Tag: World War I

Education and Ambiguity Awareness: A Polyvalent World

Sleepwalkers and sleepwalking are both destructive and constructive and show us the ambiguity in all phenomena.

The World War I chronicle of Professor Christopher Clark, The Sleepwalkers, from 2012, is described this way:

On the morning of June 28, 1914, when Archduke Franz Ferdinand and his wife, Sophie Chotek, arrived at Sarajevo railway station, Europe was at peace. Thirty-seven days later, it was at war. The conflict that resulted would kill more than fifteen million people, destroy three empires, and permanently alter world history.

The Sleepwalkers reveals in gripping detail how the crisis leading to World War I unfolded. Drawing on fresh sources, it traces the paths to war in a minute-by-minute, action-packed narrative that cuts among the key decision centers in Vienna, Berlin, St. Petersburg, Paris, London, and Belgrade.

Distinguished historian Christopher Clark examines the decades of history that informed the events of 1914 and details the mutual misunderstandings and unintended signals that drove the crisis forward in a few short weeks.

How did the Balkans—a peripheral region far from Europe’s centers of power and wealth—come to be the center of a drama of such magnitude? How had European nations organized themselves into opposing alliances, and how did these nations manage to carry out foreign policy as a result? Clark reveals a Europe racked by chronic problems—a fractured world of instability and militancy that was, fatefully, saddled with a conspicuously ineffectual set of political leaders. These rulers, who prided themselves on their modernity and rationalism, stumbled through crisis after crisis and finally convinced themselves that war was the only answer.

On the other hand, the great science writer and intellectual Arthur Koestler (died in 1983) in his own book, The Sleepwalkers, (originally, 1959) argues that the revolution in cosmology associated with the names of Copernicus, Kepler, Galileo, et al depended on visionary thinking, a kind of “sleepwalking.”

Lastly, the classic novel, The Sleepwalkers by Hermann Broch (died in 1851) condemns sleepwalking as the basis of Europe and Germany’s descent into nightmare.

Important works by Broch are The Sleepwalkers (German: “Die Schlafwandler,” 1932) and The Guiltless (German: “Die Schuldlosen,” 1950). The Sleepwalkers is a trilogy, where Broch takes “the degeneration of values” as his theme. Various generations are depicted as sleepwalking through their times and eras without any ability to “see past” their time, place, era. They were “sleepwalking.” This made them liable to demagogic deceptions and recruitment.

On the other hand, the experience and story of Kekulé (died 1896) and his scientific discoveries prodded by dreams and reveries and sleepwalking give us a story that argues against seeing sleepwalking as always negative:
Kekulé’s dream and “good kinds of sleepwalking.”

Friedrich August Kekulé, later Friedrich August Kekule von Stradonitz (7 September 1829 – 13 July 1896), was a German organic chemist. From the 1850s until his death, Kekulé was one of the most prominent chemists in Europe, especially in theoretical chemistry. He was the principal founder of the theory of chemical structure.

The new understanding of benzene (C6H6), and hence of all aromatic compounds, proved to be so important for both pure and applied chemistry after 1865 that in 1890 the German Chemical Society organized an elaborate appreciation in Kekulé’s honor, celebrating the twenty-fifth anniversary of his first benzene paper.

Here Kekulé spoke of the creation of the theory.

He said that he had discovered the ring shape of the benzene molecule after having a reverie or day-dream of a snake seizing its own tail (this is an ancient symbol known as the ouroboros).

Kekulé’s story of “dreaming up” the structure of benzene (C6H6) gives us another historical example of Arthur Koestler-type “good sleepwalking” ie visionary dreams and reveries that really enhance “objective” concrete scientific analysis and not only art works.

It is educational to see the inner ambiguity of words and phenomena (such as sleepwalking) because this duality and “polyvalence” applies to many cases.

Science and Its Discontents: The Case of Natsume Sōseki (夏目 漱石) in Japan

Natsume Sōseki (夏目 漱石) is and was the most prestigious and respected novelist in modern Japan and every student has to engage with such novels of his as Botchan (坊っちゃん, “Young Master”) and Kokoro (こゝろ, or in post-war orthography こころ, “Heart”). Sōseki died in 1916.

