1) First encounter
When I hear the word chaos theory, I immediately think of this sentence here: “…the flap of a butterfly’s wings can change the world…”. So basically it contains the statement that the smallest possible cause can have a maximum effect. And in my opinion, there is also a lot of truth in that. On the other hand: you will never be able to test it. Unless the time machine is invented after all. And as in “Back to the Future II”, even a “parallel timeline” can be created and then cut off again (thanks, Michael J. Fox!) by going back to the point in the past where it was created (all chaos? Even the chapter order; elsewhere there is talk of Biff Tannen, who found all the sports results of the future in the football almanac and built a world empire on them…; please find the chapter).
Now one does not necessarily feel comfortable with the thought: “Everything is coincidence.” I can be born (have been born) or not: coincidence. I can live to be 100 or 52, determined by chance. I can find the woman of my life or stay alone forever. And the latter only because of this stupid butterfly. If only it had flown to the left instead of to the right… In this respect, as a human being you also like to look for indications that it is not random after all. Somehow predetermined. That perhaps there is also someone who guides all our steps. Or that everything is written in the big book, fate. And then this huge coincidence happens to you that you can’t quite explain and you think you’ve found proof that there is a connection after all, that perhaps fate means well with you or that such a big (happy) coincidence can’t just happen like that and you ask yourself who had a hand in it.
This search for meaning or, more generally, these philosophical questions are basically the search for order in chaos. Intuitively, one may feel that there can simply be these giant coincidences and that there is actually no explanation for them. But being at the mercy of this principle of chaos makes you a little afraid, so you defend yourself against it.
And as much as I fundamentally believe in the chaos theory, I still gratefully accept every hint that there is something else that is responsible for fate. The story of my twins is an almost seductively good example that this is indeed the case (Chapter: “My Twins”).
Nevertheless, I have virtually internalised many of the basics of chaos theory and believe in it rock-solidly. For example, when a reporter tries to explain to me that this team’s victory was “deserved”. Then I always think: Has he already forgotten that great chance, that shot against the post and that wrong decision by the referee? And if the goal had gone in for the others, then everything would have been different, not only in terms of the result.
I can even remember my first encounter with the chaos theory: it was 1970, it was the World Cup. It was in Mexico. The games were at night. I was 11 years old. I was allowed to watch the games if I had slept before. I had seen all the German games. The day of the semi-final came, Germany – Italy. I was extremely excited, a football fan, no, crazy, I wasn’t allowed to love football quite as much as mathematics, because football is male; nothing, but nothing at all could have stopped me from watching this game. So I slept through it. I had to, condition of my parents.
I woke up one night. Something was strange, something wasn’t right. I ran into my parents’ bedroom. I woke up my father. He, drunk asleep “4:3 for Italy after extra time”. I was stunned. I didn’t want to have heard it. It couldn’t be, it was impossible, not that Germany had lost, but that I had missed it. I skipped school the next morning, the game was repeated in the morning programme. But I could feel neither excitement nor anything. Everything was dull and depressing. Italy took a 1-0 lead after seven minutes and it was a boring game. The final whistle was approaching, so what I thought I heard in my two-sided half-sleep wasn’t true after all. But then, in the last minute, it was actually 1:1 for Germany, with Schnellinger scoring his only(!) international goal and… was it supposed to be?
In extra time, I can’t say I was excited, I just kept doubting: how is it going to be 4:3? Then 2:1, a curious goal by Gerd Müller, 2:2 again, then even 3:2 for Italy, Gerd Müller again for 3:3, gradually it became certain, the last shot, 4:3 for Italy by Gianni Rivera, Sepp Maier threw himself on the floor in despair, so it was true, Germany was out, by a 3:4 after extra time. The match of the century, and I was in a trance, unable to feel or think anything at all.
But I philosophised afterwards, And I thought about whether it was possible that if I had seen it, everything would have turned out very differently. I went on and on, trying to imagine it. The neighbour’s family would have seen me at the window, would therefore have made a phone call just 3 seconds later, the phone call went to the other side of the world, everything turns out differently. Just to describe a spreading possibility of change. No one could understand me. But it was my personal birth of the “Chaos Theory”. I found no proof that it was bound to happen anyway and inevitably. It could also have remained quite boringly at 1:0. Thanks to me, you experienced the game of the century. Doubts? Oh, my parents later assured me that they had done everything humanly possible to get me awake. I still don’t believe them to this day.
