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## adpihis and reptigans rules about marrying halfsiblings spouses halfsiblings

In order to prevent or at least reduce some of the duplication in names between groups of double-parallel-first-cousins and double-parallel-half-cousins and so on;

Consider the following rules:

———

Notice what isn’t prohibited:

A half-brother and a half-sister who share a father, but not a mother, could marry a wife and a husband who share a mother, but not a father.

———

I’ll have to work it out; but:

I’m guessing that will cut down on the odds that two double-half-cousins (or closer) will have exactly the same name.

———

I have to wake up on time tomorrow, so I’ll figure this out tomorrow early evening or late afternoon at the earliest.

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chiarizio

After thinking about it some more, I’ve only come up with three (or five) situations that (I’m pretty sure) would cause trouble.

They are:

. . . . . . . .

In such cases the two couples’ children share either:

—————

There might not be a problem if two half-brothers marry two half-sisters;

whether the two couples’ children share two grandfathers, or share two grandmothers, or share an FF and an MM, or share an FM and an MF.

That’s what I strongly suspect now. I’ll have to see whether I can prove it.

—————

There also might be no problem if the sibling-pairs were opposite-sex siblings.

For instance if a man and a woman are each the other’s full-sibling, sharing both the same mother and the same father;

And the brother’s wife and the sister’s husband are also full-siblings to each other;

Then even though the two couples’ children will share all four grandparents, being double-full-cross-cousins,

One bunch of kids’ FF and FM will be the other brood’s or litter’s MF and MM, and vice-versa.

So they won’t have the same FF, nor the same FM, nor the same MF, nor the same MM.

I think that means there won’t be any forced duplication of names for some of one couple’s children to be named the same as some of the children of the other couple.

chiarizio

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chiarizio

Note that in an “FB=F and MZ=M” classificatory kinship system, which is also a prescriptive marriage system, the brides of two brothers must be each other’s classificatory sisters, and the husbands of two sisters must be each other’s classificatory brothers.

So these restrictions on affinity apply to what we’d call “actual siblings” rather than classificatory siblings.

Also note that in my discussions of such things so far, the purpose, and/or main effect, of the system of “alterclans” (or “ropes” or “geuns”), is to prevent that a man’s wife’s brother (WB) could be his sister’s husband (ZH) (or equivalently that a woman’s HZ could also be her BW). So when there are few enough “spirit-robes”, and restrictions against marrying someone who’s in one’s own or one’s parents’ spirit-robe, or whose parent is in one’s own spirit-robe, etc., are strict enough; a brother-sister pair couldn’t marry a sister-brother pair anyway. However the stringency varies, and the number of alterclans varies, over the history of Adpihi/Reptigan; at times no eponym-exogamy prohibits every such pair of marriages.

Right now, I’m just concerned about duplication of individual names among parallel double-(half)-cousins.

—————

The first part of the individual names of a man’s odd-numbered (1st, 3rd, 5th, 7th, etc.) sons, are derived from the first part of the individual names of the grandfathers and uncles of the man’s father.

The first part of the individual names of a man’s even-numbered (2nd, 4th, 6th, etc.) sons, are derived from the first part of the individual names of the grandfathers and uncles of the man’s mother.

So if two men share a father, their odd-numbered sons will share the first parts of their individual names;

And if two men share a mother, their even-numbered sons will share the first parts of their individual names.

The second part of the individual names of a woman’s odd-numbered (1st, 3rd, 5th, 7th, etc.) sons, are derived from the second part of the individual names of the father and brothers of the woman’s mother. (?)

The second part of the individual names of a woman’s even-numbered (2nd, 4th, 6th, etc.) sons, are derived from the second part of the individual names of the father and brothers of the woman’s father. (?)

So if two women share a mother, their odd-numbered sons will share the second parts of their individual names;

And if two women share a father, their even-numbered sons will share the second parts of their individual names.

So, if two men who share a father marry two women who share a mother, all the odd-numbered sons of both couples will share both parts of their individual names with the same-birth-ordered son of the other couple.

If two men who share a mother marry two women who share a father, it will be the even-numbered sons of both couples who share both parts of their individual names.

Where I put the (?) question-marks above, I may have swapped the women’s father with their mother. If so, the duplication among odd-numbered sons applies to agnate half-brothers marrying agnate half-sisters; and the duplication among even-numbered sons applies to enate (uterine) half-brothers marrying enate half-sisters.

—————

Something similar applies, ceteris parabus and mutatis mutandis, to duplication of complete individual names among their daughters.

Either agnate half-brothers shouldn’t marry agnate half-sisters, and enate half-brothers shouldn’t marry enate half-sisters;

Or agnate half-brothers shouldn’t marry enate half-sisters, and enate half-brothers shouldn’t marry agnate half-sisters.

In any case; full-brothers shouldn’t marry full-sisters, nor agnate half-sisters, nor enate half-sisters;

And full-sisters shouldn’t marry full-brothers, nor agnate half-brothers, nor enate half-brothers.

It may be safe for half-brothers to marry half-sisters in certain cases.

Either it’s safe if the shared parents are the same sex, but not if they’re opposite sex;

Or it’s safe if the shared parents are opposite sex, but not if they’re same sex.

—————

I still have to check out what if any hazard there is to a brother and a sister marrying a sister and a brother.

———

I remind myself (and my readers) that we are referring to “actual” parents and siblings (full or half), rather than classificatory relationships, unless stated otherwise!

chiarizio

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chiarizio

I’m going to go with a guess. (Or, at least, that’s what I now think I’ll do!)

Adpihi and Reptigan just want “Wife’s Brother” and “Sister’s Husband” to be two distinct and disjoint kinds of relatives.

Not because of any danger that if your wife’s brother marries your sister, you’ll end up naming one of your children exactly the same name they name one of their children;

but, rather, “Just Because”.

......

They want W <> ZHZ and Z <> WBW

and WB <> ZH and BW <> HZ

and H <> BWB and B <> HZH.

...

But I suppose they’re OK with WBW = ZHZ and HZH = BWB.

chiarizio

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chiarizio

The Dwarves and Elves and Men of Ataivsh not only have

WBW <> ZHZ ;

they also have

WBWB <> ZHZH .

However they allow WBWBW = ZHZHZ .

chiarizio

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chiarizio

I think that under the naming systems I’ve been considering here, I wouldn’t want two men who have the same father to marry two women who have the same father; nor want two men who have the same mother to marry two women who have the same mother.

So we wouldn’t want two full brothers to marry two full or half sisters, nor would we want two full sisters to marry two full or half brothers,

nor would we want two agnate half brothers to marry two agnate half sisters, nor two uterine half brothers to marry two uterine half sisters.

