Russians, Meta Intelligence

“Fog Everywhere” Continued

Consider mathematics and the aspect of fog. Nietzsche argued that the world is not knowable to us as a whole. This includes trying to express it with numbers. A recent example is Max Tegmark’s assertion that the universe is not something explained by mathematics; rather, it is itself mathematics. To contrast, Karl Jaspers, summarizing Nietzsche, wrote:

We cannot say what the world as a whole is. It is false to change all processes into a familiar world of our own, and then say: “All is will (everything wills); all is pleasure or pain (everything endures); all is motion (everything flows); all is tone (everything sounds); all is spirit (everything thinks); all is number (everything reckons).” Nietzsche warns us against all notions of the whole: “Let us guard against thinking that the world is a living being…or that the universe is a machine…Let us guard against saying that there are laws of nature…Let us guard against thinking that the world eternally creates novelties.” All these “shadows of God” darken actuality. We are within the world, and the whole of the world is, as a whole, not accessible to us.
Karl Jaspers, Nietzsche: An Introduction to the Understanding of His Philosophical Activity, Henry Regnery Company, 1966, p. 293

Notice in the paragraph quoted above that Nietzsche specifically excludes reducing everything to numbers, in opposition to Tegmark and the simulation hypothesis.

Robert Kanigel describes Srinivasa Ramanujan as “the man who knew infinity” in his biography of the same title, but mathematicians disagree on the ontological status and utility of infinity. The discussion of applying Ramanujan’s sum to arrive at -1/12 is very intricate and complex.

To make things even more puzzling, math students are confronted with the Gaussian integral, with its positive and negative infinities.

You can gain additional insight into infinity with:

Cauchy and Weierstrass had eliminated infinitely small and infinitely great numbers from analysis and replaced them by limits. But the theory of limits that thereby became so central required a clearer theory of the real line, that is to say, a theory of the irrational numbers. And that theory promptly reintroduced the infinite into analysis. The old infinity of infinitesimal and infinite numbers was simply replaced by the new infinity of infinitely large collections.¹²

In 1831 Carl Friedrich Gauss said [Kli72, p. 994], “I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits to which certain ratios can come as near as desired, while others are permitted to increase without bound.” But only 52 years later, we find this in Cantor’s Grundlagen [Can76, p. 75]: “The idea of considering the infinitely large not only in the form of the unlimitedly increasing magnitude and in the closely related form of convergent infinite series…but to also fix it mathematically by numbers in the definite form of the completed infinite was logically forced upon me, almost against my will since it was contrary to traditions which I had come to cherish in the course of many years of scientific effort and investigations.”

12 See Russell’s Principles of Mathematics [Rus03, p. 304] for a related sentiment.
Shaughan Lavine, Understanding the Infinite, Harvard University Press, 1994, pgs. 38-39

In 1961, the great Russian physicist George Gamow’s popular math and physics overview was republished to great acclaim among science and math aficionados. Intriguingly titled One, Two, Three…Infinity, the book gives you a hint that the relationship of numbers and integers to the concept of infinity is still intriguing even after the intricate analyses of Cauchy, Weierstrass et al.

Let us conclude by considering Zeno’s dichotomy paradox of motion, in which “That which is in locomotion must arrive at the half-way stage before it arrives at the goal.” As the goal is divided into halves, one must complete an infinite number of tasks, which Zeno maintains is an impossibility.

[read the previous essay on this topic]

Why Is the World So Nightmarish?

The phrase, “La Belle Époque” (French: “The Beautiful Era”) refers to the atmosphere in Europe and especially France, the high point of which lasted from 1900 to 1914, with the outbreak of World War I. The whole era was characterized by the phrase, “la douceur de la vie” (French: “the sweetness of life”). People of the time would say that if you weren’t alive then, they could not communicate how charming life was at the time.

The sinking of the Titanic in April, 1912 is the symbolic catastrophe that heralded the end of the era. Anyone who watched Downton Abbey would perhaps remember the opening scene, which depicts the newspaper announcing it with a screaming headline.

