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

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.

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?

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.

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.

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.

Photo Credit: Pixabay

The Bright Side of the Blight Side of Minneapolis

As we know, the 55411 zip code, which is in Minneapolis’ 5th Ward on the north side of the city, has the most depressed economic system in Minneapolis. It has the highest concentration of condemned and vacant buildings; it has the second highest concentration of foreclosures (the 4th Ward has the most); it has the highest unemployment rate in the city; and it has the second highest crime density in the city (the 3rd Ward has the highest).

But we also know from our previous articles that the 55411 zip code is a subsystem of the Minneapolis system. This means that the 55411 satisfies 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.

It has a system’s boundary and behavior (how a system’s performance changes over time) for which condemned and vacant buildings, foreclosures, the unemployment rate, and crime are all examples of in this economic system. But how does the systems’ behaviors of educational attainment of the 55411 zip code compare to the educational attainment of Minneapolis?

Do the residents of the 55411 experience greater earnings with greater attainment of education? Is it the case that a person from the north side zip code would earn more with a college degree than a person from the north side without a college degree? Is there a correlation between education and earnings in the 55411 zip code?

As Graph 1 of the Minneapolis system illustrates, there is an obvious increase in wages as a person’s education increases. That is, the odds are good that a person with a high school diploma will make more than a person with less than a high school education; a person with some college will more than likely make more than a person with a high school education; a person with a college degree will more than likely make more than a person without a college degree; and a person with a graduate level education will more than likely make more than a person with only a college degree.

And so the question is, will the 55411 zip code follow this system’s behavior? Indeed it will.

Considering the sensitivity of the marketplace on the north side, this is really remarkable. And despite the number of adverse economic conditions in the 55411 zip code, education is still a game changer. The question is now, would this behavior remain stable during a great recession just like a few years ago? And would Minneapolis policy makers utilize this data?

Indeed there are obvious differences in earnings from educational attainment between the 55411 and Minneapolis. But the fact remains, this is a bright side to blight side of Minneapolis.

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.

Photo Credit: army.mil

Chicagoland: 2017 Homicides through June, Update!

In a previous article Chicagoland: Systems Axioms, Boundaries, and 2017 Homicides through June this blog reported the total number of homicides for the first 6 months of 2017 was 329. This total was taken from the most current data provided by the Chicago Tribune.

However, these numbers do change from time to time. According to the most current Chicago Tribune data, the total number of homicides through 2017 now stands at 333. This means that 2017 homicide data is now on pace with 2016 homicide data: 333 homicides in 2016 through June and 333 homicides in 2017 through June.

We’ve built a system’s foundation over the past few articles. We’ve established the (3) systems’ axioms, we’ve provided examples of systems’ boundaries, and we’ve illustrated systems’ behaviors; and now we can these axioms and notions to provide a greater understanding of what the homicide data is telling us.

We know Chicago is a system with boundaries and behaviors. If we differentiate 2016 from 2017, we can identify similarities and differences in Chicago’s homicide behavior; that is, how a system’s performance changes over time. In this case, we mean the lower the number of homicides, the better the performance of this system.

Why is this the case? This is because economic utility is inversely proportional to crime and therefore homicides. In other words, as crime increases, economic utility decreases, and as crime decreases, economic utility increases. However, it should be noted that there are exceptions to this rule, for example, Downtown Minneapolis.

By observing the data in Graph 1, we can see that there aren’t many significant differences between 2016 data and 2017 data. Of course, there are months in 2016 that contain a greater number of homicides than there are months in 2017 and visa versa.

For example, there were more homicides in January, March, and May of 2016 than in those same months in 2017. In contrast, there were more homicides in February, April, and June of this year than those same months in 2016.

The greatest difference between the two years has been the months of May and June. For instance, there were 12 more homicides in May of 2016, 68 in total or approximately 17.5 percent, than in May of 2017. In comparison, there were 11 more homicides in June of 2017, 84 in total or approximately 15 percent, than in June of 2016. But overall, the behavior of the Chicago system of 2017 has been similar to the behavior of the Chicago system of 2016.

Either way, this system’s behavior is going to continue to depress economic utility in some parts of Chicago where these homicides are concentrated. And as the readers of this blog now, homicide distribution is not equal throughout Chicago.

This is because the neighborhoods of Austin, Englewood, Garfield Park, and North Lawndale to name a few continue to experience high numbers of homicides and high numbers of crime in general year after year. In contrast, the neighborhoods of Edison Park, North Park, Forest Glen, and Hegewisch to name a few do not experience such adverse systems’ variables, and of course this is good.