Sōseki’s feeling that the modern world is some kind of runaway train with no brakes is expressed clearly in his 1913 novel, Kōjin (行人 , “The Wayfarer”).

One of Sōseki’s dialogues in the novel is about the current science and technology world, which was quite visible already then, and has a very nerve-racking or frightening tempo of a turbulent tsunami.

One character says:

“Now what you call insecurity is the insecurity of the entire human race, and it isn’t peculiar to you alone. Constant motion and flow is our very fate.

“Man’s insecurity stems from the advance of science. Never once has science, which never ceases to move forward, allowed us to pause. From walking to ricksha, from ricksha to carriage, from carriage to train, from train to automobile, from there on to the dirigible, further on to the airplane, and further on and on, no matter how far we may go, it won’t let us take a breath. How far it will sweep us along, nobody knows for sure. It is really frightening.”

Yes, it is frightening, indeed, I agreed.

“It is frightening because the fate that the whole of humanity will reach in several centuries, I must go through—in my own lifetime—and at that all alone. That’s why it is frightening. In short, I gather within myself the whole insecurity of the human race, and distill that insecurity down into every moment, that is the fright that I am experiencing.”

(Natsume Sōseki, Kōjin [行人], Charles E. Tuttle Company, 1991, 9th printing, page 285)

Comment: There’s no need to dismiss these feelings as Luddite. They represent a reaction to the vertiginous or dizzying pace of the modern techno-protean change machine with no pause button.

Notice that Sōseki’s life (1867-1916) is basically congruent with Globalization I (i.e., the period of 1870-1913) discussed in the previous essay on Arthur Lewis’s classic Growth and Fluctuations, 1870-1913.

Sōseki has been, like his spokesmen in the citation above, swept up into a change-storm which led to a globalization backlash from 1914-1945, the era of deglobalization. WWI is the beginning bookend of all this.

Notice that the micro world of feelings and moods in the novel are resonant with the macro world though people at a certain time, such as the Sōseki protagonists, are not rigorous or prophetic theoreticians but rather groping in the dark.

What We Mean by “Towards a Composite Understanding of Education”

(MI slogan, motto or catchphrase)

Let’s be concrete and start with the title of the classic 1978 book by the Princeton professor and 1979 Nobel Prize winner, Sir Arthur Lewis, Growth and Fluctuations, 1870-1913 (introduced in the previous essay on “Looking Backwards and Forwards at the Same Time”).

Notice the following other dimensions that have to be included to “compositize” our understanding:

  1. The period 1870-1913/4 is called Globalization I by economic historians. Globalization in this view is not about Marco Polo, but the rise of world prices, such as for wheat.

  2. Paul Kennedy (Yale), who is known for his Rise and Fall of the Great Powers classic, wrote a tighter book called The Rise of the Anglo-German Antagonism, 1860-1914 (1980), described as follows:

    “This book gives an account of the rivalry between Great Britain and Germany in the period leading to the First World War. It gives readers a thorough comparison of the two societies, their political cultures, economies, party politics, courts, the role of the press and pressure groups, and so on. …”

  3. The first treaty between a European power and an Asian country was signed in 1902, “The Anglo-Japanese Alliance.”

    “In this book, Professor Nish deals with one of the most important aspects of far eastern politics in the critical period between 1894 and 1907. His object is to demonstrate how Britain and Japan, at first separately and later jointly, reacted to Russian encroachments in China and east Asia; he is concerned also with the policies of the other European powers and of the U.S., to whose hostility towards the Anglo-Japanese alliance after 1905 Britain showed…”

  4. The first defeat of a European by an Asian nation (i.e., the Russo-Japanese War, 1904-5). The famous Indian writer Pankaj Mishra wrote a recent book on this, showing how this defeat of a European country sent shock waves through the world and especially through the anti-colonial movements of Asia and Africa…

  5. Partition of Africa:

    “Between 1870 and 1914 the whole of Africa, apart from one or two small areas, was partitioned by the European powers.”

