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  • Ava & Emmett's Grandparents 1st - 9th
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1.  My goal is to try to answer the following question (at least to the correct magnitude).
Question:
  How many grandparents does my 5 year old Granddaughter  & 2 year old Grandson have in the history of the world?

   At first I thought this was going to be an easy problem because I had already shown that they have 4 Grandparents, 8 Great Grandparents, 16 Great Great Grandparents, 32 Great Great Great Grandparents, and 64 Great Great Great Great Grandparents because I had already found the names of over half of them.
So if my grandkids parents are generation 1 and my wife & myself generation 2 then if n = the number of generations, the total number of grandparents in a given generation would be 2 ^ (n) as generation 2 has 2 ^ 2 or 4 grandparents and generation 3 has 2 ^ 3 or 8 grandparents, etc.  So, all you have to do is figure out how many generations have occurred and take 2 to that power.
Estimates put the time since the great flood (scientists agree that there was a great flood) is either 4,364 years ago minimum or 5,516 years ago maximum.  Estimates put a generation to be a minimum of 30 years and a maximum of 35 years.  This makes the total number of generations since Noah's Ark and the great flood to be 4,364 yrs/35 yrs/generation = 124.6857 or 125 minimum and 5516 yrs/30 yrs/generation = 183.86666666 or 184 generations maximum.
Raising 2 ^ 125 or 2 ^ 184 are very large numbers.  And raising 2 to the 36.65490954 power is the total number of humans that have ever lived on planet Earth.  Obviously, our grandkids cannot have 2 raised to the 125 power (let alone the 184 power of 2) grandparents.  Not even close!!!

​After much thought, I resorted to the internet for ideas.   The cool things I discovered is this is a very challenging math problem AND every site I studied came down to mathematically the Bible must have it correct as in Darwins scientific time frame, we mathematically cannot have as little population as we do.

Example:  Here's a quote from the website http://www.ldolphin.org/popul.html 
"It may be claimed that none of these calculations really prove anything, since no one really has any way of knowing exactly what birth and death rates and what population figures existed in prehistoric times. This is quite true, of course, but the known facts of population growth do fit the Biblical chronology very well and they do not fit the assumed evolutionary chronology at all.

Scientists work in terms of "models" and try to evaluate each proposed model of a particular process in terms of the "degree of fit" of the known data into that model. On this basis, we are abundantly justified in concluding that the creationist model with its brief chronology fits the actual known data of population statistics far better than does the million-year evolutionary model. In terms of scientifically-accepted standards of evaluation, this can only mean that, on this issue at least, creationism is much more "scientific" than evolutionism.

It is possible, of course, to specify changing growth rates of family sizes on any arbitrary basis one chooses, in order to make the results come out to any predetermined value. This is what evolutionists have to do in order to account for such a small present world population after such a long imagined evolutionary history. Nevertheless, the simplest and most straightforward population models, based upon all the real population statistics that are available, clearly correlate with the Biblical chronology as the true framework of human history."

Occam's Razor is a line of reasoning that says the simplest answer is often correct.

Plan A:  Work the problem from both ends and hopefully meet in the middle.

 My thought is to graph y = 2 ^ n on the same graph as the equation that gives the population of planet Earth going back in history and see where the two graphs meet.  I propose that the year the two graphs meet in is where the number of grandparents go from exponentially increasing to exponentially decreasing.

I am already hypothesing that it will not be as far back in time as one would think.

click here for graphs of Year vs Population of  World     AND   Year vs Total Grandpartents (infant born 2016-2017)
​
​click here to see the data for the graphs that I combined into the one graph above

​
analyzing the above graphs (click on prior two lines to see graphs)

NOTE:
​That in April of 1058 AD (2017 - 1058 = 959 years ago) the number of grandparents Ava & Emmett would have is 300,000,000 grandparents at the same time the population of the world is 300,000,000 people.  That is 300 million grandparents and 300 million living people occupying the world.

Ok, the 300 million grandparents are how many are in the 28.16038726 generation of grandparents that live about 959 years ago and had the child, who had the child, who had child, .... 27 times total who had the four grandparents, the two pair who each had a child that had Ava Joycelyn born to them.  If you add up all the grandparents over the 959 years 568,435,452 would be the total.   The population of the U.S.A on Oct 5, 2017 at 3:52 pm Central Standard Time is 325,069,810 living people.which is about the population of the whole world in 1058 A.D.

Now we have to figure out what happened in that 29th generation the year following 959 years ago because the world began having fewer people whereas the grandparents doubled again.  Another way to say it is, since it takes two (a man and a woman) to give birth to a child, and two pair of people (4 grandparents) to each have a the mentioned man and woman who had the child above; how can the it go from 4 grandparents having only two grandparents having the father & mother of the child?

