akrophonobolos 0.0.2

Ancient Athenian acrophonic numeral converter

Akrophonobolos

Python package for handling Ancient Athenian monetary values in talents, drachmas and obols, including input and output in Greek acrophonic numerals (such as 𐅎, 𐅍, 𐅌, 𐅋, 𐅊, etc.)

The denominations of Ancient Athenian money were the tálanton (τάλαντον, or talent), the drakhmḗ (δραχμή, or drachma), and the obolós (ὀβολός, or obol). Six oboloí made a drakhmḗ, and 6,000 drakhmaí a tálanton (which was 57 lbs. of silver).

Large sums of money are found in forms like “1 tálanton 813 drakhmaí 1½ oboloí.” Math with these figures can be very annoying, so Akrophonobolos simpfifies this.

Installation

pip install akrophonobolos

Usage

Akrophonobolos provides a class, Khremata (χρήματα, "money") and function for manipulating instances of this class.

Initializing

An instance of Khremata can be initialized in several different ways:

With a string that gives amounts with the abbreviations t, d, and b or o:

>>> import akrophonobolos as obol
>>> obol.Khremata("1t 813d 1.5b")
Khremata (1t 813d 1½b [= 40879.5 obols])

You can use upper or lowercase letters, and spaces do not matter:

>>> obol.Khremata("1T 813D 1.5B")
Khremata (1t 813d 1½b [= 40879.5 obols])

>>> obol.Khremata("1t813d1.5b")
Khremata (1t 813d 1½b [= 40879.5 obols])

You can use o for obols, but since this is too similar to a zero, b is better:

>>> obol.Khremata("1t 813d 1.5o")
Khremata (1t 813d 1½b [= 40879.5 obols])

>>> obol.Khremata("1T 813D 1.5O")
Khremata (1t 813d 1½b [= 40879.5 obols])

Internally, the Khremata class stores the value as a (possibly fractional) number of oboloí, and this number can be used directly to initialize an instance:

>>> obol.Khremata(40879.5)
Khremata (1t 813d 1½b [= 40879.5 obols])

Finally you can use a string of Unicode Greek acrophonic numerals:

>>> obol.Khremata("Τ𐅅ΗΗΗΔ𐅂𐅂𐅂Ι𐅁")
Khremata (1t 813d 1½b [= 40879.5 obols])

Formatting

There are methods to format the value as an abbreviation, which is the default string representation:

>>> m = obol.Khremata("1t 813d 1.5b")
>>> m.as_abbr()
'1t 813d 1½b'
>>> print(m)
1t 813d 1½b

It can also be output as a phrase:

>>> m.as_phrase()
'1 talent, 813 drachmas, 1½ obols'

And as Greek numerals:

>>> m.as_greek()
'Τ𐅅ΗΗΗΔ𐅂𐅂𐅂Ι𐅁'

Math

You can do basic math with instances of Khremata

>>> obol.Khremata("1t") + obol.Khremata("3000d")
Khremata (1t 3000d [= 54000.0 obols])

>>> obol.Khremata("1t") - obol.Khremata("3000d")
Khremata (3000d [= 18000.0 obols])

>>> obol.Khremata("1t") * 2
Khremata (2t [= 72000.0 obols])

>>> obol.Khremata("1t") / 2
Khremata (3000d [= 18000.0 obols])

Comparisons:

>>> obol.Khremata("1t") == obol.Khremata("1t")
True

>>> obol.Khremata("1t") > obol.Khremata("3000d")
True

>>> obol.Khremata("1t") < obol.Khremata("3000d")
False

Most of these operators work both between two instance of Khremata and between a Khremata and anything that can be converted into a Khremata:

>>> obol.Khremata("1t") + "3000d"
Khremata (1t 3000d [= 54000.0 obols])

>>> obol.Khremata("1t") - "ΧΧΧ"
Khremata (3000d [= 18000.0 obols])