    (David Thomson, England in the Nineteenth Century, 1815-1914, 1978, Penguin Books, page 203)

  6. Rise of Suburbia:

    “The 1890s saw the coming of the first electric trams, the first “tubes,” and the first motor-cars. By 1914, almost any provincial city of any size had its electric trams, mostly under municipal control, and London had its buses and underground (i.e., subway). “These changes in urban transport created suburbia.”

    (David Thomson, England in the Nineteenth Century, 1815-1914, 1978, Penguin Books, page 202)

In other words, the world itself is a crisscrossing composite of processes at different scales.

We have growth and fluctuations, the partition of Africa, suburbanization, Anglo-German tensions, techno-revolutions (including those in urban transport), interacting with Globalization I.

All of this culminated in the “guns of August” (i.e., World War I).

We are downstream from World War I, what the Germans call the “Urkatastrophe” (i.e., original calamity), and its reincarnation in World War II and its progeny, the Cold War.

The more you can “compositize” the elements of this “historical matrix,” the deeper your MetaIntelligence will be. Hence the catchphrase for the MI site:

“Towards a Composite Understanding of Education”

Education and the Problems of Intellectual Fashions

One of our tasks is to avoid “captive mind” syndrome. A key ingredient in this is avoiding being “vacuumed up” in group mental pressures of the moment. Here’s an example:

Think back to the movie 2001: A Space Odyssey, the Kubrick classic from the sixties.

Why is it structured the way it is? The “killer ape” discovers the use of skeletal remains as weapons for killing and a bone flies out of his grasp and becomes the spaceship with Keir Dullea and HAL 9000 (the computer), and the monolith and the space “Mysticism” of Kubrick/Arthur C. Clarke.

All of this comes out of Robert Ardrey’s best seller African Genesis from 1961 which obsessed Kubrick. (Ardrey wrote many famous anthropology books such as The Territorial Imperative).

It starts, “Not in innocence or in Asia was mankind born.”

The “not in innocence” refers to the killer-ape aspect of man: man is a talking murderous ape, according to this view.

Not in Asia refers to Africa as “cradle of humanity,” hence “not in Asia.”

All of this Robert Ardrey mental fashion imbued Kubrick and the movie. It comes out of Ardrey’s encounter with Raymond Dart of Witwatersrand University who argued that fossils of early man show signs of blunt force trauma (such as the find, Taung Child) and this indicates that man is basically a kind of killer by nature. This confirmed Dart’s experience as a medic in World War I, where he was traumatized by all the brutality. From 1925 and Dart’s announcements from Africa, these beliefs began to infect all thinking worldwide and the writer Robert Ardrey was the “Saint Paul” of these beliefs with Dart as the origin.

By the time one gets to Arthur C. Clarke/Stanley Kubrick and the movie 2001, this “mindset” (i.e., Dart/Ardrey/World War I/killer ape view) tyrannizes the atmosphere worldwide.

All of these beliefs were refuted later but at the time it was most difficult to fend off this “vacuum cleaner” of intellectual atmosphere.

Thus a task of education is realizing the rigid “pre-shaping” of the mind that can easily sweep one along since one is semi-blind to the very existence of such a “Zeitgeist bullying” and its grip on our intellectual “invisible axioms.”

“Nervous Breakdowns” for Countries or Regions?

Hannah Arendt who became world famous with her Eichmann in Jerusalem 1960s book, says in her essays that Europe in the twentieth century was determined by a kind of national “nervous breakdown” in and centered on Germany.

If we allow for the fact that this is a “façon de parler” (way of expressing something) and not a rigorous comparison (a country is not one person writ large) Arendt’s figure of speech is suggestive and evocative.

