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Showing posts with the label invariant

Recursive Perceptual Differentiation

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Introduction What is the most fundamental particle? If my assumption is correct then it is P resence and A bsence or at least, there is a unique isomorphism between any other set of fundamental particles and $\{P, A\}$ which is sufficient as far as I concern. I have talked about them in [this] previous blog post of mine. Now, let's try to find the most fundamental operation, or action, or function that could be applied to the fundamental perceptions. I am going to denote such function as $π_Δ$ from now on. I still don't know much about the nature of this function, however, I can start to define, at least, some of its properties and describe them. Well, first thing first - because everything is made out of the fundamental particles PA , I can also say that the output of $π_Δ$ function is no exception. If we embrace the assumption that the inputs and outputs of this function are essentially of the same type then we can start imagining how beautiful recursive behavior(s) could ...

P.I.P. Theorem - my favorite theorem from the high school

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Background. When I was high schooling at TDV-BTL (Türkiye Diyanet Vakfı - Bakü Türk Lisesi), I happened to be thinking about functions and their properties during the 10/11$^\text{th}$ grade(s). I was mainly thinking about what happens when we change the formula of a function a little bit; do its outputs completely change by large offset or is it predictable what the function looked like before changing its formula syntactically just by looking at its new inputs and outputs? One day something interesting occurred to me as I was playing with arbitrary linear and quadratic functions - when I fixed the inputs and outputs on a table vertically, so that the (euclidean) difference between each successive input was the same, the consequent differences in the Y column did not change after some iteration, no matter how many rows(i.e., data points or x and y pairs) I added to the table as long as I respected the same-successive-difference rule on X column. For linear functions, I just observe...