debkeepr integrates non-decimal currencies that use tripartite and tetrapartite systems into the methodologies of Digital Humanities and the practices of reproducible research. The package makes it possible for historical non-decimal currencies, such as the tripartite system of pounds, shillings, and pence, to behave like decimalized numeric values through the implementation of the
deb_decimal vector types. These types are based on the infrastructure provided by the vctrs package.
debkkeepr simplifies the process of performing arithmetic calculations with non-decimal currencies — such as adding £3 13s. 4d. sterling to £8 15s. 9d. sterling — and also provides a basis for analyzing account books with thousands of transactions recorded in non-decimal currencies. The name of the
debkeepr package derives from this latter capability of analyzing historical account books that often used double-entry bookkeeping.
You can install
debkeepr from GitHub with remotes:
# install.packages("remotes") remotes::install_github("jessesadler/debkeepr")
Please open an issue if you have any questions, comments, or requests.
debkeepr package uses the nomenclature of l, s, and d to represent pounds, shillings, and pence units in non-decimal currencies. The abbreviations derive from the Latin terms libra, solidus, and denarius. The libra was a Roman measurement of weight, while the solidus and denarius were both Roman coins. The denarius was a silver coin from the era of the Republic, in contrast to the golden solidus that was issued in the Late Empire. As the production of silver coins overtook that of gold by the 8th century, a solidus came to represent 12 silver denarii coins, and 240 denarii were — for a time — made from one libra or pound of silver. The custom of counting coins in dozens (solidi) and scores of dozens (librae) spread throughout the Carolingian Empire and became ingrained in much of Europe. However, a variety of currencies or monies of account used other bases for the solidus and denarius units. Some currencies and other value systems, such as those for weights, added a fourth unit.
debkeepr provides a consistent manner for dealing with any set of bases within tripartite or tetrapartite systems through the
bases attribute of
Translations of libra, solidus, and denarius units:
- English: pounds, shillings, pence
- French: livres, sols or sous, deniers
- Italian: lire, soldi, denari
- Flemish: ponden, schellingen, groten
- Dutch: guilders, stuivers, penningen
Getting Started with debkeepr vignette: An introduction to the
deb_decimaltypes and their use as vectors and as columns in data frames.
- Transactions in Richard Dafforne’s Journal vignette: Examples of financial and arithmetic calculations dealing with various currencies taken from the practice journal in Richard Dafforne’s Merchant’s Mirrour (1660), a 17th-century textbook for learning accounting practices.
Analysis of Richard Dafforne’s Journal and Ledger vignette: An analysis of the practice journal and ledger in Dafforne’s Merchant’s Mirrour using the
dafforne_accountsdata provided in
- A PDF copy of Dafforne’s practice journal can be consulted to further investigate the practices of early modern double-entry bookkeeping.
deb_decimal types are implemented to deal with two interrelated problems inherent in historical non-decimal currencies and other value systems.
- Historical currencies consist of three or four separate non-decimal units. Most often: pounds, shillings, and pence with sometimes a fourth unit, such as the farthing, added on.
- The bases of the shillings, pence, and optionally farthing units differed by region, coinage, and era.
deb_lsd type maintains the tripartite structure of non-decimal currencies and provides a
bases attribute to record the bases for the shillings and pence units. The
deb_tetra type extends the concept of the
deb_lsd type to incorporate currencies and other types of values that consist of four units. The
deb_decimal type provides a means to decimalize both
deb_tetra types while keeping track of the two or three non-decimal bases and the unit represented.
Let’s see how this works in practice, beginning with
deb_lsd vectors. Note that all of the functions in
debkeepr begin with the prefix
deb_, which is short for double-entry bookkeeping.
deb_tetra vectors work similarly but add an
f unit that defaults to a base of four.
A primary reason for the creation of the
deb_tetra types is to simplify arithmetic calculations with non-decimal currency. Doing calculations by hand requires the use of compound unit arithmetic and normalization.