>>> obol.Khremata("1t") == 36000
True

>>> 18000.0 < obol.Khremata("1t")
True

You cannot multiply two instances of Khremata since "talents squared" does not have any meaning (this raises an UndefinedMonetaryOperation error). If you divide a Khremata by a Khremata though the units cancel out and the operation returns a unitless Fraction:

>>> obol.Khremata("1500d") / obol.Khremata("1t")
Fraction(1, 4)

Fractions, part 1

Above, we said that the Khremata class stores the value internally as a (possibly fractional) number of oboloí. The more correct way to state that is that internally, the Khremata class stores the value, in oboloí, as a Python Fraction. You can access this directly as the b property of the class. In many cases, of course, this fraction is equivalent to a whole number (with a denominator of 1):

>>> m = obol.Khremata("100t")
>>> m.b
Fraction(3600000, 1)

But monetary sums could be recorded down to the quarter-obol:

>>> m = obol.Khremata("1t 1d 1.25b")
>>> m.b
Fraction(144029, 4) 

which is the Fraction form of 36,007.25 oboloí. Storing the value as a Fraction avoids some issues with floating point math and better approximates how Ancient Greeks did math, since they did not use decimal numbers.

Loans and Interest

Figures in tálanta, drakhmaí, and oboloí are found in many ancient Athenian inscriptions, and the most interesting of these involve loans, such as the so-called "Logistai Inscription" (IG I³ 369) which records loans from the money held in the Parthenon and temples of other gods to the Athenian state. Loans were made at simple interest, most commonly at the rate of 1 drakhmḗ per 5 tálanta per day.

Akrophonobolos provides functions for working with loans like this. To start, you can calculate a more useful version of the rate. Given an amount of principal, a number of days, and an amount of interest to be returned, you get back the amount of simple interest to be added for one day:

>>> obol.interest_rate("5t", 1, "1d")
Fraction(1, 30000)

That is, the interest is 1/30,000th of the principal per day.

For any loan, the amount of interest is simply the principal times the rate times the term of the loan. If we borrowed 25 tálanta for a year at the common rate we would be expected to pay 1,825 drakhmaí of interest:

>>> rate = obol.interest_rate("5t", 1, "1d")
>>> obol.Khremata("25t") * rate * 365
Khremata (1825d [= 10950.0 obols])

Of course Akrophonobolos has a function for this:

>>> rate = obol.interest_rate("5t", 1, "1d")
>>> obol.interest(obol.Khremata("25t"), 365, rate)
Khremata (1825d [= 10950.0 obols])

1/30000th is the default rate, so you can leave it out if that's the rate you're using:

>>> obol.interest(obol.Khremata("25t"), 365)
Khremata (1825d [= 10950.0 obols])

And instead of an instance of Khremata you can provide something that can be turned into a Khremata:

>>> obol.interest("25t", 365)
Khremata (1825d [= 10950.0 obols])

If you have the interest and the rate, you can use those to get the principal:

>>> obol.principal("1825d", 365)
Khremata (25t [= 900000.0 obols])

If you have the principal and the interest, you can get the loan term, in days:

>>> obol.loan_term("25t", "1825d")
365

This last scenario is what we usually find in the inscriptions. For instance, line 7 of the Logistai Inscription records one loan as

𐅊· τόκος τούτον ΤΤΧ𐅅ΗΗΗΗ𐅄ΔΔ

or "50 tálanta. Interest on this 2 tálanta 1,970 drakhmaí." We can plug these values into loan_term() and see the the loan was for 1,397 days, just under 4 years:

>>> obol.loan_term("𐅊", "ΤΤΧ𐅅ΗΗΗΗ𐅄ΔΔ")
1397

Fractions, part 2: Rounding

Line 88 of the Logistai Inscription records another loan as 3,418 drakhmaí 1 obolós, with interest of 1 drakhmḗ 5½ oboloí:

ΧΧΧΗΗΗΗΔ𐅃𐅂𐅂𐅂Ι, τόκος τούτο 𐅂ΙΙΙΙΙ𐅁

This loan, it turns out, was for just 17 days.

