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Lineages, Names, & Marriage in 3-Sex 3-Parent Species - Gtx0 ?>


Lineages, Names, & Marriage in 3-Sex 3-Parent Species
Posted: Posted February 10th, 2017
Edited Friday by chiarizio
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Please also see the following threads:
http://gtx0.com/merge/thread/1478&highlight=three+three
http://gtx0.com/merge/thread/1473&highlight=three+three
http://gtx0.com/merge/thread/1474&highlight=three+three
http://gtx0.com/merge/thread/1471&highlight=three+three
http://gtx0.com/merge/thread/1477&highlight=three+three
http://gtx0.com/merge/thread/775&highlight=three+three
[color=#AA5500](edit) Also:
jump to http://gtx0.com/merge/post/20625#20625 for an afterthought intro to this thread. (/edit)

_______________________________________________________________

In this thread we'll be talking about the culture(s) of a species which has three sexes -- A, B, and C -- and in which each specimen has three parents, one of each sex.

The 3rd-person-singular pronouns for a person of sex A will be:
ne/nem/nis/nemself

The 3rd-person-singular pronouns for a person of sex B will be:
de/dem/dis/demself

The 3rd-person-singular pronouns for a person of sex C will be:
ve/vem/ver/vemself

I will use they/them/their/themsel(f/ve) for 3rd-persons of unspecified sex and also for plural 3rd-persons.

_______________________________________________________________

There can be eight kinds of lineages that a child can inherit from one of their parents, in a way that depends on the sex of the parent, and possibly also on the sex of the child;
in such a way that no-one belongs to more than one lineage of any given type.

Everyone can inherit their A-line from their A-parent.
Everyone can inherit their B-line from their B-parent.
Everyone can inherit their C-line from their C-parent.

There can be a set of AB-ropes for which:
every A-child inherits membership from nis B-parent; and
every B-child inherits membership from dis A-parent.
(Individuals of sex C don't belong to any AB-rope.)

There can be a set of AC-ropes for which:
every A-child inherits membership from nis C-parent; and
every C-child inherits membership from ver A-parent.
(Individuals of sex B don't belong to any AC-rope.)

There can be a set of BC-ropes for which:
every B-child inherits membership from dis C-parent; and
every C-child inherits membership from ver B-parent.
(Individuals of sex A don't belong to any BC-rope.)

There can also be a set of "honeysuckles" for which:
every A-child inherits membership from nis B-parent;
every B-child inherits membership from dis C-parent; and
every C-child inherits membership from ver A-parent.

And there can be a set of "woodbines" for which:
every A-child inherits membership from nis C-parent;
every B-child inherits membership from dis A-parent; and
every C-child inherits membership from ver B-parent.

Assuming the culture divides itself into named lineages according to all eight of these methods, every individual will belong to one and only one lineage of each of seven of these eight types; which seven will depend on their sex.

Everyone will belong to
exactly one A-line, and
exactly one B-line, and
exactly one C-line, and
exactly one honeysuckle, and
exactly one woodbine.

Every A-person will also belong to
exactly one AB-rope, and
exactly one AC-rope.

Every B-person will also belong to
exactly one AB-rope, and
exactly one BC-rope.

Every C-person will also belong to
exactly one AC-rope, and
exactly one BC-rope.


_______________________________________________________________


Note that everyone inherits a line-membership from seven of their nine grandparents.

Everyone inherits their A-line from their A-parent's A-parent.
Everyone inherits their B-line from their B-parent's B-parent.
Everyone inherits their C-line from their C-parent's C-parent.

An A-person
inherits nis AB-rope from nis B-parent's A-parent; and
inherits nis AC-rope from nis C-parent's A-parent.

A B-person
inherits dis AB-rope from dis A-parent's B-parent; and
inherits dis BC-rope from dis C-parent's B-parent.

A C-person
inherits ver AC-rope from ver A-parent's C-parent; and
inherits ver BC-rope from ver B-parent's C-parent.

Additionally:
An A-person inherits nis honeysuckle from nis B-parent's C-parent, and
inherits nis woodbine from nis C-parent's B-parent.
A B-person inherits dis honeysuckle from dis C-parent's A-parent, and
inherits dis woodbine from dis A-parent's C-parent.
And a C-person inherits ver honeysuckle from ver A-parent's B-parent, and
inherits ver woodbine from ver B-parent's A-parent.

So, an A-child inherits:
  • nis A-line from nis A-parent's A-parent;
  • nis AB-rope from nis B-parent's A-parent;
  • nis B-line from nis B-parent's B-parent;
  • nis honeysuckle from nis B-parent's C-parent;
  • nis AC-rope from nis C-parent's A-parent;
  • nis woodbine from nis C-parent's B-parent; and
  • nis C-line from nis C-parent's C-parent.

    A B-child inherits:
  • dis A-line from dis A-parent's A-parent;
  • dis AB-rope from dis A-parent's B-parent;
  • dis woodbine from dis A-parent's C-parent;
  • dis B-line from dis B-parent's B-parent;
  • dis honeysuckle from dis C-parent's A-parent;
  • dis BC-rope from dis C-parent's B-parent; and
  • dis C-line from dis C-parent's C-parent.

    And, a C-child inherits:
  • ver A-line from ver A-parent's A-parent;
  • ver honeysuckle from ver A-parent's B-parent;
  • ver AC-rope from ver A-parent's C-parent;
  • ver woodbine from ver B-parent's A-parent;
  • ver B-line from ver B-parent's B-parent;
  • ver BC-rope from ver B-parent's C-parent; and
  • ver C-line from ver C-parent's C-parent.


    So an A-child inherits some kind of lineage-membership from every grandparent except nis A-parent's B- and C-parents;
    a B-child inherits some kind of lineage-membership from every grandparent except dis B-parent's A- and C-parents; and
    a C-child inherits some kind of lineage-membership from every grandparent except ver C-parent's A- and B-parents.