All implemented arithmetic calculations with
deb_tetra types —
-, etc. — automatically normalize the values according to the
bases attribute. In addition, you can manually normalize non-standard values with
# Perform arithmetic lsd1 + lsd2 #> <deb_lsd> #>  12:9s:1d #> # Bases: 20s 12d lsd2 - lsd1 #> <deb_lsd> #>  5:2s:5d #> # Bases: 20s 12d lsd2 * 2 - lsd1 #> <deb_lsd> #>  13:18s:2d #> # Bases: 20s 12d tetra2 + tetra1 #> <deb_tetra> #>  12:9s:2d:1f #> # Bases: 20s 12d 4f # Normalize a non-standard value to default bases deb_normalize(deb_lsd(132, 53, 35)) #> <deb_lsd> #>  134:15s:11d #> # Bases: 20s 12d # Can also normalize numeric vectors of length 3 or 4 # Must provide the bases for tetrapartite value deb_normalize(c(132, 53, 35, 18), bases = c(20, 12, 4)) #> <deb_tetra> #>  134:16s:3d:2f #> # Bases: 20s 12d 4f
All types allow the user to define the bases for the solidus, denarius, and optionally farthing units of values, enabling integration of currencies that do not use the standardized bases. For example, the Polish florin found in Dafforne’s practice journal used the non-standard bases of 30 gros of 18 denars.
# Create deb_lsd vector with standard bases of 20s. 12d. (lsd3 <- deb_lsd(l = c(28, 32, 54, 18), s = c(15, 8, 18, 12), d = c(8, 11, 7, 9))) #> <deb_lsd> #>  28:15s:8d 32:8s:11d 54:18s:7d 18:12s:9d #> # Bases: 20s 12d # Same numerical values as Polish florins (florins <- deb_lsd(l = c(28, 32, 54, 18), s = c(15, 8, 18, 12), d = c(8, 11, 7, 9), bases = c(30, 18))) #> <deb_lsd> #>  28:15s:8d 32:8s:11d 54:18s:7d 18:12s:9d #> # Bases: 30s 18d # Different outcome with sum due to the different bases sum(lsd3) #> <deb_lsd> #>  134:15s:11d #> # Bases: 20s 12d sum(florins) #> <deb_lsd> #>  133:24s:17d #> # Bases: 30s 18d # Vectors with different bases cannot be combined since # their relationship is unknown. Doing so results in an error. sum(lsd3, florins) #> Error: #> ! Incompatible `bases`. #> ℹ `bases` must be compatible to combine <deb_lsd>, <deb_tetra>, or #> <deb_decimal> vectors. #> ✖ Cannot combine: `..1` <deb_lsd> vector with `bases` s = 20 and d = 12. #> ✖ Cannot combine: `..2` <deb_lsd> vector with `bases` s = 30 and d = 18. #> ℹ Use `deb_convert_bases()` to convert one or more of the vectors to compatible #> `bases`.
deb_decimal vectors represent non-decimal values in the more familiar decimal form. Internally,
deb_decimal vectors are built on
double() vectors. These decimalized vectors are linked to their non-decimal form through the
bases attributes. They can represent either tripartite or tetrapartite values. The only differences are the length of the
bases (2 or 3) and the option to choose the “f” unit with tetrapartite values.
# Create deb_decimal from numeric vector (dec1 <- deb_decimal(c(5.525, 12.235, 8.45))) #> <deb_decimal> #>  5.525 12.235 8.450 #> # Unit: libra #> # Bases: 20s 12d # Same currency values in solidus unit (dec2 <- deb_decimal(c(110.5, 244.7, 169), unit = "s")) #> <deb_decimal> #>  110.5 244.7 169.0 #> # Unit: solidus #> # Bases: 20s 12d # Equality between different units dec1 == dec2 #>  TRUE TRUE TRUE # Use the bases argument to create tetrapartite values deb_decimal(c(5.525, 12.235, 8.45), bases = c(20, 12, 4)) #> <deb_decimal> #>  5.525 12.235 8.450 #> # Unit: libra #> # Bases: 20s 12d 4f # Equality between deb_lsd and deb_decimal vectors # £5 10s. 6d. is equal to 1,326 pence deb_lsd(5, 10, 6) == deb_decimal(1326, unit = "d") #>  TRUE # Which is also equal to 5,304 farthings with default tetrapartite bases deb_lsd(5, 10, 6) == deb_decimal(5304, unit = "f", bases = c(20, 12, 4)) #>  TRUE
When working with decimalized data is preferable, the
deb_decimal type makes casting from and to
deb_tetra possible without losing any metadata about the
bases and therefore the actual value being represented.
