# Ahnentafel

An Ahnentafel (or Ahnenreihe), also known as the Sosa-Stradonitz System, is a genealogical numbering system that allows one to list a person's ancestors in a particular order. It is a construct used in genealogy to display a person's ancestry compactly, without the need for a diagram such as a family tree, which is particularly useful in situations where one may be restricted to using plain text, for example in e-mails or newsgroup articles. The term Ahnentafel is a loan word from the German language, however its German equivalent is Ahnenliste. In German Ahnentafel means a genealogical chart showing the ancestors of one person in the form of a binary tree.

An Ahnentafel may also be called a Kekulé after Stephan Kekulé von Stradonitz, the genealogist.

An Ahnentafel is effectively a method for storing a binary tree in an array by listing the nodes in level-order. The subject of the Ahnentafel is listed as #1, their father as #2 and their mother as #3, then their grandparents as #4 to #7, and so on back through the generations. In this scheme, any person's father has double that person's number, and a person's mother has double the person's number plus one. Apart from #1, who can be male or female, all even-numbered persons are male, and all odd-numbered persons are female. Using this knowledge, you can find out some things without having to compile a list.

## How to find the Ahnentafel number, knowing the relation

To find out what someone's number would be without compiling a list, you must first trace how they relate back to the person of interest, meaning you must record that they are their father's mother's mother's father's father's... Once you have done that, you can use two methods.

### First method

Use the knowledge that a father's number will be twice the subject's number, or a mother's will be twice plus one, and just multiply and add to 1 accordingly. For instance, we can find out what number Electress Sophia of Hanover would be on an Ahnentafel of Peter Mark Andrew Phillips. Sophia is Peter's mother's mother's father's father's father's mother's father's father's father's father's father's mother. So, we multiply and add.

1×2 + 1 = 3
3×2 + 1 = 7
7×2 = 14
14×2 = 28
28×2 = 56
56×2 + 1 = 113
113×2 = 226
226×2 = 452
452×2 = 904
904×2 = 1808
1808×2 = 3616
3616×2 + 1 = 7233

So, if we were to make a list of ancestry for Peter Phillips, Electress Sophia would be #7233.

### Second method (binary representation)

This is an elegant and concise way to visualize the genealogical chain between the subject and the ancestor.

1. Write down the digit "1", which represents the subject, and, writing from left to right, write "0" for each "father" and "1" for each "mother" in the relation, ending with the ancestor of interest. The result will be the binary representation of the ancestor's Ahnentafel number. Let's try with the Sophia example, translating the chain of relations into a chain of digits.
Sophia = "Peter's mother's mother's father's father's father's mother's father's father's father's father's father's mother"
Sophia = 1110001000001
2. If needed, convert the Ahnentafel number from its binary to its decimal form. A conversion tool might prove handy.
Sophia = 1110001000001 (binary)
Sophia = 7233 (decimal)

## How to find the relation, knowing the Ahnentafel number

We can also work backwards and find what the relation is from the number.

### Reverse first method

1. One starts out by seeing if the number is odd or even.
2. If it is odd, the last part of the relation is "mother," so subtract 1 and divide by 2.
3. If it is even, the last part is "father," and one divides by 2.
4. Repeat steps 2–3, and build back from the last word.
5. Once one gets to 1, one is done.

On an ahnentafel of Prince William, John Wark is number 116. We follow the steps:

 116/2 = 58 58/2 = 29 29 − 1 = 28 and 28/2 = 14 14/2 = 7 7 − 1 = 6 and 6/2 = 3 3 − 1 = 2 and 2/2 = 1 father father mother father mother mother

We reverse that, and we get that #116, John Wark, is Prince William's mother's mother's father's mother's father's father.

### Second method (binary representation)

1. Convert the Ahnentafel number from decimal to binary.
Mr John Wark = 116 (decimal)
Mr John Wark = 1110100 (binary)
2. Replace the leftmost "1" with the subject's name and replace each following "0" and "1" with "father" and "mother" respectively.
Mr John Wark = 1110100
Mr John Wark = "Prince William's mother's mother's father's mother's father's father"

## Demonstration

decimal binary relation
1 1 self
2 10 self's father
3 11 self's mother
4 100 self's father's father
5 101 self's father's mother
6 110 self's mother's father
7 111 self's mother's mother
8 1000 self's father's father's father
9 1001 self's father's father's mother
10 1010 self's father's mother's father
11 1011 self's father's mother's mother
12 1100 self's mother's father's father
13 1101 self's mother's father's mother
14 1110 self's mother's mother's father
15 1111 self's mother's mother's mother
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