1 What is science?

Last modified on 06. February 2026 at 19:54:23

“This is your last chance. After this, there is no turning back. You take the blue pill - the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill - you stay in Wonderland and I show you how deep the rabbit hole goes.” — Morpheus, Matrix

“Anything goes” is Paul Feyerabend’s famous dictum¹. Therefore, you can stop here. If you are not interested in the historical or philosophical background of what we call science, then skip ahead to the next chapter. You don’t really need the background. Think of a theater actor. The actor doesn’t need to know how the stage is built, how the lights work, or where the music comes from. The actor just performs the play. Nothing more is required. Or, to say it in the words of David Mermin, “Shut up and calculate!”² With this statement, Mermin describes the Copenhagen interpretation as a philosophy of quantum physics that prioritizes mathematical results over foundational philosophical questions.

For everyone else, I have written this introduction chapter. Maybe you’re puzzled about what this science thing is all about. That’s perfectly normal. Today, education strips away the historical and philosophical context and jumps directly into biological, chemical, or physical topics. History tells the story of countries and people, not the combination of history and the natural sciences. There is so much to learn. Therefore, there is seldom room for philosophy in any rushed school schedule. However, humans do science. What humans do becomes history. The reasons and ways in which humans do things are strongly connected to their thoughts and beliefs. Therefore, they have a philosophy, even if they are not aware of it. So, if you do science, you do so with a particular way of thinking. Therefore, you have a philosophy, whether you are aware of it or not. It’s time to talk about it a little bit.

1.1 Why history and philosophy?

What could possibly be a better argument for something than the thought of a genius and Nobel Prize winner? Therefore, we begin this section with a quote from Albert Einstein.

“I fully agree with you about the significance and educational value of as well as history and philosophy of science. So many people today - and even professional - seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is - in my opinion - the mark of distinction between a mere craftsman or specialist and a real seeker after truth.” — Albert Einstein

Don’t worry, we won’t start with the science of the Stone Age. Instead, we will focus on the modern era and the knowledge gathered during this time. In this section, we will also focus on science itself. We will discuss data and models later. For now, we will focus solely on the meaning of science. Science is hard to pinpoint. I thought it would be easy to define. What could be the problem? Then I thought about it, read about it, and thought about it again. There are three big books. The fact that there are three big books alone shows you that it cannot be so easy to define science. Yes, it is complicated. In the end, I will give you all the sources, but for now, there are three books: The Logic of Scientific Discovery by Karl Popper³, The Structure of Scientific Revolutions by Thomas S. Kuhn⁴, and Against Method: Outline of an Anarchistic Theory of Knowledge by Paul Karl Feyerabend¹. You can read these books or not. I will give you a brief introduction and refer to them. As always, a brief summary cannot encompass all the ideas of these books.

Before we continue, I would like to present a brief example of knowledge generation. How can we obtain enterprise knowledge? In this case, we will explore cholera as a human curse through the lens of a famous German scientist and his concepts.

1.1.1 Cholera and breathing walls

In 1854, cholera visited the city of Munich in Bavaria, Germany. This was not a pleasant visit, as many citizens died of cholera and its consequences. However, not all parts of the city were affected equally. By the end of the 19th century, Munich would become one of the cleanest cities in Europe. Max von Pettenkofer achieved this by building and renovating the canalization system. When cholera arrived, not all parts of the city had equal access to the canalization and fresh water supply. Some parts of the city had easy access to fresh water and working toilets. In other parts of the city, sometimes only divided by a street, construction of the canalization had not yet begun. It was observed that the death toll from cholera varied by district.

In the following Figure 1.1 (A) we see a fictional pattern. It is of two districts of Munich. On the left, the sewerage and freshwater systems are already installed and operational. We can call this area the “hygienic area.” On the right, the canalization has not been finished or even started. We will call this area “filthy” or “dirty.” After the cholera epidemic outbreak, the number of deaths in each district was counted. There were ten deaths in the hygienic area and twenty-nine in the filthy area. We assume that both areas have roughly the same number of inhabitants.

Pettenkofer observed the lower death rates in hygienic areas and concluded that canals and fresh water would stop cholera from spreading and killing people. Therefore, more sewage systems must be installed, and the city must be cleaned up. But wait a minute. What is the cause of the deaths? Yes, it is the illness cholera. But how does it work? What causes the illness? Pettenkofer discovered a way to cure or prevent cholera, even though he did not understand the cause of the illness. He did not know how it was transmitted or why people died from it. He proposed that the cause should be found in specific soil and groundwater processes.

In 1883, Robert Koch discovered the cholera bacillus to be the cause of the illness. Pettenkofer did not believe in unobservable bacteria. In 1892, at a cholera conference, his belief was so strong that he drank a cholera culture. He survived with mild symptoms. According to Pettenkofer, the cholera culture could not be the reason people died. He was still alive.

Another example of Pettenkofer’s thinking is the breathing wall. Figure 1.1 (B) shows the experimental setup. Pettenkofer sealed off his office. He sealed the doors and windows with glue. From his point of view, the room was perfectly contained. Then, he measured the airflow inside the room. The room’s pressure stayed constant while an influx could be measured. Therefore, Pettenkofer concluded that air could pass through the walls’ pores. Thus, the breathing wall model was born. However, it has been suggested that Pettenkofer might have forgotten to seal a chimney, or that the wooden floor and ceiling might have been leaking.

Figure 1.1: Visualization of two erroneous theories by Max von Pettenkofer (1818–1901). As a positivist, he only believed in facts that he could see, like the results of experiments. **(A)** Schematic example of the influence of soil conditions, here represented as fresh water/sewage (blue), on cholera cases. The district with a fresh water supply has fewer cholera cases than the district without access. Pettenkofer was able to contain cholera through hygiene, even if he could not determine its cause. **(B)** The breathing wall concept, which states that the exchange of fresh air in a room mainly occurs through the walls’ pores. Pettenkofer likely failed to properly seal the chimney and ceilings for the air exchange measurements.

That’s where we come to a halt. What is Pettenkofer doing? He was a very successful scientist. But he was sometimes wrong. Interestingly, Pettenkofer came up with one of the precursors to the periodic table of elements. He had to stop his work due to a lack of funding from the Bavarian state. In 1869, however, Dmitri Mendeleev, the discoverer of the periodic system, mentioned Pettenkofer in his articles as one of the few who influenced his work. Pettenkofer only looked at what he could see. His thought process was bound to the observable.

Now, we will learn about the philosophy of science. We will use Pettenkofer as an example. We will meet other people with strange ideas later on. Strange ideas are also science. It’s thinking outside the box. From a philosophical point of view, who was Pettenkofer? He was a positivist. This is a specific philosophical approach to acquiring knowledge. Positivists only believe in what can be seen or observed. If you wear glasses, you may notice a slight flaw in the argument about what is and isn’t observable while reading this book. Now, let’s take a closer look at the concepts of empiricism to logical positivism.

1.1.2 From empiricism to logical positivism

How does the human mind learn? How do we gather information? Humans are born in a blank state. No ideas are implanted in the brain; only instincts guide the infant through the first weeks and months. Shortly after, the infant begins to learn through the senses. This is mostly true and forms the basis of empiricism. I will not focus on human development. Therefore, we will only focus on the origin of empiricism as a basis for generating knowledge. The idea of empiricism is simple and appealing. In my experience, common sense often begins with empiricism to gather knowledge. Therefore, we will start with this simple idea and explain its history.

Empiricism: The source of knowledge comes from observation and sensory experience. We learn through the five senses, which guide our ideas. The focus is on the human mind.

Next, we will broaden the scope of empiricism by asking how science and society should function. Since we have learned through our senses, we can apply this idea to science and society in general. Since we will focus only on observable things and dismiss invisible entities, we will call our concept “positivism.” Positivism comes from the Latin word positum, meaning “that which is given” or “laid down.” No, this does not make it any better. Furthermore, we must distinguish between two completely different concepts that often pop up in our minds. Positivism is often confused with positive thinking. This is a common linguistic mistake, but positivism and positive thinking are not related. One is a rigorous philosophy of science, while the other is a psychological mindset or self-help technique.

Positivism: The validity of knowledge comes from observation and sensory experience by ignores everything invisible or immeasurable. If you cannot measure it or observe it, it shouldn’t be part of a serious discussion.

Now, let’s turn the wheel of positivism a bit further towards the extreme. Therefore, we must visit Vienna in the early 19th century. The Vienna Circle was a group of philosophers who met at the University of Vienna from 1924 to 1936. They had a big influence on the study of philosophy and science. In 1929, the Vienna Circle wrote “The Scientific Conception of the World”, also known as “The Manifesto.” The manifesto had two aims. First, it introduces the group and Vienna. At the beginning of the text, it reads more like an advertisement for Vienna and the Vienna Circle. More scientists should join the club. The philosophical main points are somewhat buried in the text. The Vienna Circle proposed that science is both empirical and positivist; knowledge comes only from experience. Furthermore, the process of scientific world conception involves applying logical analysis to observed objects, or, in other words, experience.

