Deus ex homo
Connecting the dots
When I was born, I was in a nuclear network of three: mum, dad, me.
That made for three individual connections: me and mum; me and dad; mum and dad.
When my brother was born, our network became four nodes and six connections.
Now, me and my wife have my own nuclear network of five: dad, mum and three kids. That’s 10 connections.
You can easily work out how the sequence progresses mathematically.
It’s the number of nodes multipled by the number of connections (which is the number of nodes -1), then divided by 2, because a connection is shared between two nodes, so each has been duplicated.
So that’s c=(n*(n-1))/2, where c is the number of connections and n is the number of nodes.
Now, the nuclear family is a particular thing, being relatively small and hopefully ‘perfectly’ connected.
And, when I was born, my actual network was much higher. Taking into account grandparents and close family friends (who all knew each other), all in the total number of connections in my little world was likely something closer to 200.
Of course, working up the theory to the wider world — aka social network analysis— we wouldn’t assume everyone we know knows everyone else we know.
Indeed, much of the impact of social network analysis is looking at the level of connectedness (or not) of disparate groups (say Trump supporters and renewable energy supporters, 0r NRA members and vegans), and the outlying individuals who may connect such groups.
In the case of a self selected group such as my 444 Facebook friends, perfect theory would be where all 444 know each other, leading to 98,346 connections.
However, the real number is likely to be much lower as these 444 people are split into a couple of different unconnected groups: work; family and friends; sports teams.
Indeed, research suggests that individuals can only maintain 150 friends in any realworld sense of the word. That would suggest a theoretical maximum of 11,175 connections.
But given the explosion of computer social networks, the figures can get very big, very fast.
For example, in terms of total Facebook users — 1.8 billion — we get the perfect figure of 1.6191 trillion connections.
And if everyone knew everyone else in the global population of 7.4 billion, that would be 54.8 quadrillion connections (54,800,000,000,000,000).
As some sort of comparison, there are 100 billion neurons in the human brain, which has an estimated 100 trillion total connections.
Getting even more theoretical, we can work out the total number of connections for every human being estimated to have ever live: 108 billion.
That’s 11.6 x 10**21 or 11.6 sextillion connections — 11,600,000,000,000,000,000,000 if that means anything.
To date our approach has been externalized. There’s a strong argument that our initial starting point was imprecise.
As soon as I was conscious, I was in an internal network with myself. Hence my nuclear network of three was more complex as each node had a connection back to itself.
Hence instead of three connections, there were six.
Our equation become n+((n*(n-1))/2) or c=(n(n+1))/2.
It’s not a radical mathematical change. The sequence goes: 3 nodes, 6 connections; 4 nodes, 10 connections; 5 nodes, 15 connections etc.
As the numbers get bigger, the impact of adding a big number to the product of the big number squared is marginal. Nevertheless, it is significant in terms of linking theory to actuality.
Self awareness is surely the most important connection. Or is it? Maybe we’re missing out the most important connection of all?
Without getting involved in the specificities of belief, the existence of a god who has an individual relationship to everyone, alive or who has ever lived and ever will, doesn’t change the basic math much.
It becomes 2N+((N x (N-1))/2), simplified to c=(n(n+3))/2.
(Or c=(n(n+3)/2)+3 if you’re trinitarian!)
Yet, if you do believe in a personal creator god, and given the individual comparator of 150, it does provide a modest idea about the intellectual scale of the ultimate being.