The Mathematics of the Unknown
The Mathematics of the Unknown
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The Mathematics of the Unknown

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Last updated on 2018-10-11

About the Book

The quest for knowledge always starts by identifying a set of research entities we would like to understand. The elements of this collection can be almost anything. If we are mathematicians, our set of interest will be composed by mathematical concepts; if we are biologists, the set will be living things; and if we are engineers, it will be practical problems. Our goal, as scientists, is to understand as much as possible about those entities. We want to understand how things work because that allows us to forecast both, future events in environments with high uncertainty, and the consequences of our own actions. Also, and more challenging, looking at events/consequences we can try to infer the causes; for example, if I have fever, maybe it is because I have been infected with a virus. Understanding is how humankind makes progress, and understanding means to find patterns or regularities that allows us to provide models of the original entities under study.

If we want to study a research entity, first we have to provide a representation of that entity. A representation is a string that captures as many details of the original entity as possible. In science, traditionally, these representations have had the form of texts (e.g. mathematics), collection of facts (e.g. sociology), or the result of experiments (e.g. physics). Recently, and due to the huge advances in the capacity of computers to collect and store data, a new and powerful way to encode entities has emerged: the use of large collections of data as representations.

This book is a comprehensive, self-contained, introduction to the Theory of Nescience, a new and powerful mathematical theory that has been developed with the aim of automatically understand research entities and discover new knowledge.The theory is based on the fact that randomness effectively imposes a limit on how much we can know about the representation of a particular entity. Far from being a handicap, the proper understanding of this absolute epistemological limitation opens new opportunities in science and technology, both, to solve open problems, and to discover new knowledge. In the book it is also described some of the (surprisingly) large number of practical applications of this new theory, including artificial intelligence (data science, machine learning), the scientific method, computational creativity and software engineering (quality assurance).

About the Author

R. A. García Leiva
R. A. García Leiva

R. A. García Leiva has a Bachelors degree in Computer Science by the University of Córdoba, a Master degree in Computational Sciences by the University of Amsterdam, and a Diploma of Advanced Studies in Telematics by the Universidad Autónoma de Madrid. He worked during four years in the University of Córdoba as a scientific programmer in the areas of Geographical Information Systems and Remote Senging. He worked during three years in the Universidad Autónoma de Madrid as research engineer in the area of High Energy Physics. He worked during three years as R&D Director at Andago Ingeniería in the areas of open source software and e-government. In 2008 he funded Entropy Computational Services, where he worked for five years in the areas of Social Networks, Mobile Applications, and Quatintative Trading. In 2014 he joined to the Institute IMDEA Networks, as research engineer, working in the areas of Machine Learning and Big Data.

More information about my research can be found at http://www.mathematicsunknown.com/

Table of Contents

Chapter 1 Introduction

PART I Background

Chapter 2 Discrete Mathematics

Chapter 3 Computability

Chapter 4 Coding

Chapter 5 Complexity

Chapter 6 Probability

PART II Foundations

Chapter 7 Entities, Topics and Descriptions

Chapter 8 Miscoding

Chapter 9 Surfeit

Chapter 10 Inaccuracy

Chapter 11 Nescience

Chapter 12 Creativity

Chapter 13 Advanced Nescience

PART III Applications

Chapter 14 Machine Learning

Chapter 15 Scientific Method

Chapter 16 Computational Creativity

Chapter 17 Software Engineering


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