The Mathematics of the Unknown
The Mathematics of the Unknown
Bringing to the present the knowledge of the future
About the Book
The main idea of this book is that perfect knowledge implies randomness. This is a counterintuitive idea, since a lot of effort in science deals with the task to name and organize our chaotic world. Even the kind of knowledge that explains how things work requires a previous ordering and classification. Knowledge, apparently, is anything but random, yet this is not the case. If a theory is perfect, that is, it presents no redundant elements we can remove, it description must be an incompressible string of symbols. Thus, a model is random if it contains the maximum amount of information in the less space possible.
In this book it is described the minimum nescience principle, a novel mathematical theory that address the problem of what it is science and how scientific knowledge can be acquired. Our main assumption is that it is easier to measure how much we do not know than measuring how much we do know, because randomness posses a limit to how much we can know. A second assumption is that the computer is the right tool that can provide this quantitative measure.
That randomness effectively imposes a limit on how much we can know about a particular problem or area, far from being a handicap, opens new opportunities in science and technology. Its proper understanding allow us to automate the solution of problems, and use computers to discover new interesting research topics.
In the book we describe in detail the practical applications of the new theory of nescience, not only in the context of artificial intelligence, but also to computational creativity and software engineering.
- Chapter 1 Introduction
- Chapter 2 Discrete Mathematics
- Chapter 3 Computability
- Chapter 4 Coding
- Chapter 5 Complexity
- Chapter 6 Learning
- Chapter 7 Philosophy of Science
- Chapter 8 Entities, Representations and Descripitons
- Chapter 9 Miscoding
- Chapter 10 Inaccuracy
- Chapter 11 Surfeit
- Chapter 12 Nescience
- Chapter 13 Interesting Questions
- Chapter 14 Advanced Properties
- Chapter 15 Machine Learning
- Chapter 16 Software Engineering
- Chapter 17 Measuring Current Knowlege
- Chapter 18 Computational Creativity
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