Knowledge on evolving physical fields is of paramount importance in science, technology, and economics. Dynamical field inference (DFI) addresses the problem of reconstructing a stochastically-driven, dynamically-evolving field from finite data. It relies on information field theory (IFT), the information theory for fields. Here, the relations of DFI, IFT, and the recently developed supersymmetric theory of stochastics (STS) are established in a pedagogical discussion. In IFT, field expectation values can be calculated from the partition function of the full space-time inference problem. The partition function of the inference problem invokes a functional Dirac function to guarantee the dynamics, as well as a field-dependent functional determinant, to establish proper normalization, both impeding the necessary evaluation of the path integral over all field configurations. STS replaces these problematic expressions via the introduction of fermionic ghost and bosonic Lagrange fields, respectively. The action of these fields has a supersymmetry, which means there exists an exchange operation between bosons and fermions that leaves the system invariant. In contrast to this, measurements of the dynamical fields do not adhere to this supersymmetry. The supersymmetry can also be broken spontaneously, in which case the system evolves chaotically. This affects the predictability of the system and thereby makes DFI more challenging. We investigate the interplay of measurement constraints with the non-linear chaotic dynamics of a simplified, illustrative system with the help of Feynman diagrams and show that the Fermionic corrections are essential to obtain the correct posterior statistics over system trajectories.

The rational solution of the Monty Hall problem unsettles many people. Most people, including the authors, think it feels wrong to switch the initial choice of one of the three doors, despite having fully accepted the mathematical proof for its superiority. Many people think the chances are 50-50 between their options, but still strongly prefer to stay with their initial choice. Is there some sense behind these irrational feelings? Here, the possibility is entertained that intuition solves the problem of how to behave in a real game show and not the abstract textbook version. A real showmaster sometimes plays evil, either to make the show more interesting, to save money, or because he is in a bad mood. A moody showmaster erases any information advantage the guest could extract by him opening other doors which drives the chance of the car being behind the chosen door toward 50%. Furthermore, the showmaster could try to read or manipulate the guest's strategy to the guest's disadvantage. Given this, the preference to stay with the initial choice turns out to be a very rational defense strategy of the show's guest against the threat of being manipulated by its host.

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