Which theorists are smarter physicists or mathematicians

Of terrestrial and extraterrestrial mathematics

The mathematician and physicist Christian Blohmann from the MPI for Mathematics in Bonn on soccer predictions, "Paul the Octopus" and Co. and the winner of the World Cup in Brazil

In 1981 the Max Planck Institute for Mathematics put down roots in Bonn, which is similar in structure and operation to other renowned research institutes abroad and, as a guest research institute, is entrusted with the task of bringing mathematicians from all over the world together in order to encourage creative discourse between the researchers promote and brainstorm at the highest level. To this end, around 400 scientists are invited to Bonn every year, whose length of stay varies from a few days to two years.

One of the important contacts at the MPIM, who in addition to teaching and research activities there, also looks after the press and public relations, is the 43-year-old mathematician and physicist Christian Blohmann, who can look back on an eventful academic career and numerous specialist publications. The versatile researcher is not only interested in mathematics, physics, astronomy and literature, but also deals critically with football-mathematical questions and has been thinking about the sense and nonsense of predictions and statistics in football for some time. At the start of the soccer World Cup in Brazil, a mathematical physicist should finally have his say to put an end to "Octopus Paul" & Co.

Mathematics does not have a very good reputation among the general public. Many people still shudder at this word or remember an unhappy school days with bad memories of Pythagoras and Co. Do you think that mathematics in general still has an image problem these days?
Christian Blohmann: No, from my point of view this is hardly the case anymore. Of course, many are put off by mathematics and associate negative memories with it. After all, mathematics poses enormous intellectual hurdles that many struggled with in their school days. However, if you take a look at the popular media or literature, you will see that mathematics is rather overrepresented there. There are quite a few films and TV series in which the heroes are real mathematicians. They often appear as likable nerds. They're cool now. Please find a series in which a chemical engineer or biochemist plays the part of the cool nerd. Although there are ten times more of them than mathematicians in real terms, they play a subordinate role in the TV landscape. Of course, there are also many clichés here that are exhausted to the last. We may not always be liked, but we are always recognized and a little admired - perhaps because of the abstract nature of our subject or the fact that we are extremely brainy people.
Physicists or astronomers see mathematics as nothing more than a kind of auxiliary science. Math as a necessary evil to understand what holds the world together at its core, as Albert Einstein practiced. Is math just an auxiliary science?
Christian Blohmann: No, we don't see each other like that. For example, I am a mathematical physicist myself. And yet I don't associate mathematics with an auxiliary science, but the driving force behind many developments. Mathematics is also playing an increasingly important role in the supposedly softer natural science subjects. Biology, for example, no longer consists of walking around in the forest with a botanizing drum and studying plush animals on site. In the last 100 years it has become more and more precise and is constantly moving in the direction of a thoroughly mathematic science. What is significant for this development is that biologists are currently increasingly interested in the methods of theoretical physics and mathematics. And the need for biomathematics is now enormous. Keyword: big data. This is sophisticated modern mathematics that has opened up new areas of research for biologists.
Do you see mathematics as a basic science, a science that does not have or need no auxiliary science?
Christian Blohmann: Especially here at the Max Planck Institute for Mathematics, which deals with pure mathematics, we are increasingly turning to physics - not in the sense of an application or real experiments, of course, but as a source of ideas and interesting mathematical problems. I myself come from physics. To refer to this itself as a mathematical auxiliary science, I consider just as exaggerated. We draw our inspiration from all areas of life. I am thinking of areas that did not exist in this form 20 years ago - such as Econo-Mathematics ("Economath"), ie the application of advanced mathematical and physical methods to stock exchange prices.
Can the universe be described in and with mathematical formulas?
Christian Blohmann: That depends on what you mean by the universe!