Logical Positivism: The validity of knowledge is acquired through sensory experience, by integrating modern methods of mathematics and logic. For a statement to be meaningful, it must be testable by observation. It must be proven true either by logic (an analytic statement) or by experimentation (a synthetic statement). Thus, the verification principle is introduced.

Or to write it in the words of John Passmore, who said: “Logical positivism is dead—or as dead as a philosophical movement can be.”

Figure 1.3: Dramatis personae in this chapter and their biographical details, as well as important scientific discoveries or hypotheses. We consider a selection of scientists who have contributed to the philosophical background of science and positivism. The dates refer roughly to the year of publication or when the discovery became known to the public.

epistemically

Paul Feyerabend’s famous dictum ‘Anything goes’ is at the heart of his methodological anarchism, which states that there are no universally valid rules in science. Feyerabend argued that progress often arises from breaking rules, which is why rigid methodology hinders rather than promotes the acquisition of knowledge.¹

“Shut up and calculate” is a philosophy in quantum physics advocating a focus on mathematical results over interpreting foundational, philosophical questions.²

Three fields of science Theoretical Experimental Instrumental

Paradigm shift⁴

Even witchcraft has an paradigm

Not piling up knowledge but a process thorough knowledge

Figure 1.4: The three types of science working fields are as follows: Theoretical science is the brain of science, where new, fundamental concepts are born. Thought experiments and guesswork are the main tasks. Experimental science uses suggestions from theory to conduct tests. This testing is based on the falsification principle. Finally, instrumental science uses blueprints from theory to invent new devices usable in experimental science. Each type of science can be done without using the other fields. It can be done in a passive manner.

Figure 1.5: The paradigm shift cycle, also known as the Kuhn Cycle after its inventor. The cycle describes how science evolves over time. Normal science is stable and attempts to solve puzzles and problems within a given framework. From time to time, anomalies occur that do not fit the common sense of the current science. These anomalies are usually seen as experimental error, resulting in a social pushback. Eventually, the anomalies pile up, and a crisis occurs. This marks a crack in the stable science. From there, a revolution occurs, and candidates of reality comes into being. Finally, a new paradigm of reality emerges. In this new paradigm, new languages and a new framework of science are established. Then, normal science begins again. There is a strong social component to this cycle because humans often resist fundamental changes.

Incommensurability, a terrible word, meaning that something can not be compared. Maybe incomparable

observations are theory-laden

Observation = Sensory Input + Theoretical Framework

Language shapes data: We use theoretical words to describe what we see. If you say, “The electron moved,” you are already assuming the “theory” that electrons exist and are particles that move.

⁵

1.2 Old start

The first chapter of this book is already the hardest. I started writing this chapter very early on, perhaps even before any of the others. Yet it took the longest to finish. The question is simple: What is science? The more I researched, the more complicated the answer became. Or the other way around. I followed the advice of Wolfgang Pauli. Pauli defined the scientific method as “taking up a subject repeatedly. Thinking about it. Setting it aside. Gathering new empirical material. And continuing this process for years if necessary. In this way, the conscious mind stimulates the unconscious mind. If anything, this is the only way to achieve results.” Therefore, I tried to read and find answers to the question of what science might be. Perhaps science is, at its core, something personal. However, science also has objective aspects that I want to present here. Ultimately, decide for yourself what science truly is.

The following Figure 1.6 shows the demarcation line between science and non-science. In the next sections, we will discuss each specific part, but I think it’s important to start with a clear overview. Science is distinguished from non-science through experimentation and falsification. This is true in this book. There are many subtle definitions, but I will keep it simple here. If an experiment is not possible, then it is not science. We also need the ability to build a falsification framework. Therefore, we need hypotheses that can be rejected by experimentation. These two requirements are met by the natural sciences, including physics, chemistry, and biology, in order of their purity. Biology includes medicine and all other fields of knowledge gathered from living things. In addition to natural science, there is formal science, which can be seen as a tool of science. This is due to the lack of experimentation, falsification, or both. Therefore, we will not include mathematics, logic, or theoretical computer science as sciences. True non-science fields are intuition-based or subjective at their core. There are many of these fields, and we will discuss them shortly. The humanities are undoubtedly different from non-science, but this book is not about the humanities, so we will put them aside.

Figure 1.6: Visualization of the demarcation line of science. This line divides science from non-science through experimentation and the principle of falsification. The purity of science fields is taken from xkcd comic #435 (https://xkcd.com/435). According to this definition, natural science, including physics, chemistry, and biology, is separated from formal science, including mathematics. Formal science must be clearly distinguished from other intuition-based and subjective non-science, such as pseudoscience or anti-science. The humanities are indisputably different but are also considered non-science in this schematic.

Perhaps we should start with the supposedly easy part. What is the opposite of science? In doing so, we will gain an understanding of the term “science” and what it means to us. This may be the deepest lesson for me: we cannot really grasp science. Science is connected to each person in a different emotional way. Science seems cold and rational, but humans are not. Therefore, our relationship with science is strange and complex. Science is its own way of thinking, perhaps a philosophy. Therefore, there are as many ways of thinking as there are human minds.

1.3 What is the opposite of science?

As I found out, there is no direct opposite of science. That’s interesting. Sometimes, you can define something by knowing what it is not. You might think this is not so problematic. Take a few minutes to ask yourself: “What is the opposite of science?” Okay, good to have your focus back on the page. Maybe you thought science was cold and rational. I will share my personal story with science. For me, science was Star Trek: Enterprise. But I’m too young for Kirk and Spock. So, I was socialized with Captain Jean-Luc Picard and Star Trek: The Next Generation (TNG). That’s where I first encountered Shakespeare, but that’s another story. In TNG, science was determined by the exploration of new worlds. I would sit comfortably on the open bridge in front of the gigantic viewscreen. Commander Data was the embodiment of science. He was an android. He was rational and cold, devoid of emotion and humor. Let’s flip these attributes.

If an android is science, then what is a human? Then is the human the opposite of science? Perhaps there is some truth to that. Humans have lived on this planet for thousands of years, but science as we know it began during the Enlightenment. So perhaps humans are the opposite of science. Human beings are full of emotions and feelings. Each one is very subjective and interested in their own development. They feel love and romance. Neither of these is very scientific. Humans also believe. Some believe in a more structured manner, like in big churches, while others believe in a more individual manner. However, believing in something has nothing to do with science. But humans do science. Therefore, science is part of humanity. As Joshua Schimel said, “Knowledge is a product of human hopes and fears. Our emotions are crucial to its development, and it cannot be truly understood as some bloodless, emotionless enterprise.”⁶ Science is a human endeavor.

According to Arthur C. Clarke’s Third Law, “Any sufficiently advanced technology is indistinguishable from magic.”⁷ Is magic therefore the opposite of science? We cannot perform magic. We do not have the power to do so. However, some humans believe that we can perform magic. Who is “we”? The advanced part of humankind. We come into contact with our brothers and sisters who are at a different technological level, such as tribal cultures on isolated islands in Indonesia. To a tribe with a primitive culture, our technology seems like magic. Here, we can observe the cargo cult. A cargo cult is named after its appearance in World War II. The US Army faced the challenge of determining the best island-hopping route to mainland Japan. Since no one knew and the tides of war were constantly changing, the US Army Logistics Corps decided to drop cargo everywhere. This way, if US soldiers approached an island, there would already be plenty of supplies.

What happened to the indigenous population? They believed that the gods had come to bring them cargo. They could not think of any other explanation for what they observed. They observed hardened silver birds dropping and landing on the islands. After a while, the gods stopped showing up. The war was over. But nobody told them. Therefore, the people of the islands copied the gods’ behavior. They built the control room, and they made a radar station out of grass and wood. They even built plans out of grass. Nothing could work. They did everything perfectly, but they missed the point entirely. It was a cargo cult, not science. They copied someone else’s routine and hoped to experience what the gods experienced when they did the same.

Do you follow a cargo cult in your daily routines? Do you do things that you have seen but don’t understand? Do you believe that they will work even though you don’t know why? This is totally human and from my point of view totally necessary to be a working community member. Some stuff must be done, even if I don not really understand the why. But what if we do it in science? Then we will do cargo cult science⁸. It is a danger of enormous proportions if done in the wrong place with the wrong intentions. Still, most intentions are good and are twisted by the circumstances. There are several examples of following dogmatic rules and getting a catastrophic outcome. Later, we will explore different models of reality, including the Fukushima nuclear accident.

For now, I would like to conclude that the opposite of science is difficult to grasp. On the one hand, we could argue that human emotions and feelings are the opposite of cold, rational science. However, emotions are also the driving force behind human scientific inquiry. Therefore, we are doing something scientific by leaving the topic open for further research and looking for things that are not science.