This despite the fact that two brothers’ wives will always be each other’s Classificatory sisters, and two sisters’ husbands will always be each other’s classificatory brothers.

It should be safe for two agnate half brothers to marry two uterine half sisters, or two uterine half brothers to marry two agnate half sisters.

Or at least one of those arrangements should be safe.

The “rope” or

*geun*or “spirit-robe” proscribed coeponymy will prevent a sister and brother from marrying a brother and sister, I think.

I could be wrong. If I am wrong there might be no problem with that.

chiarizio

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chiarizio

Because of the systems of assigning “official” first and second individual names to offspring in Adpihi and Reptigan,

there is sometimes a danger that, if two men who share an actual* GGF (greatgrandfather) or an actual* granduncle marry two women who share an actual* GF (grandfather) or an actual* uncle, that some son of each couple will share both their first and their second individual names with some son of the other couple.

And there is sometimes a danger that, if two women who share an actual* GGM (greatgrandmother) or an actual* grandaunt marry two men who share an actual* GM (grandmother) or an actual* aunt, that some daughter of each couple will share both their first and their second individual names with some daughter of the other couple.

*”actual” as opposed to classificatory.

If the marriages take place at a time and in a location in which circumstances don’t require prescriptive marriage, it’s possible the two sons or two daughters won’t share any clan-names, so that will be OK.

Sometimes they’ll have to share one clan-name, but circumstances may permit that they don’t have to share more than one.

Whether or not that’s OK, and how OK it is, may vary.

Sometimes they’ll share two clan-names. If so I think social pressure will recommend against both these marriages taking place; either one may be OK provided the other doesn’t happen, but both shouldn’t happen. But this might not be an absolute.

In times and places where the prescriptive marriage system is in force, if the husbands are one another’s classificatory brothers and the brides are one another’s classificatory sisters, then their sons all share all three clan-names and their daughters will also share all three clan-names. Therefore it will be very much deprecated to give any offspring both the same first individual name and the same second individual name as a child of the other couple.

From now on in this post, if I mention a kinship, I mean the “actual” kinship, unless I specifically say “classificatory”.

(That’s the opposite of how I’ll use the terms in most posts about Adpihi and Reptigan; in most posts I’ll talk like my conpeople would talk, as if the “classificatory” kinterms were the only kinterms.)

.......... .......... .......... .......... ..........

If two men who share their actual FFF marry two women who share their actual FF, then each couple’s S1 (firstborn son) will, if both couples follow the standard, share their first individual name with their fathers’ shared FFF, and share their second individual name with their mothers’ shared FF. They’ll also share their fathers’ shared patriclan. Each will receive their mother’s respective matriclans and their mother’s respective alterclan. Their mothers share their FF’s patriclan with each other; if they are each other’s classificatory sisters, as they’re likely to be since they are parallel cousins (their fathers are agnate half brothers, and half brothers are brothers, and father’s brothers are fathers, so my FBD is my FD is my sister), then the result would be that each couple’s S1 has exactly the same full official name as the other couple’s S1.

So I’m going to hypothesize about variable likelihood-of-compliance to the standard.

I’m going to consider making it depend on the birth-order of the child being named and on the birth-order of the parent doing the naming.

.......... .......... .......... .......... ..........

Concerning the first individual names of the sons of a man H:

If H is HF’s S1, then, 95% of the time, H will name H’s own S1 after H’s FFF like he’s supposed to.

If H is HM’s S1, then, 85% of the time, H will name H’s own S2 after H’s MFF like he’s supposed to.

If H is HF’s S1, then, 75% of the time, H will name H’s own S3 after H’s FMF like he’s supposed to.

If H is HM’s S1, then, 65% of the time, H will name H’s own S4 after H’s MMF like he’s supposed to.

If H is HF’s S1, then 55% of the time, H will name H’s own S5 after H’s FFB1 (HFF’s oldest brother) like he’s supposed to.

If H is either HF’s S1 or HM’s S1, then 45% of the time, H will name H’s own S6+ (H’s sixth or subsequent son) after one of H’s granduncles, like he’s supposed to, but not necessarily the granduncle he’s supposed to.

Otherwise:

If H is HF’s S2, then, 85% of the time, H will name H’s own S1 after H’s FFF like he’s supposed to.

If H is HM’s S2, then, 75% of the time, H will name H’s own S2 after H’s MFF like he’s supposed to.

If H is HF’s S2, then, 65% of the time, H will name H’s own S3 after H’s FMF like he’s supposed to.

If H is HM’s S2, then, 55% of the time, H will name H’s own S4 after H’s MMF like he’s supposed to.

If H is either HF’s S2 or HM’s S2, then 45% of the time, H will name H’s own S5+ (H’s fifth or subsequent son) after one of H’s granduncles, like he’s supposed to, but not necessarily the granduncle he’s supposed to.

Otherwise:

If H is HF’s S3, then, 75% of the time, H will name H’s own S1 after H’s FFF like he’s supposed to.

If H is HM’s S3, then, 65% of the time, H will name H’s own S2 after H’s MFF like he’s supposed to.

If H is HF’s S3, then, 55% of the time, H will name H’s own S3 after H’s FMF like he’s supposed to.

If H is either HF’s S3 or HM’s S3, then, 45% of the time, H will name H’s own S4+ (H’s fourth or subsequent son) after one of H’s GGFs or granduncles, like he’s supposed to, but not necessarily the GGF or granduncle he’s supposed to.

Otherwise:

If H is HF’s S4, then, 65% of the time, H will name H’s own S1 after H’s FFF like he’s supposed to.

If H is HM’s S4, then, 55% of the time, H will name H’s own S2 after H’s MFF like he’s supposed to.

If H is either HF’s S4, or HM’s S4, then, 45% of the time, H will name H’s own S3+ (H’s third or subsequent son) after one of H’s GGFs or granduncles, like he’s supposed to, but not necessarily the GGF or granduncle he’s supposed to.

Otherwise:

If H is HF’s S5, then, 55% of the time, H will name H’s own S1 after H’s FFF like he’s supposed to.

If H is either HF’s S5, or HM’s S5+, then, 45% of the time, H will name H’s own S2+ (H’s second or subsequent son) after one of H’s GGFs or granduncles, like he’s supposed to, but not necessarily the GGF or granduncle he’s supposed to.

Otherwise, if H is either HF’s S6+, or HM’s S6+ then, 45% of the time, H will name H’s own S (any son) after one of H’s GGFs or granduncles, like he’s supposed to, but not necessarily the GGF or granduncle he’s supposed to.

Otherwise, for any situation not covered above, 45% of the time, H will name any son S of H, after one of H’s GGFs or granduncles, like he’s supposed to, but not necessarily the GGF or granduncle he’s supposed to.

