# Years with an era

Archaeologists, geologists, and other palaeoscientists use different systems for numbering years in the distant past. For example, the year 10,000 BCE is 11,950 Before Present or 11.95 ka. It is usually fine to store years as a plain numeric vector in R, but sometimes it helps to be explicit about which system is being used:

• When you have data that mixes different systems
• When you want to transform years between different systems
• When you need to do arithmetic with years

The era package helps in these cases by providing classes which define the ‘era’ associated with a vector of years and functions for formatting, combining, and transforming years with different eras. This vignette is an introduction to the main features of the package.

library("era")
library("tibble")
library("dplyr")

## Years with an era: the yr class

Vectors of years with an era are represented by the yr (era_yr) class, which is constructed with yr():

yr(c(10000, 11000, 12000), "BP")
#> # BP years <yr[3]>:
#> [1] 10000 11000 12000
#> # Era: Before Present (BP): Gregorian years (365.2425 days), counted backwards from 1950

The first argument is a numeric vector of years. These can be integers or doubles.

The second argument, era, defines the numbering system associated with the years. This is an object of class era which defines the parameters of the calendar, epoch and time scale. Most of the time, you can simply specify the abbreviated label of the era, which will be looked up in the standard eras defined by eras():

yr(c(10000, 11000, 12000), "BCE")
#> # BCE years <yr[3]>:
#> [1] 10000 11000 12000
#> # Era: Before Common Era (BCE): Gregorian years (365.2425 days), counted backwards from 0
yr(c(10000, 11000, 12000), "uncal BP")
#> # uncal BP years <yr[3]>:
#> [1] 10000 11000 12000
#> # Era: uncalibrated Before Present (uncal BP): radiocarbon years (NA days), counted backwards from 1950
yr(c(10000, 11000, 12000), "ka")
#> # ka years <yr[3]>:
#> [1] 10000 11000 12000
#> # Era: kiloannum (ka): 1000 Gregorian years (365.2425 days), counted backwards from 1950

yr_era() returns details of the era associated with a yr vector:

neolithic <- yr(11700:7500, "BP")
yr_era(neolithic)
#> <era[1]>
#> [1] Before Present (BP): Gregorian years (365.2425 days), counted backwards from 1950

yr_era(), and its pipe-friendly alias yr_set_era(), can also be used to set the era of an existing object:

chalcolithic <- 7500:6000
yr_era(chalcolithic) <- yr_era(neolithic)
yr_era(chalcolithic)
#> <era[1]>
#> [1] Before Present (BP): Gregorian years (365.2425 days), counted backwards from 1950

Note that this only updates the vector’s era attribute; it doesn’t change the data itself. To convert years from one era to another, you need to use the yr_transform() function.

yr vectors fit nicely into tables, both base data frames and tibbles:

postglacial <- tribble(
~period,           ~start_ka,
"Late Holocene",   4.2,
"Mid Holocene",    8.326,
"Early Holocene",  11.7,
"Younger Dryas",   12.9,
"Bølling-Allerød", 14.7,
"Heinrich 1",      17.0
)

postglacial %>%
mutate(start_ka = yr(start_ka, "ka"))
#> # A tibble: 6 x 2
#>   period          start_ka
#>   <chr>               <yr>
#> 1 Late Holocene     4.2 ka
#> 2 Mid Holocene    8.326 ka
#> 3 Early Holocene   11.7 ka
#> 4 Younger Dryas    12.9 ka
#> 5 Bølling-Allerød  14.7 ka
#> 6 Heinrich 1         17 ka

