and recreation of the world. The Aztec calendar system was less precise than that of the Maya but it shared a number of features common to Central America. There was a 365-day agricultural cycle called the year count and a 260-day ritual cycle called the day count. These two cycles together formed a 52-year cycle called the calendar round.

The Incas

The Incas regarded space and time as a single concept named pacha, translated as ‘world’ or whole cosmos in their language of Quechua, but including also a temporal context, such as a specific moment in time.

The Far East

The Chinese

In common with all cultures, the traditional Chinese view of time impacts on daily life. Time is valued, so punctuality is important. However, time is spent in thought and mental preparation, reflecting on actions to be taken.

The Japanese

In Japanese traditional culture, time is not measured according to its duration but to the quality of what is done. This is exemplified by the famous Tea Ceremony, a ritual that requires respect for the proper order of the ceremony, courtesy, and tradition. On the other hand, the modern Japanese worker will be meticulous in their work rate and attention to time schedules.