1.4 What is not science?

Besides things that are the opposite of science, there are things that are similar to science or that use attributes and tools in a distorted way to imitate science. Conspiracy theories^9,10 look like science and use science terms and tools. They play on a stage that looks like science but has no deeper foundation. It’s more like a nice story about humans harming other humans. However, conspiracy theories attempt to explain the world and often generate money for the storyteller. Therefore, I do not see conspiracy theories as the opposite of science. These conspiracy theories are non-science. Some theories have a historical basis, such as the hollow earth conspiracy theory. We will discuss the origin later. Conspiracy theories like to be retold, and in the process, they grow and multiply. To circumvent the proliferation of conspiracy theories, I will provide an illustration of the anti-conspiracy theory “Birds Aren’t Real” by Peter McIndoe.

What does the movement claim? In short, the US government kills all birds in the US and replaces them with bird-looking drones. Birds sit on power lines to recharge and defecate on cars to mark them visually. The bird drones are there to spy on American citizens. The specifications are inconsistent and vary. This is a typical sign of a conspiracy theory. Finally, U.S. President John F. Kennedy was assassinated by the government due to his reluctance to kill all the birds as cherry on top.

What do conspiracy theories have in common? They all tell a good story. I personally find them more similar to fairy tales, with the standard Greek dramatic structure of one hero against an anonymous horde of evil. In addition, they all have in common a lack of experiment. They don’t even conduct a small experiment or propose a hypothesis to test. A testable hypothesis is rarely claimed. Even if a hypothesis is present, the story can easily be changed to maintain its purpose: to tell a good story. Here, we will not focus on conspiracy theories and how they work. This topic is beyond the scope of this book.

There is another field in which personal stories are the focus. Psychoanalysis uses direct dialogue between two people to help one of them. In psychoanalysis, there are also no experiments. History knows of long debates about whether psychoanalysis is a science or not, or to what extent. Psychoanalysis shares a similar fate to the Humanities in general. They are not considered science in the scope of this book either. Just because something is not a science does not make it bad. Many important things in life have nothing to do with science.

1.5 What is science?

I have discussed what the opposite of science could be. We have thought about what science not to meant. Know I want to make a little bit more clear, what science supposedly is. We divide science into two parts. The natural sciences, which include beside others physics, chemistry and biology. With biology we include all the life sciences. The other part is the formal science. We see here the formal science as tools to do science. As formal science we have as the main fields the mathematics, logic and theoretical computer science.

Experimentation and falsification lie at the core of science. We cannot reject an experiment. An experiment either takes place or it does not. However, a testable hypothesis can be rejected. This is sometimes referred to as the demarcation line of science, which is used to determine whether a field belongs to the natural sciences. In this book, we will use formal science to study the natural sciences. We need formal science as a tool.

Meters of books have been written about the sciences. As at the beginning stated, there are different version and definitions. While I was writing what you are now reading, I found some literature I party read and find intriguing. We meet Karl Pearson again as a founder of statistics, but in 1892 he wrote the book “The grammar of science”¹¹, which also inspired Einstein on his way to relativity.

Can science be objective? “Science is in reality a classification and analysis of the contents of the mind. […] In truth, the field of science is much more consciousness than an external world.”

“The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiased by personal feeling is characteristic of what may be termed the scientific frame of mind.” Karl

Ersnt Mach (1838-1916) “Ernst Mach’s positivism is a subjective, anti-metaphysical philosophy of science that restricts legitimate knowledge exclusively to directly observable sensations and measurements. He rejected unobservable entities like atoms as”hypothetical fictions”,”

¹² What is this thing called Science?

“In the same way, it is possible to follow form and call it science, but that is pseudo-science.”

“It should not be”science has shown” but “this experiment, this effect, has shown.”

“the result of the discovery that it is worthwhile rechecking by new direct experience, and not necessarily trusting the [human] race[’s] experience from the past.”

¹³ What is science

¹⁴ What is science?

David Deutsch claimed that science is guessing and falsification. Or in his words, “Tte whole [scientific] process resembles biological evolution. A problem is like an ecological niche, and a theory is like a gene or a species which is being tested for viability in that niche.”¹⁵

We conclude the following: A hypothesis should be testable through experimentation. The experiment should be designed in such a way that the hypothesis can be rejected. We need falsification. The experiment should also be reproducible; we will come to this point later.

1.6 Observables and beables

Liebig war Pettenkofer ein Positivist

Wheel of fortune

Figure 1.7: The wheel of knowledge combines science (the why), data (the what), and models (the how) in a framework. In an ideal world, all three would be active in generating knowledge. However, at least two must be chosen. Combining science and data is done in exploratory data analysis, where storytelling and visualization guide the explanation. The combination of science and models is used in theoretical works, such as general and special relativity. At its core, it is a thought experiment that generates laws and models. Most likely, data is combined with a model. The models reveal patterns in the data. These models can be used for prediction and inference. For example, standard quantum mechanics can be used as a powerful tool even though the reality of atoms, which the models predict, is unknown.

Ole Roemer (1644-1710)

https://www.amnh.org/learn-teach/curriculum-collections/cosmic-horizons-book/ole-roemer-speed-of-light

Eleven minutes (Cosmic Horizons: Astronomy at the Cutting Edge)

Pettenkofer vs. Koch

Definition: Beables sind Elemente der Realität, die existieren, unabhängig davon, ob sie beobachtet werden oder nicht. Unterschied zu Observablen: Während Observable Messwerte (z.B. Position oder Impuls) sind, die ein Beobachter erhält, sind Beables die grundlegenden physikalischen Fakten, aus denen die Welt besteht.

Experiment vs real world data

Clinical study vs observable study

An experiment has the randomisation included.

Why not observe something and than do science?

1.7 Why do science?

To find a good explanation

To help people

To reduce suffering and pain

To make the plant earth more habitable

To live longer

Because the human is lazy@price2021laziness

1.8 How to do science?

From now on I had to do a harsh decision. Science is broad, this book is in contrast slim. Therefore I will focus on the natural science. Especially, the life science, which includes all living things. Yes, some parts will also applicable to more technical fields like mechanical engineering and engineering sciences but only in a limited way. A building and the humans inside does not accept a error in its structure.

“As a scientist, you are a professional writer,” Joshua Schimel said.⁶

Pauli defined the scientific method as “taking up a subject repeatedly. Thinking about it. Setting it aside. Gathering new empirical material. And continuing this process for years if necessary. In this way, the conscious mind stimulates the unconscious mind. If anything, this is the only way to achieve results.”¹⁶. This is more or less about taking a chair and sitting in the middle of the room and getting bored as long as possible. Doing so sparks creativity.

Otto Kruse stated in his book, “many scientific topics can only be solved once all aspects have been explicitly formulated. The mind is not sufficiently prepared for this, as it can only ever focus on small sections at a time. Systematic thinking is only possible when writing, i.e. recording the results of one’s thinking and relating them to other aspects.”¹⁷

The two paths of logic.

Figure 1.9: The difference between the two logical pathways: On the left is the inductive logic, which is a bottom-up approach that goes from specific to general. First, we observe and collect data, then we look for patterns in the data. Then, we draw a general conclusion about the pattern. After observing something a few times, we conclude that it is probably a rule. On the right is the deductive logic, a top-down approach from general to specific. We have a general theory and conduct an experiment to test it. Then, we draw a conclusion. From a more common perspective, the two logical pathways have things in common but differ in their train of thought.

Erst Mach and observational things.

Karl Pearson what is reality.

Quantum mechanics, we do not know what reality is.

The measurement paradox. When there is no agent wo is measuring, does atoms exist? What does measuring mean? A interaction between a large and a small atomic object. Where is the border between large and quantum objects?

1.9 What is statistics in science?

On a warm spring day, I was sitting in my first statistics lecture. I don’t remember everything, but one quote from the beginning of the lecture has stuck with me: “Statistics is the engine room of science.” I think this quote might not have been spoken in this form. Rather, it was the underlying theme of the lecture.

A toolbox of mathematical models to do science.

In this book we will use Fisherian statistics, which is inductive logic reasoning. Or in other words the logic of inductive inference.

Fisher switched from a mathematical deductive reasoning to a inductive reasoning in science. This is remarkable for me, because he changed the way he does science.

Statistics by Fisher and quantum mechanics have in common that both do inductive probabilistic reasoning. Scientific models are deductive

Statistical models are inductive

Figure 1.10: Inductive reasoning is a probabilistic process in statistics. First, a hypothesis is stated. Then, an experiment is conducted based on the hypothesis, and data is collected. This data is a random representation of observables. This is where the probabilistic process begins. Then, statistical modeling is applied to the experimental data to minimize noise. Finally, a conclusion is drawn. Sometimes the aim is to make a probabilistic decision or explanation, with or without prediction.

