The Newtonian paradigm, also called the clockwork universe, is the scientific paradigm that supports modern science being characterized by its materialistic and atomistic vision of isolated inert objects(matter) that interact in a linear cause and effect fashion, giving a vision of the universe that is analogs to a big machine, or clock which is both orderly, knowable and predictable.[1]

### Science

Science is engaged in the enterprise of trying to describe some subset of phenomena in our world by amassing empirical data and developing logically consistent theoretical models to effectively interpret patterns within that data. But this scientific enterprise does not happen in a vacuum, it happens within a certain cultural context and depends on a certain set of philosophical assumptions about the way the world is. Physicists do not go into the laboratory every day and question whether there really is such a thing as some objective universe out there, this is a philosophical question rather than a scientific one. Researchers go into their lab every day and operate based upon a certain set of assumptions about the way the world is, what important questions to ask, what valid processes of reasoning there are, etc. and as long as the whole community of researchers shares those assumptions then they have the supporting context within which to conduct their collaborative research enterprise.

### Paradigms

This set of assumptions that supports a scientific domain and constitutes the whole philosophical framework within which they work is called a paradigm. The Oxford dictionary defines a paradigm as “a worldview underlying the theories and methodology of a particular scientific subject”[2]. The paradigm or set of assumptions within which the enterprise of modern science operates was born approximately five hundred years ago with the massive cultural transformation of the renaissance and scientific revolution that give us the cultural foundations of our modern world.

This new paradigm really came together and first found its most coherent full expression within the work of Sir Isaac Newton, whose work was extremely influential for centuries to come and laid the foundations for modern science, and of course, built into this foundation was a set of assumptions about how the world works. This whole set of assumptions is called the Newtonian paradigm or the clockwork universe; in slightly more technical terms it can also be called linear systems theory. Linear systems theory forms the backbone to virtually all of modern science. It is used in every domain from physics to biology to economics to psychology.[3]

### The Clockwork Universe

The Newtonian paradigm is materialistic and atomistic in nature. It sees the world as a set of isolated objects that interact in a linear, cause and effect fashion. The Newtonian clockwork universe receives its name because within this paradigm the universe is seen to be compared to a big mechanical clock. It continues ticking along like a perfect machine with its gears governed by the laws of physics, making every aspect of the machine perfectly orderly and predictable. Within this paradigm, we can understand and know this whole machine of the universe by understanding all the parts and the linear interactions between these parts. The whole clock is clearly nothing more than the sum of its parts and thus, to understand it we can use the process of inquiry called reductionism. Whereby we break the whole thing down into these isolated individual parts and study the properties of those parts in isolation and how they interact with each other. If we can then create a set of equations that describe this then it is game over. We have completed this process of inquiry and now know everything that there to know.

### Linear Systems Theory

The clockwork universe is a paradigm but this paradigm supports a modeling framework called linear systems theory. Linear systems theory deals with relatively simple systems, that is to say, systems that have a finite amount of independent, homogeneous elements interacting in a well-defined fashion with a relatively low level of connectivity. In its essence linear systems theory fundamentally describes closed systems at or near equilibrium. Linear systems theory forms the backbone to almost all of modern science, it is based on an assumption that the superposition principles hold, that is to say, the additivity and homogeneity principles. The additivity principle states that we can add the effect or output of two systems together and the resulting combined system will be nothing more that the simple addition of each system’s output in isolation. The homogeneity principle states that the output of a linear system is always directly proportional to the input, so if we put twice as much into the system we will, in turn, get out twice as much.[4]

By imposing these conditions we can use standard mathematics to model and analyze the system and this approach can describe simple linear interactions, the interaction between two, three or four variables within closed and relatively static systems. It works well on the micro level, and this was the primary focus of science before the eighteen hundreds where we were dealt with things like the relationship between temperature and pressure, population and time, production and trade etc. During the eighteen hundreds, scientists developed methods for dealing with macro systems composed of many parts by using statistical methods and probability theory, with most of this happening within the domain of statistical mechanics. Where they were trying to model such phenomenon as a gas in a chamber with billions of atoms, phenomena of this kind are sometimes called disorganized complexity. In such cases, we are dealing with systems composed of many disorganized parts, that is to say, a large set of random variables; the variables have to be independent and identically distributed, what is called I.I.D.[5]

If each random variable has the same probability distribution as the others and all are mutually independent then these statistical methods will work. These assumptions only hold within linear systems but by imposing them we can say things about the macro system without actually getting our hands dirty and looking at what is really going on inside. We can say that it will follow the law of large numbers, the central limit theorem. We can use mean field theory and make estimations, talk about the average normal person and so on.[6] Due to this linear systems theory is often used as a proximation for complex phenomena due to its inherent tractability and the closed-form solutions that it offers. Linear systems theory is the modeling framework within the Newtonian paradigm. The Newtonian paradigm forms the set of assumptions and linear systems theory the set of modeling tools.

1. Wikiwand. (2020). *Clockwork universe | Wikiwand*. [online] Available at: https://www.wikiwand.com/en/Clockwork_universe [Accessed 9 Sep. 2020].

2. Lexico Dictionaries | English. (2020). *Paradigm | Definition of Paradigm by Oxford Dictionary on Lexico.com also meaning of Paradigm*. [online] Available at: https://www.lexico.com/definition/paradigm [Accessed 9 Sep. 2020].

3. Ufl.edu. (2020). *Clockwork Universe*. [online] Available at: https://users.astro.ufl.edu/~guzman/ast7939/glossary/clockwork_universe.html#:~:text=Copernicus%2C%20Kepler%2C%20and%20Galileo%20were,by%20Newton’s%20analysis%20of%20forces.&text=Newtonian%20physics%20was%20used%20to,world%20machine%20or%20Clockwork%20Universe. [Accessed 9 Sep. 2020].

4. Wikiwand. (2020). *Linear system | Wikiwand*. [online] Available at: https://www.wikiwand.com/en/Linear_system#:~:text=In%20systems%20theory%2C%20a%20linear,use%20of%20a%20linear%20operator.&text=As%20a%20mathematical%20abstraction%20or,%2C%20signal%20processing%2C%20and%20telecommunications. [Accessed 9 Sep. 2020].

5. Wikiwand. (2020). *Independent and identically distributed random variables | Wikiwand*. [online] Available at: https://www.wikiwand.com/en/Independent_and_identically_distributed_random_variables [Accessed 9 Sep. 2020].

6. Wikiwand. (2020). *Mean-field theory | Wikiwand*. [online] Available at: https://www.wikiwand.com/en/Mean-field_theory [Accessed 9 Sep. 2020].