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\centerline{\bftwenty  Identification System}%
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\mni
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As explained in the introduction this is an {\it ascending\/} genealogy. In order to precisely identify each  
person and to clearly indicate their relationships with descendants and ancestors, the following method is 
used:
\mni
 Each person  is assigned a unique identification number consisting of 1s and 2s, where the digit 1 
indicates a female and the digit  2  a male. The number of digits in the identification number  depends on 
how many generations back they are from 
Eliane Herz, who is identified by the number 1. Her mother, 
Coralie Weill is 11,  and Coralie Weill's father is 112.
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\mni
In addition to giving an identification number to individuals we want to arrange them in a definite order. 
The 
idea is analogous to the  system used in dictionaries as illustrated in the following example with \lq 
before\rq\ being indicated by the symbol\TH
{\bfsixteen <}\TH .
\sni
{\leftskip =45pt
\nin
{\it aa\/}\gl rdvark   {\Th \bf   <\Th} {\it abac\/}\gl a {\Th \bf   <\Th} {\it abac\/}\gl k {\Th \bf   <\Th} 
{\it abac\/}\gl us
\par}
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\mni
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We use the same general idea for identification numbers. Consider the following couple:
\sni
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{\tt 111\|21}\en  {\bf Sophie Lang} 
\sni
{\tt 111\|22}\en  {\bf David \wr}
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 \mni
Being a couple, their identification numbers are identical except for the last place and because the wife has 
a 1 in the last place she is listed before her husband who has a 2 in the last place. 
\mni
Given the identification number \({\tt 112\|21}\) of Sophie Lang we immediately know that:
\sni
\item{} The male child \(Gottschau \wr\) of Sophie Lang has identification number {\tt 112\|2},
\item{} The parents of Sophie Lang have  identification numbers {\tt 112\|211} and {\tt 112\|212} \(Dina 
Naphtaly and Baruch Lang respectively\).
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Similarly consider the following three men:
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{\tt 111\|22}\en  {\bf David \wr}
\sni
{\tt 112\|22}\en  {\bf Jacques Weil }
\sni
{\tt 111\|212}\en  {\bf  Baruch Lang}
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  \mni
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  David \wr\ precedes Jacques Weil  because he has a 1 in the third place and  Jacques Weil has a 2.
  \mni
  Baruch Lang is after  Jacques Weil  even though he has a 1 in the first three places, because his  
identification number  has one more  digit and this in turn means that he is one generation earlier than 
Jacques Weil.
\mni
In each of  the seven groups of ancestors of \cw\
the group  is divided into generations and within a generation the lists of people follow the  order just 
described. To illustrate this consider the ancestors of Gottschau \wr.
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His parents are listed as follows:
\sni
{\leftskip = 2.0truecm
{\tt 111\|21}\en  {\bf Sophie Lang}
\sni
{\tt 111\|22}\en  {\bf David \wr}
\par}
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\sni
Next we have the  grandparents of  Gottschau \wr\  as follows:
\sni
{\leftskip = 2.0truecm
\hskip  2.1cm{\bf The Parents of Sophie Lang}
\sni
{\tt 111\|211}\en {\bf Dina Napthtaly}
\sni
{\tt 111\|212}\en {\bf Baruch Lang}
\mni
\hskip  2.1cm{\bf The Parents of David \wr}
\sni
{\tt 111\|221}\en {\bf Fromet David}
\sni
{\tt 111\|222}\en {\bf Schmulen Solomon}
\par}
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\mni
In the examples given so far there was only one  identification number, but
because the two grand\-mothers of Coralie \we\ were sisters, their parents and all preceding generations 
will have {\it two\/} numbers. Thus, since Marie \kl\ was the mother of both   Caroline \ml\ \({\tt 111\|1}\) 
and  Pauline  \ml\ \({\tt 112\|1}\) she will have the two numbers obtained by adding a 1 to the numbers of 
her 
daughters and we find the same situation with Salomon \ml, the husband of Marie \kl.
\sni
{\leftskip =45pt  
{\tt 111\|11\fsl 112\|11}\en  {\bf Marie \kl}
\sni
{\tt 111\|12\fsl 112\gl\|12}\en  {\bf Salomon \ml}
\par}
\mni
Further, since the Mandel and \wr\ lines have  common ancestors, these common ancestors will have {\it 
three\/} numbers.
\mni
Another consequence of both grand\-mothers being sisters is that,  instead of {\it eight\/}
great-grand\-parents,  Coralie Weill  had only {\it six\/} great-grand\-parents,  twelve  
great-great-grand\-parents\dots . The number of possible ancestors is reduced even further when we arrive at 
the ancestors with three numbers.
\mni
The length of the identification number also shows the degree of ancestry with respect to \cw. Thus her 
parents are identified by three digits and her grandparents by four. Next come the   great-grandparents 
with five digits and great-great-grandparents with six. From this we see that the number of \lq greats\rq\ is 
given 
by the number of digits minus four and conversely to find the number of digits in a designation we simply add 
four to the number of greats. The longest designation numbers belong to the three, six 
times 
great-grandparents of   \cw\ who have ten  digits. The oldest of these three would have been born ca.\th 1650.
\mni
\centerline{\bf Summary}
\mni
\item{1.} A female ancestor is indicated by a 1, a male ancestor is indicated by a 2.
\sni
\item{2.} Couples are listed in pairs and their identification numbers only differ in the last number, 
namely a 1 or a 2.
\sni
\item{3.} The identification number of a child is obtained by {\it taking off\/} the last digit.
\sni
\item{4.} The identification numbers of the parents of a person are obtained by {\it adding on\/} a 1 and a 2.
\sni
\item{5.} The ancestors of any person are discussed one generation at a time. Within any generation people 
are listed according to the order described above.
\sni
\item{6.}  Marie \kl\ and Salomon \ml\ each have two identification numbers. Their ancestors will also have 
two identification numbers with some of the very early ancestors of Salomon \ml\ 
 having three numbers. People with multiple numbers are listed according to their {\it first\/} 
identification number.
\sni
\item{7.} \cw\ had only six {\it distinct\/} great-grandparents,  twelve {\it distinct\/} 
great-great-grandparents\dots . When we arrive at the ancestors with three identification numbers there will 
be a further reduction in the number of actual ancestors.
\sni
\item{8.}The length of the identification number indicates the degree of ancestry with respect to \cw:
\sni
{\leftskip = 31.6pt
\pni \cw\  \({\tt 11}\) has an  identification number of length 2.
\pni Her parents  \({\tt 111} and  {\tt 112}\) have an  identification number of length 3
\pni Her grandparents  have an  identification number of length 4.
\pni Her great-grandparents  have an  identification number of length 5.
\pni Her two times great-grandparents  have an  identification number of length 6.
\pni Her three times great-grandparents  have an  identification number 
of length 7.
\pni Her four times great-grandparents  have an  identification number of length 8.
\pni Her five times great-grandparents  have an  identification number of length 9.
\pni Her six times  great-grandparents  have an  identification number of length 10.
\par}
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