Tag: Urban Dynamics

Distinguishing between sets and systems through mathematics, economics, and chemistry

A set with objects

So far, we’ve presented the (3) systems’ axioms and the notions of system’s behavior and system’s boundary. We have also explored these ideas via different examples. And we’ve touched on the idea of a set. However, we now want to differentiate between what a set is and what a system is. Once we show the difference between the two, then we will be able to demonstrate the difference between a subset and a subsystem. And most importantly, we will be able to better observe, analyze, and make sense of different kinds of systems, albeit economic systems, political systems, or political systems.

So how can we differentiate between a set and a system? First, we can address this question by referencing back to the (3) systems’ axioms:

  1. A system consists of a set of elements.
  2. Elements in a system interact.
  3. A system has a function, or purpose.
Set A is a subset of set B

The difference between a set and a system is that a set satisfies the first axiom; whereas, a system satisfies all three axioms. More specifically, a set B is a collection of well-defined objects (we will use Naive Set Theory for now), for instance B = {2,4,6,8,10}. Further more, the elements in this set interact with each other. For example, the element ‘2’ interacts with element ‘8,’ or element ‘4’ interacts with element ’10,’ or some combination of possible interaction. And finally, there is a function that is produced, or purpose, via the interactions.

As we can see, a set satisfies the first axiom; whereas, a system satisfies all three axioms. Now we have the tools to delve into the subsets and subsystems. We will see that subsets satisfy the first axiom while subsystems satisfy all three axioms.

As stated before, a set B is a collection of well-defined objects, for instance B = {2,4,6,8,10}. However, a subset of B can be partitioned and observed. For instance, a subset A is a subset of set B if all of the elements in the set A are contained in the set B. That is, A = {2,4,6} so since all of the elements in the set A are contained in  the set B, the set A = {2,4,6} is a subset of set B = {2,4,6,8,10}.

Thus, this subset or any combination of subsets with any of the five elements – 2,4,6,8,10 – satisfies the first system’s axiom.

To illustrate the second axiom with respect to a subsystem, we want to show that if elements interact in a subsystem, then they interact in a parent system. There are a few ways we can do this. For this article, we can do this by observing the interactions in set A = {2,4,6}. Thus if ‘2’ interacts with ‘4’ and ‘6,’ and ‘4’ interacts with ‘6’ in set A, then these elements also interact in set B because set A = {2, 4, 6} is a subset of set B = {2, 4, 6, 8, 10} because set A is contained in set B.

The final step is to show that a subsystem has a function, or purpose. It could be the case that a subsystem has the same function as its parent system, or it could be the case that it has a function different from its parent system. But either way, it ought to have a function no matter if it is the same or different from its parent system. So how can this be illustrated?

Example 1

As Donella Meadows conveyed in her book Thinking in Systems: A Primer identifying the function of a system can sometimes be difficult. Indeed, there are instances where the function or a system is fairly obvious.

One way this can be done is by mapping the elements in set B to the elements in set A. In other words, the elements in set B will go to the elements in set A.

The sketch in Example 1 illustrates this point. For instance, 1 goes to 3, and 2 also goes to 3; 4 goes to 7; and 5 goes to 8.

And so something is imputed through 1, 2, 4, and 5, and something is outputted through 3, 7, and 8. This means the elements in set B = {1, 2, 4, 5} would be the inputs of the system and the elements in set A = {3, 7, 8} would be the outputs.

To illustrate this point further, one could view a system that includes labor and wages as the elements. That is, a person exchanges their labor, hours worked, for a wage. If, for example, the wage was set at $30 per hour, then a person would obviously make more for every hour worked as Graph 1 shows.

That is, if 5 hours are imputed into the system, then $150 will be outputted from the system; if 6 hours are imputed into the system, then $180 will be outputted from the system; and if 7 hours are imputed into the system, then $210 will be outputted from the system. And of course this game could be played over and over again. Thus, as the number of hours imputed into the system increases, the number of dollars outputted from the system increases.

Example 1

Another demonstration of a function can be illustrated through an interaction between an oxygen molecule, O2, and two hydrogen molecules, 2H2. If a gaseous oxygen molecule interacts with two gaseous hydrogen molecules at a high temperature, these molecules are known as the reactants in chemistry, then two gaseous H2O molecules, known as the products in chemistry, will be produced. In other words, if one gaseous oxygen molecule and a two gaseous hydrogen molecules are imputed into a system, then the system will output two gaseous H2O molecules as Example 2 demonstrates.