Here’s an example. In 1919, Walter Gropius (died in 1969) gave a speech to students of his “Bauhaus” school, which sounds like a person picking up on a kind of national nervous breakdown:

First of all, Walter Adolph Georg Gropius was a German architect and founder of the Bauhaus School, who, along with Alvar Aalto, Ludwig Mies van der Rohe, Le Corbusier and Frank Lloyd Wright, is widely regarded as one of the pioneering masters of modernist architecture. He is a founder of Bauhaus in Weimar.

Gropius says (July 1919, speech to Bauhaus students):

“We find ourselves in a tremendous catastrophe of world history, a transformation of the whole of life and the whole of inner man.
We now have to forget the time before the war, which was totally different.

The more quickly we adapt to the new changed world, to its new, if austere beauties, the sooner the individual will be able to find his subjective happiness.
We will be more spiritual and profound as a result of the German distress.
As the economic opportunities sink, the spiritual ones have already risen enormously.”

(quoted in German Expressionism, University of California Press, 1990, edited by Rose-Carol Washton Long, page 250, “July 1919 Gropius speech to Bauhaus students”).

We are reminded of Kierkegaard’s (died in 1855) anatomy of the kinds of human despair in his The Sickness unto Death.

The Gropius despair is a bit different because it mirrors a real or imagined German national catastrophe which is folded into a “catastrophe of world history.”

World War I and its aftermath loom as a kind of infinite “desolation row” for Gropius and we cannot judge what percentage of the despair is German and what percentage has to do with Gropius’s subjective state of mind.

In any case, we do have the sense of a “nervous breakdown” atmosphere, nationally and personally.

Might we also wonder if Anglo-America is flirting with such a “nervous breakdown” in 2019?

Education and the Question of a “Scheme of Things”

The French classic The Thibaults (Les Thibault) from 1922 has a dialog about the presence or absence of “a scheme of things” behind everything. This Roger Martin du Gard (died 1958, Nobel 1937) classic gives us an insight into the relationship between education and this “scheme of things.”

First:

The Thibaults is a multi-volume roman-fleuve (saga novel) by Roger Martin du Gard, which follows the fortunes of two brothers, Antoine and Jacques Thibault, from their upbringing in a prosperous Catholic bourgeois family to the end of the First World War.

Antione, one of the Thibault brothers, has a conversation with a priest at the very end of the novel:

“I talked just now about a Universal Order and a Scheme of Things…actually we’ve as many reasons to question the existence of a Scheme of Things as to take it for granted. From his actual viewpoint, the human animal I am observes an immense tangle of conflicting forces. But do these forces obey a universal law outside themselves, distinct from them? Or do they, rather, obey—so to speak—internal laws, each atom being a law unto itself, that compels it to work out a ‘personal destiny’? I see these forces obeying laws which do not control them from outside but join up with them, but do nothing more than in some way stimulate them…And anyhow, what a jumble it is, the course of natural phenomena! I’d just as soon believe that causes spring from each other ad infinitum, each cause being the effect of another cause, and each effect the cause of other effects.

“Why should one want to assume at all costs a Scheme of Things?

“It’s only another bait form our logic-ridden minds. Why try to find a common ‘purpose’ in the movements of atoms endlessly clashing and glancing off each other? Personally, I’ve often told myself that everything happens just as if nothing led to anything, as if nothing had a meaning.”

Antione shook his head. “that blind appeal—to what? To that problematic Scheme of Things! To a deaf and dumb abstraction, that takes no heed of us.”

(Roger Martin du Gard, The Thibaults, Bantam Modern Classic, 1968, pages 768-770)

All bodies of knowledge like religion, philosophy, science posit a scheme of things which is perhaps subtle or occluded (“The Occluded Imam” or “mystery of the Holy Trinity”) or “the mind of God” (Steven Hawking’s way of getting at this) or “the Method of Absolute Doubt” leading to final certainty (Descartes).

String theory talks this way too.

In our own educational remediation effort, we are agnostic about any Scheme of Things and do not try to link books, lectures, courses to some pre-existing schema or “final layer underlying everything” at all.