## Era definitions: the era class

Eras are defined by the era class. Many common eras are defined by the eras() function and can be referenced in yr() or era() by their abbreviated label:

eras()
label epoch name unit scale direction
BP 1950 Before Present Gregorian years (365.2425 days) 1e+00 -1
cal BP 1950 Before Present Gregorian years (365.2425 days) 1e+00 -1
BC 0 Before Christ Gregorian years (365.2425 days) 1e+00 -1
BCE 0 Before Common Era Gregorian years (365.2425 days) 1e+00 -1
AD 0 Anno Domini Gregorian years (365.2425 days) 1e+00 1
CE 0 Common Era Gregorian years (365.2425 days) 1e+00 1
a 1950 annum Gregorian years (365.2425 days) 1e+00 -1
ka 1950 kiloannum Gregorian years (365.2425 days) 1e+03 -1
Ma 1950 megaannum Gregorian years (365.2425 days) 1e+06 -1
Ga 1950 gigaannum Gregorian years (365.2425 days) 1e+09 -1
kya 1950 thousand years ago Gregorian years (365.2425 days) 1e+03 -1
mya 1950 million years ago Gregorian years (365.2425 days) 1e+06 -1
bya 1950 billion years ago Gregorian years (365.2425 days) 1e+09 -1
b2k 2000 years before 2000 Gregorian years (365.2425 days) 1e+00 -1
uncal BP 1950 uncalibrated Before Present radiocarbon years (NA days) 1e+00 -1
RCYBP 1950 Radiocarbon Years Before Present radiocarbon years (NA days) 1e+00 -1
bp 1950 Before Present (uncalibrated) radiocarbon years (NA days) 1e+00 -1
bc 1950 Before Christ (uncalibrated) radiocarbon years (NA days) 1e+00 -1
bce 1950 Before Common Era (uncalibrated) radiocarbon years (NA days) 1e+00 -1
ce 1950 Common Era (uncalibrated) radiocarbon years (NA days) 1e+00 1
AD O.S. 0 Anno Domini (Old Style) Julian years (365.25 days) 1e+00 1
BC O.S. 0 Before Christ (New Style) Julian years (365.25 days) 1e+00 1
AH 622 Anno Hegirae Islamic lunar years (354.36708 days) 1e+00 1
BH 622 Before the Hijra Islamic lunar years (354.36708 days) 1e+00 -1
SH 622 Solar Hijri Gregorian years (365.2425 days) 1e+00 1
BSH 622 Before Solar Hijri Gregorian years (365.2425 days) 1e+00 1
HE -10000 Holocene Era Gregorian years (365.2425 days) 1e+00 1
BHE -10000 Before Holocene Era Gregorian years (365.2425 days) 1e+00 -1
AL -4000 Anno Lucis Gregorian years (365.2425 days) 1e+00 1
ADA -8000 After the Development of Agriculture Gregorian years (365.2425 days) 1e+00 1

Eras are defined by the following parameters:

• label: an abbreviated label that uniquely identifies the era
• name: the full name of the era
• epoch: the origin year from which years are counted
• unit: the unit of years counted, defined as its length in solar days
• scale: the number of years represented by one unit
• direction: whether years are counted forwards (1) or backwards (-1) from the epoch

These parameters are passed to era() to construct an era object. epoch, unit, scale, and direction determine the transformation between eras; label and name are purely descriptive.

You can define arbitrary eras by using the era() function directly:

era("T.A.", epoch = -9021, name = "Third Age", direction = 1)
#> <era[1]>
#> [1] Third Age (T.A.): Gregorian years (365.2425 days), counted forwards from -9021

As long as all the parameters are specified correctly, user-defined eras can also be used in yr_transform().