Example 2

These systems’ functions and purposes are obviously not what we often think of as a function or purpose of a system. They are in one instance somewhat familiar and in another instance esoteric.

In this article, we have used mathematics along with a couple of examples from economics and chemistry to distinguish the difference between a set and a system. Moving forward, we will be able to continue building off of these axioms, notions, and examples as we begin to apply these ideas to more familiar systems such as economic systems, political systems, and social systems.

Let us now, as we have done before, attempt to disprove our notions and work in the tradition of natural philosophy until the next blog.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News.

Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. He is also a professional member of the Society of Industrial and Applied Mathematics and the International Society for the Systems Sciences and a scholarly member of Omicron Delta Epsilon, which is an International Honors Society for Economics. 

You can connect with him directly in the comments section, and follow him on Facebook

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Copyright ©2017 – The Systems Scientist

Minneapolis: How do we partition a city into sub-systems?

By Matt Johnson

So far we’ve established the (3) systems’ axioms; we’ve touched on the notion of systems’ boundaries by using examples of cities; and we’ve established what a system’s behavior is by analyzing the labor force, average weekly wages, and unemployment rate of Minneapolis. Today, we are going to begin to partition the Minneapolis system into its respective subsystems and we are going to do it by ward.

In the next blog, we will decompose Minneapolis by zip-code. And in a future article, we will decompose Minneapolis’ wards into their respective subsystems – neighborhoods – which will introduce us to the notion of systems’ levels.

Minneapolis is a city with 413,651 residents as of July 1, 2016 according to the U.S. Census Bureau. Furthermore, those 413,651 residents obviously live in different parts of the city. Those parts of the city are called wards and Minneapolis has 13 Wards. According to Minneapolis City Government data, each ward contains about 32,000 residents, which of course varies every few years.

This means that each ward in Minneapolis contains about 32,000 residents; those residents interact with each other; and each ward has a function, which in this case is to provide political opportunity in voting and representation, and allocation of resources.

Thus, we have just shown that all 13 wards in Minneapolis satisfy the (3) systems’ axioms:

  1. A system consists of a set of elements.
  2. Elements in a system interact.
  3. A system has a function, or purpose.

Besides illustrating that these 13 wards are systems, we have also established that these wards are themselves subsystems of the general system of Minneapolis. This is because we have shown they satisfy the systems’ axioms, they are contained within Minneapolis, and they have established boundaries, i.e., political boundaries.

And this is a great place for us to dig a little deeper into the notion of boundary. Boundaries can be fuzzy or concrete; and boundaries can be regular or irregular. In the case of political boundaries, which are the wards we are observing, they are concrete and irregular. If we look at any of the 13 wards in Minneapolis, we can observe that the boundaries of the wards are well-defined, i.e., concrete. And we know this is because of the Minneapolis City Charter. But we can also observe that these boundaries are irregular. That is, they are not squares, rectangles, triangles, or circles.

In this short blog, we established that these 13 wards are subsystems of Minneapolis. We also established, with the help of the map, that the boundaries of these wards are concrete and irregular. As we keep moving forward, we will see that our new-found knowledge of systems will pay dividends when we begin to compare and contrast the different wards, neighborhoods, zip-codes, and other Minneapolis subsystems. And we will do this by adding a new tool to our systems’ took-kit – systems dynamics.

Let us now, as we have done before, attempt to disprove our systems’ notions and work in the tradition of natural philosophy until the next blog.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News. Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. 

You can connect with him directly in the comments section, and follow him on Facebook

You can also follow The Systems Scientist on Twitter or Facebook.

 

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Minneapolis: How is the city’s economic system performing?

By Matt Johnson

Over the past couple of blogs, we have illustrated the power of the (3) systems’ axioms (we will review the axioms very shortly) and we have introduced the idea systems’ boundaries. But in our quest to understand what a system is and how we can use system’s knowledge to find real-world applications, we must endeavor to keep testing the validity of our ideas while we add new notions to them.

In today’s blog, we will test the idea of an economic system against our (3) axioms with respect to Minneapolis. We will do this by introducing the notion of systems’ behavior via data and graphical representation. And in doing so, we will ask three questions to facilitate this discovery. First, does Minneapolis satisfy the (3) systems’ axioms? Second, does an economic system satisfy the (3) systems’ axioms? And third, what is systems’ behavior?