Students create an evolving overview by “circum-spective” “walking around” or meta-intelligence and there is no ultimate “Eureka moment” where “everything is illuminated” (to use the title of the contemporary novel by that name.) We also do not deny the possibility of the existence of a Scheme of Things. Education thought of this way is an exploration and quest that does not end and there does not have to be a final “knowledge map“ or “truth atlas” other than home-made student “composite sketches” which are tentative and not final or “apodictic.”

Movies as an Off-Campus “Open University:” Antonioni’s La Notte (The Night, 1961)

Michelangelo Antonioni was an Italian film director, screenwriter, editor, painter, and short story author.  

Antonioni died on July 30, 2007 (aged 94) in Rome, the same day that another renowned film director, Ingmar Bergman, also died.

He is best known for his “trilogy on modernity and its discontents”—L’Avventura, La Notte, and L’Eclisse from the early sixties.

One “hidden pillar” of the world Antonioni depicts in his movies is that “you are what you read.” This gives the viewer a “meta-intelligent” (latent overview signal) handle on the world being depicted:

In La Notte of 1961, Antonioni starts with an image of the Pirelli Tower in Milano, the most famous skyscraper of its time in Italy. In contrast to the impressiveness of the building, the characters in his movies are trying to “navigate” boredom and the enveloping sense of ennui.

One of the characters in the movie is said to be reading the masterpiece by Herman Broch, The Slkeepwalkers:

The Sleepwalkers (original title Die Schlafwandler), is a 1930s novel in three parts, by the Austrian novelist and essayist Hermann Broch. 

Opening in 1888, the first part is built around a young Prussian army officer; the second in 1903 around a Luxembourger bookkeeper; and the third in 1918 around an Alsatian wine dealer.  Each is in a sense a sleepwalker, living between vanishing and emerging ethical systems just as the somnambulist exists in a state between sleeping and waking.  Together they present a panorama of German society and its progressive deterioration of values that culminated in defeat and collapse at the end of World War I.

Antonioni implies the characters he depicts are a new version of “sleepwalker.”

When the movie starts, the characters played by Marcello Mastroianni and Jeanne Moreau visit a friend in the hospital who mentions his new work on Adorno.  Adorno (1903-1969) was a German-Jewish theoretician who wants to understand how the world has gone off the rails leading to WWII and the death factories of the Nazis.  He argues that this is connected (paradoxically) to the relentless rationality of “The Enlightenment” and works in a “dialectical” way (i.e., something becomes its opposite).

In the movie, there’s a scene where the author played by Mastroianni is at a book talk concerning his new book.

In other words, the world Antonioni is depicting, a kind of “odyssey” of ennui made confusing by gleaming architecture such as the Pirelli Tower of Nervi (built from 1955-1958) shown in the opening shot of the movie.

The books mentioned in the movie confirm the director’s “you are what you read” motif.

The recent book: The Sleepwalkers: How Europe Went to War in 1914 by Christopher Clark is consistent with this sense of things.

Novels as a Kind of University Demonstrating Storms of Global Finance and Technification

Edith Wharton began writing The Age of Innocence in 1917 as a way of recalling and criticizing the world of her youth, which had not yet experienced the devastation of World War I (1914–18).  Beginning in July 1920, the novel was published in serial form in New York’s monthly Pictorial Review.

The centrality of finance and technical change can be seen. We are reminded of the very first line in The Magnifcent Ambersons of Booth Tarkington, which tells the reader that the basis of the magnificence of the Ambersons was established when they somehow benefited from the 1873 financial crisis which destroyed many others. (Whether the Ambersons were shrewd or lucky or wily is not clarified.)

The Age of Innocence is set in New York in the 1870s and the financial storm and “techno-storm” become vital:

The Panic of 1873:

In The Age of Innocence, the investment bank run by Julius Beaufort collapses, bringing shame upon him and his wife and throwing New York into a tizzy. Beaufort’s business failure is a fictionalized version of the Panic of 1873, industrial capitalism’s first worldwide depression. Then, the United States backed its currency with both silver and gold, but when Germany and several other countries stopped using silver to back their currency, the price of silver fell precipitously, devaluing U.S. currency. The U.S. Treasury made matters worse by releasing large amounts of paper money into the economy. Speculators and bankers now had to immediately pay off their debts with gold.

