From reading the philosopher Immanuel Kant it appears he holds mathematics to be more accessible than philosophy, it being more difficult and involved. But philosophy is more complete in that Kant ascribes validity to philsophy's inclusion of: "the concept of representation, the concept of being next to or after one another; other concepts can be only partially analysed at all, as the concept of space, time, of various feelings of the human soul, of the feeling of the sublime, of the beautiful, of the disgusting, etc." (Kant Selected Pre-critical Writings, Kerferd and Walford, Manchester University Press, 1968) These philosophical ideas are not subject to statistical analysis; which brings to mind the words of a good friend, a Planning Director of a public agency serving two million people. He said there are lies, damn lies and statistics, the point of this being that statistics are typically mathematically given in numbers, and [...]
In the tumultuous last election, we have experienced the most divisive ever seen in America. But to find equilibrium I want to bring forth the time honored benefits of racial and ethnic diversity we have here and to which we must dearly hold on to. This has never been a subject in its underlying and sub conscious existence that we can comfortably talk or write about; because, on the one hand it is threatening, but on the other hand it is valuable as a unifying social attribute. This is the ‘conservative’ vs. ‘liberal’ conflict, on going, in America. There is, unmistakably, the frequent pairing of love ones, who are by nature searching for a partner, to seek out a ‘black’, (or brown) mate to compliment their ‘whiteness’ and a comparable seeking out a ‘white’ partner to compliment their ‘black’ and ‘brownness’. These desires are not spoken about openly because they [...]
When humans (homo sapiens) came to central Europe some 54,000 years ago, they encountered other humans: Cro-Magnons. It was thought by some that these “other humans” were killed off by the newly arrived Homo Sapiens, but through DNA evidence it is now thought they simply coupled with one another and were absorbed. Further study shows they had a larger brain cavity than Homo-Sapiens. The physical statures were somewhat different, with Cro-Magnons shorter but more muscular than Homo-Sapiens.
In the local paper I read a letter from a young woman, named Marisa, expressing her “feeling stupid in school” and her propensity to not do well in mathematics. I am an architect, now retired having had a successful practice of many years in the design and building of hospitals throughout California. As you may well know, this required a lot of technical skill and engineering knowledge. In high school some 70 years ago, I was tested and did not score well in mathematics. In order to gain entrance to college, I had to take a makeup course in calculus. With the help of friends, I managed to get through the course, but to this day I cannot recall a single useful principle of my calculus class. To be sure, I have been able to apply some basic principles of algebra in my work. Like all of us I use [...]
In my architectural practice, in the 1960s, in Berkeley California I had seen the affects of drug use, so much a part of the social scene of that time. I had employees come and go, not always surviving their experimenting with drugs. I knew, from a one time use of marijuana that my sense perceptions, which affected and distorted my space perceptions and momentarily affected my work, such that I wanted nothing more to do with it. One day, while alone in my office, I went to a large drawing surface on a wall and, without knowing why I was doing it, I drew a large circle. This was my unconscious coming to the fore and with this event I knew this was significant - It would become my Mandala. About this time I was reading Carl B. Boyer’s History of Mathematics. He tells of the inverse geometry of Professor [...]
As a young man with a desire to be an architect I enrolled in Mies Van Der Rohe’s School of Architecture at the Illinois Institute of Technology in Chicago. He had designed the entire campus in his severe Modern style. In my beginning class I was to draw straight line with a lead pencil. The second semester we would advance to drawing brick masonry patterns. Mies examined my work and gave his approval. However, I was dissatisfied with this training as a knew I already had these elementary skills. Late one night a classmate told me about the School of Design on the North side of Chicago. The next day I enrolled there. Most of the faculty were Europeans who taught at the German Bauhaus, who had come to America to escape the Nazis. I entered their Foundation Course which was patterned after the Bauhaus method. I was a young [...]
I was fascinated with geometry at age ten. Living on a farm in Midwest America, I attended a one room schoolhouse where the library consisted of a metal cabinet next to my desk. I could reach over and pull out a book of Euclidean geometry, which I often did. I intuitively understood, that my sense perceptions of geometry preceded and were more important than the written analysis of Euclid. I think of them, or as Euclid termed them the Propositions as being apperceptions of the geometric figures. I’m now in my eighties and the place of ‘perceptions’, that is to say ‘sense perceptions’ preceding the text is ever more correct in all matters of mathematics. In my book, Geometric Wholeness of the Self, I describe this philosophically. Not far from our farm in the Midwest, was the Farnsworth House. This famous house was designed by the world famous architect, Mies [...]
This is my first official blog post and I am excited to introduce my book Geometric Wholeness of the Self. It was recently printed by Ingram and will soon be available at Amazon.com. You can see an excerpt from the book HERE.