I mean the metagalaxy, i.e. that area of ​​the universe that is observable for us and from which and from which we can collect data!
Christian Blohmann: I understand …
I would like to clarify my question. How can the mathematician help the cosmologist? Or to put it another way: How much mathematics does a cosmologist need to understand the universe?
Christian Blohmann: Well, now I'm speaking as a mathematical physicist who did his doctorate at the Max Planck Institute for Physics and not at the MPI for Mathematics. For me, many fundamental questions in physics are essentially mathematical questions. We have reached our limits in many areas. We cannot always define the physical theories that we have created in a mathematically consistent manner. Sometimes you can't get rid of the feeling that we haven't fully understood mathematics, and that is generally a huge barrier to understanding science.
I deliberately use string theory as an example here. It is actually not a theory in the epistemological, for example Popperian, sense, because it makes practically no predictions that can be measured or checked. Rather, it consists of a complex mathematical apparatus in which one would like to embed the existing theories. As a physicist, it seems like an act of desperation for me as a physicist to propose ever more extensive, abstract theories that are further removed from the experiment. For me as a mathematician, however, this presents some of the most fascinating and difficult challenges in our field.
There is what is known as the cosmological principle in cosmology. It says that the universe is homogeneous and isotropic, that there is no excellent, special place in it. So shouldn't there also be a mathematical-cosmological principle according to which mathematics in the universe is the same everywhere?
Christian Blohmann: It's an interesting thought, but by no means an easy one. Many mathematicians are secretly Platonists and believe that everything they can mathematically prove in ten years, for example, is already somehow in some form. At the other end of the spectrum there is the Strong Program in the Sociology of Knowledge, the "Edinburgh Program". I come to this because in October this year a sociologist from Edinburgh is going to conduct a field study for a month. The core question here is whether not only the organizational aspects of mathematics, i.e. the structure of the institutes, specialist societies or universities, but the knowledge itself is socially determined.
How would mathematics created by extraterrestrial intelligences differ from ours?
Christian Blohmann: It is quite possible that the alien intelligent plasma balls on Alpha Centauri have a different mathematics than we do (laughs). But this thought is really very speculative.
I know. Let your imagination run wild!
Christian Blohmann: Given what we know on earth, it is certainly not wrong to refer to mathematics itself as language. But when you open a math book, a considerable part of it consists of natural language, which is terminologized but otherwise has the commonly used linguistic and syntactic structures. The over-formalization of mathematics, i.e. the use of a pure symbolic language, has proven to be impractical or inefficient. Nevertheless, the idea that certain types of information can be translated into a mathematical formula language that extraterrestrials could understand, at least in theory, is legitimate.
But Homo sapiens did not invent mathematics, at best only discovered it. So shouldn't this premise also apply to aliens?
Christian Blohmann: That's exactly the question. I dare to say that if you ask mathematicians what they think about constructivism, that is, the view that mathematical objects only exist from the moment they are defined by a mathematician, there are likely to be major differences between the various disciplines. A number theorist will probably be more inclined to view numbers as something God-given. From his perspective, these are simply always there. A geometer, a topologist or a numeric technician, on the other hand, is more likely to be more aware of the constructed nature of his concepts.
But the number Pi would logically be discovered by all extraterrestrial cultures at some point and determined as a mathematical constant and could be the basis of communication.
Christian Blohmann: Yes, I think so, too. On the other hand, with the curvature of space, the ratio of circumference to diameter of a circle also changes, which is the geometric meaning of the circle number Pi. So if you grew up as an alien near a black hole, you may not even get the idea that the number of circles is constant. But seriously, this is the kind of speculation we mathematicians better not get involved in. Maybe you should ask a xenobiologist.

