Neuroscientists are able to detect physical changes in information entropy in available neurodata. However, the information paradigm is inadequate to fully describe nervous dynamics and mental activities such as perception. This paper provides an effort to build explanations to neural dynamics alternative to thermodynamic and information accounts. We recall the Banach–Tarski paradox (BTP), which informally states that, when pieces of a ball are moved and rotated without changing their shape, a synergy between two balls of the same volume is achieved instead of the original one. We show how and why BTP might display this physical and biological synergy meaningfully, making it possible to tackle nervous activities. The anatomical and functional structure of the central nervous system’s nodes and edges allows to perform a sequence of moves inside the connectome that doubles the amount of available cortical oscillations. In particular, a BTP-based mechanism permits scale-invariant nervous oscillations to amplify and propagate towards far apart brain areas. Paraphrasing the BPT’s definition, we could state that: when a few components of a self-similar nervous oscillation are moved and rotated throughout the cortical connectome, two self-similar oscillations are achieved instead of the original one. Furthermore, based on topological structures, we illustrate how, counterintuitively, the amplification of scale-free oscillations does not require information transfer.

For a long time, physicists always directly use mathematical tools to deal with physical problems, and few people pay attention to the difference between mathematical theory and physical theory. Just like the dilemma that physicists once faced when dealing with the problem of blackbody radiation function.By analyzing the difference between the theoretical basis of mathematics and the theoretical basis of physics, this paper draws the following conclusions: (1) The theoretical basis of mathematics and the theoretical basis of physics are different, so when we use mathematical tools for physics research, we need to be very careful. (2) Finiteness and discreteness should be the basis of the whole physical theory; This paper points out that it is not advisable to use infinite " " and infinitesimal "0" without restriction and demonstration in physics, as well as the continuity of functions, which will bring a lot of trouble to physical theory.At the same time, through the analysis of Banach-Tarski paradox and Bertrand paradox, this paper proposes that if we revise the basic assumptions of probability theory: assuming that "points" have quantized sizes, and "lines" also have quantized widths. After the correction, we can not only avoid the troubles caused by Bertrand paradox, but also make probability theory better for practical application.

This paper presents four key results in the philosophy of language. Firstly, it distinguishes between partial and consistent assertion of a sentence, and introduces the concept of an equivocal sentence, which is both partially asserted and partially denied. Secondly, it proposes a novel definition of truth, stating that a true sentence is one that is consistently asserted. This definition avoids the Liar paradox, does not restrict classical logic, and applies to declarative sentences in the language used by any particular person. Thirdly, the paper introduces an epistemic model of language, called assertional language, which formalizes the definition of truth. Finally, it provides an argument for the falsity of so-called Liar sentences. The proposed definition of truth can be viewed as a formal account of the correspondence theory. The epistemic model is a powerful concept that allows for combining different languages in a meaningful way. This model is uniquely capable of reflecting on epistemic inconsistencies, such as logical paradoxes, in a consistent manner and without resorting to non-classical solutions.