My first thoughts were:

Genesis 19:30:38 Lot and his two daughters left Aoar and settled in the mountains, for he was afraid to stay in Zoar.  He and his two daughters lived in a cave.  One day the older daughter said to the younger,  "Our father is old, and there is no man around here to give us children -as is the custom all over the earth.  Let's get our father to drink-wine and then sleep with him and preserve our family line though our father."
​This would make the father of the children also the grandchildren and their mothers also their grandmothers so only two grandparents instead of four and one being their mother also.  But that keeps grandparents equal and not declining and would have to be repeated generation after generation and not just once or once in awhile.

Then the Bible said that King David had eight wives and Solomon had 700 wives and 300 concubines.  In Solomon's case then 1000's of the same generation children would still have different mothers but the same father and their children were much more likely to marry first cousins.

Next thought is that I don't think the number of grandparents is exponential at all.  I think it is more like how pipes are laid in a city.  The wider pipes from the source then smaller diameter pipes to different regions then smaller yet to subdivisions then the smallest to the individual households.   Inventions, weather, subdividing of the families when pieces would migrate away from the main group as it became to large to support the group all played a hand in the diameter to the pipe that signifies how the number of grandparents changed from generation to generation.   I the show Naked & Afraid strangers volunteer to be thrown in with a naked stranger of the opposite sex with one item each (like a primitive fire starter, a pot, or a cutting device) and attempt to survive for 21 days and larger groups 40 days.  The point is that the need to survive takes over and how one thinks about the person you have to survive with changes.

For Noah's three sons and their wives to start out after the great flood (and Noah & his wife) there had to be reproduction going on within those few individuals.  That being the norm could have continued for many generations.  When family groups got larger and subdivided to new lands this norm would be taken with them so the diameter of the pipe would increase some but again not be exponential.

You know the above over half billion grandparents in the last 900 and some years, I don't think happened that way at all.  My moms generation had very large families living in very small shelters.  The girls and mom & dad had a long bedroom on one side of the main home and the boys had one long bedroom on the other side if you were lucky enough to have a home to split them up this way.  My folks did not have an indoor toilet until my middle sister was born.  Hunting, gardening & canning, fishing, collecting nuts, mushrooms, berries off the land was required to survive.  This is only two and three generations back from Ava (our infant granddaughter).

My next plan is to look at the graph of the population of the world throughout history and draw a new graph of how the number of grandparents flucuated over time and not the exponential graph of grandparents doubling each generation.
​
​Here's an interesting website that may help:  https://waitbutwhy.com/2014/01/your-family-past-present-and-future.html

Tim Urban, in Jan 2014, starts by saying to go visit the oldest living relative and asked about the family that you never got to know.  His  fathers mother does share stories about family he never knew that would have been lost forever in the mind of this oldest relative if he hadn't taken the time to listen.  Here's his diagram of what it was all about having just visited that one time:

Picture
Tim Urban finishes this thought with:  "​The widest point of the Ancestor Cone happens for most of us around 1200AD,3 when our family tree is near the total world population at the time. From that point on, pedigree collapse becomes a stronger factor than the normal upward x2 multiplier, and the tree converges inwards."
Later Mr. Urban gets to what I need to share here.  Here is a great image of how grandparents appear to exponentially grow each generation that he shares:​​
Picture
First here's Tim's image of the dilema that is simpler than my graphs above as he used a logarithmic scale that makes exponential curves straight lines.
Picture

