MATHEMATICAL ELEMENTS ON NATURAL REALITY


Book Description

All matters are in colorful, mystery and also with a complex mechanism to humans even if vegetables or animals, we are embarrassed hardly know their true face unless images. Usually, we understand things by the reality for promoting the survival and development of humans ourselves and then, construct a harmonious system of humans with the nature.




Mathematics and Reality


Book Description

Mary Leng offers a defense of mathematical fictionalism, according to which we have no reason to believe that there are any mathematical objects. Perhaps the most pressing challenge to mathematical fictionalism is the indispensability argument for the truth of our mathematical theories (and therefore for the existence of the mathematical objects posited by those theories). According to this argument, if we have reason to believe anything, we have reason to believe that the claims of our best empirical theories are (at least approximately) true. But since claims whose truth would require the existence of mathematical objects are indispensable in formulating our best empirical theories, it follows that we have good reason to believe in the mathematical objects posited by those mathematical theories used in empirical science, and therefore to believe that the mathematical theories utilized in empirical science are true. Previous responses to the indispensability argument have focussed on arguing that mathematical assumptions can be dispensed with in formulating our empirical theories. Leng, by contrast, offers an account of the role of mathematics in empirical science according to which the successful use of mathematics in formulating our empirical theories need not rely on the truth of the mathematics utilized.




Our Mathematical Universe


Book Description

Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.




Reconstructing Reality


Book Description

Attempts to understand various aspects of the empirical world often rely on modelling processes that involve a reconstruction of systems under investigation. Typically the reconstruction uses mathematical frameworks like gauge theory and renormalization group methods, but more recently simulations also have become an indispensable tool for investigation. This book is a philosophical examination of techniques and assumptions related to modelling and simulation with the goal of showing how these abstract descriptions can contribute to our understanding of the physical world. Particular issues include the role of fictional models in science, how mathematical formalisms can yield physical information, and how we should approach the use of inconsistent models for specific types of systems. It also addresses the role of simulation, specifically the conditions under which simulation can be seen as a technique for measurement, replacing more traditional experimental approaches. Inherent worries about the legitimacy of simulation "knowledge" are also addressed, including an analysis of verification and validation and the role of simulation data in the search for the Higgs boson. In light of the significant role played by simulation in the Large Hadron Collider experiments, it is argued that the traditional distinction between simulation and experiment is no longer applicable in some contexts of modern science. Consequently, a re-evaluation of the way and extent to which simulation delivers empirical knowledge is required. "This is a, lively, stimulating, and important book by one of the main scholars contributing to current topics and debates in our field. It will be a major resource for philosophers of science, their students, scientists interested in examining scientific practice, and the general scientifically literate public."-Bas van Fraassen, Distinguished Professor of Philosophy, San Francisco State University




The Pythagorean World


Book Description

This book explores precisely how mathematics allows us to model and predict the behaviour of physical systems, to an amazing degree of accuracy. One of the oldest explanations for this is that, in some profound way, the structure of the world is mathematical. The ancient Pythagoreans stated that “everything is number”. However, while exploring the Pythagorean method, this book chooses to add a second principle of the universe: the mind. This work defends the proposition that mind and mathematical structure are the grounds of reality.




Mathematical Combinatorics: My Philosophy Promoted on Science Internationally


Book Description

Mathematical science is the human recognition on the evolution laws of things that we can understand with the principle of logical consistency by mathematics, i.e., mathematical reality. So, is the mathematical reality equal to the reality of thing? The answer is not because there always exists contradiction between things in the eyes of human, which is only a local or conditional conclusion. Such a situation enables us to extend the mathematics further by combinatorics for the reality of thing from the local reality and then, to get a combinatorial reality of thing. This is the combinatorial conjecture for mathematical science, i.e., CC conjecture that I put forward in my postdoctoral report for Chinese Acade- my of Sciences in 2005, namely any mathematical science can be reconstructed from or made by combinatorialization. After discovering its relation with Smarandache multi-spaces, it is then be applied to generalize mathematics over 1-dimensional topological graphs, namely the mathematical combinatorics that I promoted on science internationally for more than 20 years. This paper surveys how I proposed this conjecture from combinatorial topology, how to use it for characterizing the non-uniform groups or contradictory systems and furthermore, why I introduce the continuity ow GL as a mathematical element, i.e., vectors in Banach space over topological graphs with operations and then, how to apply it to generalize a few of important conclusions in functional analysis for providing the human recognition on the reality of things, including the subdivision of substance into elementary particles or quarks in theoretical physics with a mathematical supporting.




The Nature of Consciousness, the Structure of Reality


Book Description

This book describes how understanding the structure of reality leads to the Theory of Everything Equation. The equation unifies the forces of nature and enables the merging of relativity with quantum theory. The book explains the big bang theory and everything else.




MATHEMATICAL REALITY


Book Description

A thing is complex, and hybrid with other things sometimes. Then, what is the reality of a thing? The reality of a thing is its state of existed, exists, or will exist in the world, independent on the understanding of human beings, which implies that the reality holds on by human beings maybe local or gradual, not the reality of a thing. Hence, to hold on the reality of things is the main objective of science in the history of human development.




The Nature of Mathematical Modeling


Book Description

This is a book about the nature of mathematical modeling, and about the kinds of techniques that are useful for modeling. The text is in four sections. The first covers exact and approximate analytical techniques; the second, numerical methods; the third, model inference based on observations; and the last, the special role of time in modeling. Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area. The text is complemented by extensive worked problems.




MATHEMATICAL COMBINATORICS (INTERNATIONAL BOOK SERIES), Vol. 4, 2019


Book Description

The mathematical combinatorics is a subject that applying combinatorial notions to all mathematics and all sciences for understanding the reality of things in the universe, motivated by CC Conjecture of Dr. Linfan MAO on mathematical sciences. The International J. Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly, which publishes original research papers and survey articles in all aspects of mathematical combinatorics, Smarandache multi-spaces, Smarandache geometries, non-Euclidean geometry, topology and their applications to other sciences.