Derivation of the formula for kinetic energy

Inductive reasoning seems a bit difficult to follow. Therefore, I conducted a small experiment to derive the formula for an object’s genetic energy, focusing on velocity. To make things easier, we will keep the mass constant. The formula is well-known; Newton discovered it. The formula for kinetic energy is $E_{kinetic} = \tfrac{1}{2}mv^2$. Therefore, we will take the mass of an object in kilograms and multiply it by the square of the velocity. Velocity is defined as follows: $v = \tfrac{d}{t}$. We divide the distance traveled by the time it takes the object to travel that distance. Now, I want to find the dependency between velocity and kinetic energy. To do so, I built the following apparatus. A $30$-gram ($0.03kg$) ball lies on a height-adjustable tower. The ball will travel a ramp without friction, covering a distance of $60cm$ ($0.6m$) to the ground. At different heights, we will measure how long it takes the ball to reach the ground. Then, we can calculate the velocity in each trial. We know the ball’s energy at the top. At the top, we find the potential energy with $E_{potential} = mgh$. We will multiply the ball’s mass by the acceleration due to gravity, which is $9.81 m/s^2$, and the height of the tower. Since we are changing the height, the ball’s energy will also increase.

Figure 1.11: The formula for kinetic energy can be derived through the following example experiment. A ball of fixed mass rolls down a fixed ramp from different heights. For each trial, the time it takes the ball to reach the bottom is measured with a stopwatch. The velocity can be calculated from the traveled distance and time. As the height increases, the ball will reach the ground in less time. Friction can be ignored. However, a measurement error will most likely occur in each trial.

Let’s write everything down. We have the mass of the ball, $m = 0.03kg$, the length of the ramp, $d = 2m$, and the acceleration due to gravity, $g = 9.81 m/s^2$. We put the tower at five different heights and let the ball roll. The ball runs surprisingly fast. Because we cannot perfectly adjust the height, and manual time measurement is error-prone, we obtain noisy velocity measurements. The observed data has an error. The table Table 1.1 includes the measured and calculated data.

Table 1.1: Results table from the experiment to determine the formula for kinetic energy. The height was changed five times. Using the acceleration due to gravity, the potential energy of the ball can be determined from its height and fixed weight. The ball’s speed can be determined from the rolling time and the fixed ramp length.

Height [m]	Potential energy [J]	Time [s]	Velocity [m/s]
$0.1$	$0.1 \cdot 0.03 \cdot 9.81 = 0.029$	$1.58$	$2/1.58 = 1.27$
$0.2$	$0.059$	$0.95$	$2.11$
$0.3$	$0.088$	$0.85$	$2.36$
$0.4$	$0.118$	$0.65$	$3.09$
$0.5$	$0.147$	$0.72$	$2.78$

A table of data is nice, but most of us cannot really see anything in a table. Therefore, we will visualize our data throughout the book. The Figure 1.12 displays the five data points for the energy of the balls and the final velocity. The blue line shows the result of a statistical model. I ran a nonlinear regression to find the perfect line through the points. How did I do this? We will discuss modeling later in the book. In contrast, the purple line shows the actual dependency of velocity on energy. There is a deviation in our statistical model. We can visualize this deviation as an area of uncertainty in our plot. Due to this deviation, we cannot find the perfect formula. There are different ways to show statistical deviation. In general, the deviation is related to how far the individual observations or points are from the line drawn by the model. This process is called fitting a line through points.

Figure 1.12: Visualization of the relationship between energy and velocity. The points represent calculated velocities from different heights. Due to measurement errors, the points do not fit perfectly on a line. The blue line is the formula derived from the data using a nonlinear model. The shaded area shows the uncertainty caused by measurement errors. The purple line shows the true dependency using the formula for kinetic energy.

What can we learn from our small experiment? No matter what we do, there will always be an error, noise, or deviation. There are different names for nearly identical concepts. This is the core of inductive reasoning using statistics. We will always have errors, and we want to minimize them. The main topic of this book is what this error is and how we describe these errors. Not really the errors themselves, but rather the concept of drawing lines through points by minimizing error.

Randomization and random observations

1.10 What is a good explanation?

1.11 What is real?

Sometimes we need a model to know what is real.

Fukusima¹⁸ ¹⁹

1.12 What is a probability?

1.13 What is the replication crisis?

²⁰

Not here, move to p-value chapter:²¹

1.14 Age of enlightment

Romantic as the answer to enlightment.

1.15 General background

Full quote

“Reality is negotiable. Outside of science and law, all rules can be bent or broken, and it doesn’t require being unethical.” — Tim Ferriss

“This is your last chance. After this, there is no turning back. You take the blue pill - the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill - you stay in Wonderland and I show you how deep the rabbit hole goes.” — Morpheus, Matrix

Idea of hypotheses

Science is guessing and falsification

²² Models Demystified: A Practical Guide from Linear Regression to Deep Learning

²³ Statistical Thinking for the 21st Century

David Deutsch > Quotes

1.16 Alternatives

*“The truth is out there.” — The X files

Disappointed about this chapter? You wanted more but have gotten less? There are other books and ideas outside.

Against Method: Outline of an Anarchistic Theory of Knowledge by Paul Karl Feyerabend¹

The Structure of Scientific Revolutions by Thomas S. Kuhn⁴

The Logic of Scientific Discovery by critical rationalism by Karl Popper³

The beginning of infinity: Explanations that transform the world by David Deutsch¹⁵

1.17 Dramatis personae

1.18 Glossary

experiment: what does it mean.
epistemic: Counterpart of aesthetic. Keep in mind the saying, “It is too beautiful (‘aesthetic’) to be true (‘epistemic’).”

1.19 The meaning of “Models of Reality” in this chapter.

Science is divided in formal and natural science
Formal sciences provide tools for natural sciences
Science and non-science is divided by experiment and falsification
An experiment must include testable hypothesis

1.20 Summary

References

[1]

Feyerabend P. Against Method: Outline of an Anarchistic Theory of Knowledge. Verso Books; 1970.

[2]

David Mermin N. What’s wrong with this pillow? Physics Today. 1989;42(4):9-11.

[3]

Popper KR. The logic of scientific discovery. Published online 1959.

[4]

Kuhn TS, Hacking I. The Structure of Scientific Revolutions. Vol 2. University of Chicago press Chicago; 1970.

[5]

Boyd NM, Bogen J. Theory and observation in science. Published online 2009.

[6]

Schimel J. Writing Science: How to Write Papers That Get Cited and Proposals That Get Funded. OUP USA; 2012.

[7]

Clarke AC. Clarke’s third law on UFO’s. Science. 1968;159(3812):255-255.

[8]

Feynman RP. Cargo cult science. In: The Art and Science of Analog Circuit Design. Elsevier; 1998:55-61.

[9]

Douglas KM, Sutton RM. What are conspiracy theories? A definitional approach to their correlates, consequences, and communication. Annual review of psychology. 2023;74(1):271-298.

[10]

Grimes DR. On the viability of conspiratorial beliefs. PloS one. 2016;11(1):e0147905.

[11]

Pearson K. The grammar of science. Nature. 1892;46(1185):247-247.

[12]

Chalmers AF. What Is This Thing Called Science? Hackett Publishing; 2013.

[13]

Feynman R. What is science. Published online 1966.

[14]

Campbell NR. What is science? Published online 1952.

[15]

Deutsch D. The Beginning of Infinity: Explanations That Transform the World. penguin uK; 2011.

[16]

Fischer EP. Die Stunde Der Physiker: Einstein, Bohr, Heisenberg Und Das Innerste Der Welt. CH Beck; 2022.

[17]

Kruse O. Keine angst vor dem leeren blatt. Ohne Schreibblockaden durchs Studium. 2007;12:112.

[18]

Sevón T. Analysis of reactor water level measurements during the fukushima unit 2 accident. Nuclear Engineering and Design. 2020;366:110760.

[19]

Sevón T. Analyzing reactor water level measurements in the fukushima daiichi 1 accident. Progress in Nuclear Energy. 2023;160:104707.

[20]

Romero F. Philosophy of science and the replicability crisis. Philosophy Compass. 2019;14(11):e12633.

[21]

Benjamin DJ, Berger JO, Johannesson M, Nosek BA, Wagenmakers EJ, Berk R, et al. Redefine statistical significance. Nature human behaviour. 2018;2(1):6-10.

[22]

Clark M, Berry S. Models Demystified: A Practical Guide from Linear Regression to Deep Learning. CRC Press; 2025.

