Category Archives: Causality, Chance, and Connections

Symbolic Algebra Timeline

As I am sure is common with most mathematicians, I had become interested in the history of the development of mathematical symbols, first for numbers (numerals) and then for algebra (symbolic algebra).  Joseph Mazur’s book Enlightening Symbols provided an excellent history of this evolution.  His focus on the development and significance of symbolic algebra in the Renaissance was especially illuminating.  I also augmented Mazur’s information with details from Albrecht Heeffer’s work.

Such a subject cries out for a timeline to appreciate the order and timing of discoveries, which Mazur provided, concentrating on the Renaissance.  I decided to both simplify Mazur’s version and expand it to cover the evolution of numbers and their notation, as well as to set the whole enterprise in the context of historical periods.

See Symbolic Algebra Timelines

Greek-Indian Connection — Alexander’s Legacy

In my post, “Causality, Chance, and Connections,” I have already alluded to one of the biggest mysterious connections that has bedeviled me over the years, namely, the brief suggestion I found in an art book over 50 years ago in the mid-1960s that the human images of Buddha that appeared in statues some four to five hundred years after his life came from the influence of Greek settlers left by Alexander the Great around 300 BC in the Gandhara region of then northwest India (now Pakistan).

I spent decades trying to verify this story.  For some time I have wanted to write an article about what I found.  But it was such a vast and nebulous tale, that I was reluctant to hazard my limited view of the matter.  Nevertheless, I finally could not resist, so here is my sketch of the great Greek Buddha mystery.

See the Greek-Indian Connection

(Update 1/8/2024)  Buddha in Egypt
 Continue reading →

Turkey Red

The Columbus story shows the intervention of chance in history at its most capricious. The following tale has its own logic, but the confluence of serendipitous events makes it marvelous and uplifting, especially in our current dark times. It was first brought to my attention by my father back in the early 1960s at the height of America’s role as wheat breadbasket of the world. America, and especially Kansas, was supplying essential wheat to the recently independent country of India and to the Soviet Union, whose long struggle with collective farming (and other factors), especially in the Ukraine, had led to its dependency on imports.

I will not try to narrate the story O’Henry-like with a surprise ending, but announce the amazing coincidence from the start—America was supplying the USSR its own wheat! The Kansas wheat was derived from a special hardy winter variety called Turkey Red that had originated in the Ukraine and was brought to America by Mennonites. So the story is how this all came about. See Turkey Red.

(Update 2/24/2022)  Russian Invasion of Ukraine

More ironic coincidences.  Who would have thought a story about wheat from a distant land over one hundred years ago would become timely in the 21st century.  But terms like Catherine the Great’s “New Russia” are being uttered by a modern despot Vladimir Putin and port cities like Mariupol are again in the news.  All attention has been on focused on the effect of Putin’s folly on oil and gas, but I have been wondering about its consequences for the wheat.  And sure enough, such concerns are finally in the news.

See the Russian Invasion.

(Update 2/28/2022)  Russia May Weaponize Food Supply Chain

Politico has a more expansive article on the implications of the grain production in Ukraine by Ian Ralby et al., “Why the U.S. Needs to Act Fast to Prevent Russia from Weaponizing Food Supply Chains”.  For example, the article asserts, “Amid the chaos of this conflict and the threat to Ukrainian lives and independence, one critical implication has been grossly underexamined: how Russia could rely on China’s support to weaponize global food supply chains.”  Though Russia’s gas and oil production has garnered the most attention, “Russia’s control of Ukrainian grain shipments will likely have far greater consequences.  After just one day of the invasion, Russia effectively controlled nearly a third of the world’s wheat exports, three quarters of the world’s sunflower oil exports, and substantial amounts of barley, soy and other grain supply chains.”  The article examines in detail the implications of this control.

See Russia and Food Supply Chain.

Chemical Determinism – Motor Proteins

It was reading Peter Hoffmann’s 2012 book Life’s Ratchet that drove home the role of determinism in biological processes, which he characterizes as a ratchet, a process that filters random behavior into a particular “purposeful” direction. Since Hoffmann is a biophysicist, his presentation is heavily guided by the physical principles of energy conversion, thermodynamics, and entropy, which makes for a fresh approach to a traditionally biological subject. The startling thing Hoffmann’s book introduced me to was the subject of molecular machines or motor proteins. These were amazing engines that harnessed the chemical and physical energy within a cell to act like miniature workers hauling materials around and constructing other molecules. The intelligent design crowd would go bonkers. See Chemical Determinism – Motor Proteins

Columbus and the Irony of Chance

One of the all-time examples of chance intervening in history is Christopher Columbus’s putative discovery of America. Moreover, the legend of this discovery is filled with erroneous information that was traditionally foisted upon unsuspecting elementary school children. One of the most egregious errors was the assertion that Columbus was trying to prove the earth was round and not flat. I had a picture book when I was young that showed sailors tumbling off the edge of a flat earth.

I first came upon the demythologizing of the Columbus legend from reading Isaac Azimov’s anthologized 1962 column “The Shape of Things”. His tale is so well-written, that I want to include it in its entirety. I have augmented it with some more detailed footnotes and illustrations.

See Columbus and the Irony of Chance.

Causality, Chance, and Connections

This essay introduces a topic I have been thinking about for a number of years. It also may allow me to connect the math impulse to a wider range of thoughts than just those based on math or even science.

It all begins with the perennial question of “why” that drives our curiosity about the nature of things and how various situations came about, such as our physical universe, our biology, the origin of life, or historical events. The explanations are usually couched in terms of causal links: such and such happened because some other thing happened. In the physical sciences we think the causal links follow certain physical, chemical, or biological laws that we provisionally hypothesize. In the historical realm we think there are still causes, such as the physical environment (geography, climate, weather, etc.) or the imprint of individuals. But the historical chains of events are often disrupted by chance and coincidences, and some supposed links degenerate into imagined connections or associations.

In the future I plan to write a number of essays that explore and illustrate these ideas. See Causality, Chance, and Connections.