Essay 6: Enchantment as an “Engine of Education”

We started this book mentioning Wittgenstein’s assertion, “Light dawns gradually over the whole.”

There are two “players”—light (illumination) and the whole.

The learner, especially the deeper variety of learner, then has two quests: the flashlight or searchlight that gives off the light and the “problem” of defining “the whole.”

We argue in this book only something called “enchantment” (seeing the magic in some question or phenomenon or thing) can be the engine that gives you the impetus to go on in this double search.

For example:

  1. Think of the opening line in the great novel from 1959, The Last of the Just, which won the Goncourt Prize, the highest literary award in France.

The opening line, which serves as a kind of “overture” for the entire book, is: 

“Our eyes register the light of dead stars.”

The author uses this as a figure of speech which captures the lasting influence of people who came before you who somehow are “stars” in the sense of principal actors in your mental life. When you begin the novel, you don’t know if the writer is going to use this concept not as a statement about stellar objects in the sky, as understood by astronomy or cosmology or optics, but in the personal influence sense, as he does. 

This is a beautiful “overture” because it links the physical to the personal in a “dual metaphor.” There’s a secondary poetical device since stars could mean shiny objects in the sky or people as in “movie stars.”

Great writing has this “enchanting” quality and it addresses a deep human hunger for so-called “words to live by.”

  1. Go back to our elementary math example where 1=.9 recurring.

A student gets intrigued by this and senses “how can that be? how can you add these decimal nines infinitely?

In fact, this is a deep and “enchanting” question. If you look into something called infinitesimals (smallest math “objects”) you will find that this issue is still an “argument without end” to use Pieter Geyl’s phrase.

Furthermore: If something is or seems to be “an argument without end,” what does that imply about our ability to “nail” things down in our minds?  That’s an enchanting question in itself which resonates with the Descartes “epistemology” and certitude quest we have seen previously.

Then there’s the other elusive “player” in the Wittgenstein sentence: “the whole.”

Does one mean the whole of a novel or math problem? The whole of the world of metaphors and numerical thinking (i.e., math)? Does one mean everything that exists? It’s not a set or static “thing.”

The point is not to decide any of this in a “once-and-for-all” way. The point is only to allow the enchantment engine to carry the student into these realms and domains without insisting on an eternal “final answer.”

This is why this kind of meta-intelligent self-education or re-education parts company with quests such as Stephen Hawking’s, to “know the mind of God” as mentioned in the last lines of his 1988 book, A Brief History of Time.

Enchantment gives you some pre-understanding which pulls you higher and you can relax the insistence on finality or absolute certainty which characterizes the whole trajectory from Descartes through Husserl, who died in 1938 (think of his book, Cartesian Meditations) through contemporary “scientism” such as exemplified by Hawking with his undoubted analytical genius.

Essay 5: How to Sneak Up on a Field With Types of Meta-Intelligence

If you look at a typical economics book and are coming at it with no particular background (e.g., your dad was an economist at the World Bank, say, so you’ve “swum” in this water via your background and dinner table conversations), you will find it “remote” and “foreign.”

What to do? You need to “sneak up” on a field and find a door into it or a window to climb through that brings you inside.

This foreignness and remoteness is true for any field you can think of since unfamiliar fields are disorienting at first. You need a pre-understanding.

Let’s do two simple examples of how one gets a pre-understanding:

During the foreclosure crisis following the Great Recession of 2008 and thereafter, you might have asked yourself about the size in dollars of US residential housing stock to see what it might mean if values declined. You found perhaps that it was surprising difficult to come up with some “ballpark” sense of US housing as you looked through Google and other entries.

Here’s a sample of a kind of made-up workaround that points you in the right direction:

Suppose we say the population of the USA is 320 million at the time, in round figures that are convenient and approximate only.  Assume, for no reason, that all Americans are members of households of four (i.e., families with two parents and two children). This is of course utterly false but serves our “guesstimating” purpose we hope.