[23]

Cox D, Efron B. Statistical thinking for 21st century scientists. Science advances. 2017;3(6):e1700768.

```{r echo = FALSE, warning = FALSE, message = FALSE} source("init.R") source("images/part_0/part_0_science.R") source("images/part_0/part_0_history.R") ``` # What is science? {#sec-what-is-science} *Last modified on `r format(fs::file_info("chapter-01-what-is-science.qmd")$modification_time, '%d. %B %Y at %H:%M:%S')`* > *"This is your last chance. After this, there is no turning back. You take the blue pill - the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill - you stay in Wonderland and I show you how deep the rabbit hole goes." --- Morpheus, Matrix* "Anything goes" is Paul Feyerabend's famous dictum @feyerabend1970against. Therefore, you can stop here. If you are not interested in the historical or philosophical background of what we call science, then skip ahead to the next chapter. You don't really need the background. Think of a theater actor. The actor doesn't need to know how the stage is built, how the lights work, or where the music comes from. The actor just performs the play. Nothing more is required. Or, to say it in the words of David Mermin, "Shut up and calculate!" @david1989s With this statement, Mermin describes the Copenhagen interpretation as a philosophy of quantum physics that prioritizes mathematical results over foundational philosophical questions. For everyone else, I have written this introduction chapter. Maybe you're puzzled about what this science thing is all about. That's perfectly normal. Today, education strips away the historical and philosophical context and jumps directly into biological, chemical, or physical topics. History tells the story of countries and people, not the combination of history and the natural sciences. There is so much to learn. Therefore, there is seldom room for philosophy in any rushed school schedule. However, humans do science. What humans do becomes history. The reasons and ways in which humans do things are strongly connected to their thoughts and beliefs. Therefore, they have a philosophy, even if they are not aware of it. So, if you do science, you do so with a particular way of thinking. Therefore, you have a philosophy, whether you are aware of it or not. It's time to talk about it a little bit. ## Why history and philosophy? What could possibly be a better argument for something than the thought of a genius and Nobel Prize winner? Therefore, we begin this section with a quote from Albert Einstein. > *"I fully agree with you about the significance and educational value of as well as history and philosophy of science. So many people today - and even professional - seem to me like someone who has seen thousands of trees but has never seen a forest. A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is - in my opinion - the mark of distinction between a mere craftsman or specialist and a real seeker after truth." --- Albert Einstein* Don't worry, we won't start with the science of the Stone Age. Instead, we will focus on the modern era and the knowledge gathered during this time. In this section, we will also focus on science itself. We will discuss data and models later. For now, we will focus solely on the meaning of science. Science is hard to pinpoint. I thought it would be easy to define. What could be the problem? Then I thought about it, read about it, and thought about it again. There are three big books. The fact that there are three big books alone shows you that it cannot be so easy to define science. Yes, it is complicated. In the end, I will give you all the sources, but for now, there are three books: *The Logic of Scientific Discovery* by Karl Popper @popper1959logic, *The Structure of Scientific Revolutions* by Thomas S. Kuhn @kuhn1970structure, and *Against Method: Outline of an Anarchistic Theory of Knowledge* by Paul Karl Feyerabend @feyerabend1970against. You can read these books or not. I will give you a brief introduction and refer to them. As always, a brief summary cannot encompass all the ideas of these books. Before we continue, I would like to present a brief example of knowledge generation. How can we obtain enterprise knowledge? In this case, we will explore cholera as a human curse through the lens of a famous German scientist and his concepts. ### Cholera and breathing walls In 1854, cholera visited the city of Munich in Bavaria, Germany. This was not a pleasant visit, as many citizens died of cholera and its consequences. However, not all parts of the city were affected equally. By the end of the 19th century, Munich would become one of the cleanest cities in Europe. Max von Pettenkofer achieved this by building and renovating the canalization system. When cholera arrived, not all parts of the city had equal access to the canalization and fresh water supply. Some parts of the city had easy access to fresh water and working toilets. In other parts of the city, sometimes only divided by a street, construction of the canalization had not yet begun. It was observed that the death toll from cholera varied by district. In the following @fig-chap-01-petten (A) we see a fictional pattern. It is of two districts of Munich. On the left, the sewerage and freshwater systems are already installed and operational. We can call this area the "hygienic area." On the right, the canalization has not been finished or even started. We will call this area "filthy" or "dirty." After the cholera epidemic outbreak, the number of deaths in each district was counted. There were ten deaths in the hygienic area and twenty-nine in the filthy area. We assume that both areas have roughly the same number of inhabitants. Pettenkofer observed the lower death rates in hygienic areas and concluded that canals and fresh water would stop cholera from spreading and killing people. Therefore, more sewage systems must be installed, and the city must be cleaned up. But wait a minute. What is the cause of the deaths? Yes, it is the illness cholera. But how does it work? What causes the illness? Pettenkofer discovered a way to cure or prevent cholera, even though he did not understand the cause of the illness. He did not know how it was transmitted or why people died from it. He proposed that the cause should be found in specific soil and groundwater processes. In 1883, Robert Koch discovered the cholera bacillus to be the cause of the illness. Pettenkofer did not believe in unobservable bacteria. In 1892, at a cholera conference, his belief was so strong that he drank a cholera culture. He survived with mild symptoms. According to Pettenkofer, the cholera culture could not be the reason people died. He was still alive. Another example of Pettenkofer's thinking is the breathing wall. @fig-chap-01-petten (B) shows the experimental setup. Pettenkofer sealed off his office. He sealed the doors and windows with glue. From his point of view, the room was perfectly contained. Then, he measured the airflow inside the room. The room's pressure stayed constant while an influx could be measured. Therefore, Pettenkofer concluded that air could pass through the walls' pores. Thus, the breathing wall model was born. However, it has been suggested that Pettenkofer might have forgotten to seal a chimney, or that the wooden floor and ceiling might have been leaking. ```{r} #| echo: false #| message: false #| warning: false #| label: fig-chap-01-petten #| fig-align: center #| fig-height: 4.5 #| fig-width: 10 #| fig-cap: "Visualization of two erroneous theories by Max von Pettenkofer (1818–1901). As a positivist, he only believed in facts that he could see, like the results of experiments. **(A)** Schematic example of the influence of soil conditions, here represented as fresh water/sewage (blue), on cholera cases. The district with a fresh water supply has fewer cholera cases than the district without access. Pettenkofer was able to contain cholera through hygiene, even if he could not determine its cause. **(B)** The breathing wall concept, which states that the exchange of fresh air in a room mainly occurs through the walls' pores. Pettenkofer likely failed to properly seal the chimney and ceilings for the air exchange measurements." p_cholera + p_wall + plot_layout(ncol = 2) + plot_annotation(tag_levels = 'A', tag_prefix = '(', tag_suffix = ')') & theme(plot.tag = element_text(size = 16, face = "bold")) ``` That's where we come to a halt. What is Pettenkofer doing? He was a very successful scientist. But he was sometimes wrong. Interestingly, Pettenkofer came up with one of the precursors to the periodic table of elements. He had to stop his work due to a lack of funding from the Bavarian state. In 1869, however, Dmitri Mendeleev, the discoverer of the periodic system, mentioned Pettenkofer in his articles as one of the few who influenced his work. Pettenkofer only looked at what he could see. His thought process was bound to the observable. Now, we will learn about the philosophy of science. We will use Pettenkofer as an example. We will meet other people with strange ideas later on. Strange ideas are also science. It's thinking outside the box. From a philosophical point of view, who was Pettenkofer? He was a positivist. This is a specific philosophical approach to acquiring knowledge. Positivists only believe in what can be seen or observed. If you wear glasses, you may notice a slight flaw in the argument about what is and isn't observable while reading this book. Now, let's take a closer look at the concepts of empiricism to logical positivism. ### From empiricism to logical positivism How does the human mind learn? How do we gather information? Humans are born in a blank state. No ideas are implanted in the brain; only instincts guide the infant through the first weeks and months. Shortly after, the infant begins to learn through the senses. This is mostly true and forms the basis of empiricism. I will not focus on human development. Therefore, we will only focus on the origin of empiricism as a basis for generating knowledge. The idea of empiricism is simple and appealing. In my experience, common sense often begins with empiricism to gather knowledge. Therefore, we will start with this simple idea and explain its history. Empiricism : The source of knowledge comes from observation and sensory experience. We learn through the five senses, which guide our ideas. The focus is on the human mind. Next, we will broaden the scope of empiricism by asking how science and society should function. Since we have learned through our senses, we can apply this idea to science and society in general. Since we will focus only on observable things and dismiss invisible entities, we will call our concept "positivism." Positivism comes from the Latin word *positum*, meaning "that which is given" or "laid down." No, this does not make it any better. Furthermore, we must distinguish between two completely different concepts that often pop up in our minds. Positivism is often confused with positive thinking. This is a common linguistic mistake, but positivism and positive thinking are not related. One is a rigorous philosophy of science, while the other is a psychological mindset or self-help technique. Positivism : The validity of