### Dating schemes

(To those of you seeking a utility for converting BP and BC dates, scroll down to the applet at the bottom. You will need the JRE.)

In the west, we number years counting up from the birth of Jesus Christ. The year 2009 literally means in the 2009th year of Christ's age (although Christ is no longer around on earth, he is still, in Christian belief, very much alive). This is the 'Dionysian era', named after the monk, Dionysius Exiguus, who introduced it in 525. It became widespread when it was adopted by the Venerable Bede in the 700s.

One way of representing the Dionysian era is with the phrase 'In the Year of Our Lord' or the Latin equivalent 'Anno Domini'. Hence, we can say 'In the Year of Our Lord 2009' or 'Anno Domini 2009', abbreviated to AD 2009. Notice that the letters 'AD' should logically come before the year number, although it is now so common to write 2009 AD that the logical version might be considered almost pedantic.

The plaque left behind by the Apollo 11 astronauts reads: "Here men from the planet Earth first set foot upon the Moon, July 1969 AD. We came in peace for all mankind." Its author, William Safire, who later wrote a newspaper column on language and grammar, was mortified when he realised he should have put AD 1969 instead of 1969 AD.While the term "AD" is standard in English-speaking countries, alternative but equivalent terms are sometimes used in other parts of the west. E.g. the French use "l'an de grĂ¢ce" = "the year of grace".

To refer to dates before AD 1, we count backwards, using the term "Before [the birth of] Christ", abbreviated to BC.

The introduction of the Dionysian era greatly simplified the problem of dating, which until then had used a series of weird and wonderful schemes, such as naming years after the annually elected Roman consuls, or specifying the year of a particular king's or emperor's reign.

However, the AD scheme still has one quirk, stemming from the fact that there is no year 0 (1 BC was followed by AD 1). It means that BC dates cannot be treated as simply negative AD dates. E.g. the difference between 1 BC and AD 1 is just 1 year, not 2 years as it would be if we used the mathematics of negative numbers, saying 1 - (-1) = 1 + 1 = 2. Obviously, this is not really a problem, and we just need to remember that to calculate the year-difference between a BC date and an AD date, we add the BC date to the AD date, then subtract 1.

As the traditional Christian ethos of western society has been called into question under the influence of multiculturalism, some have wished to distance themselves from the terms AD and BC, which are closely tied to Christian doctrine. Instead, the terms Common Era (CE) and BCE (Before Common Era) are increasingly in vogue, especially in academic works, as replacements for AD and BC respectively. (In calendrical terminology, an 'era' is a date from which other dates are reckoned.) The CE/BCE scheme still uses the year of Christ's birth as its era, but this is treated as just a convenient point that happens to be in common use, and its significance is not explicitly acknowledged.

When we look at dates in the past, it can be difficult to get a real feel for their significance. Suppose we are told for example that two European countries fought each other in 1530 and again in 1580. Anyone with a reasonable awareness of history can probably conjure up a mental picture of the 1500s, such as the costumes and technologies of that century and some of its more famous personalities and events. However, unless one has made an in-depth study of the period, the distinction between the 1530s and 1580s is much hazier. The result is that the dates 1530 and 1580 sound quite close together, and subconsciously, we think of the two wars as following pretty much one after the other, and involving the same people and the same issues. This in turn reinforces our view of the past as relatively unchanging when compared to the kaleidoscopic unfolding of events in our own lifetimes.

A similar thing applies when we are told the Athenians did something in 600 BC and something else in 400 BC, or the Hittites arose in 1600 BC and their empire collapsed in 1200 BC, or people built Stonehenge in 3000 BC, extended it in 2600 BC and buried someone there in 2000 BC. The numbers are rather abstract and lose their meaning, while the Athenians, Hittites or users of Stonehenge tend to exist in our minds as though they are the same people, doing first one thing then another. However, the later Athenians, Hittites etc. were in fact the many-times-great-grandchildren of the earlier ones, and the earlier and later sets of people would not in general have had the same thoughts, attitudes or experiences.