>>> obol.loan_term("ΧΧΧΗΗΗΗΔ𐅃𐅂𐅂𐅂Ι", "𐅂ΙΙΙΙΙ𐅁")
17

Now, if we want to double-check this:

>>> obol.interest("ΧΧΧΗΗΗΗΔ𐅃𐅂𐅂𐅂Ι", 17)
Khremata (1d 5¾b [= 11.75 obols])

We get an answer that is ¼ obolós too high (11.75 instead of 11.5). We do not know how the ancient Greeks did this math, how they rounded, or what kind of approximations they used. The smallest unit they recorded was ¼ obolós, so in Akrohobolos the interest() and principal() functions round up to this by default. You can get an unrounded answer:

>>> obol.interest("ΧΧΧΗΗΗΗΔ𐅃𐅂𐅂𐅂Ι", 17, roundup=False)
Khremata (1d 5b [= 11.621766666666666 obols])

We can see what the precise fraction is:

>>> precise = obol.interest("ΧΧΧΗΗΗΗΔ𐅃𐅂𐅂𐅂Ι", 17, roundup=False)
>>> precise.b
Fraction(1635618250918339, 140737488355328)

1,635,618,250,918,339/140,737,488,355,328ths is a quite a fraction. Clearly the Greeks did some approximating. Maybe you can play around with Akrophonobolos and figure out how they arrived at 11.5 obols for this amount.

loan_term() rounds to the nearest integer, but you can change this as well:

>>> term = obol.loan_term("ΧΧΧΗΗΗΗΔ𐅃𐅂𐅂𐅂Ι", "𐅂ΙΙΙΙΙ𐅁", roundoff=False)
>>> term
Fraction(345000, 20509)
>>> float(term)
16.82188307572285

Command Line Scripts

Akrophonobolos provides two command line scripts: obol for converting and simple math, and logistes for working with loans and interest

obol

If you give obol one or more amounts in either akrophonic numerals or abbreviated with "t", "d" and "b" (or "o"), it will show the equivalent forms

$ obol 𐅉𐅉𐅈 348d "1d 5.5b" 14T1800D4O
𐅉𐅉𐅈 = 25 talents
348d = ΗΗΗΔΔΔΔ𐅃𐅂𐅂𐅂
1d 5.5b = 𐅂ΙΙΙΙΙ𐅁
14T1800D4O = 𐅉ΤΤΤΤΧ𐅅ΗΗΗΙΙΙΙ

You can also give obol numbers to add and subtract

$ obol 1t + 1000d
ΤΧ = 1t 1000d
$ obol 1t - 1000d
𐅆 = 5000d

logistes

logistes will calculate principal, interest or loan terms based on its inputs (-p for principal, -i- for interest, '-d for days of loan):

$ logistes -p 50t -d 1397
𐅊 (50t) at 10 drachmas per day for 1397 days = ΤΤΧ𐅅ΗΗΗΗ𐅄ΔΔ (2t 1970d) interest
$ logistes -p 50t -i ΤΤΧ𐅅ΗΗΗΗ𐅄ΔΔ
𐅊 (50t) at 10 drachmas per day for 1397 days = ΤΤΧ𐅅ΗΗΗΗ𐅄ΔΔ (2t 1970d) interest
$ logistes -d 1397 -i ΤΤΧ𐅅ΗΗΗΗ𐅄ΔΔ
𐅊 (50t) at 10 drachmas per day for 1397 days = ΤΤΧ𐅅ΗΗΗΗ𐅄ΔΔ (2t 1970d) interest

By default the rate is the common one, 5 tálanta yield 1 drakhmḗ in one day. You can change this with --int-p, --int-i, and --int-d. To calculate the above at 2 drakhmaí per day per 5 tálanta:

$ logistes -p 50t -d 1397 --int-p 5t --int-i 2d --int-d 1
𐅊 (50t) at 20 drachmas per day for 1397 days = ΤΤΤΤΧΧΧ𐅅ΗΗΗΗΔΔΔΔ (4t 3940d) interest

Contributing

Bug reports and pull requests are welcome on GitHub at https://github.com/seanredmond/akrophonobolos