But how can adverse systems’ variables be addressed either by economic and public policy or by market solutions in these depressed subsystems of Chicago? Or perhaps these systems’ challenges could be addressed with a combination of government and marketplace solutions in these depressed subsystems of Chicago?

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.

Photo Credit: Pixabay

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.

Photo Credit: The Systems Scientist

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.

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.

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.

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.

Photo Credit: Wikimedia Commons

Chicagoland: Systems Axioms, Boundaries, and 2017 Homicides through June

By Matt Johnson

Last year, Chicago experienced the highest number of homicides since 1996. There were 786 homicides in 2016. In 1996, there were 796 homicides according to the Chicago Tribune. So why did homicides begin to increase after a couple of decades of decreasing?

This blog will not address this question or the reasons behind the sudden increase in violence. Rather, this blog will focus on applying the systems’ axioms to this issue. In addition, this blog will focus on introduce and apply the notion of “boundary” from systems science to Chicago.

This notion will be important because it will allow us to differentiate which parts of Chicago are experiencing these homicides and which parts of Chicago are not experiencing these homicides. Indeed, this idea of partitioning different parts of Chicago seems obvious, but these systems science notions will help us to zoom in on the boundaries of these sub-systems and illustrate the differences between these sub-systems and their characteristics in greater detail. Being able to compare and contrast sub-systems will be a powerful tool for us. But first a little review will be necessary.

In our last blog, we illustrated the three axioms of a system. We used the House of Representatives as our example to satisfy all three axioms. Now let’s see if Chicago satisfies our systems’ axioms. For those readers who are new, here are the axioms:

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

First, does Chicago satisfy the first axiom; that is, does a system consists of a set of elements? According to the U.S. Census Bureau, the population of Chicago as of July 1, 2016 was 2,704,958. In other words, the set of elements, or residents, of Chicago was a little more than 2.7 million. Thus, the first axiom is satisfied.

Second, does Chicago satisfy the second axiom; that is, do elements in a system interact? This axiom is a bit more difficult to visualize because the human brain cannot imagine 2,704,958 people interacting with each other on a daily, hour, minute, or second basis.

And of course two natural question derive from this lack of perception. First, do all of the elements need to interact with each other? And second, is it possible for all of the elements to interact with each other? Eventually these questions will be answered via recognizing sub-systems from their respective general (prime) systems; and mathematics will be necessary to answer these questions. For now, the second axiom in this case will be accepted as true without mathematical proof.

Finally, does Chicago satisfy the third axiom; that is, does a system have a function, or purpose? In this case, Chicago could have several functions: ecological, economic, political, and/or social. In this case, the function, or purpose, of Chicago will be accepted as the ability to increase utility and stability while decreasing crime and instability. Thus, the third axiom is satisfied.

Now that the axioms are satisfied, let’s address the second question: what are the boundaries of Chicago? We don’t have to go far to find the answer to our question. We only need to visit the City of Chicago for such information. It is the city government that is responsible for setting such boundaries including the boundaries of neighborhoods and wards.

There are 50 Wards in Chicago, which are parts of the Chicago system that make up the whole system. Moreover, each part of the system, or ward, is represented by an alderman (city council member). And as stated before, each ward also has its own geographical area. For example, the “Chicago aldermen…voted to set new boundaries for the city’s wards” in January of 2012. In systems science, these type of boundaries are called political boundaries.

These political boundaries, as this interactive map from WBEZ 91.5 Chicago demonstrates, are concrete and irregular (an example of a regular shape would be a square, rectangle, triangle, or circle). This interactive map also illustrates the political constraints of the Ward within Chicago, for instance Ward 29 and Ward 37, that have their own political boundaries. This is because these wards are also political sub-systems of Chicago.  Again, these boundaries are set by the city representatives, or aldermen, who pass policy for the City of Chicago.

As stated before, Chicago experienced 786 homicides in 2016 and 329 homicides this year. But these homicides did not occur equally throughout the windy city. For example, there were 88 homicides in the Austin neighborhood in 2016 according to the Chicago Tribune. This is important to know because the Austin neighborhood overlaps both the 29th and 37th Wards of Chicago. And this year, the Austin neighborhood has experienced 43 homicides through June 30th.

In contrast, North Park, which is in the north central part of Chicago and in the 39th Ward, experienced no homicides in 2016, or 2017 so far, according to data pulled from the Chicago Tribune. The same can be said for the Edison Park neighborhood which is in the 41st Ward and the north-west part of Chicago.

