The Issue of The Datum Data, as finite, can never be merely fit without presupposition. The theory of the data, as what it is, is the presupposition that discloses the data in the first place through the act of measurement. As independent and identical (i.i.d.) measurements, there is not...

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## A Tutorial in Data Science: Lecture 7 – The Elements of Fourier Analysis

Fourier Analysis is the decomposition of any square-integrable functions into an infinite series of trigonometric functions. Here we show that the trigonometric polynomial functions are dense in the space of periodic continuous functions, and thus can be used as good approximations. This implies...

## A Tutorial in Data Science: Lecture 8 – The Functional Theory of Communication in Stochastic Processes

From Laplace's Calculus of Probability (Lecture 3), a finite difference equation explains probabilistically how a game evolves over discrete time, defining thus a stochastic process and specifically a Markov Chain where there is finite recursion or limited historical dependence. While one can...

## A Tutorial in Data Science: Lecture 9 – The Functional Theory of Communication in Dynamic Systems

We consider thus the functional notion of communication within the theory of dynamic systems, where the finite difference equation, or flow of a differential equation, is iterated upon as a function. Within this framework, there is a true underlying deterministic system which can be explained by a...

## A Tutorial in Data Science: Lecture 10 – The Fundamental Law of Data Science (Inter-Communication is Functional Chaos)

We will prove below that a system is inter-communicating if and only if it is chaotic. This is the fundamental law of data science, since it is both analytical, as coming from definitions, and synthetic, as explaining empirical observation, thus satisfying the Kantian transcendental deduction for...