knowledge comes from observation and sensory experience by ignores everything invisible or immeasurable. If you cannot measure it or observe it, it shouldn't be part of a serious discussion. Now, let's turn the wheel of positivism a bit further towards the extreme. Therefore, we must visit Vienna in the early 19th century. The Vienna Circle was a group of philosophers who met at the University of Vienna from 1924 to 1936. They had a big influence on the study of philosophy and science. In 1929, the Vienna Circle wrote "The Scientific Conception of the World", also known as "The Manifesto." The manifesto had two aims. First, it introduces the group and Vienna. At the beginning of the text, it reads more like an advertisement for Vienna and the Vienna Circle. More scientists should join the club. The philosophical main points are somewhat buried in the text. The Vienna Circle proposed that science is both empirical and positivist; knowledge comes only from experience. Furthermore, the process of scientific world conception involves applying logical analysis to observed objects, or, in other words, experience. Logical Positivism : The validity of knowledge is acquired through sensory experience, by integrating modern methods of mathematics and logic. For a statement to be meaningful, it must be testable by observation. It must be proven true either by logic (an analytic statement) or by experimentation (a synthetic statement). Thus, the verification principle is introduced. ```{r} #| echo: false #| message: false #| warning: false #| label: fig-chap-01-emp-to-logical #| fig-align: center #| fig-height: 2.25 #| fig-width: 7 #| fig-cap: "D" p_emp_to_logical ``` Or to write it in the words of John Passmore, who said: "Logical positivism is dead—or as dead as a philosophical movement can be." ```{r} #| echo: false #| message: false #| warning: false #| label: fig-chap-01-person-positiv #| fig-align: center #| fig-height: 4 #| fig-width: 8 #| fig-cap: "Dramatis personae in this chapter and their biographical details, as well as important scientific discoveries or hypotheses. We consider a selection of scientists who have contributed to the philosophical background of science and positivism. The dates refer roughly to the year of publication or when the discovery became known to the public." p_persons_positiv ``` epistemically Paul Feyerabend's famous dictum ‘Anything goes’ is at the heart of his methodological anarchism, which states that there are no universally valid rules in science. Feyerabend argued that progress often arises from breaking rules, which is why rigid methodology hinders rather than promotes the acquisition of knowledge. @feyerabend1970against "Shut up and calculate" is a philosophy in quantum physics advocating a focus on mathematical results over interpreting foundational, philosophical questions. @david1989s Three fields of science Theoretical Experimental Instrumental Paradigm shift @kuhn1970structure Even witchcraft has an paradigm Not piling up knowledge but a process thorough knowledge ```{r} #| echo: false #| message: false #| warning: false #| label: fig-chap-01-types-science #| fig-align: center #| fig-height: 2.4 #| fig-width: 7 #| fig-cap: "The three types of science working fields are as follows: Theoretical science is the brain of science, where new, fundamental concepts are born. Thought experiments and guesswork are the main tasks. Experimental science uses suggestions from theory to conduct tests. This testing is based on the falsification principle. Finally, instrumental science uses blueprints from theory to invent new devices usable in experimental science. Each type of science can be done without using the other fields. It can be done in a passive manner." p_theo_exper_instr ``` ```{r} #| echo: false #| message: false #| warning: false #| label: fig-chap-01-kuhn #| fig-align: center #| fig-height: 3.5 #| fig-width: 8 #| fig-cap: "The paradigm shift cycle, also known as the Kuhn Cycle after its inventor. The cycle describes how science evolves over time. Normal science is stable and attempts to solve puzzles and problems within a given framework. From time to time, anomalies occur that do not fit the common sense of the current science. These anomalies are usually seen as experimental error, resulting in a social pushback. Eventually, the anomalies pile up, and a crisis occurs. This marks a crack in the stable science. From there, a revolution occurs, and candidates of reality comes into being. Finally, a new paradigm of reality emerges. In this new paradigm, new languages and a new framework of science are established. Then, normal science begins again. There is a strong social component to this cycle because humans often resist fundamental changes." p_kuhn_cycle ``` Incommensurability, a terrible word, meaning that something can not be compared. Maybe incomparable observations are theory-laden Observation = Sensory Input + Theoretical Framework Language shapes data: We use theoretical words to describe what we see. If you say, "The electron moved," you are already assuming the "theory" that electrons exist and are particles that move. @boyd2009theory ## Old start The first chapter of this book is already the hardest. I started writing this chapter very early on, perhaps even before any of the others. Yet it took the longest to finish. The question is simple: What is science? The more I researched, the more complicated the answer became. Or the other way around. I followed the advice of Wolfgang Pauli. Pauli defined the scientific method as "taking up a subject repeatedly. Thinking about it. Setting it aside. Gathering new empirical material. And continuing this process for years if necessary. In this way, the conscious mind stimulates the unconscious mind. If anything, this is the only way to achieve results." Therefore, I tried to read and find answers to the question of what science might be. Perhaps science is, at its core, something personal. However, science also has objective aspects that I want to present here. Ultimately, decide for yourself what science truly is. The following @fig-overview-sience-non-science shows the demarcation line between science and non-science. In the next sections, we will discuss each specific part, but I think it's important to start with a clear overview. Science is distinguished from non-science through experimentation and falsification. This is true in this book. There are many subtle definitions, but I will keep it simple here. If an experiment is not possible, then it is not science. We also need the ability to build a falsification framework. Therefore, we need hypotheses that can be rejected by experimentation. These two requirements are met by the natural sciences, including physics, chemistry, and biology, in order of their purity. Biology includes medicine and all other fields of knowledge gathered from living things. In addition to natural science, there is formal science, which can be seen as a tool of science. This is due to the lack of experimentation, falsification, or both. Therefore, we will not include mathematics, logic, or theoretical computer science as sciences. True non-science fields are intuition-based or subjective at their core. There are many of these fields, and we will discuss them shortly. The humanities are undoubtedly different from non-science, but this book is not about the humanities, so we will put them aside. ```{r} #| message: false #| echo: false #| warning: false #| fig-align: center #| fig-height: 5 #| fig-width: 10 #| fig-cap: "Visualization of the demarcation line of science. This line divides science from non-science through experimentation and the principle of falsification. The purity of science fields is taken from xkcd comic #435 ([https://xkcd.com/435](https://xkcd.com/435/)). According to this definition, natural science, including physics, chemistry, and biology, is separated from formal science, including mathematics. Formal science must be clearly distinguished from other intuition-based and subjective non-science, such as pseudoscience or anti-science. The humanities are indisputably different but are also considered non-science in this schematic." #| label: fig-overview-sience-non-science p_science_overview ``` Perhaps we should start with the supposedly easy part. What is the opposite of science? In doing so, we will gain an understanding of the term "science" and what it means to us. This may be the deepest lesson for me: we cannot really grasp science. Science is connected to each person in a different emotional way. Science seems cold and rational, but humans are not. Therefore, our relationship with science is strange and complex. Science is its own way of thinking, perhaps a philosophy. Therefore, there are as many ways of thinking as there are human minds. ## What is the opposite of science? As I found out, there is no direct opposite of science. That's interesting. Sometimes, you can define something by knowing what it is not. You might think this is not so problematic. Take a few minutes to ask yourself: "What is the opposite of science?" Okay, good to have your focus back on the page. Maybe you thought science was cold and rational. I will share my personal story with science. For me, science was Star Trek: Enterprise. But I'm too young for Kirk and Spock. So, I was socialized with Captain Jean-Luc Picard and Star Trek: The Next Generation (TNG). That's where I first encountered Shakespeare, but that's another story. In TNG, science was determined by the exploration of new worlds. I would sit comfortably on the open bridge in front of the gigantic viewscreen. Commander Data was the embodiment of science. He was an android. He was rational and cold, devoid of emotion and humor. Let's flip these attributes. If an android is science, then what is a human? Then is the human the opposite of science? Perhaps there is some truth to that. Humans have lived on this planet for thousands of years, but science as we know it began during the Enlightenment. So perhaps humans are the opposite of science. Human beings are full of emotions and feelings. Each one is very subjective and interested in their own development. They feel love and romance. Neither of these is very scientific. Humans also believe. Some believe in a more structured manner, like in big churches, while others believe in a more individual manner. However, believing in something has nothing to do with science. But humans do science. Therefore, science is part of humanity. As Joshua Schimel said, "Knowledge is a product of human hopes and fears. Our emotions are crucial to its development, and it cannot be truly understood as some bloodless, emotionless enterprise."@schimel2012writing Science is a human endeavor. According to Arthur C. Clarke's Third Law, "Any sufficiently advanced technology is indistinguishable from magic."