  • There are 33 Replies
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    I (and maybe some other conworlders?) would probably like, in at least some conworlds, to make it that, not only would every parent welcome the birth of any child regardless of the child's sex, but also that every grandparent would welcome the birth of any grandchild, regardless of the grandchild's sex (and regardless of the child's sex!).

    For instance, there can be a custom that a child's personal, individual name, should be chosen by, or should be inherited from, one or both of the grandparents from whom the child does not inherit any lineage-membership.

    Examples:
    Every A-person names nis first-born A-child after nis B-parent,
    and names nis second-born A-child after nis C-parent. (Or vice-versa.)
    And every B-person names dis first-born B-child after dis C-parent,
    and names dis second-born B-child after dis A-parent. (Or vice-versa.)
    And every C-person names ver first-born C-child after ver A-parent,
    and names ver second-born C-child after ver B-parent. (Or vice-versa.)

    _____________________________________________________________

    Perhaps after the births of the first two grandchildren of a given sex through a child of that sex, the grandparents of the other two sexes can take turns choosing the name of the grandchild.

    E.g. an A-person's third A-child's name will be chosen by nis A-parent's B-parent; and an A-person's fourth A-child's name will be chosen by nis A-parent's C-parent; and so on.

    Similarly for a B-person's A- and C- parents will take turns naming dis third and fourth (etc.) B-children, and a C-person's A- and B- parents will take turns naming ver third and fourth (etc.) C-children.

    _____________________________________________________________

    Or, instead, the third and subsequent children of a given sex, will just be numbered, or otherwise assigned names that just reflect birth-order and sex.

    Posted February 11th, 2017 by chiarizio
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    In this post we will be talking about using "surnames" -- that is, the names of lineages -- in order to avoid consanguinity in marriage and mating.

    Suppose an A-person and a B-person want to mate or marry.
    The A-person belongs to seven lineages;
    nis A-line, nis B-line, nis C-line, nis honeysuckle, nis woodbine, nis AB-rope, and nis AC-rope.
    The B-person also belongs to seven lineages;
    dis A-line, dis B-line, dis C-line, dis honeysuckle, dis woodbine, dis AB-rope, and dis BC-rope.

    There are six kinds of lineage for which each of them belongs to a line of that kind; A-line, B-line, C-line, honeysuckle, woodbine, and AB-rope.

    There might be a rule that no two spouses in any marriage (or no two partners in any mating) can belong to the same line of any type.

    If the A-person and the B-person don't belong to any of the same lines, then they can share at most one grandparent; the A-person's A-parent's C-parent could be the same person as the B-person's B-parent's C-parent.

    Similarly there are six kinds of line for which both an A-person and a C-person belong to a line of that kind; A-line, B-line, C-line, honeysuckle, woodbine, and AC-rope. And if they don't belong to any of the same lines, they can share at most one grandparent; the A-person's A-parent's B-parent could be the same person as the C-person's C-parent's B-parent.

    And if a B-person and a C-person don't share any of the same lines, they can also have at most one grandparent in person; the B-person's B-parent's A-parent might also be the C-person's C-parent's A-parent.

    So, if no two of the three spouses can belong to any of the same lines as any other spouse, the most consanguineous they can be is that each of the three spouses can be a 1/3 - first-cousin of each other spouse.

    _____________________________________________________________

    In order for that to be possible, there'd have to be at least 3 each of A-lines, B-lines, C-lines, honeysuckles, and woodbines, and at least 2 each of AB-ropes, AC-ropes, and BC-ropes.

    For each sex there'd be at least (3^5)*(2^2)=243*4=972 possible combinations of lineages.
    If that were the case, each person could "legally" mate with (2^5=32)/972 = slightly less than 3.3% of the otherwise-eligible people of each other sex.
    Given two individuals of different sexes who are eligible to mate with each other, only 1 out of every 972 (just over 0.1%) otherwise-eligible people of the third sex would be "legal" for them to marry.

    So if there are barely enough lineages of each type to go around, this "proscriptive marriage system" -- it tells who you can't marry, namely anyone in any of the same lines as you -- is, de facto and in effect, a "prescriptive marriage system", or nearly so -- there's only one (type of) person you can marry.

    _____________________________________________________________

    OTOH if there are at least 4 or more A-lines, 4 or more B-lines, 4 or more C-lines, 4 or more honeysuckles, 4 or more woodbines, 3 or more AB-ropes, 3 or more AC-ropes, and 3 or more BC-ropes, then there are at least (4^5)*(3^2)=1024*9=9216 combinations of lineages for each sex; and each person can mate with people from (3^5)*2 = 486 of those combinations for each other sex (486/9216 being about 5.3%); and each eligible-to-each-other pair of possible mates can choose from (2^5)*(2^2)=128 (almost 1.4%) lineage-combinations of the remaining sex.


    _____________________________________________________________

    Suppose I (or we) wanted everyone to be marriageable to (at least) half of the members of each other sex?

    If there are the same number N of lines of each kind, then there are N^7 combinations of lineages of each sex, and any person is marriageable to each of ((N-1)^6)*N such combinations of each other sex.
    So we need to find N such that ((N-1)/N)^6 >= 1/2 .
    The smallest such N is ten (10).
    Given two people of two different sexes who are marriageable to each other, there are ((N-2)^5)*((N-1)^2) lineage-combinations of the remaining sex who are marriageable simultaneously to the both of them.
    For N=10 that's (8^5)*(9^2) = 32768 * 81.
    ((0.8)^5)*((0.9)^2) = over 0.265, or more than 26.5%, of the people in the remaining sex would be eligible.