The great masterpiece, Journey to the End of the Night (French: Voyage au bout de la nuit, 1932), describes the whole world around World War I as a nightmarish battlefield of previously unseen scope. Céline’s protagonist, Ferdinand, travels the world, from battles in Europe to Africa, then to New York and Detroit’s Ford assembly line before returning to France, finding that the nightmare is global and inescapable.

Céline died within 24 hours of Ernest Hemingway. Hemingway is famous for the quote from The Sun Also Rises (set in the 1920s), “The world breaks everyone and afterward many are strong at the broken places. But those that will not break it kills.”

The question is how could we ever explain complete evaporation of the sweetness of life and transformation into such a nightmare, culminating into the world of today.

Lastly, think of the point made in Sebastian Haffner’s The Meaning of Hitler, how Hitler fit into this nightmarization of the world. Haffner writes:

It is impossible for a serious historian to maintain that without Hitler world history in the twentieth century would have taken the course it has taken. It is by no means certain that without Hitler a second world war would even have taken place; it is quite certain that if it had taken place it would have taken a different course — possibly even with different alliances, fronts and outcomes. Today’s world, whether we like it or not, is the work of Hitler. Without Hitler there would have been no partition of Germany and Europe; without Hitler there would be no Americans and no Russians in Berlin; without Hitler there would be no Israel; without Hitler there would be no de-colonization, at least not such a rapid one; there would be no Asian, Arab or Black African emancipation, and no diminution of European preeminence. Or, more accurately, there would be none of this without Hitler’s mistakes. He certainly did not want any of it.

(The Meaning of Hitler, Harvard University Press, 1979, page 100)

No-one has yet captured how the nightmarish feeling of 2025 is itself downstream from the preceding era.

Education and the Kinds of Wholeness

We have stated several times that we seek more educational holism in particular, the tentative kind made by students themselves after they study these “exercises in holism.” Let’s explore this.

There’s a short story by Anton Pavlovich Chekhov (29 January 1860 – 15 July 1904), a Russian playwright and short-story writer, who is considered to be among the greatest writers of short fiction in history. In his classic “A Boring Story,” he tells the reader about his inner yearning for some wholeness in his life:

“In my predilection for science, in my wish to live, in this siting on a strange bed and trying to know myself, in all the thoughts, feelings and conceptions I form about everything, something general is lacking that would unite it all into a single whole.

Each feeling and thought lives separately in me, and in all my opinions about science, the theater, literature, students, and in all the pictures drawn by my imagination, even the most skillful analyst would be unable to find what is known as a general idea or the god of the living man.

And if there isn’t that. there’s nothing.”
(Selected Stories of Anton Chekhov, Anton Chekhov, Richard Pevear and Larissa Volokhonsky (translators), Modern Library, 2000, page 104, “A Boring Story”)

The author wants to unite everything (i.e., “something general is lacking that would unite it all into a single whole,” as he puts it).

This is not what we have in mind because there is no “scheme of things” or “unified field theory” that we impart to students. That is for various kinds of “madrasas” (Arabic: مدرسة) including secular ones.

Rather, we encourage students to “walk around” topics, fields, educations, discussions, books, movies, quizzes and exams, lectures, assignments to develop a more “circum-spective” view of knowledge.

Remember “Husserl’s rhomboid.” Edmund Husserl (Heidegger’s teacher, died in 1938) would bring a matchbox to his classes in Germany and get students in his classroom to see that one cannot view the whole matchbox at once nor can rotating it capture all of it. Parts are visible, the whole matchbox is not.

We apply this principle to education and knowledge acquisition and offer the mental habit for students of “homemade” exercises in making more holistic views.

The narrator in Chekhov’s story, yearning to have a god-like view of reality and knowledge and experience (theatre, science, etc.) as a unified “thing” is not our interest since it too elusive.

William James (died in 1910) says several times in his writings that “one mind can’t swallow the whole of reality.” Therefore we avoid such “totalizing” visions in favor of much more modest attempts at connecting things better.