Mathematician Stephen Wolfram has posted a lengthy and interesting dissection of Facebook user data collected through a free tool his company Wolfram Alpha offers that analyzes and visualizes your friend network.

Wolfram is most interested in looking for signals about how a person and their life changes over time, and Facebook data provides plenty. (Although Wolfram talks about “trajectories,” his data doesn’t track individuals, so snapshots of different age groups seem a reasonable substitute.)

One part of the analysis shows that people in different age groups have very distinctive patterns of friendship with other age groups. In Wolfram’s sample – he doesn’t say how large it is – people between 20 and 30 are mostly Facebook friends with people close to their own age. People that are 35 or older have an increasingly large contingent of younger friends. An interesting double peak appears in the chart for 50-year-olds, perhaps due to their connecting with their children’s generation as it comes online. Facebook users aged 60 and 70 have friends spread across all age groups younger than themselves.

An interactive version of the chart posted above allows you to zoom through the changing patterns for people of different ages.

One of Wolfram’s most interesting analyses comes when he begins mapping Facebook friend collections as network diagrams. Looked at this way, each person’s connections form into clusters, which might represent discrete groups of friends from their hometown, college, and family.

Wolfram’s sample suggests that people accumulate more clusters over time. The average 15-year-old sample in his data has between two and three clusters of Facebook friends; the average 35-year-old just over four.

Another analysis Wolfram does reveals how the topics people talk about in text they post on Facebook are very different for different age groups.

Says Wolfram:

“It’s almost shocking how much this tells us about the evolution of people’s typical interests. People talk less about video games as they get older, and more about politics and the weather…People get less interested in talking about ‘special occasions’ (mostly birthdays) through their teens, but gradually gain interest later. And people get progressively more interested in talking about career and money in their 20s. And so on. And so on.”

The results of Wolfram’s analysis are thought-provoking, if sometimes unsurprising. They are also reminder of the value of Facebook’s data. The company has a team of social science researchers (see “What Facebook Knows”) that do a mixture of exploratory, published research, and work to boost Facebook’s business. Often those things overlap. Using Facebook’s data to understand how a person’s life and priorities tend to change over time – and are likely to change in future – is something that could both benefit society at large and Facebook’s ad business.