(+) Kekule Numbering System

The following is a Plus Edition article written by and copyright by Dick Eastman. 

Genealogists often use terms that are not familiar to others. Most of these terms become familiar soon after we get involved in searching for our family trees. We soon speak of pedigree charts, enumerators, Henry numbers, fan charts, and more. However, one term we do not hear often pops up occasionally: Kekule Numbers. 

The German mathematician Stephan Kekule of Stradonitz (1863-1933) was a genealogist as well as the son of famed mathematician and chemist Friedrich August Kekulé. He used a numbering system to show relationships in text format. In German-speaking counties, lists of names created with Stephan Kekule’s numbers are still referred to by his name: Kekule numbers. However, in English-speaking countries the same numbers in lists would be called “numbers.” 

Indeed, ahnentafel numbers and the Kekule numbers for listing ancestors are the same. However, Stephan Kekule also created a similar system for listing descendants, a system I have rarely seen in English-language publications.

Ahnentafel is a word commonly used in genealogy although it probably confuses most newcomers. Ahnentafel is a German word that literally translates as “ancestor table.” It is a list of all known ancestors of an individual and includes the full name of each ancestor as well as dates and places of birth, marriage, and death whenever possible. It also has a strict numbering scheme. 

Note: Ahnentafel numbers for ancestors did not originate with Stephan Kekule. He simply popularized the system in his 1896 Ahnentafel Atlas. Spanish genealogist Jerome de Sosa first used the same ancestor numbering system in 1676, and ahnentafel/Kekule numbers are sometimes called “Sosa-Stradonitz system.” Kekule’s contribution was the numbering system for descendants.

Once the reader is accustomed to ahnentafels or Kekule numbers, it becomes very easy to read these lists, to move up and down from parent to child and back again, and to understand the relationships of the listed people. Ahnentafels are very good at presenting a lot of information in a compact format. However, the numbering system is the key to understanding ahnentafels or Kekule numbers. 

The starting-person receives the number 1. For an example, let’s create a list of your ancestors and give each person a number. You are number one. 

The father of the starting-person receives the number 2, and the mother gets the number 3. In our example, your father is #2 and your mother is #3. As we continue, a pattern emerges: your paternal grandfather is #4, your paternal grandmother is #5, your maternal grandfather is #6 and your maternal grandmother is #7. Moving up another generation continues the numbers: your father’father’father is #8 and so on. 

Here is an excerpt from a list of one famous American’ancestors:

1. George Walker Bush

2. George Herbert Walker Bush

3. Barbara Pierce

4. Prescott Sheldon Bush

5. Dorothy Walker

6. Marvin Pierce

7. Pauline Robinson

8. Samuel Prescott Bush

9. Flora Sheldon

10. George Herbert Walker

11. Lucretia [Loulie] Wear

As you continue listing ancestors, you will soon see a pattern developing: 

Male ancestors have always even numbers.

Female ancestors always have odd numbers.

The number of the father of a person is always twice as large as that of the original person.

The number of the mother is twice as large as the original person’s plus one.

To visualize the numbers, first consider a typical pedigree chart: 

Carefully observe the numbers in the chart. You will notice that every person listed has a number and that there is a mathematical relationship amongst the individuals listed: 

Gender: Male ancestors always have even numbers (ignore the starting person, or #1); female ancestors have odd numbers.

Parents: The father of any person has a number of double that of his child (2n), and the mother of any person always has number of double that of her child plus one (2n + 1).

Mate: A male ancestor’s mate has number n + 1, and a female ancestor’s mate has number n – 1.

Relationship: The exact relationship between any ancestor n and the individual at position 1 is found by successively dividing n by 2, discarding fractions at each stage, until reaching the number 1. The resulting list of integers identifies the ancestral positions that form the lineage. The number of times that n is halved equals the number of generations between the individual and the ancestor at position n.

Ancestors per generation: The first ancestor number in every generation (1, 2, 4, 8, 16, etc.) corresponds to the number of ancestor positions in that generation.

Generation numbers: The above numbers are also exponentiations of 2 (i.e., 20, 21, 22, 23, 24, etc.), and the exponent may be used as the generation number (i.e., 16 – or, 2 to the fourth power – represents the fourth ancestral generation).

Now, let’s take a typical ancestry chart and write it in ahnentafel format: 

1. person

2. father

3. mother

4. paternal grandfather

5. paternal grandmother

6. maternal grandfather

7. maternal grandmother

8. paternal great-grandfather

9. paternal great-grandmother

10. paternal great-grandfather

11. paternal great-grandmother

12. maternal great-grandfather

13. maternal great-grandmother

14. maternal great-grandfather

15. maternal great-grandmother

Notice that the numbers are exactly the same as in the pedigree chart. The rules of father=2 times child, mother=2 times child+1, child=one-half of parent, etc., remain the same. This is an ahnentafel chart. 

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