@clarke1968clarke Is magic therefore the opposite of science? We cannot perform magic. We do not have the power to do so. However, some humans believe that we can perform magic. Who is "we"? The advanced part of humankind. We come into contact with our brothers and sisters who are at a different technological level, such as tribal cultures on isolated islands in Indonesia. To a tribe with a primitive culture, our technology seems like magic. Here, we can observe the cargo cult. A cargo cult is named after its appearance in World War II. The US Army faced the challenge of determining the best island-hopping route to mainland Japan. Since no one knew and the tides of war were constantly changing, the US Army Logistics Corps decided to drop cargo everywhere. This way, if US soldiers approached an island, there would already be plenty of supplies. What happened to the indigenous population? They believed that the gods had come to bring them cargo. They could not think of any other explanation for what they observed. They observed hardened silver birds dropping and landing on the islands. After a while, the gods stopped showing up. The war was over. But nobody told them. Therefore, the people of the islands copied the gods' behavior. They built the control room, and they made a radar station out of grass and wood. They even built plans out of grass. Nothing could work. They did everything perfectly, but they missed the point entirely. It was a cargo cult, not science. They copied someone else's routine and hoped to experience what the gods experienced when they did the same. Do you follow a cargo cult in your daily routines? Do you do things that you have seen but don't understand? Do you believe that they will work even though you don't know why? This is totally human and from my point of view totally necessary to be a working community member. Some stuff must be done, even if I don not really understand the why. But what if we do it in science? Then we will do cargo cult science @feynman1998cargo. It is a danger of enormous proportions if done in the wrong place with the wrong intentions. Still, most intentions are good and are twisted by the circumstances. There are several examples of following dogmatic rules and getting a catastrophic outcome. Later, we will explore different models of reality, including the Fukushima nuclear accident. For now, I would like to conclude that the opposite of science is difficult to grasp. On the one hand, we could argue that human emotions and feelings are the opposite of cold, rational science. However, emotions are also the driving force behind human scientific inquiry. Therefore, we are doing something scientific by leaving the topic open for further research and looking for things that are not science. ## What is not science? Besides things that are the opposite of science, there are things that are similar to science or that use attributes and tools in a distorted way to imitate science. Conspiracy theories [@douglas2023conspiracy; @grimes2016viability] look like science and use science terms and tools. They play on a stage that looks like science but has no deeper foundation. It's more like a nice story about humans harming other humans. However, conspiracy theories attempt to explain the world and often generate money for the storyteller. Therefore, I do not see conspiracy theories as the opposite of science. These conspiracy theories are non-science. Some theories have a historical basis, such as the hollow earth conspiracy theory. We will discuss the origin later. Conspiracy theories like to be retold, and in the process, they grow and multiply. To circumvent the proliferation of conspiracy theories, I will provide an illustration of the anti-conspiracy theory "Birds Aren't Real" by Peter McIndoe. What does the movement claim? In short, the US government kills all birds in the US and replaces them with bird-looking drones. Birds sit on power lines to recharge and defecate on cars to mark them visually. The bird drones are there to spy on American citizens. The specifications are inconsistent and vary. This is a typical sign of a conspiracy theory. Finally, U.S. President John F. Kennedy was assassinated by the government due to his reluctance to kill all the birds as cherry on top. What do conspiracy theories have in common? They all tell a good story. I personally find them more similar to fairy tales, with the standard Greek dramatic structure of one hero against an anonymous horde of evil. In addition, they all have in common a lack of experiment. They don't even conduct a small experiment or propose a hypothesis to test. A testable hypothesis is rarely claimed. Even if a hypothesis is present, the story can easily be changed to maintain its purpose: to tell a good story. Here, we will not focus on conspiracy theories and how they work. This topic is beyond the scope of this book. There is another field in which personal stories are the focus. Psychoanalysis uses direct dialogue between two people to help one of them. In psychoanalysis, there are also no experiments. History knows of long debates about whether psychoanalysis is a science or not, or to what extent. Psychoanalysis shares a similar fate to the Humanities in general. They are not considered science in the scope of this book either. Just because something is not a science does not make it bad. Many important things in life have nothing to do with science. ## What is science? I have discussed what the opposite of science could be. We have thought about what science not to meant. Know I want to make a little bit more clear, what science supposedly is. We divide science into two parts. The natural sciences, which include beside others physics, chemistry and biology. With biology we include all the life sciences. The other part is the formal science. We see here the formal science as tools to do science. As formal science we have as the main fields the mathematics, logic and theoretical computer science. Experimentation and falsification lie at the core of science. We cannot reject an experiment. An experiment either takes place or it does not. However, a testable hypothesis can be rejected. This is sometimes referred to as the demarcation line of science, which is used to determine whether a field belongs to the natural sciences. In this book, we will use formal science to study the natural sciences. We need formal science as a tool. Meters of books have been written about the sciences. As at the beginning stated, there are different version and definitions. While I was writing what you are now reading, I found some literature I party read and find intriguing. We meet Karl Pearson again as a founder of statistics, but in 1892 he wrote the book "The grammar of science" @pearson1892grammar, which also inspired Einstein on his way to relativity. Can science be objective? "Science is in reality a classification and analysis of the contents of the mind. […] In truth, the field of science is much more consciousness than an external world." "The classification of facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiased by personal feeling is characteristic of what may be termed the scientific frame of mind." Karl Ersnt Mach (1838-1916) "Ernst Mach’s positivism is a subjective, anti-metaphysical philosophy of science that restricts legitimate knowledge exclusively to directly observable sensations and measurements. He rejected unobservable entities like atoms as "hypothetical fictions"," @chalmers2013thing [What is this thing called Science?](https://www.pmf.unizg.hr/_download/repository/1._Dodatna_literatura_%28filozofija_znanosti%29%5B3%5D.pdf) "In the same way, it is possible to follow form and call it science, but that is pseudo-science." "It should not be "science has shown" but "this experiment, this effect, has shown." "the result of the discovery that it is worthwhile rechecking by new direct experience, and not necessarily trusting the [human] race['s] experience from the past." @feynman1966science [What is science](https://www-oc.chemie.uni-regensburg.de/diaz/media/docs/feynman_what-is-science_68.pdf) @campbell1952science [What is science?](https://www.whatisscience.info/files/what_is_science_rd1.pdf) David Deutsch claimed that science is guessing and falsification. Or in his words, "Tte whole [scientific] process resembles biological evolution. A problem is like an ecological niche, and a theory is like a gene or a species which is being tested for viability in that niche." @deutsch2011beginning We conclude the following: A hypothesis should be testable through experimentation. The experiment should be designed in such a way that the hypothesis can be rejected. We need falsification. The experiment should also be reproducible; we will come to this point later. ## Observables and beables Liebig war Pettenkofer ein Positivist Wheel of fortune ```{r} #| echo: false #| message: false #| warning: false #| label: fig-chap-01-triangle #| fig-align: center #| fig-height: 9 #| fig-width: 10.5 #| fig-cap: "The wheel of knowledge combines science (the why), data (the what), and models (the how) in a framework. In an ideal world, all three would be active in generating knowledge. However, at least two must be chosen. Combining science and data is done in exploratory data analysis, where storytelling and visualization guide the explanation. The combination of science and models is used in theoretical works, such as general and special relativity. At its core, it is a thought experiment that generates laws and models. Most likely, data is combined with a model. The models reveal patterns in the data. These models can be used for prediction and inference. For example, standard quantum mechanics can be used as a powerful tool even though the reality of atoms, which the models predict, is unknown." p_wheel_knowledge ``` Ole Roemer (1644-1710) https://www.amnh.org/learn-teach/curriculum-collections/cosmic-horizons-book/ole-roemer-speed-of-light Eleven minutes (Cosmic Horizons: Astronomy at the Cutting Edge) ```{r} #| echo: false #| message: false #| warning: false #| label: fig-chap-01-triangle-jupiter #| fig-align: center #| fig-height: 1.5 #| fig-width: 7 #| fig-cap: "fooo" p_io_speed_of_light ``` Pettenkofer vs. Koch Definition: Beables sind Elemente der Realität, die existieren, unabhängig davon, ob sie beobachtet werden oder nicht. Unterschied zu Observablen: Während Observable Messwerte (z.B. Position oder Impuls) sind, die ein Beobachter erhält, sind Beables die grundlegenden physikalischen Fakten, aus denen die Welt besteht. Experiment vs real world data Clinical study vs observable study An experiment has the randomisation included. Why not observe something and than do science? ## Why do science? To find a good explanation To help people To reduce suffering and pain To make the plant earth more habitable To live longer Because the human is lazy@price2021laziness ## How to do science? From now on I had to do a harsh decision. Science is broad, this book is in contrast slim. Therefore I will focus on the natural science. Especially, the life science, which includes all living things. Yes, some parts will also applicable to more technical fields like mechanical engineering and engineering sciences but only in a limited way. A building and the humans inside does not accept a error in its structure. "As a scientist, you are a professional writer," Joshua Schimel said. @schimel2012writing Pauli defined the scientific method as "taking up a subject repeatedly. Thinking about it. Setting it aside. Gathering new empirical material. And continuing this process for years if necessary. In this way, the conscious mind stimulates the unconscious mind. If anything, this is the only way to achieve results." @fischer2022stunde. This is more or less about taking a chair and sitting in the middle of the room and getting bored as long as possible. Doing so sparks creativity. Otto Kruse stated in his book, "many scientific topics can only be solved once all aspects have been explicitly formulated. The mind is not sufficiently prepared for this, as it can only ever focus on small sections at a time. Systematic thinking is only possible when writing, i.e. recording the results of one's thinking and relating them to other aspects."