Brain science is upending traditional notions of brain performance. The brain was thought of as a machine that accepts inputs and produces a variety of outputs.
Modern brain science has proved that this traditional viewpoint is not just simplistic, but actually misrepresents the brain’s performance in a fundamental way. The insight is now that the brain continuously modifies itself and adapts for the tasks at hand.
We just completed a book titled Magic, Error, and Terror: How Models in Our Brain Succeed and Fail. It interprets the new insight into the brain using the language of models. They reside at both the conscious and subconscious level. The book consists of three distinct parts.
Part I examines a number of cases where conscious thought modifies subconscious models. Part II looks at conscious models that are claimed to be correct, but in reality inflict considerable damage. Part III examines how models can be used to decided complicated philosophical questions, including the age-old question “Do we have free will?”
As you can see, the book covers a kaleidoscope of cases that, we hope, will prompt the reader to explore on their own how models in the brain impact our lives.
Over centuries, John Napier was considered the sole inventor of the logarithm concept. Based on this notion, he created a large table of logarithms that drastically reduced computational effort for multiplication and division of numbers.
However, independently and at the same time if not earlier, Jost Bürgi created a table of logarithms that required less construction effort, yet was more precise and just as effective in use as Napier’s.
The strange claim that Napier was the sole inventor came to be because Bürgi didn’t publish his invention in a timely fashion, and then only by a table and terse handwritten instructions for its use.
That situation changed in the middle of the 19th century, when Bürgi’s became more widely known. But even after that point in time there have been debates whether Bürgi should be considered an independent inventor of the logarithm concept.
These strange developments got our attention a few years ago, and we began to investigate the work of Bürgi and Napier. The results just appeared in the book The Daring Invention of Logarithm Tables. The main conclusion is that, without any doubt, Bürgi and Napier are independent co-inventors of logarithms.
We have completed the translation of F. Hülster’s Introduction to Wittgenstein’s Tractatus Logico-Philosophicus into German. The translation also made extensive use of Hülster’s original German manuscript. The book, Einführung in Wittgensteins Tractatus Logico-Philosophicus, is now in print. For details, go to the More Books section.
During the past several months we worked on a German edition of the book Introduction of Wittgenstein’s Tractatus Logico-Philosophicus by F. Hülster. During that process we decided to update the existing English version so that it would be in full agreement with the upcoming German edition. At the same time, we corrected some minor errors. That updating effort of the English version is now complete, and the updated edition is available.
The book The Construction of Mathematics: The Human Mind’s Greatest Achievement includes creation of tables of the logarithm function by the Swiss craftsman, engineer, and mathematician Jost Bürgi around 1600 CE, with delayed publication in 1620. The book includes the title page of Bürgi’s tables, then explains that the black numbers of the inner ring are on a logarithmic scale.
Due to that feature, two copies of that ring of numbers can be arranged in nested fashion depict a circular slide rule.
Bürgi did not realize this, or rather, there is no evidence that he did. Instead, William Oughtred invented the circular slide rule two years later, in 1622.
We couldn’t rest until we had implemented the circular slide rule based on Bürgi’s title page. For an authentic look, we created with Photoshop two differently sized copies of the black ring of numbers of Bürgi’s title page. The resulting rings were encased in Lexan and connected by a center bolt. It is fun to multiply and divide numbers by rotating the inner, smaller disk, all the time thinking that this is based on the work of genius done almost 400 years ago.