    _____________________________________________________________

    But that pre-supposes that every combination of lineages in every sex will have at least one member who is available for marriage. Since there would be 10^7 = 10,000,000 lineage-combinations for each sex, that would mean that the culture's population would have to be very large, for this number of lineages of each type to actually be used to control consanguinity in marriage, and still allow everyone to find half-or-more of the otherwise-eligible (for instance, age-appropriate and not already over-mated) members of each other sex to be marriageable.

    In real life, avoiding same-surname marriages is useful for avoiding consanguinity, only in medium-to-smallish populations (for instance, where, if two people have the same surname and come from the same village, there's a "high" (whatever that means) chance that their fathers are related, or that their mothers are related if they're matrilineal.)
    Once people have a chance to pick mates from many, many different villages, or even a few big cities, having the same family-name no longer implies very much consanguinity. Likewise, once the number of people with a given surname grows very large, the odds that two of them will be too closely consanguineous to marry, drops to a safe level.


    _____________________________________________________________


    What if "half" is too big a fraction? What fraction would be the smallest that could be tolerated/enforced/mostly-obeyed?

    If N=8, there'd be 8^7 = 2,097,152 lineage-combinations in each sex. IMO that's still too large.
    But each person would be marriageable to (7/8)^6 = almost 44.9% of the (otherwise-eligible) members of each other sex. Two such persons would be marriageable to ((6/8)^5)*((7/8)^2) = almost 18.2% of the remaining sex.
    I figure that might be tolerable -- i.e. not too strict.

    If N=6, there'd be 6^7 = 279,936 lineage-combinations in each sex.
    Perhaps that might not be too large.
    But each person would be marriageable to (5/6)^6 = almost 33.5% of the (otherwise-eligible) members of each other sex. Two such persons would be marriageable to ((4/6)^5)*((5/6)^2) = a bit more than 9.1% of the remaining sex.
    I figure that might be barely tolerable.



    _____________________________________________________________


    OTOH, how big would N need to be so that, once an A-person and a B-person "hook up" or get engaged (or, for that matter, and A-person and a C-person, or a B-person and a C-person), at least half of the otherwise-eligible members of the remaining sex are mutually marriageable to both of them?

    We need to find the smallest N such that
    (((N-2)/N)^5)*(((N-1)/N)^2) >= 1/2

    It turns out that smallest N is 19.
    That would allow 19^7 = 893,871,739 lineage-combinations in each sex.
    Population would need to be near 2.7 billion (2.7 * 10^9) for there to be just one person of each sex in each such combination.


    _____________________________________________________________


    And we're still allowing each spouse to be a 1/3 -first-cousin of each other spouse!

    Posted February 11th, 2017 by chiarizio
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    One way of still using the "no two spouses can have a same surname (belong to the same lineage of the same type)" to limit consanguinity even further, so that 1/3 -first-cousins are not marriageable to each other, would be to require that, for instance, no spouse's parent could belong to any of the same lines as any other spouse's parent.
    That would require a minimum of 9 each of A-lines, B-lines, C-lines, honeysuckles, and woodbines, and 6 each of AB-ropes, AC-ropes, and BC-ropes.

    A less strict requirement, still stricter than just "no two spouses can both belong to any of the same lines", is that:
    No spouse can belong to any of the same lines as any parent of any other spouse.
    Equivalently;
    No spouse's parent can belong to any of the same lines as any other spouse.

    This requires a minimum of 5 each of A-lines, B-lines, C-lines, honeysuckles, and woodbines; and a minimum of 4 each of AB-ropes, AC-ropes, and BC-ropes.

    But, again, if there are only the minimum number of each of them, choice will be constrained so that the proscriptive marriage system would be, in effect, a prescriptive marriage system.

    So it would seem that, once an industrial and technological society took hold among these people, and their population got large and everyone's trade-area got large and they started being able to travel a lot and meet people from far-away places and possibly fall in love with them and marry them, they would start just calculating actual consanguinity, even if they kept up the named-lineages.

    (The named lineages might continue to be culturally important for some other reason than controlling consanguinity.)

    _____________________________________________________________

    Under the circumstances for evolving three-sex-three-parent reproduction that bloodb4roses proposed in (some of) the threads referred to in the beginning of the first post on this thread;
    It might be that there is more pressure for diversity and against consanguinity among these people than there is among RL humans *here* on Earth-Prime in OurTimeLine.

    So perhaps the following matings would be proscribed:
  • parents
  • children
  • any direct ancestors
  • any direct descendants
  • siblings
  • full siblings
  • 2/3 -siblings
  • 1/3 -siblings
  • niblings (children of siblings)
  • full niblings
  • 2/3 -niblings (children of 2/3 -siblings)
  • 1/3 -niblings
  • reciprocally, siblings of parents
  • parents' full siblings
  • parents' 2/3 -siblings
  • parents' 1/3 -siblings
  • any collateral ancestors (siblings or part-siblings of direct ancestors)
  • any collateral descendants (direct descendants of siblings or part-siblings)
  • first-cousins (a parent's sibling's child)
  • part-first-cousins (a parent's part-sibling's child)
  • first-cousins and part-first-cousins removed any number of generations; viz. a collateral ancestor's child or a parent's collateral descendant)
  • second-cousins and part-second-cousins (a grandparent's full- or part- sibling's grandchild)
  • second-cousins and part-second-cousins one generation removed (a grandparent's full- or part- sibling's great-grandchild, or a great-grandparent's full- or part- sibling's grandchild)

    The most restrictive consanguinity proscription I'm aware of in real life, prohibits marriage between first-cousins-once-removed or closer.

    The above proscription is, in a sense, one step more strict. It proscribes first-cousins-twice-or-more-removed, and also second-cousins-once-removed or closer.

