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Ancestral Mathematics

January 31st, 2021, 2:16 pm

I came across this little calculation recently and it might make a simple but interesting brainteaser.

ANCESTRAL MATHEMATICS

When you were born, your ancestral tree looked like this:

2 parents
4 grandparents
8 great-grandparents 
16 second great-grandparents 
32 third great-grandparents
64 fourth great-grandparents 
128 fifth great-grandparents
256 sixth great-grandparents 
512 seventh great-grandparents
1,024 eighth great-grandparents
2,048 ninth great-grandparents

So, looking back at the previous 11 generations, you will discover 4,094 direct ancestors in the last 400 years.  

But that only dates back to the year 1620!

Build a little program that can take us back to the year 0 AD - what nth generation is that and how many ancestors have you had since then?

For a little more challenge, assume that a generation is 35 years. Build a calculator where you can plug in a year anywhere from 0 to the present and it will put that year into a 35-year bucket, tell you how many generations have existed since then, and calculate the number of ancestors you would have from that point in time.
family tree.jpg
 
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bearish
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Re: Ancestral Mathematics

January 31st, 2021, 4:40 pm

I object to the notion of year 0 AD. Evidently we skipped straight from -1 to 1. Anyway, this Julia code should do the trick:

function g(y)
b=numerator(ceil((2021-y)//35))
b-1, 2^b-2
end

Example call:

g(1620)
(11, 4094)
 
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bearish
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Re: Ancestral Mathematics

January 31st, 2021, 4:48 pm

Of course, the assumption of no intermarriage among one’s ancestors gets increasingly implausible as we move back in time. The model seems to predict a plethora of Eves.
 
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Cuchulainn
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Re: Ancestral Mathematics

January 31st, 2021, 5:30 pm

Of course, the assumption of no intermarriage among one’s ancestors gets increasingly implausible as we move back in time. The model seems to predict a plethora of Eves.
All that begetting turns the tree into a graph.
 
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Cuchulainn
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Re: Ancestral Mathematics

January 31st, 2021, 5:30 pm

Of course, the assumption of no intermarriage among one’s ancestors gets increasingly implausible as we move back in time. The model seems to predict a plethora of Eves.
All that begetting turns the tree into a graph.
 
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Re: Ancestral Mathematics

January 31st, 2021, 6:07 pm

Good point about 0 AD - ha ha - I was obviously not thinking that through. So, 1 AD is the starting point indeed.

As for inbreeding, cross breeding, begets, begats, and begotting, you guys can take the thread wherever you want. : ) The Julia code is very nice and maybe we can also beget some C, C++, Java, Python, R, and whatever else. Like "Hello, World." in all languages. 

But maybe not - it is Sunday - people are watching football and I am preparing for a Nor'easter, which is supposed to hit here tomorrow.  Up to a foot of fresh snow! I also am working on some logic and gambling brainteasers, but it will take awhile to make them good enough to post.
 
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Cuchulainn
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Re: Ancestral Mathematics

January 31st, 2021, 7:05 pm

And the Monday morns, o the Monday morns
The roses are blooming in Picardy.

www.youtube.com/watch?v=nVI5cz8H0M4

BTW my mum turned 96 yesterday.
 
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Re: Ancestral Mathematics

January 31st, 2021, 7:22 pm

And the Monday morns, o the Monday morns
The roses are blooming in Picardy.

www.youtube.com/watch?v=nVI5cz8H0M4

BTW my mum turned 96 yesterday.
Happy birthday to her!  
pink roses.jpg
The Beckett is great - Waiting for Godot one of my favorites going way back. Like a primer for a pandemic.
I had an idea for a new and very sustainable thread on this Forum, so keep an eye on it!