A Method of proof on recursion stemming from neurological determinism and the implications of its existence

This is a Method of proof regarding recursion occurring due to neurological determinism. Our assumptions are: determinism at the neurological level, and the equivalence of logical functions starting from a certain level of . These functions are equivalent with respect to the logical and mathematical operations of a formal system that satisfies the conditions required by Gödel for a system to be incomplete. i will claim that our brain is capable of generating a specific type of recursion, which will indeed manifest within the aforementioned logical system. I will construct a recursive formula in which it is easier to demonstrate equivalence to the recursion our brain can enter deterministically due to physical necessity. This recursion, which the brain is capable of conceptualizing, will be equivalent to a recursion that employs modal logic and satisfies Gödel's conditions, such that only a component external to its own logical system can terminate it. I will conclude that this component must utilize physiological dimensions. Furthermore, I hypothesize that there are compelling neurological insights to be discovered by conducting measurements while engaging in this recursion. This recursion will initiate due to physical necessity, and I argue that the recursive equation I have constructed is structured in such a way that this physical necessity can be translated into the obligations of modal logic. Each recursive iteration also represents a specific energy expenditure, due to its equivalence to the recursion the brain actually enters. This implies that the brain must exit the process without the need for an internal logical component to monitor or check the recursion from within. These research methods can be referred to Deterministic Recursive Neurological methods. Update 18.1.26: Added addendum1 file containing new ideas, corrections, and clarifications. This is an idea about representation using a sequence of finite matrices, axioms for the input and output of certain information, the relation between logical and arithmetic expressions and sequences of collections of elements from subsequences of sequences of matrices, with a connection to the completeness and incompleteness of sequences of collections, as well as to sequences and elements that are not part of certain sequences . keywords: mathematics, Neurology, Gödel's Incompleteness Theorems, Determinism, Recursion