    _____________________________________________________________

    In one of my concultures, at a certain time in its con-history and evolution, two people may not marry if:
  • either of them is a direct ancestor of the other,
  • or the child of such a direct ancestor (and therefore a collateral ancestor),
  • or the grandchild of such a direct ancestor (and therefore a first-cousin, or a first-cousin-some-number-of-times-removed);
  • or a direct descendant of the other,
  • or a direct descendant of a parent of the other (and thus a collateral descendant),
  • or a direct descendant of a grandparent of the other (and thus a first-cousin, maybe-some-number-of-times-removed)
  • or the two have more than one great-grandparent in common.

    Thus, full-second-cousins are prohibited to each other; and so are double-half-second-cousins.
    (Double-half-second-cousins might come in two varieties.
    (Maybe one grandparent of one person is half-sibling to each of two grandparents of the other person;
    (or maybe each person has two grandparents, each of whom is half-sibling to a grandparent of the other.)

    However, half-second-cousins are not prohibited each other.
    Neither are second-cousins-once-(or-more)-removed.

    Full-second-cousins (and double-half-second-cousins) average about 1/32 of their variable genes in common from the same source(s).

    Relatives permitted above, average about 1/64 (or less) of their variable genes in common from the same source.

    _____________________________________________________________


    In the three-sex-three-parent species, 1/3 -second-cousins average about 1/729 of their variable genes in common from the same source; and 1/3 -second-cousins-once-removed average around 1/2187 of their variable genes in common from the same source.

    Full-second-cousins, however, average about 1/243 of their variable genes in common; so full-second-cousins-twice-removed average about 1/2187 of their variable genes in common.
    Yet full-second-cousins-twice-removed are not proscribed each other, but 1/3-second-cousins-once-removed are.

    Maybe it should be:
    If there are three or more cases where a great-grandparent of one is a great-grandparent or great-great-grandparent or great-great-great-grandparent of the other, they are proscribed from each other.
    Or just:
    Unless they average less than 1/2187 of their variable genes in common from the same source (their index of consanguinity is less than 1/2187), they are proscribed from each other.

    Or whatever.

  • Edited Friday by chiarizio
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    Next up:
    What if we ditch the complicated lines (honeysuckles, woodbines, and ropes), and just concentrate on the A-lines, the B-lines, and the C-lines?

    (Later. It's late.)

    Posted February 11th, 2017 by chiarizio
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    This is a lot to think about. It is possible, much as it is Here TM, on Earth Prime and in our Time Line, that different cultures might prescribe or proscribe different things in regards to consanguinity.

    For example, Here TM, some cultures proscribe against quite a few individuals, but usually only through some type of traceable relation. Sally Smith and Allen Smith could both marry each other despite having the same last name, assuming they can't be should to be related far enough back. In other cultures, like some in China iirc, prescribe a specific person who is relatively closely related (if someone fitting the prescription exists), BUT anyone with the same family name is proscribed.

    In parts of Europe, again iirc, they allowed first cousin marriages but not any closer relations even by adoption or "spiritual" family like the children of godparents.

    So, there could be some cultures with more or less strict systems, even on a world where more genetic diversity is needed than Here TM, especially when entire large swaths of their tree of life have evolved a specific mechanism to deal with that.

    Posted February 11th, 2017 by bloodb4roses
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    This is a lot to think about. It is possible, much as it is Here TM, on Earth Prime and in our Time Line, that different cultures might prescribe or proscribe different things in regards to consanguinity.
    ....
    So, there could be some cultures with more or less strict systems, even on a world where more genetic diversity is needed than Here TM, especially when entire large swaths of their tree of life have evolved a specific mechanism to deal with that.

    You are right about all of that, of course.
    I don't have a specific response to your post, but I wanted to thank you for your comment.
    So; Thanks!

    Posted February 13th, 2017 by chiarizio
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    To use named lineages (or, surnames, or, clan-names) to control consanguinity, there are several levels of strictness, which can be characterized by a pair of non-negative whole numbers a and b where a >= b >= 0. The number a is how many generations before the spouses the earliest generation to be compared is; the number b is how many generations before the spouses will be compared to that ath generation.

    I'm going to write those numbers with a period connecting them, like a.b .

    Considering just one lineage-type;

    0.0 ; No spouse belongs to the same line as any other spouse.
    1.0 ; 0.0, and, additionally, no spouse's parent belongs to the same line as any other spouse.
    1.1 ; 1.0, and, additionally, no spouse's parent belongs to the same line as any other spouse's parent.
    2.0 ; 1.1, and, additionally, no spouse's grandparent belongs to the same line as any other spouse.
    2.1 ; 2.0, and, additionally, no spouse's grandparent belongs to the same line as any other spouse's parent.
    2.2 ; 2.1, and, additionally, no spouse's grandparent belongs to the same line as any other spouse's grandparent.
    3.0 ; 2.2, and, additionally, no spouse's great-grandparent belongs to the same line as any other spouse.
    3.1 ; 3.0, and, additionally, no spouse's great-grandparent belongs to the same line as any other spouse's parent.
    3.2 ; 3.1, and, additionally, no spouse's great-grandparent belongs to the same line as any other spouse's grandparent.
    3.3 ; 3.2, and, additionally, no spouse's great-grandparent belongs to the same line as any other spouse's great-grandparent.

    ....

    And so on.

    _____________________________________________________________


    I personally have never experimented with any level more strict than 3.0 .
    I have never heard of any real-life restriction stricter than 2.2 .
    Some Sikh community (or communities) in India use 49 patrilines (everybody inherits from their father) eponymously named after their founding 49 sages or saints. When a marriage is being proposed, their elders make certain neither of the parties has or had a grandparent from the same patriline as some grandparent of the other party. ([citation needed], I suppose.)

    Depending on the level of strictness, and on the number of sexes and number of parents (assuming everyone has to have exactly one parent of each sex), there are different minimum numbers of lines that must exist in order for any marriages to be legal.

