Question

Ten circles meet each other : a conjecture

Abstract : Based on current state of connected profiles in WikiTree, and analysis of how the circles grow, we extrapolate figures that could be reached by systematic population of the ten first circles for an average profile of WikiTree (19th century, Western world). We derive from those figures that the ten first circles for any two such profiles have necessarily a non-empty intersection, meaning that their relative distance is at most 20 degrees.

Details on the linked free-space page. Comments welcome, as usual.

Comments

Very interesting, Bernard.  The only thing that confuses me (well...maybe not the only thing ) is why you refer to the average WT profile as a 19th-century Westerner, yet the example you use on the linked page, Samuel Lothrop, is a 17th-century man.  I wonder if your conjecture could be applied to a larger group?

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Good point, Julie.

Certainly 19th century has also to be taken as "average", and the conjecture could be extended a few centuries around it. Let's say as long as you don't go too many (more than ten) generations backwards, because time distances cannot be made shorter. If asked for a limit, suppose I would not extend beyond the 16th century. This way Samuel Lothrop is in, Marie Stuart is out.

We can be more or less bold vs how widely it applies.

That said, it would be good to have a solid 19th century example of one million/ten circles.

[edited] : We have actually one of those ... Brigham Young

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Answer 1

Bringing the cumulative population of the first ten circles for a given profile up to over the million is certainly nothing that is done singlehandedly

Comments

Sure enough, Eva! It has to be a collective endeavour. The funny thing is that, for the profiles currently in this category, those who have achieved it were certainly both unwilling and unconscious unaware to do so. And those, like both of us, who struggle for some poor Jean-Joseph and Olof, will probably not reach the goal in their lifetime ... unless some  help from our cousins.

[edited for clarity, thanks Eva!]

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"Unwilling" does not feel like the right word (comes too close to active resistance, as I hear it) - but the contributors were certainly not consciously aiming for the goal of one million within ten circles.

The nice density of the connection network in my favourite parishes, Skinnskatteberg and Gunnilbo, will also have come about unintentionally (at least in relation to the connection finder). It just so happens that several of the Swedish members who joined before me had roots there, a few more have joined after me; there are also a number of members descended from emigrants, who have roots there. Also, because the early church records, from before 1700, are so good there, these parishes have been among the targets for the huge early GEDCOMS, causing some messes - which should be mostly sorted out now.

It has been a lot of fun going through the records again and joining up the bits and pieces of families that were already there (which I was doing a couple of years ago). It is still far from a total transfer of the recorded population into WikiTree, but when I'm looking for connection possibilities for some Swedish line, I am always happy when I find somebody marrying a person from this territory. So because those parishes are already so "wet" they will attract more rain

Edit: typo

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Thanks Eva for fixing my vocabulary. Post edited, unaware seems the correct wording. It takes a French and a Swedish to produce correct English

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"Correct English" = filling a hole in the ocean. Their our know rules.

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Languages are like families. Seen from outside they seem to follow some kind of rules. When you live inside, you know better.

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I might point out that I was not asking for rules - more like savouring the meaning.

Answer 2

Continuing this thought experiment: In order to reach 1M profiles in the 10th "circle", you need (on average) about 4x growth from circle to circle (4¹⁰ = 1,048,576). To sustain this 4x growth, the average person in the n-th circle would have to have at least 4 new connections not reached yet. So this average person would have to have at least 5 connections (one which connected them into the n-th circle, 4+ connecting to new people outside of the n-th circle). If the average person has: 2 parents, 1 sibling, 1 spouse and 2 children (6 connections) this looks like it could be close to that magic number! (And for older families where large numbers of children was more common, you could imagine even faster growth.)

I really like this line of theoretical thinking, Bernard! Thinking about what the "real" tree of life/love looks like that we are trying to approximate using this website.

Comments

Shawn, I get the magic one million another way : the two first circles for a profile with a reasonably large family, are counting over 100. Then a tenfold growth every two circles (a bit less than the 4x you propose) leads to the same figure.

And those round figures look like a very conservative baseline. For my "focus" ancestor Jean-Joseph, the growth of first circles is indeed greater than that. The ongoing systematic census (easy in a very endogamic context) has already passed the one thousand threshold for the fourth circle, and it's far from completion, the final figure will certainly pass 1,500.

Of course, as Eva has pointed in her answer above, to actually identify, connect, source everyone up to the tenth circle is more than a human genealogist can achieve alone. Fortunately, we're all there together, making the target more likely to be reached at some point.

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I finally got around to making the comparison between Samuel Lothrop and Brigham Young presentable. These two patriarchs have been in competition for the shortest mean distance to all connected profiles for a long time.

Back in October 2018 (hi Shawn!), Samuel Lothrop was clearly in the lead with an average distance of 17.69 as compared to Brigham Young's 18.38

In January 2021 Lothrop was still in the lead with an average distance of 17.50 versus Young's 17.60 - obviously Young's average had shrunk faster than Lothrop's over the intervening time.