.......... .......... .......... .......... ..........

Concerning the second individual names the sons of a woman W:

If W is WF’s D1, then, 95% of the time, W will name W’s own S1 after W’s FF like she’s supposed to.

If W is WM’s D1, then, 85% of the time, W will name W’s own S2 after W’s MF like she’s supposed to.

If W is WF’s D1, then, 75% of the time, W will name W’s own S3 after W’s FB1 (WF’s oldest brother) like she’s supposed to.

If W is WM’s D1, then, 65% of the time, W will name W’s own S4 after W’s MB1 (WM’s oldest brother) like she’s supposed to.

If W is WF’s D1, then, 55% of the time, W will name W’s own S5 after H’s FB2 (WF’s 2nd-oldest brother) like she’s supposed to.

If W is either WF’s D1 or WM’s D1, then, 45% of the time, W will name W’s own S6+ (W’s sixth or subsequent son) after one of W’s uncles, like she’s supposed to, but not necessarily the uncle she’s supposed to.

Otherwise:

If W is WF’s D2, then, 85% of the time, W will name W’s own S1 after W’s FF like she’s supposed to.

If W is WM’s D2, then, 75% of the time, W will name W’s own S2 after W’s MF like she’s supposed to.

If W is WF’s D2, then, 65% of the time, W will name W’s own S3 after W’s FB1 (WF’s oldest brother) like she’s supposed to.

If W is WM’s D2, then, 55% of the time, W will name W’s own S4 after W’s MB1 (WM’s oldest brother) like she’s supposed to.

If W is WF’s D2, or W is WM’s D2, then, 45% of the time, W will name W’s own S5+ (W’s fifth or subsequent son) after one of W’s uncles, like she’s supposed to, but not necessarily the uncle she’s supposed to.

Otherwise:

If W is WF’s D3, then, 75% of the time, W will name W’s own S1 after W’s FF like she’s supposed to.

If W is WM’s D3, then, 65% of the time, W will name W’s own S2 after W’s MF like she’s supposed to.

If W is WF’s D3, then, 55% of the time, W will name W’s own S3 after W’s FB1 (WF’s oldest brother) like she’s supposed to.

If W is WF’s D3, or W is WM’s D3, then, 45% of the time, W will name W’s own S4+ (W’s fourth or subsequent son) after one of W’s uncles, like she’s supposed to, but not necessarily the uncle she’s supposed to.

Otherwise:

If W is WF’s D4, then, 65% of the time, W will name W’s own S1 after W’s FF like she’s supposed to.

If W is WM’s D4, then, 55% of the time, W will name W’s own S2 after W’s MF like she’s supposed to.

If W is WF’s D4, or W is WM’s D4, then, 45% of the time, W will name W’s own S3+ (W’s third or subsequent son) after one of W’s uncles, like she’s supposed to, but not necessarily the uncle she’s supposed to.

Otherwise:

If W is WF’s D5, then, 55% of the time, W will name W’s own S1 after W’s FF like she’s supposed to.

If W is WF’s D5, or W is WM’s D5, then, 45% of the time, W will name W’s own S2+ (W’s second or subsequent son) after one of W’s GFs or uncles, like she’s supposed to, but not necessarily the GF or uncle she’s supposed to.

Otherwise:

If W is WF’s D6+, or W is WM’s D6+, then, 45% of the time, W will name W’s own S (any son) after one of W’s GFs or uncles, like she’s supposed to, but not necessarily the GF or uncle she’s supposed to.

Otherwise, in any situation not covered above, 45% of the time, W will name any son after one of W’s GFs or uncles, but not necessarily the GF or uncle she’s supposed to.

.......... .......... .......... .......... ..........

A similar pattern of compliance occurs in the first individual names of the daughters of a woman W or the second individual names of the daughters of a man H.

Concerning the first individual names of the daughters of a woman W:

Compliance is 95% for the first daughters of first daughters;

compliance is 85% for the second daughters of first daughters, and the first daughters of second daughters;

compliance is 75% for the D3s of D1s, and the D2s of D2s, and the D1s of D3s;

65% for the D4s of D1s, the D3s of D2s, the D2s of D3s, and the D1s of D4s;

55% for the D5s of D1s, the D4s of D2s, the D3s of D3s, the D2s of D4s, and the D1s of D5s;

and 45% for any other situation, including the D6+ of D1+, the D5+ of D2+, the D4+ of D3+, the D3+ of D4+, the D2+ of D5+, and the D1+ of D6+.

And similar compliance for the second individual names of the daughters of a man H.

95% for the D1s of S1s

85% for the D2s of S1s and the D1s of S2s

75% for the D

*j*of S

*k*if

*j+k=4*

65% for the D

*j*of S

*k*if

*j+k=5*

55% for the D

*j*of S

*k*if

*j+k=6*

45% for the D

*j*of S

*k*if

*j+k>=7*

45% for any other situation not covered above

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Early in settling a planet each couple is likely to have seven children on average.

That may be a mean and a median and a mode.

I’m not sure what the variance would be.

Consider those who have exactly this many children; for the moment ignore the large minority who’ll have six, the probably smaller (but not negligible, although I’m just about to neglect it!) minority who’ll have eight, and the probably negligible minorities who’ll have five or fewer, or nine or more.

35 out of every 128 will have four sons and three daughters;

35 out of every 128 will have three sons and four daughters;

21 out of every 128 will have five sons and two daughters;

21 out of every 128 will have two sons and five daughters;

7 out of every 128 will have six sons and one daughter;

7 out of every 128 will have one son and six daughters;

1 out of every 128 will have seven sons and no daughters;

1 out of every 128 will have no sons and seven daughters.

I believe it will be safe to ignore those who have six or more sons, or one son or no sons, or six or more daughters, or one daughter or no daughters. They make up about 12.5% of these 128 but I’m going with the 87.5% who have two to five sons and two to five daughters, and a total of seven children.

Then I’m going to commit a further sin against statistics, and ignore for the time being those who have fewer than three or more than four sons, and those who have fewer than three or more than four daughters.

I’m going to concentrate on the middle 54.6875% and pretend they’re everybody.

.......... .......... .......... .......... .........

Everybody has a father F and a mother M.

So everybody has an FF and an FM and an MF and an MM.

And everybody has an FFF and an MMM and an FMF and an MFM and the other four GGPs (great grandparents.

I’ll pretend every man has at least two brothers and at least three sisters; and 50% of men have exactly three brothers and exactly three sisters, while the other 50% of men have exactly two brothers and exactly four sisters.

