# Why are scientific equations important

## Freistetter formula world: The equation for the right relationship

"But with all your math and science you still can't explain love!" As a scientist you have to listen to these and similar allegations regularly, and they are not completely false, but also a little naive. The point is probably that certain areas of scientific research are inaccessible. And of course that's true too.

The misunderstanding is that no serious mathematician or researcher would come up with the idea that science can explain everything. Mathematics in particular is deliberately a formal, logical and also emotionless language. Only in this way can it achieve what it is able to do: to serve as the basis of an objective and thus also reliable method for examining the world. If it were subjective and emotional in the same way as our everyday language, it would be useless for this.

#### This article is included in Spectrum - The Week, 37/2016

But that doesn't necessarily mean that you can't say anything about love with the help of math. If you disregard the very personal feelings that everyone associates with this word, this topic is quite accessible to a mathematical-scientific analysis. One can set up models with which the probability of finding a suitable partner can be described. Mathematical algorithms form the basis of online dating platforms; game theory approaches like the prisoner's dilemma can also be applied to relationships - and so on. If mathematics is able to describe such complex systems as the movement of celestial bodies, the development of the entire universe or the interaction of elementary particles, then a little human interaction is not a big problem for them.

It can even be used to avoid an escalating argument in the partnership. You know it: one person says something, the other gets angry; a reproach is followed by a defense that is itself a reproach, and a negative chain reaction develops, which in the worst case results in the end of the relationship. Mathematicians and psychologists have researched together how this works and summarized them in these two formulas:

These equations can be used to model and predict a couple's reaction to a conversation. "M" stands for the man and "F" for the woman (but of course the whole thing also works with any other gender combination). At the beginning of the conversation, each partner has a certain basic mood, which is described by the number "f" or "m". With r_{f}F._{t} describes the mood of the woman when she is with her husband. The mood of the man in the presence of the woman is through r_{m}M._{t} given. However, the functions I above all are important_{FM}(M_{t}) and I._{FM}(F_{t}), which describe how the woman (or the man) reacts to the actions and statements of the man (the woman). Taken together, this gives the mood F_{t + 1} or M_{t + 1} of the woman and man after the first "round" of the conversation. The conversation is continued with these values and the whole thing is recalculated. At the end of this repeated iteration there is either a big argument or a reconciliation after a good conversation.

This may all sound like a bit of humbug, but it is serious science. The numbers that are used in the equations to describe the basic moods were obtained by the scientists through studies and psychological experiments. And the "interaction functions" are also selected in such a way that they match the behavior of real couples: If one partner acts slightly negatively, this leads to a slightly negative reaction from the other. This reinforces the original negative action, which now leads to an increased negative reaction, until at some point a "negativity threshold" is exceeded, at which the conversation turns into a heated argument.

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