To get a more realistic feel for ancient dates, I suggest the technique of mentally converting them into equivalent modern dates.

- For example, when I read 1530 and 1580, I convert them in my mind into 1930 and 1980, e.g. imagining the 1530 people as being in the Depression Era, driving around in black sedans, and the 1580 people as watching 'Dallas' on TV while electing Ronald Reagan to the US presidency. Thus, I have a reasonable feel for the differences between 1930 and 1980, and this allows me to get a feel for the corresponding differences between 1530 and 1580, i.e. how personalities, costume and technology might have moved on, and how 1530 would have seemed quite old-fashioned from the perspective of 1580.
- For dates spanning centuries, I think of the earlier date as equivalent to the corresponding period before our own time. For example, to the Athenians of 400 BC, people and events of 600 BC would have seemed rather like the people and events of AD 1800 seem to us. Similarly, if the Hittite empire spanned the period 1600 BC to 1200 BC, it is rather like an empire that lasted from AD 1600 to the present. Finally, the Stonehenge dates of 3000, 2600 and 2000 BC would correspond to AD 1000, 1400 and the present. This should make it apparent that the rebuilding of Stonehenge was not just the continuation of a general programme of construction, but was a fresh initiative, undertaken by people who may have known very little about the original builders and did not necessarily think about Stonehenge in the same way. Ditto the people who performed the burial - to them Stonehenge was already an ancient monument and the way they were using it may have had little to do with the intentions of its builders.

In light of the artificiality of BC dates for their subject, archaeologists have adopted the approach of specifying dates in terms of years 'Before Present', abbreviated to BP. So something that happened 4200 years ago would be said to have happened 4200 BP. Now, if BP were taken to mean literally 'before the present', something dated to, say, 561 BP one year, would be 562 BP the next year, and 563 BP the year after that. Evidently, this is totally impractical. Therefore, archaeologists have adopted AD 1950 as the standard 'present'. Years BP means years before 1950.

In my work on this blog so far, I have felt the need for a consistent and meaningful dating scheme, as none of the existing methods seems fully satisfactory. I am conscious of the pedantry and parochialism of the BC/AD scheme, but I balk at the clumsy and merely cosmetic CE/BCE alternative. I do not want to keep switching arbitrarily between BP and BC/AD, and would like a standard approach. However, when I am dealing with events of the upper palaeolithic and rough orders of magnitude, quoting BC dates seems rather absurd, but when I refer to recent historical events the use of BP would become equally nonsensical, as I would find myself saying "the first world war broke out in 36 BP" and people would wonder what I was talking about. Furthermore, BC and BP involve counting backwards, whereas it would be preferable to be able to count forwards. It would also be good if the dating scheme could help drive home the distinction between 1530 and 1580, or between 1600 BC and 1200 BC etc.

These thoughts have led me to the idea of expressing dates in terms of 'generations' from a given starting point.

- Since I am concerned with history from the upper palaeolithic onwards, the starting point, or era, I will use is 50,000 BC.
- The generation length I choose is 25 years. This has the advantage that it divides neatly into 100 years and makes it possible to translate easily from ordinary years to generations. Obviously the 'generations' I am using are schematised but they are not wholly disconnected from reality. We won't go far wrong if we imagine that people's oldest grandchildren are being born 2 generations = 50 years after their own births.
- The idea behind using generations is that it should drive home the point that the Athenians, Hittites or Stonehenge-users of generation N were not the same people as the Athenians, Hittites or Stonehenge-users of generation N+10 or N+20, whatever it might be, but were their distant descendants.
- The use of generations also gives smaller and more manageable numbers, and I hope it should be easier to visualise and make sense of the spans of time involved.

To convert a span of years to the equivalent number of generations, we divide by 25. Alternatively, if it is an exact number of centuries, we multiply the number of centuries by 4.

