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Brownian Motion, Osmotic Pressure, and Utopias

3/16/2023

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Which do you prefer, a society evolving randomly toward some future condition or a society evolving purposefully toward some goal?


Celebration, Disney’s Utopian Community


You might think “utopia” with regard to the latter. Think Walt Disney’s EPCOT and the community called Celebration designed by Disney. Both were planned concepts for humanity though EPCOT doesn’t have residents. That it is just a “visitor” community is probably good. I can’t imagine living full-time in EPCOT even if it had homes. And the City of Celebration? Well, it’s developed into a “regular community” with a fire department, neighborhoods (villages), and schools. It has businesses and all the problems associated with pre-planned communities, including a downtown homeowners’ association filing a 2016 lawsuit because their homes were deteriorating. Shoddy workmanship? Corner-cutting at the get-go? Or just the withering heat and humidity of Florida where mold thrives? Anyway, the Disney-planned paradise isn’t paradise, is mostly white (nearly 90%), and has more than 11,000 people with all the ordinary problems that 11,000 people have just about everywhere. All evolving utopias devolve. What begins as a planned community gradually changes with randomness through succeeding generations. The buildings, even the deteriorating ones, remain, but the occupants change, and random growth occurs, adding to the initial optimistic population.


Celebration is relatively safe, but it does have crime: 11.29 crimes per 1,000 residents. According to CrimeGrade.Org, Celebration’s north neighborhoods are slightly more dangerous than its east neighborhoods (1 in 78 vs. 1 in 89). * Celebration has not yet devolved into a mini-Chicago. It’s safe, but it does have a record of some violent crimes. Maybe one reason for the low crime rate stems from character of the initial population, people enthused about moving into a Disney utopia. But all utopias devolve—randomly. Call each new member of the group a “particle.”


Brownian Motion and Osmotic Pressure


If you have ever observed dust particles moving in a stream of sunlight, you’ve seen an analog of Brownian movement that even the ancient Lucretius (60 BC) noticed. He ascribed the random motion to the action of “atoms,” foreshadowing the observation of Robert Brown (1827) who observed pollen moving in a fluid, and the mathematics of Thiele (1880), Einstein (1905), Smoluchowski (1906), and Perrin (1908) who tried to describe their probabilistic movements.. The dust particles you observe are driven more by air currents than by the random motions of atoms of the gas in which they move, but since atoms are too small to be seen and tiny particles like pollen require some magnification, those dancing dust particles are a good approximation of Brownian motion, the random movement of colloids.


Brownian motion, as it is called, is probabilistic for any particle so moved. All those randomly moving atoms in a fluid or gas just don’t get together to run like cars on one side of a four-lane. They aren’t like Celebration’s first optimistic residents all seeking a common ideal communal life. The direction of each particle’s movement occurs by chance in Brownian movement. In contrast, the motion of cars and those first residents is purposeful.


The randomness of a utopian society’s devolution stands in contrast with its initial evolution, which is a purposeful process. At its commencement, a utopian city reflects not only planning, but also social commonality. Randomness does play a role in its development. Take the political nature of Celebration. It appears to be almost evenly split between Republicans and Democrats, with Biden edging out Trump in the 2020 election. As the city ages, its makeup will change as it no longer remains a closed system. There will be pressure from “outside particles.” Eventually, the balance between the political affinities will change the way concentrations of atoms change across an osmotic membrane. The membrane around Celebration was an initial barrier between the higher crime outside and the lower crime inside. But there’s an inherent pressure for the particles to move from higher concentrations to lower concentrations just as there is a pressure exerted by the chaotic movements of atoms in Brownian motion, atoms that only get into sync by chance.


I suspect that as the initial Celebration occupants tire of deteriorating housing and an increase in crime or they die off, that the next generation of Celebration’s citizens will live in a non-utopian society, one that isn’t planned, rather one that is the product of the random bumping of “particles.” That might already have occurred because various neighborhoods in the city’s boundaries have differing levels of safety.


Any Interest in This?


I suppose all this amounts to nothing of interest unless you either live in Celebration or in some other planned neighborhood or unless you want to consider how your local community evolved.


PA (Two letters pronounced separately. Is this the only state commonly referred to by its postal designation?)


For example, I reside in western Pennsylvania, an area that grew with immigrants in the late nineteenth and early twentieth centuries arriving to work in coal mines, coke oven fields, steel mills, and limestone quarries. From those basic industries all those other supporting purposes arose: Retail sales, transportation networks, construction, schools, police forces, and fire departments. At the beginning of the process, many moved into the planned patch neighborhoods owned by the coal companies. My own countryside location sits in the midst of many such communities, each built under the auspices of a specific coal company. The more urban steel mill towns developed rather randomly as steel workers bought or rented in walking distance to the mills, most located along the four major rivers, the Youghiogheny, Monongahela, Allegheny, and Ohio.


And then the devolution occurred: Steel mills rusted into disuse during the 1970s and 1980s, coal mines closed under stringent restrictions by environmental agencies and an anti-coal government, and with all the industrial closings, the deterioration of the patch-housing and urban river cities led to a new migration. Malls then killed the once prosperous downtowns (and uptowns) until they, too, succumbed to the randomness of particle movements that included new ways of commerce like Amazon online purchasing that spread out the original close particles to a worldwide community. Most of western Pennsylvania’s small town centers died, the osmotic pressure crossing the membranes from densely populated towns and cities to suburbia. A number of towns tried to revitalize themselves, but revitalization requires a new population. Pennsylvanians make up the ninth oldest state population, and the one-time second most populous state has declined in rank to the fifth largest population with only about a million more residents than it had in the 1950s. Suffice it to say that during the time of steel mill demise, the young particles randomly left, pushing past the membranes of other state boundaries to enter growing communities.


Do Brownian and Osmotic Motion Serve as Analogs?


Mandelbrot pointed out that any attempt to apply the math of Brownian motion to human activities like movements in a  stock market fails because of the dissimilarity between continuous and discontinuous processes. The atoms in a fluid are different from human-controlled events like bull and bear markets. I suppose his criticism of attempts to associate such movements with human affairs also applies to similar attempts to associate those physical movements with the evolution and devolution of human communities.


The analogy here, like all analogies, probably “limps.” But I thought it might give you a point of departure to examine your own community and maybe to see whether it is evolving or devolving.


*https://crimegrade.org/safest-places-in-celebration-fl/
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