In our previous blog, we illustrated that Chicago satisfied the (3) systems’ axioms:

  1. A system consists of a set of elements.
  2. Elements in a system interact.
  3. A system has a function, or purpose.

That is, Chicago consists of a set of elements in the form of approximately 2.7 million residents. Chicago’s residents also interact with each other in various ways on a daily, hourly, minute, and second basis. And one of Chicago’s functions is the ability to increase utility and stability while decreasing crime and instability.

Thus, homicides are concentrated in specific neighborhoods and so it follows that the economic, political, and social systems will behave much differently in the Austin neighborhood, which has experienced 43 homicides this year, than they do in the Edison Park neighborhood, which experienced no homicides this year, for example.

Using the template that we used for Chicago, we can illustrate that Minneapolis will also satisfy the (3) systems’ axioms. This is because we know from U.S. Census data that Minneapolis had 413,651 residents as of July 1, 2016, which is our set of elements.

Graph 1

We also know that residents interact with each other in various ways. And finally, we can think of a half-dozen possible functions that Minneapolis might have. For example, we can think of three economic variables that will tell us if utility is increasing or decreasing in Minneapolis: labor force, wages, and unemployment. We know that these three variables can be systems’ functions. Thus, our (3) systems’ axioms are satisfied once again.

Now we can show if an economy is an economic system in a few different ways, but in this case we will use a similar approach to that of our city examples.

Indeed, not all of the 413,651 residents participate in the marketplace. In reality it is those residents who are 16 years of age and older. And frankly, that’s all that is needed – a set of market participants. It could be 50 percent of the population. Those 50 percent, or 200,000 and some, are a set of elements.

In addition, these participants interact with each other various ways. Some of the participants are employees; some participants are even unemployed; and some participants are business owners. No matter the capacity of these participants, they are still interacting in the marketplace in one form or another. The point here is that they are interacting.

Graph 2

And finally, does the economic system have a function? If Adam Smith and his books The Theory of Moral Sentiments and The Wealth of Nations are to be a guide, than economic utility (stability and vitality) is to be the main function of an economic system.

Indeed, this notion of economic system is more abstract, but the (3) systems’ axioms are still satisfied.

Now if economic utility is our function and we want to illustrate that function for everyone to see, how do we do it? Simple. We’ll do it graphically via data.

As we stated before, the functions of the Minneapolis system are labor force, wages, and unemployment. We also stated the function of the economic system is utility. Adding in the title of this blog How is the city’s economic system performing? we can now address the systems’ functions and question in one sitting through the notion of systems’ behavior.

Systems’ behavior – how a system’s performance changes over time – will tell us how a system is performing. In other words, if the economic system of Minneapolis is performing well, then we ought to expect to see an increase in the labor force, an increase in wages, and a decrease in unemployment over time.

Graph 3

However, if the economic system of Minneapolis is not performing well, then we ought to expect to see a decrease in the labor force, a decrease in wages, and an increase unemployment over time. For sure there are other economic variables we could consider, but for now, and for brevity, we will concentrate on these three variables.

If we take a look at Graph 1, it will tell us how the labor force of Minneapolis has been behaving over the past decade. So what are we observing? What is the graphical data telling us about the labor force in the economic system of Minneapolis?

Well, we are seeing a steady, albeit stochastic (probabilistic), increase over time, correct? Aren’t we observing an increase of about 20,000 participants in the labor force since January of 2007? If our observations are correct, we are seeing an economic system that is performing well in regards to the labor force over time.

What do we see when we observe the wages of Minneapolis in Graph 2? Doesn’t it appear that the average weekly wages for Minneapolis have increased by about $300.00 since the 1st Quarter of 2007? If so, then we are observing an economic system that is performing well in regards to wages over time.

And finally, what do we see when we observe the unemployment rate of Minneapolis in Graph 3? We see the unemployment rate decreasing from more than 8 percent in early 2009 to a little more than 3 percent in late 2016. Again, and just like the first two variables, we are observing an economic system that is performing well in regards to unemployment over time.

So with respect to the systems’ functions of the Minneapolis system, the systems’ behaviors via our graphical representations of the labor force, wages, and unemployment are telling us that the economic system in Minneapolis has been increasing in utility for the residents of the city, in general, for some time now.

