What a coincidence!
About Unpredictability, Complexity and the Nature of Time

Foreword

„How the hell could this happen? really impossible!“ We have often made such exclamations ourselves, heard them even more often and read them at least as often. We consider improbable events to be practically impossible. Experts calculate probabilities of occurrence for catastrophes that we and above all the decisive politicians trust. For nuclear power plants, apart from a „maximum credible accident“, there is theoretically nothing worse, but in practice much more happened in Fukushima than was previously conceivable as a maximum. That was „coincidence“ („there were simply too many unforeseeable things that came together“).

Successful people like to claim that they have planned everything, that they have stuck to their strategy. And yet they forget how often, by chance, they have met exactly the right people (whom they did not know beforehand) or appeared in exactly the right market situation (which they could not influence at all) with a product (which was not intended for exactly this market situation). Those who have done similarly well but unsuccessfully, blame themselves (if they are self-critical) for all kinds of mistakes, but often overlook the fact that they also happened not to meet the right people, or appeared too early (when the market situation was not yet suitable) with practically the same product, and therefore happened to fail.

August 2021 marked the thirtieth anniversary of the launch of the World Wide Web. No one could have foreseen, no one predicted how much the WWW would turn the world upside down just a few years later. Not even, and especially not, its inventor Tim Berners-Lee, who only wanted to develop it for the easier exchange of scientific documents. The path to this launch was also a chain of chances and coincidences, as he recounted.

Rather more coincidences we all experienced in 2020: presumably at a wildlife market in Wuhan, China, a novel Corona virus jumped to humans in December 2019, maybe this happened sometimes elsewhere without being noticed before, because as far as we know so far, the first infection occurred in Italy in November 2019, as it was found out afterwards. In January 2020, the founder of the biotechnology company BioNTech learned about this virus. He decided to radically shift the company’s focus from cancer therapy research to the development of a vaccine against Covid-19. In December 2020, after less than a year of work, the vaccine was approved. This research was only possible because the founders couple had come across the first indications from basic research more than twelve years earlier that mRNA might enable novel cancer therapies – we will go into this in more detail. Because, as oncologists, they founded a company for this purpose (BioNTech), happened to find two investors – two brothers – who were willing to take risks and were patient; and because by the end of 2019 they had developed the mRNA technology almost ready for application, only there was still no approved product. The vaccine became possible, although the research was actually aimed at a completely different field of application. By chance, however, they recognised this possibility of their technology platform and developed a vaccine in an incredibly short time.

Very many unpredictable events are at least annoying to us. There can be sudden rain that was not predicted, and the picnic outside falls through. Some coincidences are dangerous, such as a car suddenly taking the right of way. Some even threaten our existence, for example the accidental spread of the Corona virus to humans. Other chances, on the other hand, are welcome: We are often happy about small coincidences. For example, about the sun suddenly breaking through again after we had quickly packed up the picnic and can now unpack it again after all. We marvel smilingly at bigger ones, such as the chance that made it possible for me to meet my partner for the first time, with whom I happily live together. We shake our heads in joyful disbelief at the fact that our favourite soccer team was able to equalise in the very last second, and that only because an opposing defender’s leg happened to give the ball the right direction. The development of stock market prices is unpredictable, and that is by no means the only thing that is unpredictable in economic life. Inventions and discoveries are very often, if not predominantly, the result of coincidences.

Other coincidences are even decisive for all our lives: The extinction of the dinosaurs, which made the development of mammals possible. And even more decisive was the formation of the moon several billion years earlier, which stabilised our earth’s axis and thus made the world we live in possible. A world that we humans would not be able to write about if some crucial mutations had not happened by chance millions of years ago, shaping our brains as we find them today.

If we are honest, more unpredictable events happen, more that are actually rather improbable than those that we can plan, foresee, predict or influence. All kinds of things go wrong, although we have done nothing wrong! And just as many events that please us or advance us happen unexpectedly, or at least at a time when we did not expect it. The newspapers and all other media are full of them.

Let us now assume that chance and coincidence are normal, that is, nothing unusual, that they are, so to speak, a typical phenomenon with us on earth and thus in the whole universe; if that is so – then we also want to know: Where does this unpredictability come from, how does it come into our world, why is it normal? To answer this question, unlike mathematicians, philosophers or psychologists, I will not talk too much about „randomness“ (which is something else than a true coincidence), I will not argue with probability calculations, statistics or with chaos theory. Nor will I work with philosophical considerations or psychological analyses that are supposed to make us understand how we can enjoy, endure or cope with coincidence. We will first look – after a more detailed consideration of such events which surround us – at how it is that our world consists of nothing but structures. If all the substances in the universe were equally distributed and homogeneously mixed, we would not exist, with our complexly structured brain, nervous and circulatory system, muscles, bones, our complex skin, the sensory organs and all our fantastically finely constructed internal organs. How do such complicated structures come into being?

If all material in the universe were statistically evenly distributed and did not form highly complex structures, we would not be able to marvel at the beauty of the Cirrus Nebula. Above, there is a new image from the Hubble telescope.¹ The nebula looks like a turbulent swirling plume, but with a diameter of over one hundred light years. We will look at phenomena like this and similar ones in the book and understand the causes of their formation.

