After a hiatus of four years, Stephen Welch is back with some timely videos at Welch Labs that just coincidentally occur around the time of the new movie release of Oppenheimer. They deal with the history of the physics behind the Manhattan Project at Los Alamos. Continue reading
“I want to [link to] an insightful explanation of the history of string theory, discussing the implications of how it was sold to the public. It’s by a wonderful young physicist I had never heard of before, Angela Collier. She has a Youtube channel, and her latest video is string theory lied to us and now science communication is hard.
… It’s as hilarious as it is brilliant, and you have to see for yourself.”
Collier delivered her talk lucidly and thoroughly—all while playing a frenetic video game! She claimed she used the length of the game to time her talk. Of course we can walk and talk, and ride bicycles and talk, but I have never seen anyone split their mental concentration between a fast-paced video game and an esoteric physics explanation of the history of string theory and supersymmetry—for over 50 minutes! And there was something about her presentation that was completely captivating. It was definitely a serious scientific talk, but the ludicrousness of the game-playing echoed how ridiculous the continued, misplaced fascination with string theory is. Naturally I had to learn more about this provocative physicist.
See A New Day
I have just finished reading a most remarkable book by Alec Wilkinson, called A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age. I had read an essay of his in the New Yorker that turned out to be essentially excerpts from the book. I was so impressed with his descriptions of mathematics and intrigued by the premise of a mature adult in his 60s revisiting the nightmare of his high school experience with mathematics that I was eager to see if the book was as good as the essay. It was, and more.
The book is difficult to categorize—it is not primarily a history of mathematics, as suggested by Amazon. But it is fascinating on several levels. There is the issue of a mature perspective revisiting a period of one’s youth; the challenges of teaching a novice mathematics, especially a novice who has a strong antagonism for the subject; and insights into why someone would want to learn a subject that can be of no “use” to them in life, especially their later years.
Wilkinson has a strong philosophical urge; he wanted to understand the role of mathematics in human knowledge and the perspective it brought to life. He was constantly asking the big questions: is mathematics discovered or invented, what is the balance between nature and nurture, why does mathematics seem to describe the world so well, what is the link between memorization and understanding, how do you come to understand anything?
I thought there was nothing new we could learn about Abraham Lincoln, but I see I was quite mistaken after reading Sidney Blumenthal’s article, “Abraham Lincoln, Tech Entrepreneur”.
In the current oppressive anti-science climate it is important to look back at our history and see how integral scientific thinking was to our founding and development. Not only were our Founding Fathers scientists, such as Jefferson and Franklin who with others founded the American Philosophical Society in 1743, but it turns out that President Abraham Lincoln could also lay claim to a scientific mind. Blumenthal’s article describes in detail how Lincoln employed science to advance the development of our country. You should read the entire article, but I am including some highlights.
I thought it would be interesting to present a recent entry in the mathematician John Baez’s Diary on some extremes in mathematics from the Bourbaki school, namely, how many symbols it would take to define the number “1.”
I don’t know if the “mathematician” Nicolas Bourbaki holds any significance for students today, but in my time (math graduate school in the 1960s) the Bourbaki approach seemed to permeate everything.
My first exposure to Bourbaki was as a humorous figure described by Paul Halmos in his 1957 article in the Scientific American—the humor being that Bourbaki did not exist. As Halmos wrote:
“One of the legends surrounding the name is that about 25 or 30 years ago first-year students at the Ecole Normale Superieure (where most French mathematicians get their training) were annually exposed to a lecture by a distinguished visitor named Nicolas Bourbaki, who was in fact an amateur actor disguised in a patriarchal beard, and whose lecture was a masterful piece of mathematical double-talk. It is necessary to insert a word of warning about the unreliability of most Bourbaki stories. While the members of this cryptic organization have taken no blood oath of secrecy, most of them are so amused by their own joke that their stories about themselves are intentionally conflicting and apocryphal.”
Nicholas Bourbaki was the pseudonym for a group of French mathematicians who wished to write a treatise which would be, as Halmos stated, “a survey of all mathematics from a sophisticated point of view”.
See the Bourbaki World
Given the mathematical nature of this website I feel reluctantly impelled to address the coronavirus pandemic. The mathematics behind the spread of infection is basically the same exponential growth that I discussed in the “Math and Religion” post and has recently been explained by the ever-lucid Grant Sanderson at his 3Blue1Brown website.
What I wish to draw attention to is the series of posts on the coronavirus by Kevin Drum on his website at Mother Jones. I have collected his recent posts comparing the spread of the virus in various countries and added some mathematical commentary of my own, which is the content of this post.
But the bottom line seems to be that in virtually all the countries, including the US, the virus infection is spreading at the Italian rate of doubling every 4 days! The readers of this website are sufficiently numerate to realize the frightening import of that number. If that weren’t enough, Kevin provides additional posts on the results of the modeling at the Imperial College that are truly nerve-wracking for someone such as myself in the most vulnerable cohort. The only blessing so far seems to be that, for once, the children are spared.