Thus, we have shown that Minneapolis is a system, the city has an economic system, and that the economic system is performing well based off our established parameters.

Let us now, as we have done before, attempt to disprove our notions (systems axioms, boundaries, and behaviors) and work in the tradition of natural philosophy until the next blog.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News. Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. 

You can connect with him directly in the comments section, and follow him on Facebook

You can also follow The Systems Scientist on Twitter or Facebook.

 

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Copyright ©2017 – The Systems Scientist

Radio Jedi co-hosts Donald and Jamar invite TSS’s Matt Johnson onto the BRBD Show

By TSS Admin

brbd-v1Our very own Editor-in-chief, and research scientist, Matt Johnson will be making his radio debut as a guest on the Black Republican Black Democrat Show this Saturday, February 11th, at 6 pm on Twin Cities News Talk in Minneapolis, Minnesota.

He will join radio Jedi co-hosts Donald Allen (R) and Jamar Nelson (D) for the 6 to 7 pm central time hour. Together, they will take a closer look at the socio-economic data – crime, employment, housing, etc. – for Minneapolis, and other American cities. They will be delving into Matt’s “Number Shrewdness” to get the real scoop on the urban numbers that are not always presented in a truthful light.

What’s going on in Chicago and other cities? Why is there such disparity in economic wealth between racial groups? What might be done to address such issues? These are just a few of the questions that may be addressed during this Saturday’s show.

Where do you listen?

For our Twin Cities’ readers, just simply turn the terrestrial dial to AM 1130 or FM 103.5. For our national readers, just simply download the iHeartRadio app or you can listen LIVE via the world-wide web by going to www.TwinCitiesNewsTalk.com, which is an iHeartRadio station.

 

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TSS: 2016 Year in Review

TSS Admin

2016 was a year of growth and transition for us, and what a year it was. But it would not have been possible without the support of our readers and followes – You.

We will continue to be a source of free thought and ideas. We don’t hold to any agendas or political leanings. We are not beholden to corporations, political parties, or elites. Our views here at The Systems Scientist, we also go by TSSNewsMag, are as diverse as humanity and we like that!

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We report and write on a wide range of topics (systems) from science, politics, policy, economics, space science, and everything in between. We do this because we believe that all of these (systems) topics are interconnected to one another.

Media has for far to long tried to separate these things as a way to drive up ratings or use it to cause division amongst the people. This is a misuse of data and resources which we at TSSNewsMag have made a promise to done our best not to do.

I think this quote sums up what we do here at TSSNewsMag:

We give you the facts. I told you information is power – knowledge is power. We can’t be in an ideological battle to redeem the soul of this country if we don’t have the facts. – Tavis Smiley

Once again thank you to all our readers and suppoters for a great 2016 and we look forward to a greater 2017!

Please help us grow and become more of a presence on social media by following and liking The Systems Scientist on Twitter or Facebook Donating to TSS

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Minneapolis: The tale of two cities 

By Robert J. Garrison

The council’s decision to divest from Wells Fargo because of their investments in the DAPL is just a political ploy by the council. They most likely haven’t thought through the ramifications of that action. The ramifications of a strictly political decision that just harms those living within the community. Yet they made it a political issue to draw attention away from their failures.

2016-11-18-1Aside from the points mentioned above my question to our readers is, how does this divestment vote address the poverty in Minneapolis?

Well, it doesn’t! It’s a political ploy by politicians to divert the focus away from their failures to address the real issues that are affecting minorities living in Minneapolis – poverty. Matt Johnson has pointed this out in his recent blog In Minneapolis, Black poverty is the problem not Wells Fargo.

This inaction of dealing with real issues of those living within the community is why so many voters have become disillusioned with typical politicians and are revolting. People are tired of talk and they want action and they want it now!

This revolt has opened the door for “political outsiders” to enter the local races in Minneapolis. One of those “outsiders” is  Nekima Levy-Pounds who is a Black Lives activist and former president of the Minneapolis NAACP. Whether Levy-Pounds wins or not, the voters can be assured issues that really matter will be at least brought up during the race.

However, as always the elites always find a way to silence or undermine “political outsiders.” We saw this happen to Senator Bernie Sanders when the DNC and Hillary’s campaign colluded to beat Sanders in the Democratic primaries.