If we call the people living in 50,000 BC, generation 1, then to convert a date into a generation number, we calculate 1 plus the number of generations that have passed since 50,000 BC.

For example, the Last Glacial Maximum (LGM) was at about 18,000 BC. This is 32,000 years after 50,000 BC (50,000 - 32,000 = 18,000). In terms of generations, it is 32,000 ÷ 25 = 1280 generations later. (Alternatively, it is 320 centuries, and 320 x 4 = 1280.) Therefore, the people living at the LGM would be generation 1281 (because 1 +1280 = 1281).

When we calculate generation numbers for AD dates, we have to take into account the absence of a year 0. It was in the year AD 1 that 50,000 years = 2000 generations had passed since 50,000 BC. Therefore, AD 1 corresponded to generation 2001. For any general AD date, the total number of generations since 50,000 BC is 2000 plus the number of generations since AD 1. To find the number of generations since AD 1, we find the number of years since AD 1 and divide by 25. However, the number of years since AD 1 is not the number of the year but the number of the year minus 1. Thus, the year AD 2 was not 2 years after AD 1 but only 1 year after AD 1 (2 - 1 = 1). It was AD 3 that was 2 years after AD 1 (3 - 1 = 2). In the same way, it was AD 26 that was 25 years or 1 generation after AD 1. Therefore, AD 26 (not AD 25) was the beginning of generation 2002.

The generation number today is 2081, and it began in 2001. This is because AD 2001 was 2000 years or 80 generations (2000 ÷ 25 = 80) after AD 1, making 2080 generations since 50,000 BC.

Clearly, the generation number only narrows a date down to a 25-year window. All the years from 2001 to 2025 correspond to generation 2081, say. For my purposes, this degree of precision is usually going to be enough, even for historical dates. When talking about the colonisation of Australia or the discovery of agriculture, a 25-year window is obviously more than adequate. However, I am equally content to know, for example, that Columbus's discovery of America was in generation 2060 while the American Revolution was 12 generations later, in generation 2072. I am not writing narrative history so it is not necessary to be absolutely precise (even in ordinary history, the year is often good enough and it is not necessary to give the exact day).

Nevertheless, it would be desirable to be able to refer to the exact year if necessary. We can do this by including the phase, which means the position of the year within the 25-year generation. For instance, the 1st year within generation 2081 was AD 2001, so that AD 2001 has phase 1. The 2nd year within generation 2081 was AD 2002, which has phase 2. The 3rd year was 2003, with phase 3, and so on. This continues up to AD 2025, which will have phase 25. The next year, AD 2026, will be the 1st year of generation 2082, with a phase of 1 again.

We can now put all this together, to obtain some conversion formulas.

For these formulas we will use '%' to mean 'the remainder after dividing by' (or, for the mathematically savvy, 'modulo'). For example,

- 6 % 3 = 0
- 7 % 3 = 1
- 8 % 3 = 2
- 9 % 3 = 0
- 10 % 3 = 1
- etc.

To convert from a BC/AD date to a generation date:

. . For BC dates:

. . . . generation = 1 + (50,000 - year) / 25

. . . . phase = 1 + (50,000 - year) % 25

. . For AD dates:

. . . . generation = 2001 + (year - 1) / 25

. . . . phase = 1 + (year - 1) % 25

To convert from a generation/phase to a BC/AD date:

. . For generation <= 2000 (less than or equal to 2000): . . . . year (BC) = 50,000 - (generation - 1) x 25 - (phase - 1) . . For generation > 2000 (greater than 2000):

. . . . year (AD) = (generation - 2001) x 25 + phase

We also need a notation for dates expressed in generations:

- To represent an absolute date, we put a 'G' then the generation number, then a colon (':'), then the phase (if required). E.g. the year AD 1492, becomes G 2060:17, meaning it had phase 17 within generation number 2060.
- To represent a duration, we put the number of generations, a colon, the additional phase (if required), then a 'g'. E.g. a duration of 65 years becomes 2:15 g, meaning 2 generations (50 years) plus an extra 15 years.

