The image generation of ChatGPT started freezing while my repeated attempts to correct Kogasa’s costume continued to produce deviations from the intended design as due to some ongoing issue of ChatGPT on 30th Sept. 2026. So, I have decided to use this version an illustration of Kogasa Vs. Sanae as a compromise for now.
AI Redraw Request — Crying Umbrella Youkai Defending Against a Divine Shrine-Maiden
The following text is AI (ChatGPT plus) generated with reference to my current issue in mathematical modelling of the macroeconomic growth theory.
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This week I had an interesting little incident at the boundary between economics and mathematics.
I was checking an exponential model for an economic growth / Total Factor Productivity (TFP) problem. After going back to the mathematical formulation and implementing it carefully in MATLAB, the objective function showed a clear minimum.
At first sight, that sounds encouraging: the optimisation problem has a well-defined solution.
However, when I reconstructed the corresponding TFP trajectory using the parameters associated with that minimum, the result did not reproduce the observed trajectory satisfactorily.
So I found myself in an interesting situation:
the mathematics said, “Here is the optimum,” while the economic data replied, “Not so fast.” 😅
This does not necessarily mean that the exponential approach is mathematically wrong. Rather, it raises a more interesting question: is this particular model structure appropriate for representing the empirical behaviour of TFP?
At the moment, I am therefore also comparing the result with a penalised smoothing spline, which appears to represent the trajectory more naturally.
For me, this has been a useful reminder that finding a mathematically neat optimum is not the same thing as finding a good empirical model. Optimisation, model specification, and interpretation all have to work together.
The investigation is still ongoing, so this is not a final conclusion — just one of those small research episodes where economics and mathematics refuse to cooperate quite as politely as expected.
