This is a Python notebook along with code and examples which attempt to summarize and explain the main concepts outlined in the paper: Real numbers, data science and chaos - How to fit any dataset with a single parameter
"We show how any dataset of any modality (time-series, images, sound...) can be approximated by a well-behaved (continuous, differentiable...) scalar function with a single real-valued parameter. Building upon elementary concepts from chaos theory, we adopt a pedagogical approach demonstrating how to adjust this parameter in order to achieve arbitrary precision fit to all samples of the data. Targeting an audience of data scientists with a taste for the curious and unusual, the results presented here expand on previous similar observations regarding expressiveness power and generalization of machine learning models."
In other words, the author comes up with a methodology of encoding almost any arbitrary data set into a single real-valued number which is located between 0 and 1.
Assuming that we had an fully continuous and analog universe which allowed us to perform computations up to any arbitrary decimal precision, the above methodology would allow us to encode / decode an infinite amount of data within a single decimal value! Of course, our universe is not analog and there are constraints within it which may limit us from using the above concept, albeit it's still a very mathematically beautiful concept which is definitely worth exploring!