But in order not to make things too complicated, we will also turn to apparently simpler structures and questions: Why is mayonnaise so stiff even though the main ingredients raw egg yolk, water and oil are each far from viscous? Why do you have to proceed in certain steps when making mayonnaise or Sauce Béarnaise and cannot simply pour all the ingredients into a bowl at once and stir? Why is it not so easy to make a nice rich brown cocoa with raw cocoa powder (like you use for tiramisu) and milk, where cocoa clumps don’t sink to the bottom of the cup after a few seconds?

I will try to answer these questions partly from my own research. For I discovered complex structures in material compositions that previously were believed not to exist at all according to generally accepted ideas. In my research as a chemist, I found a common denominator and therein the cause: All these products are non-equilibrium systems. I inevitably had to break away from the idea that I had developed as a chemistry student, like everyone else, based on the lectures and textbooks: For us, the world consisted of equilibrium systems; non-equilibrium was something rare and undesirable, such systems we then only approximately described again as equilibrium systems that were just only a little bit out of equilibrium.

In my further research, I learned through studying the work of many other researchers that non-equilibrium systems are structured. I began to ask myself: Why is that? Or thinking the other way around: Why are complicated structured systems not in equilibrium? Professor Ilya Prigogine received the Nobel Prize in 1977 for explaining this with a new thermodynamics. It simply has to do with entropy, which is very crucial to what determines the course of the world. You may have heard the word „entropy“ before, but either not considered it important or possibly not understood it in the first place. I will help you to understand it. Because if you want to understand the world at least a little from the bottom up, you should have a reasonably accurate idea of entropy. But don’t worry, I will explain it in such a way that it is really easy and practical to grasp.

Then we will also deal with fundamental questions: If everything was chaotic at the Big Bang, why can order arise in the universe, the galaxies so diversely structured with countless solar/planet systems. And why can a glowing hot earth become a life-friendly blue planet? How did the „big bang“ come about in the first place? Wasn’t that already a coincidence? Can we be sure that a „big bang“ was the beginning of our universe?

I have always been fascinated by the phenomenon of chance, coincidence and accidental events. When I started working on non-equilibrium thermodynamics, at some point I noticed a connection between chance, coincidence, accidental events and non-equilibrium. But in what way can that be? Well, that is exactly what this book is about, and I will explain this little by little in the course of the book. This much is already said: Both phenomena are inseparably and closely connected. And both phenomena are just as indissolubly closely related to entropy. I was only very surprised when I searched even more deeply while writing this book that apparently no one had come up with similar ideas before. Or at least, if someone did think similarly, it was not written down in a publicly accessible (or not easily accessible) way. In any case, all I kept reading and hearing was: It is the quanta, the uncertainty principle describing the behaviour of elementary particles, that should cause chance, coincidence and accidental events in our macroscopic world. I will explain why this cannot be the case. Quite apart from the fact that there is no verifiable evidence for this at all so far and no theoretical basis indicating this.

And what is „time“? We are not going to link entropy to time as well, are we? Yes, we are not going to link time with entropy and non-equilibrium, we don’t have to and we can’t do this at all. Because time is already linked to entropy by itself.

But isn’t time simply an illusion, as Einstein said? And as some other very serious physicists and philosophers also think. But if it is not an illusion, what is the essence, what is the nature of time? We will also approach the answer to this question, which has not yet been clarified by either philosophy or the natural sciences, step by step, just as I have done in the course of my research.

And finally, the older ones among us may also expect an answer to the question (and the younger ones can put it aside for later): Why does time pass more quickly in old age? Is this really the case, or do we just feel it that way? Why does time pass even for the younger among us sometimes slowly, for example when we are waiting for something urgent, and sometimes faster, for example when the holiday is over sooner than expected?

If you have ever asked yourself these or similar questions, I invite you to join an expedition into landscapes of science that you have probably not visited before. We will span great arcs from simple mayonnaise to complex galaxy clusters, from disdainful traffic jams on the motorway to fascinating evolution, from the misunderstood big bang to the astonishing self-organisation of order from chaos, from surprising goals in overtime to unimaginably oversized black holes. And we thus embrace becoming and passing in our world, entropy, chance, coincidence, complexity and time.

During this expedition, we will also occasionally reflect on how our own thinking works. How open are we to questioning previously widely accepted explanations of the interrelationships in our world that we ourselves also find comfortable and plausible? If we are honest for a moment: Most of the time we are not very open. But we should try more often. In the words of Nobel laureate Daniel Kahneman: „Our minds normally function in such a way that we have intuitive feelings and opinions about almost everything we encounter. […] Whether we formulate them explicitly or not, we often have answers to questions we do not fully understand, and we base them on cues we can neither explain nor defend.“ In this book, you will encounter some thoughts you may not have heard or read before. This will make you sceptical because, as Daniel Kahneman explains in his profound book „Thinking, fast and Slow“², among many other aspects of our thinking, we consider statements we have read or heard many times before to be probably more correct than those we encounter for the first time. It then requires considerably more mental effort and thus energy (!) to deal with novel thoughts and phenomena than to read and hear things that we have known for a long time and have considered to be correct for a long time.

With this book I would like to motivate you to subject your previous world view to a critical examination: Is everything really in balance, should the climate, the ecosystem, our economy really be in the best of balance? I do not expect you to change or even overturn your previous ideas; but I would like to encourage you to allow some unfamiliar thoughts and to think them through calmly. For in this way we will not only be able to answer the question of how chance comes into our world. We will understand the world as a whole a little better.