Ancestry of Ava

Ava is half of what daddy's ancestry is AND half of what mommy's ancestry is.
but we need to break these halves each in two pieces
Ava is 1/4 Grandpa S and 1/4 Grandma S AND 1/4 Grandpa K and 1/4 Grandma K
but lets break these up just one more time
Ava is 1/8 Fredrick C. Savage and 1/8 Janet Burleigh AND 1/8 LeRoy Good and 1/8 Marie (?) Good
AND 1/8 Leo F Konichek and 1/8 Dorothy L Clark AND 1/8 John Jancik and 1/8 Joycelyn Ann Wald
What Year Did Each Branch Immigrate Over
OK, it is over a year since I worked on the question of how many grandparents Ava & Emmett have total in the history of the mankind and back a year ago I never really came up with a magnitude even so today on 8/17/2018 I'll take my first magnitude estimate and why and narrow in on it more in the future when more data & thoughts on this question come to light.
​If we do Tim Urban's diamond shape above as how Ava & Emmett's grandparents evolved then from my graphs meeting in April of 1058 AD Ava would have 300,000,000 grandparents till the diamond is at it's widest and another 300,000,000 grandparents if the diamond shape went back to one set of parents that started it all for all the existing population on the planet today.   This makes 300,000,000 plus 300,000,000 or 600,000,000 thus 6 X 10^8 grandparents in the known history of mankind.   Did you notice how half way to max the magnitude was eighth and the theory that this may be just half of the total made doubling the amount still the same magnitude of eighth magnitude interesting thus showing me that estimating the magnitude of Ava's total number of grandparents is probably as accurate as one can get and is probably a really great estimate within a magnitude or two magnitudes of accuracy.
Thus Ava (and every child on planet Earth within a decade or two of 2017) has had a total of less than a billion grandparents in the history of mankind should be safe to say as a maximum number.
​Now for a minimum number magnitude estimate:
If I just take the 128+64+32+16+8+4 = 252 grandparents above over the six generations which is the past about 200 years fo grandparents and go another 600 years back or 18 more generations back giving 2 x 2 ^ 19 or 1,048,576 since Tim's 1200 AD at the widest part of the diamond then doubling that or 2,097,152 grandparents since the time of Jesus Christ then use the Bible's genealogy to finish up the magnitude estimate.
The Book of Mathew states there were 14 generations in all from Abraham to David, 14 from David to the Exile to Babylon, and14 from the exile to the Messiah.  Note above from the shape of the graph that the diamond does not yet converge to a point but pretty much stays like the 256 grandparents each generation thus 256 X 14 X 3 = 10,752 grandparents which we'll round up to 90,000 grandparents which is still a 4th magnitude number.   
Thus from Abraham to Ava there are a minimum of 2,097,152 plus 90,000 or about 3,000,000.   Now we only have from Adam to Abraham.   
In Luke Chapter 3 it gives 10 generations from Adam to Noah and his sons thus if we double grandparents from Adam till the flood it would give 2,048 grandparents more grandparents.
Now we just have from the flood to Abraham which again in Luke Chapter 3 gives 10 more generations starting with one of Noah's sons to Abraham but one would have to take these 10 generations and add the 3 X 14 generations to it for a total of 52 generations from Noah's son to Jesus Christ which would be much less than 52 X 256 grandparents per generation gives 13,312 grandparents from Noah to Christ (round up to 20,000 grandparents)

Finally, taking the 2,048 grandparents from Adam to Noah and another less than 20,000 grandparents from Noah to Christ and another 2,097,152 grandparents from Christ to Ava makes around 2,119,200 grandparents for Ava in the history of mankind.

Thus the number of grandparents for Ava in the history of the human race is between 2,097,152 grandparents which is a magnitude of six and less than a billion which is a magnitude of eight.

From all the above data my final estimation is much closer to the 2 million than the 100 million because of how inbreeding within a family was much more the rule before the 17th century for the survival of mankind.   Ava's total grandparents would certainly be in the sixth magnitude or less than 10 million grandparents total.
OK, I do not agree with the above diagram at all.  I believe that marriages between 2nd cousins or closer was much more common just three or more generations ago counting generations from a newborn in 2015-2017.  Here is a great article from the Discovery magazine that may support this:  click here

Here are three quotes from the above Discovery magazine article:
1).  "  But the nature of cousin marriage is far more surprising than recent publicity has suggested. A closer look reveals that moderate inbreeding has always been the rule, not the exception, for humans. Inbreeding is also commonplace in the natural world, and contrary to our expectations, some biologists argue that this can be a very good thing. It depends in part on the degree of inbreeding. "

2).  "  The traditional view of human inbreeding was that we did it, in essence, because we could not get the car on Saturday night. Until the past century, families tended to remain in the same area for generations, and men typically went courting no more than about five miles from home—the distance they could walk out and back on their day off from work. As a result, according to Robin Fox, a professor of anthropology at Rutgers University, it's likely that 80 percent of all marriages in history have been between second cousins or closer."

3).  "   Some families have traditionally chosen inbreeding as the best strategy for success because it offers at least three highly practical benefits. First, such marriages make it likelier that a shared set of cultural values will pass down intact to the children. 

