# Mathematics of urban environments

By Matt Johnson

I remember when I was in grade school, Jr. high, and high school, my fellow students and others told me that math was useless. As they put it, “You’ll never use that stuff in real life.” So sure of themselves, and ignorant of thinking any differently, I took their word for it. But as I learned later in life and my training, boy were they wrong.

Today, mathematics is one of the most important tool kits I use to analyze, study, and make predictions about urban environments. The forms of mathematics I use probably would sound like ancient Greek to the untrained ear and stating them here isn’t useful for this discussion. Just know that the entire foundation of our civilization is based on mathematics, and this is why I can use math to analyze and understand cities and the people who live in them. This is why I can endeavor to find solutions to complicated, urban problems.

As a consequence of mathematics and the scientific method, I have been able to unlock some very interesting behaviors and patterns in depressed parts of cities. For example, the city I study and draw my systems hypotheses from is Minneapolis and the city has shown some interesting systems’ behaviors with respect to its subsystems.

Like most American cities in the United States, Minneapolis has evolved in such a way that there are parts of the city which are predominantly occupied by those who are of African ancestry; and there are parts of the city which are predominantly occupied by those who are of European ancestry.

And as plenty of studies and news articles have pointed out, there are many socio-economic discrepancies between these two groups and their respective subsystems. In fact, this blog has illustrated these discrepancies in the form of data analysis on several occasions. But these sources, although useful, still don’t get to the behaviors of the systems and how they interact with these respective groups. This is why mathematics is desperately needed.

I have been able to use math to analyze crime data from different perspectives. That is, I have analyzed crime as a time series over a one year period, and compared multiple years to each other. As a consequence, crime overall and at the very least has been decreasing in the city of Minneapolis over the past few years.

In addition, I have also analyzed crime in a non-linear format; that is, I have analyzed the behavior of crime in different parts of the city in a spatial context (a space that is multidimensional and probabilistic). What I have not been able to do yet is predict how crime will behave going forward in time series and spatial modes. This will take a combination of additional advance mathematics and game theory. But what should also be considered is how crime adversely affects traditionally disenfranchised groups, both in utility and incarceration rates.

And this is just one variable. This doesn’t account for housing issues such as foreclosures and condemned and vacant buildings, nor does it account for unemployment and education level. And it certainly doesn’t account for how all of these socio-economic factors interact with each other in these depressed systems.

As you can see, this stuff gets complicated very quickly. But it also lends a little light to why these socio-economic discrepancies can be so difficult to find solutions for, and why the mathematics of urban environments is so important.

Matt Johnson is a writer for The Systems Scientist, and a mathematical scientist. You can connect with him directly in the comments section, and follow him on Twitter or on Facebook

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Photo credit: Math Boost

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