The Long Count, a Mayan numeric system for dates.
A Mesoamerican notation for writing integers in base 20 with an 18 in the third position, where 20^3 would go.
- 1 day is called K’in.
- 20 days are called Winal.
- 360 (20 * 18) days are called Tun. This is where the number system differs from base twenty. This is likely because 360 is approximately one year.
- 7200 (20 ** 2 * 18) days are called K’atun and represent about 20 years.
- This continues until 1 Alautun, which is 20 ** 7 * 18 and represents about 63,081,429 years.
Examples
Here is how many years each number represents:
>>> import M
>>> for days, name in M.days_to_names.items():
... print(f"A {name} is {days} days, or approximately {days / 365:,.2f} years.")
A K'in is 1 days, or approximately 0.00 years.
A Winal is 20 days, or approximately 0.05 years.
A Tun is 360 days, or approximately 0.99 years.
A K'atun is 7200 days, or approximately 19.73 years.
A B'ak'tun is 144000 days, or approximately 394.52 years.
A Piktun is 2880000 days, or approximately 7,890.41 years.
A Kalabtun is 57600000 days, or approximately 157,808.22 years.
A K'inchiltun is 1152000000 days, or approximately 3,156,164.38 years.
A Alautun is 23040000000 days, or approximately 63,123,287.67 years.
Here is a factorization of each number to powers of 20 and 18:
>>> M.days
[1, 20, 360, 7200, 144000, 2880000, 57600000, 1152000000, 23040000000]
>>> for days in M.days[2:]:
... print(f"{days} days are called {M.days_to_names[days]} = 18 * 20 ** {1 + M.log20(days / 18)} days")
360 days are called Tun = 18 * 20 ** 2.0 days
7200 days are called K'atun = 18 * 20 ** 3.0 days
144000 days are called B'ak'tun = 18 * 20 ** 4.0 days
2880000 days are called Piktun = 18 * 20 ** 5.0 days
57600000 days are called Kalabtun = 18 * 20 ** 6.000000000000001 days
1152000000 days are called K'inchiltun = 18 * 20 ** 7.0 days
23040000000 days are called Alautun = 18 * 20 ** 8.0 days
Numbers are represented as numpy arrays with 9 elements. The 0th element is the first digit, the 1st is the second digit, and so on.
For example, 44 = 4 Tun + 2 Winal.
>>> M.from_integer(44) array([4, 2, 0, 0, 0, 0, 0, 0, 0])
You can add numbers with M.add. There is also:
- M.increment to add 1 to a number.
- M.shift to multiply a number by 20 or 18.
- M.repeat to apply a function N times.
>>> M.to_integer(M.add(M.from_integer(122), M.from_integer(34))) 156 >>> M.to_integer(M.repeat(M.shift, 5, M.from_integer(222))) 639360000
Testing
make test
Development
make format