    Let S be the number of sexes (also, the number of spouses, and the number of parents).
    Assuming that the lineage-type we're working with consists of lines that include all S sexes; the minimum number of such lines that must exist is:
    (S^(b+1)) + ((S^a) - (S^b)).

    Varying S from 2 to 5, and varying a.b from 0.0 to 3.3, these minimum values are as follows:
    0.0  2  3  4   5
    
    1.0 3 5 7 9
    1.1 4 9 16 25
    2.0 5 11 19 29
    2.1 6 15 28 45
    2.2 8 27 64 125
    3.0 9 29 67
    3.1 10 33 76
    3.2 12 45
    3.3 16 81


    We've been considering labeling the lineages with the (lowercase) letters of the Latin alphabet.
    Even if we use all 26 letters in each line, we'd run out of letters at 2.2 for 3 sexes, at 2.1 for 4 sexes, and at 2.0 for 5 sexes.
    But we've been thinking of using just 26/S letters for each type of lineage.
    If we do that, and if we're using just those lineage-types where everybody inherits their lineage-membership from a specific sex of parent --- (for two parents, those two lineage-types would be matrilines/matriclans and patrilines/patriclans; for three sexes (A, B, and C), those three lineage types would be A-lines (everyone inherits from their A-parent), B-lines (everyone inherits from their B-parent), and C-lines) --- then we wouldn't have enough Latin letters at 3.3 for two sexes (2*16 > 26), or at 1.1 for three sexes (3*9 > 26), or at 1.0 for four sexes (4*7 > 26), or at 0.0 for six sexes (6*6 > 26).
    Even if we were using the 74-letter Khmer alphabet, instead of the 26-letter Latin alphabet, we couldn't handle 2.2 for three sexes (3*27 > 74), nor 2.0 for four sexes (4*19 > 74), nor 1.1 for five sexes (5*25 > 74), nor 1.0 for seven sexes (7*13 > 74).

    So, for three sexes, I want the strictness level to be 1.0 or less strict.


    _____________________________________________________________

    We could label the A-lines with the eight letters a-h; and label the B-lines with the eight letters j-q; and label the C-lines with the eight letters s-z.

    Or:
    We could label the A-lines with the ten letters a-j; and label the B-lines with the ten letters i-r; and label the C-lines with the ten letters q-z.

    As I have pointed out in previous posts, if the number of lines in a lineage-type is only the minimum number required to allow any marriages at all, the system becomes close to a prescriptive marriage system.

    But as soon as there are more than the minimum number of lineages of a certain type, there is more freedom of choice for which families one's spouses come from.

    I have made a spreadsheet showing the possible legal combinations of A-lines of the A-, B-, and C- -parents of each of the spouses (the A- , B- , and C- -spouses), when there are seven (7) A-lines.
    I didn't do that for eight (8 ) A-lines because there would be more than two million legal combinations, and my version of Excel can't handle more than 1,048,576 (=2^20) rows.

    For five (5) A-lines, there are only 480 combinations.

    For six (6) A-lines, there are 25,920 combinations.

    For seven (7) A-lines, there are 362,880 combinations.

    ....

    And so on.


    _____________________________________________________________

    With three spouses, each having three parents, there are nine spouses' parents to consider. If the lineage-type is such that every spouse, and every parent of a spouse, belongs to some lineage of that type; but there are fewer than nine lineages of that type; then at least one pair (or trio) of spouse's parents must belong to the same lineage.

    Let L be the number of lineages of such a type.

    There are L*(L-1)*(L-2) combinations of parents' lineages for a spouse of the first sex we consider. (Let's consider the A-spouse first).

    Provided there are at least six (6) lineages (i.e. L >= 6), there are
    (L-3)*(L-2)*(L-3) combinations of parents' lineages who would be eligible to be the B-spouse of a given A-spouse.

    However, if L < 9, unless at least one of the A-spouse's parents is of the same lineage as one of the B-spouse's parents, then the choice of C-spouse is constrained.

    For example, if L = 5, there are 5*4*3 = 60 combinations of parents' lineages for the A-spouse.
    But although there are 2*3*2 = 12 combinations of parents' lineages for which the A-spouse is not in the same A-lineage as any of the B-spouse's parents, and the B-spouse is not in the same A-lineage as any of the A-spouse's parents:
    they won't find a C-spouse who is simultaneously eligible to both of them, unless the A-lineages of the B-spouse's B- and C- -parents, are the same as the A-lineages of the A-spouse's B- and C- parents (in either order; either A's B-parent's A-lineage is the same as B's B-parent's A-lineage and A's C-parent's A-lineage is the same as B's C-parent's A-lineage, or A's B-parent's A-lineage is that of B's C-parent's A-lineage while A's C-parent's A-lineage is that of B's B-parent's A-lineage).
    So actually only 2*2=4 combinations of B-spouse's parents' lineages will allow A and B to jointly find a C-spouse eligible for both of them.
    The C-spouse's A-lineage (and therefore the C-spouse's A-parent's A-lineage) must be the remaining one of the A-lineages that "has not yet been used", that is, that is not the lineage of any of the other two spouses' parents.
    The C-spouse's B- and C- -parents' A-lineages, must be the same as the A-lineages of the other two spouses' B- and C- parents; in either order. So there are only 1*2=2 combinations of C-spouse's parents' A-lineages eligible to both the A-spouse and the B-spouse to be a match for a C-spouse of both of them together.


    _____________________________________________________________

    Posted February 14th, 2017 by chiarizio
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    _____________________________________________________________

    In that L=5 example above, any given A-spouse can find four out of the sixty combinations of B-spouse's parents' A-lineages compatible with nem; and the A-spouse and B-spouse together can find two out of the sixty combinations of C-spouse's parents' A-lineages compatible both with nem and with dem.
    That is, about 6.67% of the B-people are not ineligible because of matching A-lineages for a given A-person; and, for a given pair of an A-person and a B-person who are eligible for each other, about 3.33% of of the C-people are not ineligible for either of them because of matching A-lineages.