If we divide the total population by 4, we get 80 million families. Assume all families live in single-family homes ignoring apartment buildings, multi-family homes and a zillion other forms. Make up a number like 300 thousand dollars per home at the time, based on radio news,  and you will get a national housing stock value of 80 million by 300 thousand which is 24 trillion dollars.

In fact, the official value of U.S. residential housing was usually given at 24-25 trillion so our “sneaking up” guesstimating was not bad at all.

Now ask how one might have perhaps done it better, more cleverly. You have to “back into” a field by something you yourself look into and figure out before you enter the “ocean” of the textbook presentation.

It requires a kind of “sneaking up” on a field with back-of-the-envelope “meta-intelligence” in order for you to attune yourself to the field, or if you want to “parachute” in like a “knowledge spy” and get what you need. This is true for all fields. Some “homemade” familiarity you make up yourself is needed.

How to “Sneak Up” on Academic Fields With Meta-Intelligence

An accepted workhorse of economics is the Cobb-Douglas production function based on two people with the names of Cobb and Douglas.

Your economy produces, say, shirts and to do that you need machines (capital), workers (labor), energy, materials.

Think of 100 women seamstresses at one hundred tables with sewing machines plugged into 100 electrical outlets (energy) and lots of fabric (raw materials for shirt-making).

Capital (e.g., machines, equipment, structures) is denoted by the letter K (from German word Kapital), workers or labor force by L (for labor) and the whole is called KLEM. (capital, labor, energy, materials). The letter A stands for “technology level.”

We simplify and worry only about K and L just to make the math much easier. Remember capital here means machines and not money.

In Cobb-Douglas “world,” the product of your economy, shirts is called Y (we don’t have the shirt prices to keep things easier).

Then Y=A multiplied by K (to the alpha) multiplied by L (to the beta). Alpha and beta are measures of responsiveness, “elasticity,” sensitivity.

Cobb-Douglas is multiplicative (i.e., A by K by L, so the algebra goes easier). A is called “technical change” or technology.

Suppose you don’t know or don’t remember log differentiation (calculus) to easily “play  with” this little equation. That’s ok.

Think of the simple identity z=xy. This could be 10=5 x 2 or 12=4 x 3. You can show that if the left side goes up by 10%, the right must grow by 10 percent so that the 5, say, becomes 5.5. 5.5 x 2 is 11 so both sides are the same again, 11=11. It’s easy to show that the percentage growth on the left side of the equation is roughly the sum of the percentage growth of each of the numbers on the right.

You can easily show that the percentage growth of Y (say 6% per year) is approximately equal to the percentage change of A plus percentage growth of K+ plus that of L with K and L modified by alpha and beta.

This is a simplified version of so-called “Growth accounting” (i.e., components of growth in Y from year to year).

You will find that once you sense how this kind of “accounting” looks and works you can proceed to other kinds of accounting in economics such as Balance of Payments accounting or National Income accounting.

These exercises are key to economics as a field with its textbooks and again you have to sneak into it, so to speak, by climbing through a door or window you made up yourself to give you some bearings.

We call all this a pre-understanding before more usual understanding through textbooks.

Pre-understanding is a deep key or prerequisite to educational mastery.

On a National Public Radio call-in talk show few years ago, there was a discussion by four economists (professors plus private sector analysts). A listener calls in and asks one of them about the growth prospect for the following year. The professor responds: about 2.88 percent. Everybody goes quiet and wonder how he figures this out.

The answer will help you “sneak in” to or “parachute” into this world.

The professor, in his mind, calls the economy Y. He realizes that Y is the same as Y/L multiplied by L, where L is labor force. In Y/L by L the l’s cancel each other out so it’s just a harmless re-write of the basic variable Y.

Y/L is average productivity (e.g., number of shirts [the economy has one product, shirts]) divided by number of workers (laborers, seamstresses making the shirts).

If Y is one hundred and L=10, then the average laborer produced 100/10=10 shirts. ie that’s the average productivity.

The professor knows that approximately the percentage growth of Y (which is what the radio show caller’s question was about) is the sum of the percentage growth of Y/L and L.

