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+% [identification_system.tex]
+
+% HEADING MATERIAL HAS BEEN REMOVED
+
+
+{\rm % rm, bf ... = 12.5pt (\it =13.0pt) in [fonts.mac]
+%
+{\verysmall .}
+%
+\vskip -20pt\nin
+%
+\centerline{\bftwenty Identification System}%
+%
+\mni
+%
+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.
+%
+\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}
+%
+\mni
+%
+We use the same general idea for identification numbers. Consider the following couple:
+\sni
+{\leftskip =45pt %
+%
+{\tt 111\|21}\en {\bf Sophie Lang}
+\sni
+{\tt 111\|22}\en {\bf David \wr}
+ \par}
+ %
+ \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} \(Dina
+Naphtaly and Baruch Lang respectively\).
+%
+\mni
+%
+Similarly consider the following three men:
+\sni
+{\leftskip =45pt %
+%
+{\tt 111\|22}\en {\bf David \wr}
+\sni
+{\tt 112\|22}\en {\bf Jacques Weil }
+\sni
+{\tt 111\|212}\en {\bf Baruch Lang}
+ \par}
+ %
+ \mni
+%
+ 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.
+%
+\vfill\eject
+%
+\nin
+%
+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}
+%
+\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}
+%
+\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}
+%
+%
+\par % seem to need \(sometimes\)
+%
+% %%%%%%%%%%%%%%%%%%%%% KEEP THIS ENDING!!! % %%%%%%%%%%%%%%%%%%%%%
+%
+\vfill\eject
+%
+ } % ends \rm
+ \par} % ends \hsize
+ \bye
+
+