    The same is true of the B-lineages and the C-lineages.
    So if we track all of those -- that is, we track A-lineages, and B-lineages, and C-lineages -- and there are only 5 (five) lineages of each type, and we require that no spouse's parent belongs to any of the same lineages that any other spouse belongs to, each person finds (4/60)^3 = (1/15)^3 = 1/3375 of the people of any other sex, to be eligible; and any two people of different sexes who are eligible to each other, find (2/60)^3 = (1/30)^3 = 1/27000 people of the third sex to be eligible to both of them.

    I am not sure such strictness would be tolerable.

    If L = 9 , then there are 9*8*7 = 504 combinations of parents' A-lineages. A given individual is eligible to 6*7*6 = 252 combinations of spouse's parents' A-lineages, and 252/504 is 1/2. Given two individuals of different sexes none of whose parents share an A-lineage with any of the other's parents, there would be at least 3*6*5 = 90 combinations of spouse's parents' A-lineages who would be eligible for both of them. (If just one of the A-spouse's parents shared an A-lineage with just one of the B-spouse's parents, there would be 4*6*5 = 120 combinations of C-spouse's parents' A-lineages eligible to both of them. If the A-spouse's B- and C- -parents came from the same A-lineages as the B-spouse's B- and C- -parents, in either order, there would be 5*6*5 = 150 eligible combinations of C-spouse's parents' A-lineages.)

    This is a lot closer to tolerable. Using the same values for B-lineages and C-lineages, an A-person would find (252/504)^3 = (1/2)^3 = 1/8 = 12.5% of the B-people to satisfy the 1.0 rule; and together they would find on the average something more than
    (90/504)^3 = (5/28 )^3 = 125/21952 > 1/176 of C-people eligible to both of them.

    When looking at two-sex two-spouse two-parent cultures, I try to arrange that each person finds at least one-half of the opposite sex to be eligible, or, at least, not ineligible due to a surname match.
    For a 3-sex 3-spouse 3-parent culture, if we wanted to make sure every A-person would find at least half of the B-people eligible, and we assume there are just as many (i.e. L) A-lineages as B-lineages and just as many C-lineages as A-lineages, then we would need:
    ( ((L-3)*(L-2)*(L-3)) / (L*(L-1)*(L-3)) )^3 >= 1/2 ;
    that is, ((L-3)*(L-2)*(L-3)) / (L*(L-1)*(L-3)) >= cuberoot(1/2).
    For that, we need L >= 24 .

    If we went further, and wanted any inter-eligible couple of an A-person and a B-person to find at least half of all C-people to be eligible for both of them, we'd need
    ((L-6)*(L-3)*(L-4)) / (L*(L-1)*(L-3)) >= cuberoot(1/2).
    This would be the case provided L >= 47 .

    (For some couples, ((L-4)*(L-3)*(L-4)) / (L*(L-1)*(L-3)) >= cuberoot(1/2) would suffice.)
    (This happens if L >= 37 .)



    _____________________________________________________________

    How effective is this scheme at preventing consanguinity?
    How much consanguinity does it allow?

    Consider the following:
                         A-lineage B-lineage C-lineage
    

    A-spouse's A-parent's a n y
    " " B-parent's d k z
    " " C-parent's e o v

    B-spouse's A-parent's b n y
    " " B-parent's d l z
    " " C-parent's e o w

    C-spouse's A-parent's c n y
    " " B-parent's d m z
    " " C-parent's e o x


    This satisfies the rule 1.0; no spouse's parent belongs to any of the same lineages that any other spouse belongs to.
    We see that the A-spouse's A-parent and the B-spouse's A-parent and the C-spouse's A-parent could all be mutually 2/3-siblings of each other; they could all share the same B-parent and the same C-parent, but would all have to have different A-parents.
    Also, we see that the A-spouse's B-parent and the B-spouse's B-parent and the C-spouse's B-parent could all be mutually 2/3-siblings of each other; they could all share the same A-parent and the same C-parent, but would all have to have different B-parents.
    And, finally, we see that the A-spouse's C-parent and the B-spouse's C-parent and the C-spouse's C-parent could all be mutually 2/3-siblings of each other; they could all share the same A-parent and the same B-parent, but would all have to have different C-parents.

    So this allows each spouse to be a triple 2/3-first-cousin of each other spouse.

    Posted February 14th, 2017 by chiarizio
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    I mentioned that I would prefer that my conculture be such that, as nearly as possible, every child would inherit a lineage-membership from every grandparent.
    If it were indeed true that everyone inherited a lineage from every grandparent, then rule 0.0 would guarantee that no spouse's grandparent shared a lineage with any other spouse's grandparent, provided the parents' sexes were the same as each other and the grandparents' sexes were also the same as each other.
    That would mean that, for instance, no spouse's A-parent's B-parent could be a full-sibling of any other spouse's A-parent's B-parent.
    So certain full-second-cousin relationships between spouses would be ruled out.
    I haven't figured it out, but, possibly, some 2/3-second-cousin or 1/3-second-cousin relationships might also be ruled out; and also, possibly, the spouses' parents needn't be the same sex as each other, and/or their grandparents needn't be the same sex.

  • =*==*==*==*==*==*==*==*==*==*==*==*==*==*==*==*==*

    However it is impossible for any child to inherit any lineage from their same-sex-parent's other-sex-parent.

    For instance, among humans, a child inherits their patriline from their father and his father, and inherits their matriline from their mother and her mother, and inherits their "rope" from their opposite-sex-parent and that parent's opposite-sex-parent (who is the same sex as the child).
    So boys inherit their rope from their mothers and their mothers' fathers; and girls inherit their rope from their fathers and their fathers' mothers.
    But their is no consistent way for a boy to inherit any lineage from his father's mother, nor for a girl to inherit any lineage from her mother's father.