deb_decimal vectors can also be combined with numeric vectors or cast from and to numeric vectors.
debkeepr uses an internal conversion hierarchy of
# deb_decimal -> deb_lsd c(dec1, lsd1, lsd2) #> <deb_lsd> #>  5:10s:6d 12:4s:8.4d 8:9s:0d 3:13s:4d 8:15s:9d #> # Bases: 20s 12d # deb_decimal -> deb_tetra c(dec1, tetra1, 8.25) #> <deb_tetra> #>  5:10s:6d:0f 12:4s:8d:1.6f 8:9s:0d:0f 3:13s:4d:3f 8:5s:0d:0f #> # Bases: 20s 12d 4f # deb_decimal -> deb_tetra -> deb_lsd c(dec1, tetra1, lsd2) #> <deb_lsd> #>  5:10s:6d 12:4s:8.4d 8:9s:0d 3:13s:4.75d 8:15s:9d #> # Bases: 20s 12d # Cast between deb_lsd, deb_tetra, and deb_decimal vectors deb_as_lsd(dec1) #> <deb_lsd> #>  5:10s:6d 12:4s:8.4d 8:9s:0d #> # Bases: 20s 12d deb_as_decimal(florins) #> <deb_decimal> #>  28.51481 32.28704 54.61296 18.41667 #> # Unit: libra #> # Bases: 30s 18d deb_as_decimal(tetra2) #> <deb_decimal> #>  8.789583 #> # Unit: libra #> # Bases: 20s 12d 4f # Provide an f unit base to cast from tripartite to tetrapartite deb_as_tetra(lsd1, f = 4) #> <deb_tetra> #>  3:13s:4d:0f #> # Bases: 20s 12d 4f # Represented by solidus/shillings unit deb_as_decimal(lsd3, unit = "s") #> <deb_decimal> #>  575.6667 648.9167 1098.5833 372.7500 #> # Unit: solidus #> # Bases: 20s 12d # Only tetrapartite values can be represented by the farthings unit deb_as_decimal(tetra1, unit = "f") #> <deb_decimal> #>  3523 #> # Unit: farthing #> # Bases: 20s 12d 4f # All three types can be cast to base numeric, which, # of course, leads to the loss of all metadata as.numeric(lsd3) #>  28.78333 32.44583 54.92917 18.63750 as.numeric(tetra1) #>  3.669792 as.numeric(dec1) #>  5.525 12.235 8.450
See the Getting Started with debkeepr vignette for an in depth discussion of the similarities and differences between the two types.
deb_tetratypes have the advantage of maintaining the structure and values used by non-decimal currencies, making it easier to identify and present such values.
deb_decimalimplements a wider array of mathematical functions and arithmetic operations than
- You can move between
deb_tetratypes and the
deb_decimaltype without losing any data through
deb_decimalare based on the vctrs package, all types act as expected in data frames or tibbles columns. From dplyr 1.0.0 — which is the minimal version used by debkeepr — all dplyr functions work on both
ggplot2 does not know how to pick a scale for
deb_tetratypes. In contrast,
deb_decimalvectors work properly with
ggplot2, though explicitly identifying the scale as continuous — with
scale_x_continuous()— is needed to avoid the appearance of a message.
deb_decimalvectors cannot be combined in a single function if their
basesdiffer. Tripartite and tetrapartite values can be combined if the bases of their solidus and denarius bases match. The only way to transform the bases of
deb_decimalvectors is explicitly with
deb_convert_bases(). This prevents mistakenly combining two different currencies together without properly converting their values.