2010-04-25 Ahnen Numbering

Ahnen Ahnung

numbering system

ancestor numbering

Ahnentafel numbering

Ahnen numbering is the simple numbering system commonly used with ahnenlist. The examples in both Ahnentafel and Ahnenlist use this numbering system.
This numbering system is historically known as ahnentafel numbering, but because it is most commonly used with ahnenlist, it would make more sense to call it ahnenlist numbering.

Eytzinger numbering

The numbering system is already known by multiple names. It is known as Eytzinger numbering because Michael Eytzinger used it when he published the first ahnentafel ever.

Eytzinger's First Ahnentafel

Sosa-Stradonitz numbering

It is known as Sosa-Stradonitz numbering because the Spanish genealogist Jerónimo de Sosa used it in his work Noticia de la gran casa de los marqueses de Villafranca (1676 GC) and German genealogist Stephan Kekulé von Stradonitz popularised it through his work Ahnentafel-Atlas. Ahnentafeln zu 32 Ahnen der Regenten Europas und ihrer Gemahlinnen (1904 GC).

Kekulé numbering

The numbering system is sometimes called the Kekulé numbering system, once again named after Stephan Kekulé von Stradonitz, and the numbers themselves are known as Kekulé numbers. This particular name is common in Germany and German speaking countries only.

ahnen numbering

The ahnentafel numbering system is most commonly used with ahnenlist. That the numbering system so ideal for ahnenlist is known as ahnentafel numbering is an unfortunate historic accident; the name derives from the aforementioned Ahnentafel-Atlas, the book that popularised both ahnentafels and the numbering system.

Because the numbering system is commonly used with ahnenlist and hardly even used with ahnentafel anymore, it does make more sense to call it an ahnenlist number. However, calling it an ahnenlist number would not only belie the etymology, but also fail to be a real improvement; it would be just be as confusing to use an ahnenlist number with an ahnentafel as it is to use an ahnentafel number with an ahnenlist.

From here on, I will avoid avoid creating either confusion, yet still respect the etymology by referring to this numbering system as ahnen numbering - ancestor numbering.

how it works

This minimal modern presentation of Eytzinger’s original ahnentafel shows how the numbering system works. It is the table from Ahnentafel again, only this time, the ahnen numbers used in the ahnentafel have been highlighted. Notice how, in the earliest generations shown here, the numbering continues even if the ancestors are not known.

Five Generation Ahnentafel for Henric III, King of France

1 Henric III	2 Henric II	4 Francisc	8 Carolu	16 Joannes
			8 Carolu	17 Margareta
			9 Iudouica	18 Philippus
			9 Iudouica	19 Margareta
		5 Claudia	10 Ludeuici	20 Carolus
			10 Ludeuici	21 Maria
			11 Anna	22 Franciscus
			11 Anna	23 Margareta
	3 Catharina	6 Laurenti	12 Petrus	24 Lauretius
			12 Petrus	25 Clarixa
			13 Alphonsina	26 N
			13 Alphonsina	27 N
		7 Magdalena	14 Joannes	28 Berijandus
			14 Joannes	29 Ludouica
			15 Joanna	30 Johannes
			15 Joanna	31 N

ancestor order

The order of ancestors in an ahnentafel is fixed. The table is ordered by generation. It always shows both parents of an individual next to that individual, and always lists the father before the mother.

enumeration sequence

The boxes in the ahnentafel are numbered sequentially, generation by generation, and from the top the bottom.
The single box for the first generation is given number one. Number 2 till 3 are given to the two boxes in the next generation, numbers 4 through 7 are given to the boxes in the third generation, and so on. Within each generation, the boxes are numbered sequentially, from the top to the bottom.

Each unknown ancestor has an ahnen number reserved for them.

fixed numbering

It is important to stress that ahnen numbering does not number the ancestors, but the boxes in the table. The same boxes always have the same numbers, regardless of whether ancestors are known or not. The same position in the diagram always gets the same number.

The ahnen number for an ancestors depends on nothing but their relation to the proband, not on how many or which ancestors are known. For example, the ahnen number for your paternal grandmother is always 5, and ahnen number 6 always refers to your maternal grandfather.

The ahnen number used for an ancestor does not depend your current knowledge of your ancestry, but only on their relationship to you. Each unknown ancestor has an ahnen number reserved for them.

If you use ahnen numbers today, and then discover another ancestor later, you do not need to renumber your entire ancestry to make the new ancestor fit in. You do not need to renumber your ancestry at all, but can simply insert that ancestor using the number that was reserved all along.

numeric properties

This simple method of ordering and numbering ancestors has a few interesting properties:

Zero is not used. Numbering starts with number 1.
Each couple in the ancestry gets two consecutive numbers.
For each couple in the ancestry, the wife’s number is the husband’s number plus one.
Fathers always get an even number, and mothers always get an odd number.
For each individual in the table, the number for their child is found by dividing their own number by two (and truncating the result).
For each individual in the table, the number for their father is double their own number, and the number for their mother is double their own number plus one.
The numbers for the ahnenstamm, the ancestors in male line, are all powers of two (1, 2, 4, 8, 16).
The numbers for the mutterstamm, the ancestors in the female line, are all powers of two minus one (1, 3, 7, 15, 31).

couples

Many ancestors had more than one partner, but the numeric properties apply to the couples in your ancestry only. Your ancestors’ other partners are not part of your ancestry and do not have an ahnen number.

children

Similarly, most couples had more than one child, but the numeric properties only apply to their child that is part of your ancestry. Other children are not part of your ancestry and do not have an ahnen number.

even and odd

Do note that it are fathers and mothers that always gets even and odd numbers respectively. You may encounter articles that claim that men always get even even numbers and women always get odd numbers respectively, but that is not correct. The proband gets number 1 regardless of gender; an odd number, even if he is male.

pedigree collapse

It does not have to happen within recorded history, but at some point, each pedigree suffers pedigree collapse; the same ancestor appears at more than one location in your ancestral tree. Those different locations may even be in different ancestral generations - for example, eight generations ago through a female line, and seven generations ago through a male line.

Each position in the ancestral tree has its own ancestral number associated with it, so an ancestors that appears more than once has more than one ancestral number associated with it.

binary tree

Binary Ahnentafel Numbering

1	10	100	1000	10000
			1000	10001
			1001	10010
			1001	10011
		101	1010	10100
			1010	10101
			1011	10110
			1011	10111
	11	110	1100	11000
			1100	11001
			1101	11010
			1101	11011
		111	1110	11100
			1110	11101
			1111	11110
			1111	11111

Those with a background in computer science or mathematics will notice that an ancestral tree is a binary tree and that ahnentafel numbering corresponds to breadth-first enumeration of a complete binary tree.

binary pattern

The binary pattern of ahnen numbering is clearly visible when you use binary numbers.

In the binary number system, converting between ahnen numbers for parents and their children becomes ridiculously easy. To find the child, remove the last digit. To find the father, append a zero. To find the mother, append a 1.

array

Binary trees, and complete binary trees in particular, have various well-understood properties. One well-known property of this particular numbering is that it allows a binary tree to be represented by an array. An array is not just a simple data structure, but - for complete binary trees in particular - a fast and memory-efficient data structure as well.

ahnenlist

This explanation used ahnentafels to explain ahnen numbering, but an ahnentafel has a such a clear structure that the ahnen numbers are hardly necessary. Ahnen numbers are most commonly used with ahnenlists. An ahnenlists always lists ancestors in ahnen sequence anyway; but the explicit use of ahnen numbers is not without purpose. The use of ahnen numbers are an aid in navigating the ahnenlist, and in distinguishing between different ancestors with the same.