    In a three-sex species, an A-child could inherit
    nis A-line from nis A-parent and nis A-parent's A-parent; and
    nis B-line from nis B-parent and nis B-parent's B-parent; and
    nis C-line from nis C-parent and nis C-parent's C-parent; and
    nis AB-rope from nis B-parent and nis B-parent's A-parent; and
    nis AC-rope from nis C-parent and nis C-parent's A-parent; and
    nis honeysuckle from nis B-parent and nis B-parent's C-parent; and
    nis woodbine from nis C-parent and nis C-parent's B-parent.
    (An A-child would not be assigned a BC-rope.)
    But an A-child cannot inherit a lineage from nis A-parent's B-parent nor nis A-parent's C-parent.

    By the same token, a B-child could inherit
    dis A-line from dis A-parent and dis A-parent's A-parent; and
    dis B-line from dis B-parent and dis B-parent's B-parent; and
    dis C-line from dis C-parent and dis C-parent's C-parent; and
    dis AB-rope from dis A-parent and dis A-parent's B-parent; and
    dis BC-rope from dis C-parent and dis C-parent's B-parent; and
    dis honeysuckle from dis C-parent and dis C-parent's A-parent; and
    dis woodbine from dis A-parent and dis A-parent's C-parent.
    (A B-child would not be assigned an AC-rope.)
    But a B-child cannot inherit a lineage from dis B-parent's A-parent nor nis B-parent's C-parent.

    And similarly a C-child cannot inherit a lineage from ver C-parent's A-parent nor ver C-parent's B-parent.

    _____________________________________________________________

    If I go on to a four-sex four-parent four-spouse species, can I glean any general principles?

    Consider my concultural desideratum that everyone inherit membership in some lineage or other from every grandparent from whom it's possible to inherit such membership.

    Call the sexes A, B, C, and D. (Because I'm just so creative!)

    First; every child, regardless of the child's sex, can inherit a lineage-membership from each grandparent who is the same sex as the child's parent (the grandparent's child).
    Every child inherits an A-lineage from their A-parent's A-parent;
    every child inherits a B-lineage from their B-parent's B-parent;
    every child inherits a C-lineage from their C-parent's C-parent; and,
    every child inherits a D-lineage from their D-parent's D-parent.

    Second; every child can inherit a lineage-membership from every grandparent who is the same sex as the child.
    So for instance every A-child can inherit an AB-rope from their B-parent, and their B-parent's A-parent, and their B-parent's A-parent's B-parent; and,
    can inherit an AC-rope from their C-parent, and their C-parent's A-parent, and their C-parent's A-parent's C-parent; and,
    can inherit an AD-rope from their D-parent, and their D-parent's A-parent, and their D-parent's A-parent's D-parent.
    And, every B-child can inherit an AB-rope from their A-parent, and their A-parent's B-parent, and their A-parent's B-parent's A-parent; and,
    can inherit an BC-rope from their C-parent, and their C-parent's B-parent, and their C-parent's B-parent's C-parent; and,
    can inherit an BD-rope from their D-parent, and their D-parent's B-parent, and their D-parent's B-parent's D-parent.

    And similarly every C-child
    inherits an AC-rope from their A-parent's C-parent, and
    inherits a BC-rope from their B-parent's C-parent, and
    inherits a CD-rope from their D-parent's C-parent.
    And every D-child
    inherits an AD-rope from their A-parent's D-parent, and
    inherits a BD-rope from their B-parent's D-parent, and
    inherits a CD-rope from their C-parent's D-parent.

    But I still want every child to inherit from an other-sex-parent's other-sex-parent who is not the same sex as the child. In other words, if the parent is not the same sex as the child, and the grandparent is not the same sex as either the child or the child's parent (grandparent's child), I need a lineage-type that can be inherited by that child from that grandparent.

    Because I have expressed no desideratum wishing that every child inherit lineage membership from as many great-grandparents as possible, there are two ways to go (more than two if there are more than four sexes).

    Either every child eventually inherits from a great-grandparent who is the same sex as the child, but different from the parent and the grandparent;
    or every child eventually inherits from a great-grandparent who is the sex different from that of the child, different from that of the parent, and different from that of the grandparent.

    The first way, there will be eighteen types of lineage in all; the four "straight lines", the six "ropes", and eight three-turn coils.
    The second way, there will be sixteen types of lineage in all; the four "straight lines", the six "ropes", and six four-turn coils.
    Either way, everyone will belong to exactly one lineage of each of thirteen types. Which thirteen types, depends on the sex of the individual.
    They will all belong to all four "straight lines"; to three of the six "ropes"; and either to six of the eight "three-turn coils", or to all six of the "four-turn coils".

    The three-turn coils are as follows.


    1. ABC-coil; an A-child inherits from their B-parent, a B-child inherits from their C-parent, and a C-child inherits from their A-parent.
    D-children are not assigned an ABC-coil.

    2. ACB-coil; an A-child inherits from their C-parent, a B-child inherits from their A-parent, and a C-child inherits from their B-parent.
    D-children are not assigned an ACB-coil.


    3. ABD-coil; an A-child inherits from their B-parent, a B-child inherits from their D-parent, and a D-child inherits from their A-parent.
    C-children are not assigned an ABD-coil.

    4. ADB-coil; an A-child inherits from their D-parent, a B-child inherits from their A-parent, and a D-child inherits from their B-parent.
    C-children are not assigned an ADB-coil.


    5. ACD-coil; an A-child inherits from their C-parent, a C-child inherits from their D-parent, and a D-child inherits from their A-parent.
    B-children are not assigned an ACD-coil.

    6. ADC-coil; an A-child inherits from their D-parent, a C-child inherits from their A-parent, and a D-child inherits from their C-parent.
    B-children are not assigned an ADC-coil.


