Klaus Truemper is Professor Emeritus of Computer Science at the University of Texas at Dallas. He started out at that university in Mathematics and Computer Science, but now also focuses on the history of mathematics and brain science. See More Books and Software for additional material.
Wittgenstein and Brain Science
What is the nature of knowledge? What is time? This book proposes answers to these and other centuries-old, and so far unresolved, questions about the world using results of modern brain science and a key method of the philosopher Wittgenstein.
The book relies on the same tools to show why some of these questions about the world simply cannot be answered. For example: Do we have free will?The arguments rely on a very general concept of subconscious and conscious neuroprocesses that acquire information and react in some way. A hypothesis consistent with the results of modern brain science specifies how these processes interact.
Why would you want to read this book?
– If you are interested in the fundamental questions about the world, this book gives you a new way to look at them.
– The tools help you deal with the flood of information produced by the media. They help you decide whether material is relevant or manipulative drivel.
Magic, Error, and Terror
How is it possible that the brain, an organ weighing less than 4 lbs., manages the body and copes with our complex world so effectively?
The answer: The brain employs a large number of subconscious and conscious models. They often produce magical results, but also lead to errors, and sometimes to terror. We explore a number of these models.
We look at subconscious models that explain how psychotherapy changes minds, why fatigue is an emotion, how breathing affects our well-being, and how we may give mind and body a rest.
In contrast with these beneficial models, there are conscious models in medicine, economics, politics and religion that inflict enormous damage.
Lastly, the models play an important role in philosophy. We use them to establish that the age-old question “Do we have free will” is nonsensical.
The Daring Invention of Logarithm Tables
In the early 17th century, both Jost Bürgi and John Napier dared to invent a logarithm table whose construction required tens of thousands of computing steps.
The Daring Invention of Logarithm Tables tells the story of Bürgi’s and Napier’s work, and how Henry Briggs built on Napier’s idea, creating a table of logarithms that was easier to use.
It reconstructs Bürgi’s thinking leading up to his table. The reader looks over his shoulder, so to speak, and learns how Bürgi came upon the idea, how he decided on the specific format of the table, and how his instructions should be interpreted. And so the reader experiences the magic of the invention of logarithms.
The final chapters examine the question “Who invented logarithms?”. For centuries, few people were aware of Bürgi’s work; John Napier was considered to be the sole inventor. This changed at the middle of the 19th century when Jost Bürgi’s work became more widely known. Since then there has been extensive debate whether Bürgi should be considered an independent co-inventor.
Careful parsing of the history of logarithm going back to Archimedes of antiquity then reveals that, without doubt, John Napier and Jost Bürgi are independent co-inventors of logarithms.
The Construction of Mathematics: The Human Mind’s Greatest Achievement
Is mathematics created or discovered? The answer has been debated for centuries. This book answers the question clearly and decisively by applying the concept of language games, invented by the philosopher Wittgenstein to solve difficult philosophical issues.
Using the results of modern brain science, the book also explains how it is possible that eminent mathematicians and scientists offer diametrically opposed answers to the question of creation vs. discovery.
Interested in the topic but intimidated by mathematics? Not to worry. If you are familiar with the elementary operations of addition, subtraction, multiplication, and division, you can follow the arguments of this book.