I’ll pretend every woman has at least three brothers and at least two sisters; and 50% of women have exactly four brothers and exactly two sisters, while the other 50% of women have exactly three brothers and exactly three sisters.

.......... ........... .......... .......... ..........

When a man is coming up with the first individual names for his sons, he looks to the first individual names of the fathers and brothers of his grandparents, taking his grandparents in the order FF, MF, FM, MM, FF, MF, FM, MM, FF, MF, FM, MM, .... and so on, repeating as often as necessary.

So.

Everybody has an FFF

Everybody has an MFF

Everybody has an FMF

Everybody has an MMF

Almost everybody has an FFB1

Almost everybody has an MFB1

Almost everybody has an FMB1

Almost everybody has an MMB1

Almost everybody has an FFB2

Almost everybody has an MFB2

Almost everybody has an FMB2

Almost everybody has an MMB2

About 50% of everybody has an FFB3

About 50% of everybody has an MFB3

Almost everybody has an FMB3

Almost everybody has an MMB3

Very few people have an FFB4

Very few people have an MFB4

About 50% of everybody has an FMB4

About 50% of everybody has an MMB4

Even fewer people have an FFB5

Even fewer people have an MFB5

Very few people have an FMB5

Very few people have an MMB5

and so on.

He can’t run out of names for his first four sons, is likely to easily name his first twelve sons, may have to skip some slots but still pretty certain to be able to name sons thirteen through sixteen, then the source might start petering out for sons seventeen through twenty, and he will have to outsource the naming if he ever has twenty-one or more sons.

(Tip: don’t have that many sons!)

.......... .......... .......... .......... ..........

Now let’s look at a man coming up with second individual names for his daughters.

He’ll look at the second individual names of his parents’ mothers and sisters.

He’ll take his parents in the order M, F, M, F, M, F, M, F, ... repeating as often as necessary.

Everybody has an MM

Everybody has an FM

Almost everybody has an MZ1

Almost everybody has an FZ1

Almost everybody has an MZ2

Almost everybody has an FZ2

About 50% of everybody has an MZ3

Almost everybody has an FZ3

Very few people have an MZ4

About 50% of everybody has an FZ4

Even fewer people have an MZ5

Very few people have an FZ5

and so on.

He can’t run out of names for his first two daughters and is unlikely to run out of names for his first six daughters.

For his seventh daughter, if he has one, he might name her after her FZ3 if he has no MZ3.

But he’s likely to have a supply of names ready for his first eight daughters, and a good shot at being able to name his first nine after his own grandmothers and aunts.

.......... .......... ............ .......... ..........

Similar considerations apply when coming up with first individual names for a woman’s daughters, or second individual names for a woman’s sons.

.......... .......... .......... .......... ..........

One reason the later-born the child being named is and the later-born the parent doing the naming is, the likelier the namer is to choose an out-of-order lineal or collateral ancestor of the appropriate sex and generation to make the child a namesake of, is that the reason for using those names as sources, is to keep them represented by living members of the naming parent’s branch of their family.

The later-born the namer is, the likelier it is that the names earlier in the rotation are already multiply represented in the to-be-named child’s generation of the family.

The naming parent, and their family, may prefer they name the child as the namesake of someone who has died, or who as yet has no namesake, or only one namesake; especially if they’ve died with no namesake, or died with only one namesake.

That really makes it sound like the later-born the namer is, the less likely they are to comply to the earlier rules. Like a third-born parent might not comply to the rules for naming their firstborn but likely would comply while naming their later offspring; and a fourth-born namer might not comply for either their firstborn or their second born but might comply while naming those children born later; and so on.

Maybe I should have set it up that way.

But I didn’t.

Maybe I’ll have to revise this feature.

But it’s after 11:00PM here now.

So I’ll sleep on it first.

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Suppose a man has two sons: they’ll be either full brothers, or agnate half brothers, to each other.

Now suppose each of those two sons also has two sons; the least closely related they can be, all having the same FF, is parallel cousins.

Suppose each of those four parallel cousins has two sons. This third filial generation will all be second-cousins, at least, to each other. They’ll all have the same FFF.

Now suppose each of those eight men has a son.

The men in the third filial generation are all supposed to give their own S1s the same first individual name that first guy — the shared FFF of the third filial generation — had.

What if they don’t all do it?

The S1’s S1’s S1 will do it for sure, let’s say.

And the S1 S1 S2 will do it;

And the S1 S2 S1 ;

And the S2 S1 S1.

But if so the original guy will now have four different namesakes already among the sons of the third filial generation; that is, among his SSSSs, the fourth filial generation.

What if the

S1 S2 S2 and the

S2 S1 S2 and the

S2 S2 S1 and the

S2 S2 S2

don’t name their own S1s after the original guy?

In my estimation his name isn’t likely to die out.

....

Or what if a man has two sons,

each of whom has two daughters,

each of whom has two sons,

each of whom has a second son?

The man’s S1’s D1’s S1,

His S1’s D1’s S2,

His S1’s D2’s S1,

His S1’s D2’s S2,

His S2’s D1’s S1,

His S2’s D1’s S2,

His S2’s D2’s S1, and

His S2’s D2’s S2,

Are all expected to name their S2’s after their shared MFF, the original guy.

I imagine the S1D1S1 definitely will do so.

Definitely at least one of, and probably at least two of, and frequently all three of, the

S1D1S2

S1D2S1

S2D1S1

Will also name their own S2 after their shared MFF (the original guy).

But then what need is there for all four, or even any three or any two, of

S1D2S2

S2D1S2

S2D2S1

or

S2D2S2

to do so?

....

Still looking at the first individual names of men’s sons.

Suppose the founding father has two daughters D1 and D2;

And each such daughter has two sons D1S1, D1S2, D2S1, and D2S2, has two sons;

And each such son DxSySz has a third son.

Each of the first man’s DSS is expected to name their own S3 after their joint FMF, the original guy.

Imagine D1S1S1 does so, faithfully.

And so do D1S1S2, and D1S2S1, and D2S1S1.

If all four of those people managed to have a third son and name him as tradition requires, then

D1S2S2, and D2S1S2, and D2S2S1, and especially D2S2S2, might not see the need to follow through with the naming system for their own third sons.

.....

Lastly suppose the founding father had two daughters, D1 and D2,

each of whom had two daughters, so the second filial generation were

D1D1 and D1D2 and D2D1 and D2D2;

and each of those granddaughters had two sons, so the third filial generation contains at least the GGrandsons

D1D1S1

D1D1S2 and D1D2S1 and D2D1S1

D1D2S2 and D2D1S2 and D2D2S1

D2D2S2

I think only about half of them will have fourth sons at all.

