I would like to follow up on Alain Connes’ statement in my last blog. The weave of mathematical thought is tight. The seeds of mathematics are found in early explorations of number relationships and in observations of what we call space. But symbol, stripped of content, has led to heightened powers of thought and discernment. […]
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I’ve thought that one of the reasons it’s difficult to resolve questions about the nature of mathematical reality is that we’re not exactly clear on what it means to ‘perceive’ something. Trying to establish whether or not even the data of our senses is somehow independently ‘real,’ has fueled centuries of philosophical debate. I found […] Many of this week’s circumstances are limiting the time I have to write but I would like to point to a few sources that contain very nice accounts of what is known as the foundational crisis in mathematics. One of them was written by Paul Bernays in 1935. Understanding the nature of some of the […] I don’t have a lot of time to write this week and next but I felt a little surge of thoughts gather when I read about the implications of Einstein’s Second Law (m = E/c^2) which is a simple rearrangement of the now famous E = mc^2. It was in The Lightness of Being by […] Let’s ask again, “What is the nature of the bridge between sense perceptions and concepts? It’s a simple question to ask, but a fairly difficult one to answer. Raphael Nunez contributed a chapter to the Springer book, Recasting Reality: Wolfgang Pauli’s Philosophical Ideas and Contemporary Science. A pdf of the chapter can be found here. […] It’s easy to neglect the detail of one person’s, now historic, philosophical discussion of math and science. But there is a moment, in Henri Poincare’s well known text Science and Hypothesis, that I would like to shine a light on today. The first English translation of the book was published in 1905. Chapter IV is […] The following exchange between M.P. Schutzenberger and A. Connes is lifted from the book Triangle of Thoughts: M. P. S. — …language begins with poetry rather than with grammar; euphony plays a big role here. A. C. — Your point of view coincides with my own, since I sincerely believe that music is at its […] In the first half of the twentieth century, physicists and mathematicians began to raise questions about what they could say about what they were actually doing. The ‘truth’ of things was beginning to elude the seekers of that truth. Both the validity of mathematical ideas and the objectivity of physics came under scrutiny. Questions about […] I like the word plasticity, the idea that something would be capable of being shaped or formed. It’s an optimistic word, pointing to the promise of change, or transformation (another word I like). Today I happened upon some of the work of Nancy Nersessian, Professor of Cognitive Science at the Georgia Institute of Technology. She’s […] |
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