He’s familiar with the latest productivity and labor force projections from the electronic newsletters he receives and the websites he checks out (e.g., BEA and the BLS, et al).

He adds them up to get 2.88 percent, the number he mentions to the questioner and the rest of the radio audience.

Once you’re familiar with these simple elements of analysis and sources of info, you can begin to lose your fearfulness and do the same as the professor, who is not solving complex differential equations in his head to answer the question for the listeners.

As a “field outsider,” you’re unfamiliar with the “landscape” and “rules of thumb” and your mind races or wanders when confronted by such a question because you don’t have these simple techniques.

You can thus “parachute” into any field and leave with what you need.

Essay 4: What Is Meta-Intelligence?

You have heard of meta-data and perhaps meta-analysis.  In meta-analysis you don’t (say) study climate change directly, rather you study all the research and all the reports and papers on climate change trying to sense a grand overall conclusion and implication rather than simply making a synopsis or summary.

Meta-intelligence is in this spirit because it wants to get an overview of other overviews, a view of views.

Let’s do one example, namely, Paul Tillich (died in 1965), the famous German-American thinker.

He “walks around” human language and notices:

“Language… has created the word ‘loneliness’ to express the pain of being alone. And it has created the word ‘solitude’ to express the glory of being alone.”

He also senses a missing dimension in all modern science:  “Whenever man has looked at his world, he has found himself in it as a part of it. But he also has realized that he is a stranger in the world of objects, unable to penetrate it beyond a certain level of scientific analysis. And then he has become aware of the fact that he himself is the door to the deeper levels of reality, that in his own existence he has the only possible approach to existence itself.”

(Systematic Theology IUniversity of Chicago Press, 1951)

In other words, we design equations and experiments that suit our ways of seeing and thinking, our brains and nervous systems and we never really know if we are glimpsing eternal laws of nature or patterns that satisfy us given the way we are.

We can’t see what part of our scientific world-view is a construct as opposed to a pure discovery.

We never really know: are these problems?  Difficulties?  Puzzles?Mysteries?

Gabriel Marcel, the French thinker who taught at Harvard in the 1950s, teaches us that a puzzle is something we might successfully surround and solve while a mystery is something that surrounds us and cannot be solved like a puzzle, an issue, a query, a question.

Meta-intelligence is aware of these levels and layers and doesn’t fall into a Descartes-type “whirlpool of doubt” since it accepts the great historian Pieter Geyl’s (died in 1966) category of the existence of “arguments without end” (i.e., finality is always “shy”).

Essay 3: Why Descartes-Type Assumptions Might Confuse This Type of Holism Quest

René Descartes, who died in 1650, and whom you remember from high school Cartesian coordinates, points the way to the modern intellectual assumption that everything should be explained by means of the mathematical sciences which then eventually gives us the Steven Hawking sense of reality (i.e., science will yield final certitude and thus we’ll know “the mind of God.”)

Hawking’s 1988 book A Brief History of Time concludes explicitly with a rousing vision of science as the ultimate triumph of the rational mind eventually revealing “the mind of God.”

To get our bearings on this set of beliefs, go back to Descartes’ masterpiece from 1641/42, Meditations on First Philosophy, one of the world’s great books. “Meditation 2” of this book starts with:

“So serious are the doubts into which I have been thrown as a result of yesterday’s meditation that I can neither put them out of my mind nor see any way of resolving them. It feels as if I have fallen unexpectedly into a deep whirlpool which tumbles me around so that I can neither stand on the bottom nor swim up to the top. Nevertheless, I will make an effort and once more make an effort and once more attempt the same path which I started on yesterday.

Anything which admits of the slightest doubt I will set aside just as if I had found it to be wholly false; and I will proceed in this way until I recognize something certain, or, if nothing else, until I at least recognize for certain that there is no certainty. Archimedes used to demand just one firm and immovable point in order to shift the entire earth; so I too can hope for great things if I manage to find one thing, however slight, that is certain and unshakeable.

I will suppose then, that everything i see is spurious. I will believe that my memory tells me lies, and that none of the things that it reports ever happened.