Each of them who does have an S4, will be expected (if they follow the rules) to name him after their shared MMF, who is that original guy.

But once two of them have done so, would the remainder feel obligated to continue the pattern?

Or if three of them have done so, would the rest feel even less obligation?

.....

In times and places when people want lots of children, most people would have three sons, most people would have three daughters, about half would have a fourth son, and about half would have a fourth daughter.

chiarizio

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Let’s look now at men giving their daughters their second individual names.

Suppose a woman has three daughters, D1 and D2 and D3;

And each of those daughters has three sons, giving the original woman a second filial generation containing at least these nine grandsons,

D1S1 D1S2 D1S3

D2S1 D2S2 D2S3

D3S1 D3S2 D3S3

Now also suppose each of those grandsons has a first daughter.

According to the formula they’re all supposed to name their first daughter after the original woman, their shared MM.

Suppose all the sons of D1 do that.

That is D1S1, D1S2, and D1S3, each name their own D1 after their MM.

Suppose also each daughter’s first son does that;

That is each of D1S1, D2S1, and D3S1, name their own D1 after their shared MM.

Then she will have five living namesakes for her second individual name in the the third filial generation.

The other four sons in the second filial generation — namely D2S2 and D2S3 and D3S2 and D3S3 — may feel less of an obligation to continue that pattern, and instead feel more of an obligation to honor and preserve the names and memories of fir instance their FZ1 or MZ2 or so on.

..... ..... ..... ..... .....

Something like that might also happen when the men name their D2s with their second individual names.

Suppose a woman has (at least) three sons, S1 and S2 and S3, each of whom has (at least) three sons, so she has in the second filial generation at least three grandsons denoted here SxSy where each of x and y varies from 1 to 3.

Now suppose each of those grandsons has a second daughter.

That gives the woman nine more greatgranddaughters, SxSyD2; if all her grandsons stick faithfully to the formula those greatgranddaughters will all share their second individual name with her.

Suppose all three sons of her first sons do so; she’ll have at least the following three living namesakes, then; S1SyD2 where y runs from 1 through to 3.

Suppose also all three eldest sons of her sons do so; then each SxS1D2 where x runs from 1 to 3, will also be her namesake.

So those five of these grandsons will have each given her, their shared FM, a namesake greatgranddaughter, namely their own respective D2s.

So I think her SxSy grandsons, where each of x and y runs from 2 to 3, might think about naming their D2s after their MZ2 or FZ1 or some other aunt, instead of their FM.

..... ..... ..... ..... .....

Again suppose a woman has an oldest sister, her Z1, and also has three sons, her S1 and her S2 and her S3.

And suppose each one of her sons has a third daughter, D3.

If they all follow the pattern her sons should name their D3s after her Z1, their shared MZ1.

But if she is her own mother’s D1 or her own father’s D1 we might expect all her sons to do say.

And even if she is the second or later daughter of each of her parents, perhaps we would ought to expect that her S1 will stick faithfully to the pattern.

But her S2 and S3 might feel they should name their D2s after their FZ1s or their MZ2s instead.

..... ..... ..... ..... .....

If a man who has a sister has three sons each of whom has a fourth daughter, then the pattern says each of those sons should give their D4 the same second individual name their shared FZ1 had.

If he’s a first son of either of his parents perhaps all three of his sons will do so.

OTOH even if he is a second or third or later son of each of his parents, his own S1 may be expected to honor the pattern. Otherwise his own second and third sons might feel they should honor the memory of their MZ2 or FZ2 instead.

chiarizio

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All of these customs grew up when people could expect to have seven children.

Everyone could expect to have three sons and about half of them would have a fourth son:

everyone could expect to have three daughters and about half of them would have a fourth daughter.

..... ..... ..... ..... .....

So what would be the math about a man’s DDSes’ naming their own S4s after him, that is, giving them his first individual name as the S4’s own first individual name?

.... .... .... ....

Assuming nobody has a fifth daughter nor a fifth son, and everybody has at least three daughters and at least three sons, and everybody has a 50% chance of having a fourth daughter or a fourth son:

There are 4*4*4=64 kinds of DDS greatgrandsons a man might have.

We’ll look at 27=3*3*3 of them as guaranteed;

DxDySz for each of x and y and z varying independently from 1 to 3 inclusive.

Another 27 = 3*3*1 + 3*1*3 + 1*3*3 have each an independent 50% chance of existing;

Nine DxDyS4

Nine DxD4Sy

And nine D4SxSy

where each of x and y varies independently from 1 to 3 inclusive.

We can assume he has an average of 13.5 of those.

Another nine each have a 25% chance of existing;

DxD4S4 and D4DxS4 and D4D4Sx where x varies from 1 to 3 inclusive.

He can expect to have 2.25 of these.

Lastly he has only a 12.5% chance of having a D4D4S4. I think I might safely ignore that one?

.... .... .... ....

Now each of those DDSes, if they exist, has only a 50% chance of having an S4 of their own to make a namesake for their MMF (the original guy), by giving them the same first individual name he had/has.

So there’s a 50% chance for each of his 27 DxDySz where {x, y, z} is a subset of {1, 2, 3} to have an S4 to think of naming after him,

and a 25% chance for each of his DxDyS4s or DxD4Sys or D4DxSys where {x, y} is a subset of {1, 2, 3} to both exist and have an S4 to name after him,

and a 12.5% chance for his DxD4S4 and his D4DxS4 and his D4D4Sx where 1<=x<=3 to both exist and have an S4 to name after him.

So I think I’ll ignore his DxD4S4 and D4DxS4 and D4D4Sx too.

... ... ...

Just letting x and y and z vary independently from 1 to 2,

and just looking at his

DxDySz and DxDyS3 and DxD3Sy and D3DxSy, that’s twenty (2*2*2=8, 2*2*1 + 2*1*2 +1*2*2 = 12, 8+12 = 20) DDSes who each have a 50% chance of having an S4.

If half of them do, there’ll be ten potential namesakes.

If half of these DDSes commit to following the pattern provided they actually have a fourth son, he’ll be guaranteed five namesakes.

Suppose all of the eight DxDySz where each of {x, y, z} varies between 1 and 2 makes such a commitment; and each of the twelve [DxDyS3 and DxD3Sy and D3SxSy for each of x and y varying independently from 1 to 2 inclusive] has, independently, one chance in six of abiding by the pattern on condition they ever actually have an S4, then he could on average expect about five namesakes.

____________________. ____________________. ____________________.

But how many does he actually need?

I don’t know.

Technically I think he needs only at least two.

I think, though, that depending on cultural reasons, most families would prefer he has at least three, and some would prefer he has at least four. — drawing probably-unreliable parallels to natcultures.