    7. BCD-coil; a B-child inherits from their C-parent, a C-child inherits from their D-parent, and a D-child inherits from their B-parent.
    A-children are not assigned a BCD-coil.

    8. BDC-coil; an B-child inherits from their D-parent, a C-child inherits from their B-parent, and a D-child inherits from their C-parent.
    A-children are not assigned a BDC-coil.

  • Posted February 14th, 2017 by chiarizio
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    _____________________________________________________________


    The four-turn coils are as follows:

    1. ABCD-coil; an A-child inherits from their B-parent, a B-child inherits from their C-parent, a C-child inherits from their D-parent, and a D-child inherits from their A-parent.

    2. ABDC-coil; an A-child inherits from their B-parent, a B-child inherits from their D-parent, a C-child inherits from their A-parent, and a D-child inherits from their C-parent.

    3. ACBD-coil; an A-child inherits from their C-parent, a B-child inherits from their D-parent, a C-child inherits from their B-parent, and a D-child inherits from their A-parent.

    4. ACDB-coil; an A-child inherits from their C-parent, a B-child inherits from their A-parent, a C-child inherits from their D-parent, and a D-child inherits from their B-parent.

    5. ADBC-coil; an A-child inherits from their D-parent, a B-child inherits from their C-parent, a C-child inherits from their A-parent, and a D-child inherits from their B-parent.

    6. ADCB-coil; an A-child inherits from their D-parent, a B-child inherits from their A-parent, a C-child inherits from their B-parent, and a D-child inherits from their C-parent.


    _____________________________________________________________

    Although each individual will belong to thirteen lineages of different type in either scheme, the number of lineage-types two spouses will both belong to a lineage in, are different in the three-turn scheme than in the four-turn scheme.

    In both schemes, everyone will belong to exactly one lineage in each of the four "straight-line" types; an A-line, a B-line, a C-line, and a D-line.
    So, every two spouses will have those four lineage-types in common.

    In both schemes, everyone will belong to exactly on lineage in each of three of the six "rope" types. But, to look at a representative example, both the A-spouse and the B-spouse will belong each to their own AB-rope; but the A-spouse will also belong to an AC-rope and an AD-rope, while the B-spouse will belong to no lineage of either of those types; and the B-spouse will also belong to a BC-rope and a BD-rope, while the A-spouse will belong to no lineage of either of those types. (Neither the A-spouse nor the B-spouse will belong to any CD-rope.)
    So, every two spouses will both belong to "ropes" of only one type.

    So far, there are five lineage-types that two spouses of different sexes will both belong each to their own lineage of that type.

    In the four-turn scheme, everyone will belong to some four-turn coil in each of the six types of four-turn coils. So in that scheme, there will be eleven types of lineages such that both spouses belong to some lineage (each to their own lineage) of each of those types.

    But in the three-turn scheme, only four of the eight types of three-turn coils will both contain a lineage to which one spouse belongs and also contain a lineage to which the other spouse belongs.
    Again, to illustrate with a representative example:
    The A-spouse belongs to an ABC-coil, an ACB-coil, an ABD-coil, an ADB-coil, an ACD-coil, and an ADC-coil.
    The B-spouse belongs to an ABC-coil, an ACB-coil, an ABD-coil, an ADB-coil, a BCD-coil, and a BDC-coil.
    The B-spouse belongs to no ACD-coil and to no ADC-coil. The A-spouse belongs to no BCD-coil and to no BDC-coil.
    Only the ABC-coil type, the ACB-coil type, the ABD-coil type, and the ADB-coil type, each contain both a lineage to which the A-spouse belongs, and also a lineage to which the B-spouse belongs.

    So, in the three-turn scheme, there are but nine types of lineage such that both the A-spouse and the B-spouse belong to some lineage (each to their own) of that type.

    The difference between a ninth-power and an eleventh-power might make it much less troublesome to find a compatible mate. 7^9 is 49 times smaller than 7^11. (OTOH 7^9 is 343^3 which is more than 27 million.)


    _____________________________________________________________


    Is there any new information to be gleaned from trying on a five-sex five-parent five-spouse culture?

    The only thing new is, now there are two great-grandparents who are not the same sex as the child, not the same sex as the parent, and not the same sex as the grandparent, when the child and the parent and the grandparent are all of three different sexes.

    Call the five sexes A and B and C and D and E, respectively.
    (Wow! I'm on fire with creativity!)

    So, say I want a lineage type wherein an A-child inherits membership through their B-parent from a C-grandparent.

    I could do this with a three-turn coil (an ABC-coil), having the lineage inherited eventually from an A-great-grandparent the same sex as the child.

    I could do this with either of two four-turn coils; an ABCD-coil or an ABCE-coil. At 4:00 AM in the morning I can think of no good reason to choose one over the other.

    Or, I could do this with either of two five-turn coils; an ABCDE-coil or an ABCED-coil. Again, I don't need both, and I don't know why I should prefer one over the other.

    It looks, to me, that, in the interests of consistency across number-of-sexes, and of simplicity in choosing the lineage types, and of reducing the number of comparable lineages of the same type that each of two spouse-hopefuls belong to a lineage of, we (or maybe just I) should always go with the three-turn coils.
    If we look at the three-turn coils, two individuals of different sexes both belong to lineages of 2*(S-2) three-turn-coil types (where S is still the number of sexes); while they'll both belong to lineages of 3*(S-2)*(S-3) four-turn-coil types. For S = 5 that's the difference between six and eighteen. 9^(5+1+6) differs from 9^(5+1+18) by quite a few. 9^12 is only the square-root of 9^24.




    _____________________________________________________________


    Alright, it's way the fuck past time for bed. I'm turning in for the night. I hope I can drive tomorrow!

    Posted February 14th, 2017 by chiarizio
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