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.