I can’t see — at the moment — why his family would want to guarantee he has at least five namesakes, at the expense of not using “namesake slots” to “rescue” the first individual names of granduncles of the fathers of fourth sons.

__________. __________. __________. __________. __________.

... ... ...

But suppose the D1D1Sx and D1DxS1 and DxD1S1, where x varies from 1 to 4 inclusive, commit conditionally to following the pattern, conditional on (actually existing and) actually having a fourth son.

D1D1S1

D1D1S2 D1D1S3

D1D2S1 D1D3S1

D2D1S1 D3D1S1

would each provide 50% of an S4 namesake;

and D1D1S4 and D1D4S1 and D4D1S1 would each provide 25% of a namesake.

So he could expect (7*0.5 + 3*0.25 = 3.5 + 0.75 = 4.25) namesakes on average this way.

... ... ...

Anyway, to sort-of guarantee he has on average at least two namesake DDSS4s, we’d need that all four of

D1D1S1, D1D1S2, D1D2S1, and D2S1S1, commit to following the namesake formula, conditional on actually having an S4.

To make the average number of namesake DDSS4s be at least three, we could make that each of D1D1S3 and D1D3S1 and D3S1S1 has at least a 66.6667% chance of following the tradition;

Or that each of D1D2S2 and D2D1S2 and D2D2S1 has at least a 66.6667% chance of following the tradition.

If both of those last two probabilities hold he’ll average four DDSS4 namesakes.

.... .... .... ....

chiarizio

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In later Reptigan, or even later Adpihi when the population is close to the planet’s and ecology’s and economy’s carrying capacity, people can count on an average of >2 but <3 children, including >1 but <2 sons on average, and >1 but <2 daughters on average.

I’m just going to assume, for no better reason than that I have to assume something, that

12.5% of people have three daughters and no sons

12,5% of people have three sons and no daughters

37.5% of people have two daughters and one son, and

37.5% of people have two sons and no daughters.

So to simplify, a guy will wind up with

100% of a S1S1S1

50% of a S1S1S2

50% of a S1S2S1

50% of a S2S1S1

25% of a S1S2S2

25% of a S2S1S2

25% of a S2S2S1

and 12.5% of a S2S2S2.

If all eight commit (conditional on actually existing and actually having an S1) on giving him, their joint FFF, an SSSS1 namesake, he can expect 3.375 such namesakes.

If just the first four make such a commitment he can still expect 2.5 such namesakes, barring the chance that any of his sons or any of his grandsons have only daughters.

Suppose S1S1S1s always follow the rule; and each of S1S1S2, S1S2S1, and S2S1S1, follow it two times out of three. He can then expect, on average, two such namesakes.

......... ......... ......... ......... ......... ......... ......... .........

Now consider SDSes who are considering naming SDSS2s after their joint MFF.

An S1D1S1 will contribute 0.5 such a namesake;

Each of S1D1S2, S1D2S1, and S2D1S1, will contribute 0.25 such a namesake;

Each of S1D2S2, S2D1S2, and S2D2S1, will contribute 0.125 such a namesake;

And S2D2S2 will contribute 0.0625 such a namesake;

In the event that they each commit to following the rule provided they can.

On average, he could expect to have

1*0.5 + 3*0.25 + 3*0.125 + 1*0.0625 =

0.5 + 0.75 + 0.375 + 0.0625 =

1.6875 SDSS2 namesakes whom his SDSs name after him, their joint MFF.

So, no way to make the average minimum number be two or more.

Unless he has a third son, or one or more of his sons has a third daughter, or one or more of his SD granddaughters has a third son; or more than one of those things happens.

....

...

.. .. .. .. .. .. .. .. .. .. .. ..

Suppose we look at a man’s DSS greatgrandsons and consider them considering naming their S3s after him. (He’s their FMF.)

He’ll have

One D1S1S1

0.5 each of a D1S1S2, D1S2S1, D2S1S1

0.25 each of a D1S2S2, D2S1S2, D2S2S1

0.125 of a D2S2S2

Each of whom can contribute 0.125 of an S3.

(1 + 3*0.5 + 3*0.25 + 0.125)*0.125 =

(1 + 1.5 + 0.75 + 0.125)*0.125 =

3.375*0.125 = 0.421875

which isn’t even 0.5.

He has less than a 50% chance of having a DSSS3 namesake at all.

.....

**====. =====. =====. =====. =====.**

So I guess I’ll say that S1S1S1s will always be devout about naming their own S1s after their FFF, but S1S1S2 and S1S2S1 and S2S1S1 will follow that rule about two times out of three, and other SSSes will name their S1s after different greatgrandfathers and granduncles.

However all DSSes will be devout about naming their S2s after their MFFs.

And all SDSes will be devout about naming their S3, if they have one, after their FMF, though that won’t come up much over 40% of the time.

......

All only on planets with controlled population, during times in which population is controlled that way.

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I’ll consider the custom of mothers naming their sons after the fathers and brothers of their parents — that is, after the grandfathers and uncles of the mothers — when giving their sons their second individual names.

Consider a group of women who are parallel (half-)cousines because they all share the same FF.

But I’ll also consider the same situation starting with that shared grandfather.

First I’ll consider this custom under the circumstances in which people usually have seven children, including at least three sons and at least three daughters, and about 50% of people have a fourth son and about 50% have instead a fourth daughter.

(Later I’ll consider it under the circumstances wherein most people have three children, including at least one son and at least one daughter, and 50% of the time a second son and 50% of the time a second daughter instead.)

So suppose some guy is wondering about how many SDS1s are going to be named after him by his various SD granddaughters who will give them the same second individual name he, their FF, has.

He has an S1 and an S2 and an S3, and half the time he also has an S4.

Each of them has a D1 and a D2 and a D3, and half the time also a D4.

So in effect he has

S1D1 S1D2 S1D3

S2D1 S2D2 S2D3

S3D1 S3D2 S3D3

“for sure”. (Not really, probably. I’m oversimplifying the stats for illustrational or exemplificational purposes.)

And he has half of

S4D1 S4D2 S4D3

and half of

S1D4 S2D4 S3D4.

(And a quarter of S4D4, but I’ll ignore her.)

If all 12 (9=3*3 + 3=(3+3)*0.5) of those SDs follow the customs he’ll have a dozen SDS1 namesake grandsons.

Suppose we say that all S1D1s follow the custom provided they can — that is, provided they get born, grow up, marry, and have an S1.

But S1D2s and S2D1s follow the custom only usually, that is, over 50% of the time, provided they can.

For instance, S1D2 will follow the custom if, upon the birth of her own S1, none of her (half-)sisters (her fathers other daughters) nor parallel (half-)cousins (FBDs) have yet named an S1 after their FF.