In 1873, a prominent investment banker by the name of Jay Cooke went bankrupt, the effects rippled throughout the entire U.S. economy, and panic ensued. Trading was suspended for two weeks on the New York Stock Exchange as company after company failed, wages dropped precipitously, and unemployment spiked. The rise of the labor movement can be traced to the widespread unrest and economic instability set off by the panic. Additionally, the panic allowed a few of the wealthiest businessmen—such as Andrew Carnegie, John Rockefeller, and Cyrus McCormick, who retained access to valuable capital—to vastly increase their wealth and snuff out competitors.

Technological Advancements

Characters in The Age of Innocence are aware their world is about to be forever changed by the culture of outsiders, brought to them in part by advancements in technology. Although inventions like the telephone were on the horizon, they seemed improbably fantastic to people living in the early 1870s world of telegrams and horse-drawn carriages. However, in the final chapter, Wharton depicts Newland Archer living in a world that has been significantly altered by these technologies, a mere quarter century later.

In 1876, for example, American inventor Alexander Graham Bell (1847-1922) patented an early telephone and wowed audiences by demonstrating the world’s first telephone call by placing a call from one telegraph station to another five miles away.  The Western Union company refused to buy Bell’s telephone patent, claiming his invention would amount to no more than a novelty. However, the first telephone line was built in 1877-78, and after that, telephone usage skyrocketed.  At the start of the 1880s, there were almost 50,000 telephones in use, a number that swelled to over half a million by the turn of the century.

A similar large-scale change was the invention and development of electricity. Although the first electric light was developed in 1835, it was not until 1879 that American inventor Thomas Edison (1847-1931) developed and patented a light bulb with a life span of 15 hours. Edison’s work also focused on the problems of electrical generation and conductivity.

At the same time that communication was becoming easier and the day was lengthened artificially through electric lighting, the distance between continents was shortened by advances in turbine steam engines. 

In the 1860s, it took between eight and nine days to cross the Atlantic Ocean; by 1907, the Mauretania (the ship that Dallas and Newland Archer take to Europe in the last chapter) makes the voyage in half that time.  This was a contributing factor to the great influx of European immigrants who arrived in the United States during the late 19th and early 20th centuries.

In Chapter 29, Newland contemplates the “brotherhood of visionaries,” who predict a train tunnel under the Hudson River as well as “ships that would cross the Atlantic in five days … and other Arabian Night marvels.” In 1904, excavation for train tunnels under the Hudson began, directed by Alexander Cassatt, president of the Pennsylvania Railroad. In 1910, New York’s Penn Station opened and began receiving traffic from electric trains that traveled through the tunnels.

Notice that the novel The Magnificent Ambersons is from 1918, Edith Wharton’s Age of Innocence from 1920. In each, the personal storms of private emotion are somewhat carried along and swept up into the storms coming from national and even global finance (1873 caused a tremendous crash in Germany and Austria called the “Grunderkrach” [founder’s crash]) as well as techno-waves that are very baffling to the people of the time.

Movies as a “Backdoor Into Financial History”

“Financial history” (the Professor Niall Ferguson PBS miniseries, The Ascent of Money, of recent years tries to “flag” this domain) can be exciting and eye-opening if the student fins the kind of “backdoor” into it that makes it all enchanting and not a tiresome slog through opaque textbooks.  Movies are a good way to “parachute” into fields, domains, areas of study:

The 1963 movie Mary Poppins is partly about bank runs and the “Tuppence” song in the movie communicates the centrality of London finance in the world of 1910, the setting of the movie:

“You see, Michael, you’ll be part of railways through Africa
Dams across the Nile, fleets of ocean Greyhounds
Majestic, self-amortizing canals
Plantations of ripening tea
All from tuppence, prudently fruitfully, frugally invested
In the, to be specific
In the Dawes, Tomes, Mousely, Grubbs
Fidelity fiduciary bank