I will now provide some example dates, converted into generations (note: I have rounded some of the figures - e.g. 18,000 BC actually equates to G 1281, but I have rounded this to G 1280, since we are only talking approximate dates):

Event | Date | |

Conventional | Generation | |

Beginning of upper palaeolithic | c. 50,000 BC | c. G 1:1 |

Last glacial maximum | c. 18,000 BC | c. G 1280 |

Invention of agriculture | c. 10,000 BC | c. G 1600 |

Founding of Egyptian 1st dynasty | c. 3100 BC | c. G 1876 |

Pyramid of Cheops | c. 2500 BC | c. G 1900 |

Beginning of bronze age | c. 2100 BC | c. G 1916 |

Beginning of iron age | c. 1000 BC | c. G 1960 |

Foundation of Rome | 753 BC | G 1970:23 |

Birth of Christ | 4 BC | G 2000:22 |

End of western Roman empire | AD 476 | G 2020:1 |

Battle of Hastings | AD 1066 | G 2043:16 |

Discovery of America | AD 1492 | G 2060:17 |

Battle of Waterloo | AD 1815 | G 2073:15 |

Apollo 11 moon landing | AD 1969 | G 2079:19 |

9/11 attacks | AD 2001 | G 2081:1 |

Today | AD 2009 | G 2081:9 |

The generational dates should give a feel for relative timescales. E.g. the founding of the Egyptian first dynasty is around 200 g ago, compared to the 2080 g of the human story as a whole. The discovery of America is very recent at only 20 g ago.

It is also useful to note that one lifetime is approximately 3 g (75 years). So the period from the Battle of Waterloo to the first moon landing, which is 6 g -- meaning we would count grandparent, parent, child, twice -- is equivalent to 2 lifetimes laid end to end. From the building of the Pyramid of Cheops to today is 180 g or 60 lifetimes.

It is commonplace to note that life expectancy has been increasing, so it would not always be true that 3G = 1 lifetime. However, most of the increase in life expectancy is due to reduction in infant mortality not to people living longer. Even the Bible considers the typical lifespan to be 70-80 years. Bones of our most ancient, upper palaeolithic ancestors suggest they may have died younger, typically in their 40s, but the 'natural' human lifespan, under reasonably favourable conditions, seems to be around 75 years, as the Bible has it.Here is an applet for converting AD/BC dates to generations and vice versa. (Instructions: (1) Enter a year into the year field, select AD, BC or BP; click "Convert to gen", and the generation number and phase appear in the generation fields. (2) Enter a generation number and phase into the generation fields; click "Convert to year", and the year appears in the year field with AD or BC selected as appropriate; click "Convert to BP" and the BP figure appears in the year field with BP selected. (3) To convert BC to BP etc., first convert to generations by (1) then convert back to AD/BC or BP by (2).)

(No program? See only a red X? You need to install the Java Runtime Environment (JRE). Click here.)

Finally, I note three other aspects of the generational dating scheme:

- If somebody was born in G n, then their parents were almost certainly born in G n-1, while their grandparents were almost certainly born in G n-2.
- If someone was born in G n, and did not die prematurely, they were probably still alive in G n+3 but dead by G n+4.
- The life of a person born in G n will typically just about overlap the lives of people born between G n-3 and G n+3.
- Each generation reacts against its predecessor, so that people tend to have more in common with their grandparents than with their parents. This implies a two-generation oscillation in social attitudes, which should show up in the generational scheme as a difference between odd-numbered and even-numbered generations. The pattern will not be exact since our standardised generation length of 25 years is not necessarily equal to the 'true' generation length. However, it might hold roughly over short periods of one or two centuries. This roughly 50-year (2 g) oscillation might be the same as the roughly 60-year Kondratiev wave.