And so what can the boundaries of the city and wards tell us about the general system of Chicago and the sub-systems of the 29th, 37th, 39th, and 41st Wards?

First, Chicago experienced 786 homicides in 2016 which was the most in two decades. Furthermore, we know that these homicides were not distributed equally. We know that more than 11 percent (88 of 786) of homicides in Chicago occurred in the Austin neighborhood in 2016; whereas, no homicides occurred in the Edison Park and North Park neighborhoods in 2016.

Second, these sub-systems will probably have a different set of ecological, economic, political, and social characteristics. For example, the aldermen of the 29th and 37th Wards are dealing with an extraordinary level of violence and ought to contribute to the lack of economic and social utility in the sub-system in the form of higher than average unemployment, lower than average median and family household incomes, and lower than average housing values.

In contrast, the aldermen of the 39th and 41st Wards are probably dealing with competitive levels of median and family household incomes, lower than average levels of unemployment, and higher than average housing values.

When we look at Chicago as a whole, this information will be lost to us. However, if we partition the Chicago system into sub-systems with concrete boundaries like wards and neighborhoods, then we will be able to see the different parts of the city in greater detail. We will be able to see that homicides really do happen in certain segments of Chicago and not just Chicago in general.

Article Questions:

Until the next blog, think about where a boundary would start and where a boundary might end. One example that might be useful is to think about where Earth’s atmosphere ends and outer space begins. Perhaps there is another example that is more localized and easier to visualize? Where does one neighborhood, or ward, begin and where does another neighbor, or ward, end? Or where does one culture start and where does one culture end? Find an example and test it.

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. And he has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University.

Photo Credit: Pixabay

What is a system?

By Matt Johnson

What is a system? I posted a similar question on The Systems Scientist Facebook page last week. I asked the following question,

In your own words, explain, or describe, what you think a system is?

A limited framework of interrelated processes that work toward a mutual output or outcome.

As the reader will see, this answer hits the third axiom of what a system is, and the answer also touches upon the structure and processes of a system as well.

Another Facebook follower hit the mark on two of the systems’ axioms on the first try: the first axiom and the third axiom. As the follower explained,

A system to me is a set of parts, each with a different function, that work in concert, complimentary way towards a common goal.

All together, there were a lot of really good answers and everyone who commented pointed out that a system has a function, or purpose. And many of the Facebook followers added that systems consist of parts and those parts are what compose the system itself, which is correct. So what is a system?

To answer this question, we will utilize Donella Meadow’s three conditions from her book Thinking in Systems: A Primer to propose the systems’ axioms, we will be using going forward. And by axiom we mean a statement that is true and will follow our thinking and logic from thusly. Here are the axioms we will be using:

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

At first, these axioms seem so obvious and simple, and that’s good, but these axioms are subtly profound. This is because they can be described through mathematics and tested via the scientific method. But perhaps putting the math and science aside for the moment would be beneficial. Instead, a familiar example will suffice.

Again, in order to have a system, the three axioms must be satisfied. For instance, does the United States House of Representatives satisfy each condition?

For the first axiom, all we have to do is count the total number of members that serve in the House, which is 435. In other words, there are 435 elements in our example. Thus, we see that axiom (1) is satisfied. For the second axiom, we should ask ourselves if the members of the House interact with each other?

Is there another answer to a question that has ever seemed so obvious? From the debates on the House floor to Twitter wars, the members of the House of Representatives do indeed interact with each other. There are a plethora of examples to illustrate this point in the form of C-SPAN, MSNBC, FOX, and CNN. Thus, we see that axiom (2) is satisfied.

And finally for the third axiom, does the House of Representatives have a function? It definitely feels like they don’t have a purpose on most days. But they do and this purpose of course derives from the United States Constitution. Thus, we see, although begrudgingly, that axiom (3) is satisfied.

Over time and as these blogs progress, we will see that these three axioms will be extremely useful for us. They will allow us to explore cities and economic systems, and most importantly they will allow us to construct describable phenomena via mathematics, test observable data, and make predictions that might not otherwise be accessible through cluttered language, hyperbolic rhetoric, and undefined terms.

One final thing, these three axioms are not the totality of a system. Systems have inputs and outputs, a structure, environment, behaviors, processes, boundaries, and other properties. Together, all of these characteristics are what make a system. But these axioms are a good start and will allow an interested party into the world of Systems Science.

Until the next blog, do the classical science thing and test these axioms for yourself. In other words, try to disprove them. If you can manage to find an example, please do share it in the comments section below so the other readers and commentors can validate your findings.

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. And he has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University.

Photo Credit: Wikimedia Commons