As much as I’d like to move on to philosophy, I’ll stick with mathematics (wasn’t there even a recognised relationship between the two?).
2) The search for order in chaosI would like to take a closer look at this concept and the connections behind it.
In a way, chaos theory deals with the (non-)predictability of future events. My observation or encounter with it at the time was a little different. I suspected that an event that had occurred might have changed its outcome by changing a tiny little parameter.
Two things can be said about this: 1) how big the influence would have to be is not fixed and 2) you can never check the alternative variant.
If it is such a small parameter as the one at the time when I was not woken up at night and missed the game of the century, it is of course questionable whether I could have made an impact with my waking up and what that impact would have been (that’s just the flapping of the butterfly’s wings…). But that leads directly to 2). Because: It will never be possible to verify it. So here is the smooth transition to philosophy.
But this consideration really does have a meaning for me almost every day. Because whenever I place a bet or, even better, don’t place a bet, it’s pointless for me to think about what would have happened if… Because I will never be able to check that. So only what was actually done, what was bet, counts. “I wanted to play those, but just at that moment my internet crashed…” doesn’t count. I don’t know how the game would have turned out without a crash. I had also experienced the little roulette story when, while going to the cashier, I (accidentally) bet 100 DM on the 27, which I had accidentally taken out of my pocket (it was supposed to be 20), I took the 100 down again, was too late for the 20 and the 27 came. That would be another example. Would things really have turned out differently? Would someone else have made a different decision when he saw my set, would he have moved differently because of it, a breath of wind, a touch, triggered by it, the kettle, anything, and the ball would have changed its course after all?
This is one aspect of chaos theory. The other is precisely this: to what extent can the probability of occurrence of events be predicted? Sure, we know the (basic) statement of Heisenberg’s uncertainty principle, according to which it is not possible to determine the location and speed of small particles at the same time: When Heisenberg got caught in a traffic control and was asked if he knew how fast he was going, he replied: “No, he doesn’t. But I know where I am. But I do know where I am.”). This points to a certain disorder even in the microcosm. This is also, in a way, the refutation of Laplace’s assumption that, as I quoted, “A demon…”, so if you knew all the parameters, every event could be predicted exactly.
So as far as I know, even the (natural) scientists are no longer entirely comfortable with the term “chaos theory” itself. Many areas of research are concerned with the question of how far order can be found or established despite the apparent chaos. Not least the consideration of fate is also proof of the search for order in chaos.
But there is another refutation, in my view. As long as one only makes and observes experiments in which only inanimate elements are set in motion (better said: remain in motion, because everything is moving all the time, but being moved specifically, the thrown cube), knowledge of the laws of physics may not even be completely sufficient (see above) to classify it as ” exactly predictable” or “calculable”. So if we take the dice out again and invoke LaPlace’s demon again, even then, even if we know all the parameters responsible for the outcome, they might not be sufficient to make the outcome of the throw exactly predictable. The reason for this is once again: the smallest particles behave chaotically themselves. At least the current state of science is not (yet?) sufficient for this. Science is only ever at the momentary state of error anyway.
But what if humans are involved? And that in the truest sense of the word “game”? How should I be able to predict their reactions? Even if they are also guided by chemical and physical processes. But that seems completely hopeless. And it is not only the participants themselves, the players, but also the game leaders whose decisions can have a decisive influence on the outcome of the events.
In summary, reality moves between the two extreme poles: exact predictability and absolute unpredictability. Something between 1 and 0, as usual in probability theory. I don’t want to philosophise about this any further or give a percentage in which direction I’m leaning.
Just this much about it: The path of life I am following is concerned with the order of chaos. I am trying to limit absolute unpredictability. Look, quite simply, football is a game, 22 players, one ball, and in the end Germany wins (Gary Lineker). Nothing seems predictable (except that). Who is going to win? Or even a draw? And absolute order, predictability, knowledge of all variables, parameters, movements, total order of chaos, would lead to setting an event at 100% (which then occurs). I try an approximation in the sense that I say 56.6% Bayern, 27.9% X, 15.5% HSV. So this form of “fixing” entails a partial ordering of chaos. Better still, it is a prerequisite for it.
The pure chaos would be the forecast 33.33% — 33.33% — 33.33%. There is no order to be found. But, as I hope I have been able to prove, there is some order. And this can even be proven in the long term.