   Second, cousin marriages make it more likely that spouses will be compatible, particularly in an alien environment. Such marriages may be even more attractive for Pakistanis in Bradford, England, than back home in Kashmir. Intermarriage decreases the divorce rate and enhances the independence of wives, who retain the support of familiar friends and relatives. Among the 19th-century du Ponts, for instance, women had an equal vote with men in family meetings.
   Finally, marrying cousins minimizes the need to break up family wealth from one generation to the next. The rich have frequently chosen inbreeding as a means to keep estates intact and consolidate power.
   Moderate inbreeding may also produce biological benefits. Contrary to lore, cousin marriages may do even better than ordinary marriages by the standard Darwinian measure of success, which is reproduction. A 1960 study of first-cousin marriages in 19th-century England done by C. D. Darlington, a geneticist at Oxford University, found that inbred couples produced twice as many great-grandchildren as did their outbred counterparts. 
   Consider, for example, the marriage of Albert and Bettina Rothschild. Their children were descended from a genetic pool of just 24 people (beginning with family founders Mayer Amschel and Gutle Rothschild), and more than three-fifths of them were born Rothschilds. In a family that had not inbred, the same children would have 38 ancestors. Because of inbreeding, they were directly descended no fewer than six times each from Mayer and Gutle Rothschild. If our subconscious Darwinian agenda is to get as much of our genome as possible into future generations, then inbreeding clearly provided a genetic benefit for Mayer and Gutle."
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Tim Urban goes onto say:
"Before you wince, absorb this fact: according to Rutgers anthropology professor Robin Fox, 80% of all marriages in history have been between second cousins or closer.1
The reason for this is that for most of human history, people spent most of their lives in the same five mile radius, and the other people in that same area tended to be immediate and extended family. To get away from their extended family when courting, men would have to walk over five miles away, which after a long day of hunting you just don’t feel like doing.
In the Western World, this is largely a phenomenon of the past, but in many parts of the world, this is still a common practice—for example, in most of the Middle East and North Africa, over 50% of today’s marriages are between second cousins or closer.2
So that group of 4,096 people above? A number of those spots are undoubtedly duplicates, meaning the real number of distinct people is likely a bit lower—and for someone a few thousand years ago, the number of 10th generation ancestors they’d have would be a lot lower than 4,096.
Because of pedigree collapse, if you extended your family tree way, way back, it would begin to get smaller, resulting in a diamond shape:"
Click here to see all the work done to figure out your Fredrick C.Savage roots.

Click here to see all the work done to figure out you Janet Burleigh roots.

Click here to see all the work done to figure out your LeRoy Good roots.  Not Enough Data

Click here to see all the work done to figure out your Marie (?) Good roots.   Not Enough Data

Click here to see all the work done to figure out your Leo F Konichek paternal roots.     & materal roots click here.
or click here for more paternal roots a different branch

Click here to see all the work done to figure out your Dorothy L Clark roots paternal.    & materal roots click here.
or for a different branch of materal roots click here

Click here to see all the work done to figure out your John Jancik roots.

Click here to see all the work done to figure out you Joycelyn Ann Jancik roots.
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What Is Ava & Emmett's Heritage

3/8 English from Ava & Emmett's paternal side (Savage, Burleigh) mainly with some from their maternal side also (Clark)
2/8 or a quarter Czech/Bohemian/Slovakia from Ava's maternal side (Jancik, Wald, Konichek,Mezera)
1/8 German from materal side (Wald & some Clark)
1/8 Norweigen/Sweden/Dutch area (Burleigh, Clark, & Wald)
1/8 Native American & European (Good, Deflores color: Mexican according to Maria's birth certificate and Maria's DNA results were 59% Native American, 28% Europe,7% Africa, 4% West Asia)

but mathematically all the heritages submerge into one heritage over a short period of time (a few thousand years) whatever you believe that heritage to be.  But to get to that one heritage the number of heritages possible quickly dwindle to just a few before getting to the one common ancestor.  If one traces the original ancestors from England back you have them coming from France/Germany/Sweden and if you trace their ancestry back further you end up in Italy durning the Roman Empire.   If ancestors came over more recently they were much harder or couldn't be trace back any further.  If ancestors came from England area they were easier to trace back much further.  If one can trace ancestory back a long way (hundreds of years) we are all related to royality as the only reason you can get this far back is that they were important enough in history to keep track of who they were (kings, queens, princes, princesses, saints, patriarchs, rulers).  It was also easier to trace back further if there was a Henry VIII, Henry VII, etc.

It will be cool if someday Ava & Emmett take the DNA test and compares that test with my findings here.  If I am still alive grandchildren of our daughter & son-in-law please let me know the comparison.