At this time, I don’t have the stomach to keep updating the post as new numbers come in. That may change. I could address the catastrophe of having ignorance and incompetence at the helm of the national ship of state, but it is too depressing.
See the Coronavirus Mathematics
(Updates 3/17/2020, 3/21/2020, 4/17/2020, 9/20/2020, 10/1/2020) Continue reading
For a number of years I have collected excerpts that portray mathematical ideas in a literary or philosophical setting. I had occasion to read a few of these on the last day of some math classes I was teaching, since there was no point in introducing a new subject before the final exam.
I thought it might be interesting to present some of these excerpts now. They roughly fall into three categories: logic, infinities (Zeno’s Paradoxes, infinite regress), and permutations.
(Update 11/16/2019) Continue reading
One of the books that has stuck with me over the years is Carl Becker’s The Declaration of Independence (1922, reprint 1942), not only for its incredibly clear and beautiful writing but also for its emphasis on the impact of the revolution most prominently caused by Isaac Newton, which was later subsumed under the term Scientific Revolution covering the entire 17th century. A consequence of this remarkable period was the so-called Enlightenment that followed in the 18th century and became the soil from which our nation’s founding ideas and documents sprang. Both these centuries have been further optimistically called the Age of Reason.
Our current times, awash in lies, corruption, and such terms as “alternative facts”, have been characterized as an assault on the rationalism and Enlightenment that shaped our founding. Any revisiting of these origins would seem to be a valuable endeavor to see if they still have validity. What makes Becker’s essay particularly relevant to me is the current pervasiveness of the mathematical view of reality that was launched by Newton some 300 years ago. Becker shows how this new way of thinking spread far beyond the bounds of mathematics and engendered a new “natural rights” philosophy that formed the foundation for the Declaration of Independence. Essentially the idea was that if the behavior of the natural world was based on (mathematical) laws, then so must the behavior of man be based on natural laws.
(Updates 10/31/2019, 9/18/2020) Steven Strogatz Confirmation and an Atlantic article
The September 2019 Special Issue of Scientific American is a must read. Unfortunately it is behind a paywall, so you should purchase a copy at a store or digitally online. All the articles are fascinating and relevant, and address basic questions of epistemology—how do we know what we know? The first section, “Truth”, is the most pertinent to my thinking, as it covers three subjects I have been pondering for years.
Physical Reality. The first article in the section is “Virtually Reality: How close can physics bring us to a truly fundamental understanding of the world?” by George Musser. I have addressed this issue of physical reality in my article Angular Momentum, with an emphasis on the role of mathematics. Musser cites the difficulties of trying to understand quantum mechanics after almost one hundred years or the failure to marry quantum mechanics with Einstein’s theory of gravitation as possible indications that there might be limits to our human endeavor to comprehend physical reality. This frustration is not new:
Over the generations, physicists have oscillated between self-assurance and skepticism, periodically giving up on ever finding the deep structure of nature and downgrading physics to the search for scraps of useful knowledge. Pressed by his contemporaries to explain how gravity works, Isaac Newton responded: “I frame no hypotheses.”
I am a regular reader of Ash Jogalekar’s blog Curious Wavefunction, but I found my way to his latest via the eclectic website 3 Quarks Daily, also highly recommended. I could not resist the title, “Mathematics, And The Excellence Of The Life It Brings”. The entirety of the post was about the mathematician Shing-Tung Yau’s recent memoir, The Shape of a Life, but Jogalekar’s introductory remarks about his personal involvement with mathematics stirred so many personal recollections of my own, that I thought I would provide an excerpt, followed by my own comments. Furthermore, he also addresses in passing the perennial question of whether math is invented or discovered.
(Update 8/9/2021) Jogalekar’s story about his embracing math and the effect Simmon’s topology book had on him is even more amazing than I thought. Throughout his younger years he had always been labeled “bad at math” and did poorly in school. But a teacher and Simmon’s book changed all that. He explains in a recent article in 3QuarksDaily, which I also provide here.
I can’t help singling out a section where he, too, extols the significance and importance of high school geometry (see my post “Down with Geometry”):
“… Purely through accident at this time, I had gotten my hands on a book on topology, a subject that I had become mildly interested in because of its deep connections to geometry; interestingly, while I was rather abysmal at algebra in school, I always did well with geometry because I was good at visualization. …
The topology book and the professor completely changed my outlook and saved me. I started doing well and tackling advanced topics and started to love math. I also got interested in physics and did well. Most importantly, I started appreciating the beauty of math. Over time I found that people interested in mathematics are generally of two kinds, although there’s some overlap: there are those who really enjoy mathematical puzzles and puzzle-like problems, relishing the raw process of problem-solving. Then there are others who simply enjoy the abstract nature of proofs and the connections between different topics: I am definitely part of this second group. In fact, another revelation I had was that most of the high school curriculum needed the students to be good at the former skill and had no appreciation of the latter, thus simply weeding out students like myself who wanted to understand the big picture and see the connections rather than just become adept at problem-solving.”
I confess I share this view and find it somewhat ironic that my website has devolved into a problem-solving source. I have tried to show the wider picture of fascinating connections, but that often takes more skill and time than I currently possess.