@kruse2007keine The two paths of logic. ```{r} #| message: false #| echo: false #| warning: false #| fig-align: center #| fig-height: 4.5 #| fig-width: 10 #| fig-cap: "The difference between the two logical pathways: On the left is the inductive logic, which is a bottom-up approach that goes from specific to general. First, we observe and collect data, then we look for patterns in the data. Then, we draw a general conclusion about the pattern. After observing something a few times, we conclude that it is probably a rule. On the right is the deductive logic, a top-down approach from general to specific. We have a general theory and conduct an experiment to test it. Then, we draw a conclusion. From a more common perspective, the two logical pathways have things in common but differ in their train of thought." #| label: fig-sience-inductive p_sience_inductive ``` Erst Mach and observational things. Karl Pearson what is reality. Quantum mechanics, we do not know what reality is. The measurement paradox. When there is no agent wo is measuring, does atoms exist? What does measuring mean? A interaction between a large and a small atomic object. Where is the border between large and quantum objects? ## What is statistics in science? On a warm spring day, I was sitting in my first statistics lecture. I don't remember everything, but one quote from the beginning of the lecture has stuck with me: "Statistics is the engine room of science." I think this quote might not have been spoken in this form. Rather, it was the underlying theme of the lecture. A toolbox of mathematical models to do science. In this book we will use Fisherian statistics, which is inductive logic reasoning. Or in other words the logic of inductive inference. Fisher switched from a mathematical deductive reasoning to a inductive reasoning in science. This is remarkable for me, because he changed the way he does science. Statistics by Fisher and quantum mechanics have in common that both do inductive probabilistic reasoning. Scientific models are deductive Statistical models are inductive ```{r} #| message: false #| echo: false #| warning: false #| fig-align: center #| fig-height: 4 #| fig-width: 4.5 #| fig-cap: "Inductive reasoning is a probabilistic process in statistics. First, a hypothesis is stated. Then, an experiment is conducted based on the hypothesis, and data is collected. This data is a random representation of observables. This is where the probabilistic process begins. Then, statistical modeling is applied to the experimental data to minimize noise. Finally, a conclusion is drawn. Sometimes the aim is to make a probabilistic decision or explanation, with or without prediction." #| label: fig-statistic-inductive p_statistic_inductive ``` ::: callout-note ## Derivation of the formula for kinetic energy Inductive reasoning seems a bit difficult to follow. Therefore, I conducted a small experiment to derive the formula for an object's genetic energy, focusing on velocity. To make things easier, we will keep the mass constant. The formula is well-known; Newton discovered it. The formula for kinetic energy is $E_{kinetic} = \tfrac{1}{2}mv^2$. Therefore, we will take the mass of an object in kilograms and multiply it by the square of the velocity. Velocity is defined as follows: $v = \tfrac{d}{t}$. We divide the distance traveled by the time it takes the object to travel that distance. Now, I want to find the dependency between velocity and kinetic energy. To do so, I built the following apparatus. A $30$-gram ($0.03kg$) ball lies on a height-adjustable tower. The ball will travel a ramp without friction, covering a distance of $60cm$ ($0.6m$) to the ground. At different heights, we will measure how long it takes the ball to reach the ground. Then, we can calculate the velocity in each trial. We know the ball's energy at the top. At the top, we find the potential energy with $E_{potential} = mgh$. We will multiply the ball's mass by the acceleration due to gravity, which is $9.81 m/s^2$, and the height of the tower. Since we are changing the height, the ball's energy will also increase. ```{r} #| message: false #| echo: false #| warning: false #| fig-align: center #| fig-height: 3.75 #| fig-width: 5.75 #| fig-cap: "The formula for kinetic energy can be derived through the following example experiment. A ball of fixed mass rolls down a fixed ramp from different heights. For each trial, the time it takes the ball to reach the bottom is measured with a stopwatch. The velocity can be calculated from the traveled distance and time. As the height increases, the ball will reach the ground in less time. Friction can be ignored. However, a measurement error will most likely occur in each trial." #| label: fig-newton-example p_newton_example ``` Let's write everything down. We have the mass of the ball, $m = 0.03kg$, the length of the ramp, $d = 2m$, and the acceleration due to gravity, $g = 9.81 m/s^2$. We put the tower at five different heights and let the ball roll. The ball runs surprisingly fast. Because we cannot perfectly adjust the height, and manual time measurement is error-prone, we obtain noisy velocity measurements. The observed data has an error. The table @tbl-newton-data includes the measured and calculated data. | Height \[m\] | Potential energy \[J\] | Time \[s\] | Velocity \[m/s\] | |--------------|------------------|--------------|--------------| | $0.1$ | $0.1 \cdot 0.03 \cdot 9.81 = 0.029$ | $1.58$ | $2/1.58 = 1.27$ | | $0.2$ | $0.059$ | $0.95$ | $2.11$ | | $0.3$ | $0.088$ | $0.85$ | $2.36$ | | $0.4$ | $0.118$ | $0.65$ | $3.09$ | | $0.5$ | $0.147$ | $0.72$ | $2.78$ | : Results table from the experiment to determine the formula for kinetic energy. The height was changed five times. Using the acceleration due to gravity, the potential energy of the ball can be determined from its height and fixed weight. The ball's speed can be determined from the rolling time and the fixed ramp length. {#tbl-newton-data} A table of data is nice, but most of us cannot really see anything in a table. Therefore, we will visualize our data throughout the book. The @fig-kenetic-energy displays the five data points for the energy of the balls and the final velocity. The blue line shows the result of a statistical model. I ran a nonlinear regression to find the perfect line through the points. How did I do this? We will discuss modeling later in the book. In contrast, the purple line shows the actual dependency of velocity on energy. There is a deviation in our statistical model. We can visualize this deviation as an area of uncertainty in our plot. Due to this deviation, we cannot find the perfect formula. There are different ways to show statistical deviation. In general, the deviation is related to how far the individual observations or points are from the line drawn by the model. This process is called fitting a line through points. ```{r} #| message: false #| echo: false #| warning: false #| fig-align: center #| fig-height: 3.5 #| fig-width: 7 #| fig-cap: "Visualization of the relationship between energy and velocity. The points represent calculated velocities from different heights. Due to measurement errors, the points do not fit perfectly on a line. The blue line is the formula derived from the data using a nonlinear model. The shaded area shows the uncertainty caused by measurement errors. The purple line shows the true dependency using the formula for kinetic energy." #| label: fig-kenetic-energy p_kenetic_energy ``` What can we learn from our small experiment? No matter what we do, there will always be an error, noise, or deviation. There are different names for nearly identical concepts. This is the core of inductive reasoning using statistics. We will always have errors, and we want to minimize them. The main topic of this book is what this error is and how we describe these errors. Not really the errors themselves, but rather the concept of drawing lines through points by minimizing error. ::: Randomization and random observations ## What is a good explanation? ## What is real? Sometimes we need a model to know what is real. Fukusima @sevon2020analysis @sevon2023analyzing ## What is a probability? ## What is the replication crisis? @romero2019philosophy Not here, move to p-value chapter: @benjamin2018redefine ## Age of enlightment Romantic as the answer to enlightment. ## General background Full quote > *"Reality is negotiable. Outside of science and law, all rules can be bent or broken, and it doesn’t require being unethical." --- Tim Ferriss* > *"This is your last chance. After this, there is no turning back. You take the blue pill - the story ends, you wake up in your bed and believe whatever you want to believe. You take the red pill - you stay in Wonderland and I show you how deep the rabbit hole goes." --- Morpheus, Matrix* Idea of hypotheses Science is guessing and falsification @clark2025models [Models Demystified: A Practical Guide from Linear Regression to Deep Learning](https://m-clark.github.io/book-of-models/) @cox2017statistical [Statistical Thinking for the 21st Century](https://statsthinking21.github.io/statsthinking21-core-site/index.html) [David Deutsch \> Quotes](https://www.goodreads.com/author/quotes/103190.David_Deutsch) ## Alternatives > *"The truth is out there." --- The X files Disappointed about this chapter? You wanted more but have gotten less? There are other books and ideas outside. *Against Method: Outline of an Anarchistic Theory of Knowledge* by Paul Karl Feyerabend @feyerabend1970against *The Structure of Scientific Revolutions* by Thomas S. Kuhn @kuhn1970structure *The Logic of Scientific Discovery* by critical rationalism by Karl Popper @popper1959logic *The beginning of infinity: Explanations that transform the world* by David Deutsch @deutsch2011beginning ## Dramatis personae ## Glossary experiment : what does it mean. epistemic : Counterpart of aesthetic. Keep in mind the saying, "It is too beautiful ('aesthetic') to be true ('epistemic')." ## The meaning of "Models of Reality" in this chapter. - Science is divided in formal and natural science - Formal sciences provide tools for natural sciences - Science and non-science is divided by experiment and falsification - An experiment must include testable hypothesis ## Summary ## References {.unnumbered}

Height [m]	Potential energy [J]	Time [s]	Velocity [m/s]
\(0.1\)	\(0.1 \cdot 0.03 \cdot 9.81 = 0.029\)	\(1.58\)	\(2/1.58 = 1.27\)
\(0.2\)	\(0.059\)	\(0.95\)	\(2.11\)
\(0.3\)	\(0.088\)	\(0.85\)	\(2.36\)
\(0.4\)	\(0.118\)	\(0.65\)	\(3.09\)
\(0.5\)	\(0.147\)	\(0.72\)	\(2.78\)