Now, pertaining to Minneapolis the same can happen and has happened for decades. Sadly, Minneapolis is a tale of two cities – North Minneapolis and the rest of Minneapolis. It’s always been that way (even while I was growing up in Minneapolis).

North Minneapolis’ problems have been ignored for far too long. The newspapers and media don’t care about the plight going on in North Minneapolis because it doesn’t sell papers or ads. Part of the problem is voting demographics. North Minneapolis only makes up a small percentage of the voting base in the city. Unless Minneapolis begins to act as one community instead of two, the problems of North Minneapolis might never change.

5th-ward-and-13th-ward-crime-pattern-dwmThe only way that Minneapolis can be united as one is if we begin to heal and address the issues that affect us all and come together. Out of sight does not mean out of mind. We must be conscious of the hurting going on around our city. We are our brothers/sisters keeper whether they live next door to us or on the other side of town.

It is only through this united sense of community that we can elect leaders who do not live inside a political bubble that just pay lip service to the voters every election cycle. It’s time to stop playing politics with people’s lives and start serving the community, all of the community. The time is ripe for change, are you ready? are you in?

Matt Johnson also contributed to this article.

Robert J. Garrison is a political and religious writer for The Systems Scientist. You can connect with him directly in the comments section, follow him on Twitter or on Facebook, or catch up on his articles in the Archives.

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Armchair urban dynamicists criticize Dr. Ben Carson for HUD secretary

By Matt Johnson

As you may know by now, President-elect Trump picked Dr. Ben Carson to head the U.S. Department of Housing and Urban Development (HUD). And in fact, the armchair urban dynamicists are out in force criticizing Dr. Carson for not being qualified for the position and criticizing Trump for appointing him.

Look. I’m not here to defend the pick. And as an urban dynamicist, a mathematical scientist who studies cities (a city scientist), I’m not even sure how I feel about it at this point.

Indeed, Dr. Carson does not have an education in urban dynamics, nor does he have city management experience. These are indisputable facts. And yes, there are probably a lot of people more qualified than him. But dismissing him outright is probably not the most productive approach.

In fairness to him, no person yet, who has sat as secretary of HUD, has provided a viable economic policy plan to address the historical discrepancies that still resonate in depressed, urban environments. Black unemployment has continuously been at least twice that of white folks since the civil rights era.

Before the civil rights acts of the 1960s, black folks experienced redlining policies and economic partitioning in resources. And what is not understood is that these past adverse policies are still being dealt with today.

It is indeed the case that utility and economic vitality and security have increased here in the United States over the past few decades. However, black folks are still behind in economic and educational competitiveness. And it’s not just black unemployment is twice that of white folks. Black business owners are far behind white business owners in creating jobs and producing revenues. Why might this be?

Resources were disproportionately distributed before the 1960s. Local governments, for example Atlanta and Detroit, would provide white citizens with desirable geography, law enforcement for safe neighborhoods, good schools plus the best educational resources, economic support and resources for white businesses, and responsive city government solutions.

In contrast, black folks received undesirable geographical locations, harassment by local law enforcement, second-rate schools and little to no educational resources, and nearly no economic support, if they ever received any.

If black families wanted to move into better neighborhoods, which were white, white families would do what they could to keep white neighbors from moving and black folks from moving in. And this was as recent as the 1960s if not the 1970s and 1980s.

However, the reader should not be fooled. Urban neighborhoods are still very much segregated. What are the reasons for this in a modern America, where everyone is equal and has the same opportunities? There are many reasons, including political philosophy disputes between liberal structuralists and conservative behaviorists. But that’s the point. It’s still happening. Segregated neighborhoods are as American as apple pie.

As secretary of HUD, these will be some of the challenges Dr. Carson will need to address. Is he qualified? Most reasonable, non character assassinating people would probably agree he isn’t. Will he be successful? Who knows? If he surrounds himself with the best of the best when it comes to urban environments and delegates authority, then it won’t matter if he’s qualified. He’ll rely on his team and their education and experience.

But until Carson is appointed by the U.S. Senate , there are going to be a lot of armchair urban dynamicists and economists criticizing the appointment.

 

Matt Johnson is a writer for The Systems Scientist and the Urban Dynamics blog; and is a mathematical scientist. He has also contributed to the Iowa State Daily and Our Black News.

You can connect with him directly in the comments section, and follow him on Twitter or on Facebook

You can also follow The Systems Scientist on Twitter or Facebook as well. 

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