Now Michael, when you deposit tuppence in a bank account
Soon you’ll see
That it blooms into credit of a generous amount
Semiannually
And you’ll achieve that sense of stature
As your influence expands
To the high financial strata
That established credit, now commands
You can purchase first and second trust deeds
Think of the foreclosures
Bonds! Chattels! Dividends! Shares
Bankruptcies! Debtor sales! Opportunities
All manner of private enterprise
Shipyards! The mercantile
Collieries! Tanneries
Incorporations! Amalgamations! Banks”

The current  U.S. Treasury Secretary Mnuchin was a foreclosure king of the Great Recession of 2008.  An American movie on “bank runs” is of course the classic It’s a Wonderful Life (with James Stewart as the local banker.)

The 1910 world of London finance show in the movie Mary Poppins can be now contextualized by realizing all of this crashed down in August 1914 which represents the beginning of post-WW 1 “deglobalization.”  Thus, finance and globalization issues haunt the present.

Walter Bagehot’s masterpiece of 1873, Lombard Street, is a kind of anticipation of this syndrome and Charles Kindleberger‘s (MIT) Manias, Panics and Crashes gives the sense of the underlying instability.

Kevin Phillips’s book Bad Money of 2008 outlines the dangers of “over financialization.”

The movie and the fun song can help a student find his or her way in to these areas and domains.

Unnoticed Dimensions of Knowledge

Let’s “get down to cases” right now:

  1. You learn decimals and fractions in school. You see that 1/2 can be written as 0.5 or 0.50 or with as many zeros as you like. That seems “clean.”

But 1/3 is equal to something more complex (i.e., 0.3 recurring or repeating, like 0.3333 and so on infinitely).  If you divide 1 by three you keep getting three.

Imagine you want to experiment a bit, and multiply the fraction 1/3 by three and the 0.3 recurring by three, thus not affecting things since you’re doing the same thing to both sides of the equation.

You get:  1 = 0.9 recurring or repeating.

You’re suddenly puzzled: How can 1 be obtained by adding “slices of 9 fractions” (i.e., 9/10 + 9/100 + 9/1000) to infinity. How do you get to the end? What end? 

It turns out that it’s not that simple to get a grip on all this.  A person who allowed themselves to become fascinated by this specific conundrum would enter a “beautiful ocean” of mathematics beginning with so elementary a phenomenon.

This shows you a deep connection between a part (e.g., the fraction and decimal 1/3 and 0.3 recurring) and the wider world or domain or universe of numbers.

How can it be that such a simple elementary “thing” becomes so intricate, deep and elusive?

  1. Let’s jump over to an entirely different kind of example. Think of Dinesen’s novel Out of Africa. Remember the movie with Meryl Streep and Robert Redford.

Suppose you turn the movie “inside out” and “upside down” and ask: is this movie about coffee and coffee bushes, coffee markets and coffee growing, in a colonial context?  The coffee plantation is near Nairobi (today’s Kenya) and involves plantation economics, colonial relations with Kikuyu peoples, German-British colonial tensions around World War I.

Suppose I take the “backstory” and make that the “frontstory”.

The story of “economic botany” (coffee growing is one case) and colonial tensions between and among Europeans as well as Europeans and Africans is the deeper and larger story while the “musical beds” of the Westerners is a colorful footnote.   

We have the perennial question of “parts and wholes” which is one theme of this book.       

  1. Why does science “orbit” some numbers such as π (pi) (i.e., 22/7)?

You learn in school that there’s a ratio called π (pi) which is 22/7. Think of π (pi) as some kind of essence of circularity. Remember πr2 and 2πr in grade school.

Why does it keep appearing in almost every equation of physics? Why would “circleness” “haunt” science and math? Probability and statistical theory are dependent on π (pi) as a variable. Why?

You could peruse:

A History of Pi is a 1970 non-fiction book by Petr Beckmann that presents a layman’s introduction to the concept of the mathematical constant π (pi). 

Why does science “orbit” some numbers such as π (pi)?

This is an example of this quest for connectedness.