The Mathematics of the Unknown

With Applications

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The Idea

The main assumption of this book is that if it requires a lot of time and effort to explain how something works, probably we do not fully understand it, and our knowledge must be necessarily incomplete. Many scientists and philosophers of science will not agree with this premise; they would argue that some theories are difficult to explain because the underline concepts are inherently difficult. However, we provide a strong evidence, based in the analysis of the history of science, that this is not the case. Long explanations usually contain a lot of redundancy: repeated ideas, unused concepts, improperly defined relations, and so on. With a better understanding, normally after considerable research, we should be able to remove that redundancy. When there is no more redundancy to remove, we say that we have achieved a perfect knowledge.

When it is not possible to further compress a string, because there are no more redundant elements to remove, we say that the string is random. Since perfect knowledge is achieved when there is no more redundancy to be removed from a description, we can conclude that perfect descriptions must be necessarily random strings. That is, perfect knowledge implies randomness.

In this book it is described in detail the Theory of Nescience, a new mathematical theory that has been developed with the aim of quantitatively measure how much we do not know. The theory is based on the fact that randomness effectively imposes a limit on how much we can know about a particular research topic. In the book are also covered some of the (surprisingly) large number of practical applications of this new theory, not only to philosophy of science, but also to psychology, engineering, finance, biochemistry and physics.


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