### Ask the Chicken Philosopher

by Olivia DeLane

Dear Olivia,
I am from a mixed-breed flock. Half of us are brown (like me) and half are white. A couple of weeks ago we were attacked in an open field by a hawk, who killed one of our white companions.

I think it is irresponsible of whites to hang around together, where they attract the attention of predators. This poses a risk not only to themselves, but to everyone in the field.

Look, I am not a member of the Ku Kluck Klan or anything, but I just feel that the world would be a better place if only every chicken was brown. Maybe, at least, we could require all light-colored chickens to wear dark wide-brim pimp hats as camouflage when they are outdoors. What do you say?

Sincerely,
“Eva Brown”

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OK, first of all, Eva, I’m going to tell you pull your beak out of your cloaca so I can get something through your little chicken head. No, it’s not OK to hate others because of the color of their feathers, nor to recommend that they all be forced to wear hats if they don’t do what you say.

You’ve ruffled my feathers already and discussions like this one can be very emotional, so maybe some mathematics can help us. In his book Micromotives and Macrobehavior, Thomas Schelling used ‘checkerboards’ of 64 squares to study mixing and segregation and I think that tool might be helpful here.

Imagine that there are two colors of chicken: Gold and Blue. There are 32 of each kind scattered on a checkerboard that has 64 squares, one chicken per square.

Gold chickens are Tolerant, in that they enjoy the company of all other chickens, both Gold and Blue. But Blue chickens are Intolerant. They like other Blues but dislike Golds. Each chicken looks to the 8 nearest squares surrounding it and gets 1 point for each neighboring chicken it likes and loses 1 point for each chicken it dislikes.

We can examine many possible configurations of chickens in that space. Each try, we pick two squares at random and have the chickens on them swap spaces. If the move increases the overall happiness, then the move is kept. If it decreases happiness, the chickens go back to their original spaces.

(To avoid boundary effects, the edges of the space wrap around to the opposite side, so that the land we’re examining is really more like a small parcel amid a much larger field.)

What happens after random chickens have tried to swap spaces, say, 10 million times?

Since the Blues want to be away from the Golds (and the Golds don’t care who they are near), the two colors of chicken will separate completely. That is, they are completley immiscible.

If all of the Blue chickens were Tolerant, like Golds, and considered each neighbor to worth +1 point instead of -1 point, then the two colors would mix completely. That is, they are perfectly miscible.

But interesting things happen when the 32 Blue chickens are a mixture of Tolerant and Intolerant kind.

Let’s say that we have 32 Gold chickens and 32 Blue chickens and all of the Blues are Intolerant. Then, we replace one of the Intolerant Blues with a Tolerant Blue. Then, we replace another, and then another.

When we had 0 Tolerant Blues, the Gold and Blue chickens separated completely. When we have 32 Tolerant Blues, the Golds and Blues mixed completely. So, between 0 Tolerant Blues and 32 Tolerant Blues, there must be some sort of transition from a society where chickens separate to one where they intermingle.

We can measure how well-mixed the checkerboard is by how many chickens neighbor someone whose color is unlike theirs. When the chickens are completely separated, as is shown in the figure above, half of the chickens have 3 neighbors who are a different color and half have no neighbors who are unlike themselves. So, on average, the number of Unalike neighbors is 1.5.

In a perfectly mixed society, each chicken on average would have 4 neighbors who are Unlike himself (and 4 who are like himself).

The graph below shows how the ‘mixedness’ of our chicken society changes as the number of Tolerant Blues changes.

In a society with 0 Tolerant Blues, we tried 10 million swaps and found that the Blue separated themselves from the Golds, resulting in an average number of Unlikes of 1.5.

We then took that configuration of chickens and randomly turned one of those Intolerant Blues into Tolerant Blue and tried another 10 million swaps.

We turned a second Intolerant Blue chicken into a Tolerant Blue and tried 10 million more random swaps, and so forth until all of the Intolerant Blues had been replaced with Tolerant Blues.

As the first few Blues become tolerant, the checkerboard becomes slightly more mixed. But after 8 of the 32 Blues become Tolerant, I find it interesting that adding Tolerant Blue chickens makes society become more separated. When there are 16 Tolerant Blues and 16 Intolerant Blues, the Tolerant Blues act as a buffer, separating the Intolerant Blues from the Golds. In this state, every single chicken is perfectly happy with his 8 neighbors, yet there is a clear separation of Golds from Blues.

It is only after more than about half of the Blues are Tolerant that the separation of colors on the checkerboard begins to approach the fully mixed state that occurs when all of the Blues are Tolerant. When the number of Tolerant Blues goes from 21 to 22, the separated bands break up into small bubbles called miscelles, with a core of Intolerant Blues separated from the Golds by a layer of Tolerant Blues.

On the graph I have also shown a gray line for when we start with 32 Tolerant Blues and then switch them one-by-one to Intolerant Blues, moving in the opposite direction down the graph. In that case, from 24 down to 12 Tolerant Blues, the checkerboard of chickens exhibits hystersis, showing patterns not seen in the other direction. But that’s a story for another day…

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Olivia DeLane has a Master’s certificate in normative ethology from Gallus College, a non-accredited online institution. Her writings are for entertainment purposes only and should not be misconstrued as being for any other use. Olivia’s smash-hit YouTube dance video ‘Shake Your Tailfeathers’ has had over 430,000 unique viewers since its debut.