The question of science itself has never been its particular object of inquiry but the existential nature, in its possibility and thereby the nature of its actuality. Science is power, and thus abstracts itself as the desired meta-good, although it is always itself about particularities as...
This lecture serves as a philosophically informed mathematical introduction to the ideas and notation of probability theory from its most important historical theorist. It is part of an ongoing contemporary formal reconstruction of Laplace's Calculus of Probability from his english-translated...
We consider here how to estimate a parameter to a distribution given a sample space of observations. It is important to recognize that the testing of any hypothesis relies upon assumptions, which may be further explicated as obtaining validity based upon the further assumptions. The system of...
When two states, i.e. possibly measured outcomes, of the stochastic sampling process of the underlying statistical object communicate, there is a probability of one occurring after the other, perhaps within the internal time (i.e. indexical ordering) of the measurement process, $t \in \pi=(1,...
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...
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...
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...
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...