Or if at most one of them have.

Similarly S2D1 will follow the custom if, by the time her own S1 is born, none, or at most one, of her father’s other daughters, or her father’s (full- or agnate half-)brothers’ daughters, have named an S1 after their FF.

That will, I assume, be true more than 50% of the time, depending on whether S1D2 or S2D1 is older than the other.

Also, even when S1D1 is older than S1D2 (which she will obviously be) and older than S2D1 (which she might not be), possibly

S1D2S1 and/or S2D1S1 will be born before S1D1S1 is born.

If both S1D2S1 and S2D1S1 are born before S1D1S1 is born, I expect both S1D2 and S2D1 will follow the custom, and both their first sons will be named after the sons’ mothers’ FF.

I suppose that will happen less often than one time in three, but it seems possible it might happen more often than one time in four?

S1D3 and S2D2 and S3D1 will also follow the custom sometimes; I’m assuming probably less often than one time in three for each of them, though.

Each of them will follow it if, by the time their own S1 is born, fewer than two of the other women who have the same FF, have given their shared FF a namesake SDS1 great-grandson.

In general, S1D3S1 will be born after S1D1S1, but not always; and after S1D2S1, but not always.

In general, S3D1S1 will be born after S1D1S1, but not always; and after S2D1S1, but not always. This sentence is even iffyer—— has more variance —— than the previous sentence, because it’s possible that S3D1 is older than one or the other or both of S2D1 or even than S1D1.

In general, S2D2S1 will be born after S2D1S1, but not always; and after S1D2S1, but not always, especially considering the <50% chance that S2D2 is actually older than S1D2.

So if when S1D3S1 is born, at most one of S1D1S1 and/or S1D2S1 has been born, then S1D3 will follow the custom (probably, depending on what’s going on with her FBD cousins).

And if when S3D1S1 is born, at most one of S1D1S1 and/or S2D1S1 has been born, then S3D1 will follow the custom (probably, depending on what’s going on with the rest of her FFSD cousins and sisters).

And if when S2D2S1 is born, at most one of S1D1S1 and/or S1D2S1 and/or S2D1S1 has been born, then S2D2 will follow the custom (probably).

I expect that’ll be less often than three times out of four for S1D3 and S3D1, and less often than half the time for S2D2.

Even if S1D1 and S1D2 and S2D1 always follow the custom.

.....

S2D3 and S3D2 may follow the custom sometimes.

Suppose S2D3 follows the custom whenever at most one of S1D1, S1D2, S1D3, S2D1, and S2D2, has already followed it; and that’s true about 6 times out of 32 (about 18.75% of the time), or less. So maybe S2D3 follows the custom about that often.

Similarly suppose S3D2 follows the custom whenever at most one of S1D1, S1D2, S2D1, S2D2, and S3D1 has already followed it, and that’s 18.75% of the time or less.

So I’ll say;

S1D1 and S1D2 and S2D1 always follow the custom;

Each of S1D3 and S3D1 follows the custom 75% of the time;

S2D2 follows the custom 50% of the time;

Each of S2D3 and S3D2 follows the custom 18.75% of the time (3/16 of the time);

And S3D3 follows the custom 3.515625% (9/256) of the time. (Let’s round that off to 3.516% of the time). In other words, rather rarely.

S1D4, S2D4, S3D4, S4D1, S4D2, and S4D3, also have their own odds of following the custom, but those are conditional on their already-problematic existence.

Say each of S1D4 and S4D1 follow the custom half the time — if they exist;

Each of S2D4 and S4D2 follow the custom 6.25% (one time in sixteen) — if they exist;

And each of S3D4 and S4D3 follow the custom 3/512 of the time — 0.5859375% of the time, round that off to 0.6% of the time. If they ever get born themselves, and go on to have first sons.

It might make sense to ignore the granddaughters who will follow the custom less often than one time in eight? Less often than 12.5% of the time?

Or, less often than 25% of the time if the chance that such a granddaughter exists is only 50% or less?

..... ..... ..... ..... ..... ..... ..... ..... ..... .....

Now we might also consider how many DDS2 namesake greatgrandsons a man can expect his DD granddaughters to give him.

If we’re still assuming everyone has exactly seven children and at least three but not more than four daughters and at least three but not more than four sons, the conclusions are similar.

D1D1 and D1D2 and D2D1 will always name their S2s after their MF;

D1D3 and D3D1 will name their S2s after their MF 75% of the time;

D2D2 will name her S2 after her MF 50% of the time;

D1D4 and D4D1 will also name their S2s after their MF 50% of the time, but they thenselves have only a 50% chance of getting born;

D2D3 and D3D2 will name their S2 after their MF 18.75% of the time;

D3D3 will name her S2 after her MF only about 3.52% of the time;

D4D1 and D1D4 will name their S2s after their MF 50% of the time if they themselves get born, but there’s only a 50% chance that they will;

D4D2 and D2D4 will name their S2s after their MF 6.25% of the time, but there’s a 50% chance each of them won’t exist; (so the net contribution of each of them is less than 3.13%, less than that of D3D3, which might be negligible);

And D4D3 and D3D4 will each produce a namesake less than 0.6% of the time, even if they exist, which for each of them is only a 50% chance.

..... ..... ..... ..... .....

There must also be some way to calculate how often each type of BD niece a man has will give him a BDS3 namesake grandnephew.

I’ll have to think that out later.

Similarly, how often each type of ZD niece will give him a ZDS4 namesake grandnephew.

.......... .......... .......... .......... .......... .......... ..........

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For one thing, if a man is not the firstborn son nor the secondborn son, he won’t be anyone’s father’s oldest brother, so none of his BD nieces will name their S3s after him.

But suppose he is the oldest brother of 2.5 of his brothers.

For simplicity I’ll assume all 3.5 men are full brothers.

There’s the man himself — should I call him EGO?

And there’s his oldest younger brother B1;

And a second younger brother B2;

And 50% of the time a third younger brother B3.

For simplicity I’m going to skip B3 for the time being.

Each of these brothers will have an average of 3.5 daughters;

B1D1, B1D2, B1D3,

B2D1, B2D2, B3D3,

50% chance each B1D4 and B2D4 I’ll skip for now,

50% chance B3D1, B3D2, and B3D3 I already said I’d skip,

25% chance B3D4 I might skip even if I included those others I said I’m skipping.

So let’s suppose his B1D1 and his B1D2 and his B2D1 always follow the custom.

(Since his B1 is an S2 for their parents, his B1D1 is an S2D1 and his B1D2 is an S2D2.)

(And since his B2 is an S3 for their parents, his B2D1 is an S3D1.)

