Simulation Science: The Parable of Polygons

Continuing the discussion from The Role of Simulation in Science:

To give one example: a famous and groundbreaking agent-based simulation was Thomas Schelling’s (1971) model of “segregation.” The agents in his simulation were individuals who “lived” on a chessboard. The individuals were divided into two groups in the society (e.g. two different races, boys and girls, smokers and non-smokers, etc.) Each square on the board represented a house, with at most one person per house. An individual is happy if he/she has a certain percent of neighbors of his/her own group. Happy agents stay where they are, unhappy agents move to free locations. Schelling found that the board quickly evolved into a strongly segregated location pattern if the agents’ “happiness rules” were specified so that segregation was heavily favored. Surprisingly, however, he also found that initially integrated boards tipped into full segregation even if the agents’ happiness rules expressed only a mild preference for having neighbors of their own type.

Thomas Schelling is a Nobel Laureate, and he writes this paper in 1971, just three years after MLK was assassinated. This is really important work to understand. In our moment, it turns out you can run versions of his experiments online really easily. I really encourage everyone to take a look at this website here:

As they write:

This is a story of how harmless choices can make a harmful world.

And they have these key lessons, all demonstrated by simulation.

1. Small individual bias → Large collective bias.
When someone says a culture is shapist, they’re not saying the individuals in it are shapist. They’re not attacking you personally.

2. The past haunts the present.
Your bedroom floor doesn’t stop being dirty just coz you stopped dropping food all over the carpet. Creating equality is like staying clean: it takes work. And it’s always a work in progress.

3. Demand diversity near you.
If small biases created the mess we’re in, small anti-biases might fix it. Look around you. Your friends, your colleagues, that conference you’re attending. If you’re all triangles, you’re missing out on some amazing squares in your life - that’s unfair to everyone. Reach out, beyond your immediate neighbors.

In the end, we have to decide if we are content with segregation. Or will we allow discontent to grow, so that we might choose the integrated Kingdom of God.


Has anyone take a look at this yet? There was a Nobel Prize granted for it. Very interesting stuff.

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Amazing! Fascinating.

This got me to thinking about various aspects of this diversity topic: We often tend to associate with churches where everybody holds opinions very similar to our own: same views on baptism, same views on origins, same views on free will vs. divine sovereignty, etc etc. etc. We may even choose based on criteria which are quite minor. (For example, I knew a family who changed churches because they were “more comfortable” with a church which took the Lord’s Supper only once per quarter instead of weekly. I was surprised they separated their children from their church friends over something like that.)

When a Christian moves to a new town, does he/she automatically check the church directory for a particular denomination or church fellowship association? Nothing wrong with that. Yet, that may only leave us with only one or two choices, and such choices may lead us to a church that happens to be far less healthy and effective in reaching its community than if we were to avoid our usual “segregation patterns.” (Of course, I’m not specifically referring to any sort of racial segregation—but it certainly can mean simply reinforcing racially segregated worship.)

So, I wonder if we end up in a church of triangles-only when we might have been greatly enriched by a diverse assortment of polygons.


I was surprised that this thread got so little activity when posted last October.

Some forum participants may need to adjust their Flash control settings to make the simulations work properly.

The simulations bring to mind another great study of how even just a little bit of sexism in a predominantly male environment can have a far greater impact upon the women than what one’s natural intuitions might first assume:

Both studies remind us that even small biases can have very significant results.


Then it was expanded by a physicist:

In conclusion, the recently introduced ‘Petrie multiplier’—which provides a majority-bias explanation to sexism in Tech companies—received notable viral interest and media coverage. Powered by concepts and tools from the theory of diffusion we presented in this paper a rather profound generalization of the basic Petrie multiplier . Namely, we applied statistical physics of normal and anomalous diffusion to comprehensively model and analyze the sociophysics of sexism, obtained Petrie multipliers of the form , and classified these Petrie multipliers to four universal behavioral types. This interdisciplinary approach demonstrates the potency of theoretical physics with regard to the modeling of timely sociological phenomena.