The Mexica number system was based on a vigesimal system, which counted in groups of twenty rather than in groups of ten. The vigesimal system was common in Mesoamerica, and it may have been related to that the Mexica used their fingers and toes to count. The Mexica counted from 1 to 19 using a series of pictographic signs, and they reached 20 by using a special sign. The Mexica then continued to count by adding multiples of 20, 400, and 8000.
The Reasons for the Vigesimal System
The vigesimal system was common in Mesoamerica, and it may have been related to that the Mexica used their fingers and toes to count. The Mexica had 20 fingers and toes (10 fingers and 10 toes), and the vigesimal system was a natural way to count using these body parts. The vigesimal system was also used by other Mesoamerican cultures, including the Maya, and it was a key part of the Mesoamerican mathematical tradition.
The vigesimal system had several advantages over the decimal system. It allowed the Mexica to count larger numbers using fewer signs, and it allowed them to perform complex calculations with relative ease. The vigesimal system was also well suited to the calendar system, which was based on cycles of 20 and 260 days.
The Use of the Vigesimal System
The Mexica number system was used in a wide range of contexts, from the calculation of the tribute to the recording of the calendar to the conduct of trade. The Mexica used the vigesimal system to calculate the amounts owed by the subject provinces, and the tribute lists typically used the vigesimal system to record the larger amounts.
The Mexica also used the vigesimal system in the regulation of the markets, and the market officials used the system to verify the weights and measures used in the markets. The Mexica used the system to calculate the value of the goods, and they used it to determine the prices of the goods.
The Use of the System in Astronomy
The Mexica number system was also used in the calculation of the astronomical observations, which were central to the Mexica calendar system. The Mexica used the vigesimal system to calculate the position of the sun, the moon, and the planets, and they used it to predict eclipses and other astronomical events.
The Mexica had a particular interest in the planet Venus, and they kept careful records of its appearances and disappearances. The Mexica calculated the synodic period of Venus, the time it takes for the planet to return to the same position in the sky, and they used this information to determine the timing of the most important rituals.
The Survival of the Vigesimal System
Many elements of the vigesimal system have survived in the modern Mexican culture, particularly in the indigenous communities, where the traditional counting system is still used in some contexts. The vigesimal system is also reflected in the modern Mexican counting of certain things, particularly in the counting of eggs and other items sold by the piece.
The Spanish conquest brought the European decimal system and the Arabic numerals to Mexico, and these gradually replaced the Mexica system. Yet the Mexica system continued to be used in many indigenous communities, and the persistence of the Mexica system is evidence of the cultural resilience of the indigenous peoples of Mexico.
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