Kinds of attraction:

Doing a bit of half-serious family history, I’m struck by the way people got together in the 19th century –lets say in the period from about 1850 to about 1950. I’m talking about country properties: they didn’t interact much with nearby towns, but people travelled from property to property – to siblings, uncles, aunts, cousins – and in the process visited those people's friends – all the time. Each family had a network, in other words, and the result was that marriages were usually within the network, and families often developed multiple links over time, as cousins married brothers, and so on. In my own family there are at least three such connections in a hundred years.

Mothers and daughters travelled to see their extended families (and perhaps in the case of mothers to take a break from childbearing); sons travelled for work experience in places where, though the environment might be demanding it would not be unfriendly; people travelled to parties, weddings and celebrations. In my mother’s family’s case the path stretched from Wangaratta to Wentworth to Menindee to Wilcannia to Thargomindah to Longreach – they were all on the circuit, and people were coming and going all the time.

The result, it seems to me, was that the likelihood of marriage between two nodes in this network would be simply (in the ideal case) the product of the number of available partners at the two places irrespective of the distance between them – whereas townspeople stereotypically married the girl next door.

We know from geographers that the mutual intercomprehension of two places is a function of the product of their populations divided by the distance between them, and Newtonian gravity, of course, is proportional to the products of two masses divided by the square of the distance between them.

It seems to me that these relations are all the same phenomenon, but applied to a one-dimensional, a two-dimensional and a three-dimensional frame of reference respectively – so for the one-dimensional case we have N₁ x N₂ / D⁰, for the two-dimensional N₁ x N₂ / D¹, and so forth.

Then I’m led to wonder whether we mightn’t see the same sort of effect at work in the outer reaches of giant galaxies, where gravitation, as I understand it, can be anomalously strong.

Just a thought.