1.  [1907 spoke Hungarian]   Ava & Emmett, on your Grandma K's  paternal side:  Her Grandpa Urban Jancik immigrated over to Ellis Island, N.Y. on 27 June 1907, on a vessel named Kaiser Wilhelm der Grosse that came from Bremen, Germany.  Urban Jancik was born in Zbiniove, Hungary.  His wife Irene Gajdos did not immigrate over with him but was from Jbiniove, Hungary.

click here for Great Great Grandpa Urban Jancik's immigration paper (this is history, read entire document)

click here for Great Great Gandpa Urban Jancik's all nine forms:  1) Declaration of Intention 2) same document (sorry) 3)  Certificate of Arrival - For Naturalization Purposes 4 & 5)  Petition for Naturalization  6 & 7) Oath of Allegiance  8 & 9) Death Certificate indicating where his parents live (note:  Urban's parents did NOT immigrate with him)  This is what your ancestors went through to become a citizen of the U.S. back then.

​2.  [1856 spoke German]   Ava & Emmett, Grandma K's  materal side:  Her Great Great Grandfather Rudolph Wald was the first immigrate from that branch on 19 Jul 1856 from Germany to N.Y.  click here to see all his immigration papers

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3.   [about 1868 spoke Bohemian]  Ava & Emmett, your 4th Great Grandfather Joseph Konichek must have brought his children over between 1866 & 1870 because his son Frank had a sister that was born in 1866 in Podborany, North Bohemia, Czech Republic when Frank was 10 and Frank's brother Fred was born in 1870 in Wisconsin.  click here to see the census that shows these facts

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4.  [ after 1867 spoke Aust Bohemian] Ava & Emmett, your 3rd Great Grandmother Anna Chvatal born 1870 in Bohemia must have either immigrated here with her father ? or was old enough to come to America on her own?  click here to see the census that shows these facts

​5.  [after 1862 spoke Scotish]  Ava & Emmett, your 8 Great Grandmother Joanna Williams born in Scotland 1862 must have immigrated after she was born to marry Aeneas George Ross born in Delaware, U.S.  click here to see the facts

6.  [around 1600 or before, spoke England English]  Ava & Emmett, both your 12 Great Grandparents on your Great Grandmother Janet Burleigh paternal side immigrated from England to what the United States was before we were a country (New England they called us) Rev William Noyes & Anne Ernley AND Captain John Cutting & Mary Ward back in around 1600.  click here to see the facts

I just noticed there is something called New England, The Great Migration and The Great Migration Begins 1620 - 1635.  This is matching the above and below Immigrations of Great Grandma Janet's branches.

7.  [around 1600, spoke England English]  again your 12 Great Grandparents Isaac 1571 - 1639 & Alice 1576- 1639 Perkins from England to New England, probably New Hampshire.  click here to see the facts

​8.  [around 1600, spoke England English] again both your 12 Great Grandparents Robert Tuck 1590 - 1664 & Johanna Bachilder 1600 - 1673 AND Thomas Philbrick 1584 - 1674 & Elizabeth Knapp 1593 - 1663 immigrated from England to New England in the Great Migration era.  click here to see the facts

​9.  [around 1700 or before, spoke German] This time on your Great Grandmother Dorothy Konichek's side through her mother Carrie Clark - Yager.  This time 10 Great Grandparents Joannes Thomas Oeswein 1671 - 1710 & Anna Elisabeth Werner 1675 - 1710 from Hoerdt, Palatinate, Bavaria, Germany AND also 10 Great Grandparents Hans Jacob Monsieur 1657 - 1725 & Anna Catharine Bohmen 1650 - ? from Testorf - Steinfort, Mecklenburg, Germany immigrated here because their children married in Poughkeepsie, Dutchess, New York, USA 
click here to see the facts

10.  [1668, spoke England, English] Again you Great Grandmother Dorothy Konichek's side through her mother Carrie Clark - Yager.  Don't know how many Greats but John Rose born 1647 married Margaret ? born 1649 on 24 Sep 1667 in Hollesley, Suffolk, England and their daughter Jamsin Rouse 1687 - 1723 & John Bradley 1678 -1763 married 24 Nov 1708 in Dorchester, Suffolk, Massachusetts  click here to see the facts

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A start on explaining the ? above is to look at how first cousins mating affects the graph.  Tim Urban explains it this way:
"With a concept called pedigree collapse, which is what happens when people end up with a mate who is somewhat or very closely related to them. So for example, if two 1st cousins had a child, that child would only have six great-grandparents, not eight. Or, to put it another way, there are eight filled great-grandparent spots on that child’s family tree, but two of the spots are duplicates of two other spots—"​ 
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In the diagram above the middle set of grandparents have two children (a boy & girl) and the other two sets each have at least a girl child and a boy child.  The siblings marry and give birth to 1st cousins (boy & girl) and the 1st cousins have a child.  Following the diagram one can easily see only six Great Grandparents were there would be eight if 1st cousins had not given birth to a child.