关于Tonalpohualli（墨西加仪式日历）的数学计算技术问询

Got it, let's break down how to compute dates in the Tonalpohualli (Mexica ritual calendar) clearly—this boils down to working with two independent cyclic sequences: the 13-day trecena numbers and the 20 unique day symbols. Here's a step-by-step breakdown with examples and code to automate the process.

Core Background #

The Tonalpohualli is a 260-day calendar formed by the least common multiple of 13 and 20 (since 13 and 20 are coprime). Each date is a pair of:

• A number from 1 to 13 (repeating every 13 days)
• One of 20 unique symbols (repeating every 20 days)

Full Symbol Sequence (Matching Your Description) #

First, let's formalize the 20-symbol order based on the examples you provided, filling in standard missing entries (adjust these if your symbol set differs):

• 1: Crocodile
• 2: Wind
• 3: House
• 4: Lizard
• 5: Serpent
• 6: Death
• 7: Deer
• 8: Rabbit
• 9: Water
• 10: Dog
• 11: Monkey
• 12: Grass
• 13: Reed
• 14: Jaguar
• 15: Eagle
• 16: Vulture
• 17: Ocelot
• 18: Snake
• 19: Rain
• 20: Flower

Step-by-Step Calculation #

For any given day number N (starting at 1 for the first day of the cycle):

1. Calculate the Trecena Number #

Use modular arithmetic to wrap the day number into the 1-13 range:

number = ((N - 1) % 13) + 1

• Why subtract 1 first? Modulo 13 gives us a 0-12 range; adding 1 shifts it back to 1-13.
• Example: Day 14 → ((14-1) %13)+1 = (13%13)+1 = 0+1 = 1 (correct, as it starts a new trecena).

2. Calculate the Day Symbol #

Similarly, map the day number to the 20-symbol cycle:

symbol_index = (N - 1) % 20
symbol = tonalpohualli_symbols[symbol_index]

• Again, subtracting 1 aligns the day number to a 0-based index for the symbol list.
• Example: Day 19 → (19-1)%20 = 18 → index 18 corresponds to Rain, which matches your "6 - Rain" example (since day 19's number is ((19-1)%13)+1 = 6).

Example Calculations #

Let's verify with your provided cases:

• Day 13: ((13-1)%13)+1 =13 | (13-1)%20=12 → symbol 13 = Reed → 13 - Reed
• Day 14: ((14-1)%13)+1=1 | (14-1)%20=13 → symbol14=Jaguar → 1 - Jaguar
• Day 19: ((19-1)%13)+1=6 | (19-1)%20=18 → symbol19=Rain → 6 - Rain
• Day20: ((20-1)%13)+1=7 | (20-1)%20=19 → symbol20=Flower → 7 - Flower

Automated Calculation Code (Python) #

If you need to compute multiple dates quickly, here's a simple script you can adapt:

# Define your 20-symbol sequence (adjust this list if your symbols differ)
tonalpohualli_symbols = [
    "Crocodile", "Wind", "House", "Lizard", "Serpent",
    "Death", "Deer", "Rabbit", "Water", "Dog",
    "Monkey", "Grass", "Reed", "Jaguar", "Eagle",
    "Vulture", "Ocelot", "Snake", "Rain", "Flower"
]

def get_tonalpohualli_date(day_num):
    # Calculate the 1-13 number
    trecena_num = ((day_num - 1) % 13) + 1
    # Get the corresponding symbol
    symbol = tonalpohualli_symbols[(day_num - 1) % 20]
    return f"{trecena_num} - {symbol}"

# Test the function with your examples
print(get_tonalpohualli_date(13))   # Output: 13 - Reed
print(get_tonalpohualli_date(14))   # Output: 1 - Jaguar
print(get_tonalpohualli_date(19))   # Output: 6 - Rain
print(get_tonalpohualli_date(20))   # Output: 7 - Flower
print(get_tonalpohualli_date(260))  # Output: 13 - Flower (last day of full cycle)

Just update the tonalpohualli_symbols list if your specific symbol order varies— the core arithmetic logic stays the same regardless of the symbol set.

内容的提问来源于stack exchange，提问作者Pablo Ivan