When does soccer math make sense?

Back to earth: before the start of the soccer world championship in Brazil, mathematicians and physicists increasingly spoke up and presented probability calculations in various media, which should be used to determine the next soccer world champion. The part that astrologers, charlatans or the octopus Paul took on in the past is now played by scientists. What do you think of this trend?
Christian Blohmann: Such predictions are of course not to be taken too seriously. In a friendly way, it is a gimmick, but in the worst case charlatanism. But it can also be very entertaining, as Stephen Hawking recently demonstrated in his Cup Study for Paddy Power.
Yes, Hawking has come up with a formula for England's success at the World Cup in Brazil. For this purpose, he analyzed the appearances of the English national teams at the past World Championships since the triumph in 1966. He sums up that the English team should appear with red shirts and a 4-3-3 formation and only nominate blonde shooters in the event of a penalty shoot-out. Statistically speaking, 84 percent of the attempts by blonde players found the target. For bald people it was 71 percent and dark-haired only 69 percent. "The reason is unclear. It will remain one of the great mysteries of science," said Hawking. So there is also a sense of humor!
Christian Blohmann: Yes, Hawking's post is quite amusing and shows that it's best not to take soccer math that seriously. I think it is understandable and appropriate to comment on this with ironic words.
Irony or not, some mathematicians and physicists seem to take their own calculations and forecasts a little more seriously.
Christian Blohmann: The fact that so many scientists go to great lengths to get into the media is nothing new. Bowing to the authority of mathematics has historical roots. As early as the 17th and 18th centuries, researchers tried to quantify things that were previously unquantifiable. This is how the first poet rankings came about, in which points were distributed and added up to determine whether Homer or Shakespeare was the better poet.
Indeed, today there are serious mathematical studies relating to football or other sports. The majority of them don't make it to the front pages of the newspapers because they are based on overly complicated calculations and do not give any predictions as to who will be world champions, etc. Football mathematics makes perfect sense when it comes to the economic dimension of sport when, for example, mathematical methods are used to judge a player and determine his market value.
Unlike the astrologers, Paul the octopus was often right at the 2010 World Cup. But how should a layman behave when he encounters football mathematical predictions and uses them as the basis for football betting. Can he risk a high bet?
Christian Blohmann: The octopus Paul area is better left to the octopus. If someone only juggles with school mathematical methods, one can see from a distance that something is wrong. There is a wide range in the seriousness scale. Just predict something - anyone can do that. Anyone can give stock market tips. If mathematicians were really accurate in their soccer predictions, many of them would have been rich by now. Anyone with a certain amount of common sense can understand this doubt. Sometimes, however, the mathematical authority is proliferated. For the layman it is then difficult to distinguish whether this is a serious study or not. That is a fundamental problem.
Physics professor Andreas Heuer from the University of Münster based his calculations on the strengths of the teams. He let the teams compete against each other on the computer tens of thousands of times. In his computer simulations, Brazil and Spain were clearly ahead. The Dortmund physics professor Metin Tolan calculated the outcome of the tournament with a complex formula and a wink. According to his probability calculations, Germany has the best chance of winning the title. He sees national coach Joachim Löw's team at 20.33 percent in the final on July 13th in Rio de Janeiro. Who is right now?
Christian Blohmann: It is perfectly legitimate to apply mathematical tools, theories, and methods to such a system. I know the work of Heuer and Tolan and consider them to be serious. If you try a mathematical method on a new object and are curious about what interesting things can come out of it, this corresponds to a scientific approach.
However, if you want to develop an empirical theory, you also have to check whether it is correct or not. For example, if newspapers give the impression that football theoretical predictions are based on an absolutely sound scientific foundation, I consider this claim to be incorrect. Because if you do not check football mathematical predictions for their correctness in retrospect, you are moving in the direction of astrology.
How was that with the predictions for the 2010 World Cup? If someone makes ten predictions and doesn't want to hear about the nonsense they once prophesied at the next soccer World Cup, or if they only ever pick out the only chance hit with which they can score, they act like an astrologer. It would be nothing more than a bogus confirmation.

Is soccer math?

Suppose there was such a thing as a generally applicable World Cup formula. How can such important factors as luck, chance and manipulation be integrated into a mathematical world championship formula? You can't determine that!
Christian Blohmann: With football in particular, one has the impression that the factor of chance plays a major role and that this is different from sports such as baseball. These consist to a greater extent of controllable individual performances that can be segmented, which is not so easily possible in football.
Karl-Heinz Rummenigge once said that football is not mathematics. Bayern professional Holger Badstuber countered that football has something to do with math, because there are certain strategies that can be used to defeat the opponent. Which of the two is right?
Christian Blohmann: Rational, systematic and logical thinking doesn't necessarily have to be called mathematics. What Mr Badstuber probably means by strategy are video analyzes and the creation of statistics or the planned formation of a team. Today every movement, every ball contact, every duel of a professional footballer is recorded statistically. Even after a game there is a small mountain of information - mostly useless details. At first, this has little to do with higher mathematics.
Does that mean that football mathematics only makes sense for statistics and not for forecasts?
Christian Blohmann: If you had really found a good prediction based on simple mathematical methods, everyone would want to copy and implement them all at once.It is of course conceivable that a given team could have a much smarter and better mathematician than the competition. Perhaps they have a scientist who not only documents the number of ball contacts, but who also knows advanced mathematics and, for example, does a topological data analysis of the game or the players.
Google and the NSA show us how to get rich and powerful with sophisticated mathematical methods. How these observations and data can be strategically implemented, on the other hand, is a completely different question. After all, apart from the strange regulars' table statistics, there are serious efforts here.
What is your personal tip? Who will be the soccer world champion?
Christian Blohmann: Even at the risk of appearing a little boring now: I'm guessing Brazil.
Does your tip have a mathematical basis?
Christian Blohmann: (laughs) Apart from the fact that my Brazilian postdocs will like that: No. For me as a mathematician, going to a soccer game with friends is part of my free time. I'll do the devil for wanting to do math as well.
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