I have no senses. Body, shape, extension, movement and place are chimeras. So what remains true? Perhaps just the one fact that nothing is certain.”

The reader will sense a radical vision of infinite doubt looking for an “Archimedean point” of one certain item. The reader can easily see why mathematical constants such as the ubiquitous pi would be something to cling to since one assumes that 22/7 or pi will be the same forever. What else could it be, one thinks.

What we are doing in this book doesn’t look for any “Archimedean point” of final certainty at all. What we want to do is to introduce exercises in holism, giving a more wide-angle view of a field, course, topic, lecture, book, educational experience. We are not in Descartes-type “new certainty” business and don’t look for eternal truths or axioms.

In fact, let’s use Descartes own words here to “extract” some connectedness on the spot:

He says:  “I have fallen unexpectedly into a deep whirlpool which tumbles me around so that I can neither stand on the bottom nor swim up to the doubt.”

Let’s call this a kind of “knowledge vertigo.” The reader might sense that there is a “family” of such dizziness. You think of Jimmy Stewart in Hitchcock’s Vertigo.  That some psychological panic attack which he tries to explain in the movie. Kim Novak, the female protagonist in the movie, has her own kind of dizziness and falls into the ocean. You can have dizziness from hunger, overtiredness, inner ear infection, salmonella, anxiety, etc. Kierkegaard (1813-1855) discusses a dizziness and vertigo of a person “lost in the world” like a sailor lost at sea with no direction.

In other words, one can use Descartes description of his own “certainty chasing” panic to build a taxonomy of dizzy feelings and get a more holistic sense of such phenomena without insisting on any “eye in the sky” perspective on everything based on a rebuilt version of certainty.

In other words, these Cartesian quests could block the reader from connecting things at a more intermediate or “meso” level, neither micro (too small) nor macro (too far away).

Essay 2: Connectivity and the Need for Meta Intelligence

Arguments without end and our attitude to them:

A reader of this book might ask:

How far does this quest for more holism go?  Are there limits on this type of inquiry?

This is a very good question.  In order to answer this, we quote something from the famous French historian, Michelet, who died in 1874:

“Woe be to him who tries to isolate one department of knowledge from the rest….all science [i.e., knowledge] is one:  language, literature and history, physics, mathematics and philosophy; subjects which seem the most remote from one another are in reality connected, or rather all form a single system.”

(quoted in To the Finland Station, Edmund Wilson, Farrar, Straus and Giroux, 1940, page 8)

Our attitude to such radical system building is non-committal. Rather we say, you the student should pursue flexible forms of increased connection and holism while you acquire knowledge and extend it and not worry about some once-and-for-all system underneath or beyond everything. We propose exercises in holism and all exercises are replaceable with new ones or better ones and there’s no “final layer” or hidden “mind of God” to use Stephen Hawking language. The existence of some underlying or final system is something like an “argument without end” (to use Pieter Geyl language).

This argument is captured by the classic “fight” between Hegel (the person that Marx and Kierkegaard rebelled against and who died in 1831) and Adorno in the twentieth century.

Hegel says: The whole is the true. Adorno (who died in 1969) says: The whole is the false.

We skip all such fights.

Thinking about University Knowledge Again:

One cannot major in every field. One cannot make everything a university offers your specialty or concentration.

“Sartor Resartus:”  The great British critic Thomas Carlyle (who died in 1881), close friend of Ralph Waldo Emerson, wrote a famous satire called “Sartor Resartus or The Tailor Retailored” where he lampoons a certain Professor Devil’s-crud who teaches at Don’t-Know-Where University and is Professor of Everything.

Obviously, we are not proposing the creation of professors-of-everything and propose nothing more than the heightened ability to “zoom out” of academic fields, topics, lectures, topics, campuses.

A person who has similar intuitions is Alfred North Whitehead of Harvard (died 1947) who says in his essays on education that the real purpose of university education is to enable the learner to generalize better using that person’s field as a help or aid.  The purpose of a university cannot be fields and monographs within fields alone. 

Essay 1: 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.