The world is complex. If we want to learn something about it, we need to use statistics

Hey, I’m Jonas!

I’m a student in the beautiful city of Heidelberg, Germany. Here I’m currently pursuing both a MSc in physics and a MA in philosophy at Heidelberg University.

My true passion lies in the question of how we can arrive at understandable macroscopic descriptions of nature and society, which are both intricately complex on their microscopic scale.

What we can learn from statistical physics

This is a question at the heart of physics, think for example of the complex behavior of the myriad of particles in the room you are currently sitting in. On a macroscopic scale, all of this is describable in the interplay of two quantities: temperature and pressure. In its most fundamental, this move from the microscopic to the macroscopic is the domain of statistical physics. If we move to infinitely many degrees of freedom, we are in the regime of quantum field theory (QFT). Note though, that the techniques of QFT not only apply to quantum systems, but they also apply to stochastical system more generally. A more accurate name for QFT would be statistical field theory.

Complexity is everywhere

The question of useful macroscopic descriptions of systems, that are too complex to comprehend on their fundamental level, is broadly relevant and is not restricted to the description of physical phenomena. Many social or economic questions we are interested in as a society run into the same problem. Descriptions on the fundamental level of these systems, the level of the individual, are hopeless because of the sheer number of people in our society and the complexity of our interactions. The same problem faces neuroscience. A description of the entire brain on the level of single neurons, even if available, would be entirely incomprehensible to us humans.

Our world in its microscopic intricacy is too complex for us to understand. We need to find sensible abstractions to move to a macroscopic level, that we can make sense of. This will always require statistics!

Models from data

In physics, we generally know the equations governing the microscopic but need methods to move to a macroscopic description to make predictions. This is entirely different for other fields. Here we often do not know the underlying microscopic dynamics or, as in the realm of the social, mathematical regularities only arise on an aggregate scale. But how can we then arrive at a description of these phenomenon?

The answer is that a lot of domain knowledge is (and always will be) required. I’m interested in developing techniques to support this process of modelling by inferring models from data.

I’m currently working at the DurstewitzLab in the field of dynamical systems reconstruction. The idea is that underlying every time series there is a (hidden) stochastic process generating the data. With the help of a special kind of recurrent neural network, we try to recover these underlying dynamics to study the process in itself(with tools from dynamical systems theory), instead of just one realization of it.

Improving the world

All this theory is interesting in its own right, but I’m sure learning how to understand the world despite its complexity will allow us to leave the world a little better than we found it…

If you have questions, insights, criticsm or more generally a topic you’d like to discuss, please feel free to reach out.