## Converting between eras: yr_transform()

Use yr_transform() to convert between eras:

postglacial %>%
mutate(start_ka = yr(start_ka, "ka")) %>%
mutate(start_bp = yr_transform(start_ka, era("BP")),
start_bce = yr_transform(start_ka, era("BCE")))
#> # A tibble: 6 x 4
#>   period          start_ka start_bp start_bce
#>   <chr>               <yr>     <yr>      <yr>
#> 1 Late Holocene     4.2 ka  4200 BP  2250 BCE
#> 2 Mid Holocene    8.326 ka  8326 BP  6376 BCE
#> 3 Early Holocene   11.7 ka 11700 BP  9750 BCE
#> 4 Younger Dryas    12.9 ka 12900 BP 10950 BCE
#> 5 Bølling-Allerød  14.7 ka 14700 BP 12750 BCE
#> 6 Heinrich 1         17 ka 17000 BP 15050 BCE

This function implements a generic algorithm for transforming years based on the era parameters described above. This means that, with a few exceptions (see invalid transformations, you can transform between any two eras that can be described by the era class.

### Transformation precision

By default, era transformations are exact:

yr(500000, "BCE") %>%
yr_transform(era("ka"))
#> # ka years <yr[1]>:
#> [1] 501.95
#> # Era: kiloannum (ka): 1000 Gregorian years (365.2425 days), counted backwards from 1950

Often, this precision is not necessary. For example, when converting years between calendar- and present-based eras, the 71 year difference between the formal definition of “Present” and the actual present is rarely significant on a geologic time scale. Use the precision argument of yr_transform to get rounded results:

yr(10000, "BP") %>%
yr_transform(era("BCE"), precision = 1000)
#> # BCE years <yr[1]>:
#> [1] 8000
#> # Era: Before Common Era (BCE): Gregorian years (365.2425 days), counted backwards from 0

yr(500000, "BCE") %>%
yr_transform(era("mya"), precision = 0.1)
#> # mya years <yr[1]>:
#> [1] 0.5
#> # Era: million years ago (mya): 1000000 Gregorian years (365.2425 days), counted backwards from 1950

### Invalid transformations

Some transformations are not possible. Notably, the length of a ‘radiocarbon year’ is not well defined on a calendar time scale without calibration. Eras that use non-calendar year unit are represented with an NA and will cause an error if passed to yr_transform():

era_unit(era("uncal BP"))
#> <era_year[1]>
#> [1] radiocarbon years (NA days)
yr_transform(yr(9000, "uncal BP"), era("cal BP"))
#> Error: Cannot transform uncalibrated Before Present to Before Present years:
#> x Calendar length of a radiocarbon year is undefined.

c14_calibrate() from the stratigraphr package implements radiocarbon calibration with yr objects.

Conversion between eras that both have an NA unit are also an error, following the R convention that NA == NA is NA. In other words, we don’t know whether two non-calendar units are the same non-calendar unit. This means that it is not possible to use yr_transform() to convert bp (radiocarbon years Before Present) to bce (radiocarbon years before the Common Era) years, for example.

## Arithmetic with year vectors

The yr class is based on vctrs, ensuring type- and size-stable computations. For example, you can do arithmetic with year vectors:

a <- yr(1500, "CE")
b <- yr(2020, "CE")
b - a
#> # CE years <yr[1]>:
#> [1] 520
#> # Era: Common Era (CE): Gregorian years (365.2425 days), counted forwards from 0

But only when they have the same era:

c <- yr(0.5, "ka")
b - c
#> Error: <yr (CE)> - <yr (ka)> is not permitted
#> Reconcile eras with yr_transform() first.

Note that, when comparing eras, only the parameters significant to the transformation are considered (i.e. not label or name). This means that it is possible to combine year vectors with differently-named but functionally equivalent eras, for example era("BP") and era("cal BP"), although doing so will print a warning about the loss of information:

era("BP") == era("BC")
#> [1] FALSE
era("BP") == era("cal BP")
#> [1] TRUE

yr(1000, "BP") + yr(1000, "cal BP")
#> Warning: era(x) and era(y) have different label or name parameters.
#> # BP years <yr[1]>:
#> [1] 2000
#> # Era: Before Present (BP): Gregorian years (365.2425 days), counted backwards from 1950

Years will be coerced to a plain numeric vector if a computation means their era no longer makes sense:

a * b
#> [1] 3030000