So we get that S2D1s and S2D2s and S3D1s always follow this part of the custom, naming their S3s after their FB1s.

Let’s also suppose B1D3s (who are, appositively, I remind the reader and myself, also, S2D3s), follow the custom 75% of the time;

And B2D2s (S3D2s) follow it 50% of the time;

And B2D3s (S3D3s) follow it 18.75% of the time.

.....

Let’s just go ahead and assume S1D1s and S1D2s and S1D3s behave like S2D1s and S2D2s and S2D3s.

So S1D1s and S1D2s follow this rule always, and S1D3s follow it 75% of the time.

.......... .......... .......... .......... ..........

What about when EGO is wondering how many of his various ZD nieces will give him a ZDS4 namesake as their MB1?

In the first place, unless he’s the S1 of one of their parents, he won’t be any woman’s B1.

To save my head from aching, let’s assume he is the full brother of three full sisters, namely Z1 and Z2 and Z3. (There’s also a 50% chance he has a Z4, but I said I’d save myself from a headache.)

Let’s assume each of those sisters has three daughters; then there are nine ZD nieces to consider, namely

Z1D1 Z1D2 Z1D3

Z2D1 Z2D2 Z2D3

Z3D1 Z3D2 Z3D3

(There’s also a 50% chance for each sister to have a D4, but ... headache ...)

Now each of those nieces has only a 50% chance of having an S4 fourth son.

So let Z1D1 and Z1D2 and Z2D1 always follow the custom.

Let Z1D3 and Z3D1 follow it 93.75% (15/16) of the time.

Let Z2D2 follow it 84.375% (27/32) of the time.

Let Z2D3 and Z3D2 follow it 63.28125% (81/128) of the time (round that up to 63.2813% or 63.29% or 63.3%)

And let Z3D3 follow it 36.71% of the time ((3^8 + 8*(3^7))/(4^8)).

..... ..... ..... ..... .....

_____. _____. _____. _____. _____.

The chance of a second-born son having any BD nieces giving him a namesake BDS5 grandnephew because he’s their FB2 uncle is negligible.

Or, if it’s not negligible, I am at least neglecting it anyway, up ‘til now.

Maybe one of his BD nieces will name their S1 or S3 after him, or one of his ZD nieces will name her S2 or S4 after him.

Or, heck, maybe a BD niece will name an S2 or S4, or a ZD niece will name an S1 or S3, after him.

If he has enough nieces who have enough sons, there might be several who break the pattern, and that might be the way they break it.

**====. =====. =====. =====. =====. =====. =====. =====.**

When everyone has three children, including at least one but not more than two sons and at least one but not more than two daughters, the stats will be affected somewhat.

chiarizio

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chiarizio

When everyone has three children — 50% having two sons and one daughter, and 50% having two daughters and one son —

A man (EGO) will have

100% S1D1

50% S1D2

50% S2D1

25% S2D2

And each of those SD granddaughters of his will have an S1 whom they can make be an SDS1 namesake greatgrandson of their FF by giving them his second individual name to be the S1’s own second name.

If we assume S1D1 and S1D2 and S2D1 all do this, that gives him an average of two such namesakes.

If S2D2 exists then S2D1 also exists, but maybe S1D2 doesn’t.

Assuming S2D2 exists, what are the odds that by the time S2D2S1 is born, two or more of

S1D1S1 and/or S2D1S1 and or S1D2S1 have already been born?

Let’s say that the odds S1D1S1 has already been born are 50%;

Likewise the odds S2D1S1 has already been born are 50%;

And the odds S1D2S1 has already been born are 25%.

Then the chance two, or all three, have already been born, are

0.5*0.5*0.25 + 0.5*0.5*0.25 + 0.5*0.5*0.25 + 0.5*0.5*0.75

**0.5*0.5*(0.25 + 0.25 + 0.25 + 0.75)**

**0.25*1.5 = 0.375**

So the odds that only one, or none at all, have been born, is 62.5%.

Suppose S2D2 — in the 25% of the cases where she exists at all — follows the rule 62.5% of the time, and names her S1 after her FF.

Second-born sons and second-born daughters are more faithful to this tradition under these circumstances.

...... ...... ...... ...... ...... ......

Something like the same sort of thing happens when considering EGO’s DD granddaughters naming their S2s after him, their MF; except now there’s only a 50% chance, for each DD, that she’ll even ever have an S2.

So EGO will have

50% D1D1S2

25% D1D2S2

25% D2D1S2

12.5% D2D2S2

For an average of 1.125 DDS2 greatgrandsons. Even if all of his DDSs abide by the tradition he probably won’t have two namesake DDS2s out of it.

............

For BD nieces to give him BDS3 namesake grandnephews because he’s their FB1, we need to consider:

50% of men won’t have a brother at all.

The other 50% will have exactly one brother, each of whom will be the other’s B1.

This brother will have at least one daughter, BD1, and 50% of the time will have a second daughter, BD2.

But neither niece is likely to have an S3 to name after him.

The odds are about 12.5% either of them will have an S3.

So assuming he has a brother at all, he has a 12.5% chance of having a BD1S3, and a 6.25% chance of having a BD2S3.

So on average, he can expect (conditional on having a brother), 0.1875 (3/16) of a BDS3 namesake.

.....

For ZD nieces giving him ZDS4 grandnephew namesakes as the nieces’ MB1, in the first place he needs to be the firstborn son; in the second place he has only a 50% chance of having a second sister; and in the third place none of his nieces will have an S4.

Furthermore every niece who is an S1D1 or an S1D2 or an S2D1, or a D1D1 or a D1D2 or a D2D1, will already have named their S1 and their S2 and their S3 after someone else.

If he has a niece who is both an S2D2 and a D2D2, and she has a son she hasn’t already named after someone else, she may name one of those sons after him; but I think it might be impossible, under the assumptions given so far, for such a niece to have such a son.

His name may nevertheless be rescued by some niece who is a daughter of his second brother (he has a 12.5% chance of having a second brother), or is a third daughter of one of his siblings (preferably his sister or one of his sisters).

I have not calculated the odds and at present have no intention of doing so.

..........

The tradition comes up less often in the limited-births situations; but also is more strictly followed in the limited-births situations.

Essentially the only significant license to deviate from the tradition comes when an S2D2 doesn’t name her S1 after her FF, which she won’t about 37.5% the time (if I remember correctly), although there’s only a 25% chance that EGO has such an SD granddaughter.

chiarizio

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chiarizio

The posts I put here between 2021/02/05 and today (2021/02/11), might have better been put in the

“Names Names Names ...” thread started by Lyndon (in Worldbuilding).

chiarizio