Young overtook Lothrop some time in the end of March/beginning of April. The difference is still very small - you have to look at three decimals.

See spreadsheet.

I suspect that Lothrop's closest circles are more or less saturated, while Young's still have the potential to grow.

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Oh wow, what a blast from the past! I haven't thought about graph center for some time. And it appears that while I wasn't paying attention, Brigham pulled into the lead :) Very interesting. How are you measuring average distances here Eva? I used custom code run on downloaded data dumps. Are you interested in graph analysis in general for the global tree? I've had many half baked ideas on this over the years that I'd love to chat with other folks interested in this stuff :)

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The initial circles idea is Bernard's.
You can see on this space page about 100Circles what we have been doing.
Aleš Trtnik of WikiTree+ has provided us with a query that yields the current population, circle by circle, for a given profile (to be used sparingly).

Me, I'm more of a case study person, listening with fascination to you maths types :-)

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multi-dimensional visualizations using z as time, graph the network using location nodes based on lat/long (wouldn't it be great if we had locations for every sourced event?), edges for immediate family connections. Highlight shortest paths/categories/DNA/whatever else you wanted. localized avg connected-ness, so we can see where the "edges" of the tree potentially are that could be improved.

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Jonathan, do you have a means of presenting such things?

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Not currently, but theoretically you could use something like R or http://sigmajs.org/ to do that.

Answer 3

Bernard, I keep thinking about your circles. Is there a difference (and if so, what is it) between the "circle" and the Connection Finder?

Secondarily, if one is more than 20 "connections" away from someone, or perhaps more than 10-15, that should be an indicator that the circles are not complete. Without complete knowledge, of course, this is only a bad estimate, but could the average connections be used as a proxy of completion within the larger tree?

Comments

I would say that the "circles" are a way to consider the  "landscape" around a profile, the Connection Finder is a tool to find paths in this landscape. We have used "focus" to name the profiles used as circles centers (could be anyone), I think now it would be clearer to call them "viewpoints".

And yes, the current distribution of circles in WikiTree for a given profile is more a measure of how much work has been achieved in her surroundings than anything else. At the end of the day, when all that could be added is added, the landscape should look about the same from any vewpoint. Mediocrity principle, if you like.

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I like "viewpoints" - for when we use them to think about the shape of the Global Tree. "Focus" suits them when we do all that work to fill out their circles. The circles idea is a multipurpose tool ;-)

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Bernard,I didn't expect you to say that the landscape would look the same from any viewpoint.

Of course, the total population of anyone's circles will be the same as anyone else's (if measured at exactly the same time), for it is the total of the connected tree.  But I thought that there would always be variations in the landscape--i.e., the shape of the graph and the locations of the peak circle and the mean--due to some profiled people coming from very endogamic populations, and others, like Samuel Lothrop or Brigham Young, being well connected from their earliest circles.

Edit:  Yielded to temptation and removed my display of ignorance.

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I think it's a truth for one individual, not the tree as a whole

 "[...] for a given profile [...] when all that could be added is added, the landscape should look about the same from any viewpoint."

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Hmmm.  That could be true for you or me, or many of us looking from a current viewpoint.  What I meant was that from, say, Jean-Joseph Marie Vatant's point of view (born 1804), the mountains might be further away and the closer landscape flatter.

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Julie, I'm surprised to find you surprised.

The mediocrity principle is not a so to speak expression. It's  underlying all important advances in our understanding of the world around us, since Copernic and Giordano Bruno. The fate of the latter shows it's not something easy to grasp and accept.  This introduction by a biologist is short and to the point : https://www.edge.org/response-detail/11272.

And seems to me in previous conversations among circlers I've already made this point. The current state of affairs in WikiTree, the differences in the distribution of circles for different profiles is mainly due to how different parts of the landscape have been more or less thoroughly explored..

But re-reading now the 100 Circles page section about those differences I understand they need rewriting, because the current wording is misleading.

The closer landscape of Jean-Joseph or Olof is not "flat" at all! It looks so now in WikiTree because I need the fingers of one hand to count WikiTreers actually working on it! If all the Brezhoneg who stubbornly (Brezhoneg are known to be stubborn, alas) keep on growing "THEIR" tree on Geneanet had been bringing their task force to WikiTree since the very beginning, it would look radically different.

The growth of the first circles I've mentioned in another answer above has no reason to stop. And Eva has very similar figures (astonishly similar, indeed) for Olof.

We tend to speak of WikiTree "bulk" or "center". Yes there is something of the kind right now because 99% of profiles are Anglo-Saxons (throwing the figure without means to support its actual value, but you see the point).

And to come back to the mediocrity principle, this very predominance of the Anglo-Saxon world is certainly an obstacle to its understanding, by giving the impression that the genealogical landscape of this world is "special". It's not, but the current figures are totally biased.

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As always, Bernard, you educate me.

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Sorry, Julie. Both my parents were teachers, and I'd been one also. Even retired, c'est plus fort que moi

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Don't apologize!  Stronger than you, but nevertheless, that's a good thing.