## Education and “The Three-Body Problem”

The brilliant math-watcher, Ian Stewart, says of this classic physics problem, the Three-Body Problem:

Newton’s Law of Gravity runs into problems with three bodies (earth, moon, sun, say).

In particular, the gravitational interaction of a mere three bodies, assumed to obey Newton’s inverse square law of gravity, stumped the mathematical world for centuries.

It still does, if what you want is a nice formula for the orbits of those bodies. In fact, we now know that three-body dynamics is chaotic–so irregular that is has elements of randomness.

There is no tidy geometric characterization of three-body orbits, not even a formula in coordinate geometry.

Until the late nineteenth century, very little was known about the motion of three celestial bodies, even if one of them were so tiny that its mass could be ignored.

(Visions of Infinity: The Great Mathematical Problems, Ian Stewart, Basic Books, 2014, page 136)

Henri Poincaré, the great mathematician, wrestled with this with tremendous intricacy and ingenuity all his life:

Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as “The Last Universalist,” since he excelled in all fields of the discipline as it existed during his lifetime.

Born: April 29, 1854, Nancy, France
Died: July 17, 1912, Paris, France.

We now think of applying in an evocative and not a rigorous mathematical way, the unexpected difficulties of the three-body problem to the n-body (i.e., more than three) problems of sociology or economics or history itself, and sense that social life is always multifactorial and not readily pin-downable, since “everything is causing everything else” and extracting mono-causal explanations must be elusive for all the planetary and Poincaré reasons and beyond.

This suggests to the student that novels are one attempt to say something about n-body human “orbits” based on “n-body” stances and “circumstances” with large amounts of randomness governing the untidy mess that dominates human affairs.

Words are deployed in novels and not numbers as in physics, but the “recalcitrance” of the world, social and physical, remains permanent.

Education and meta-intelligence would be more complete by seeing how the world, as someone put it, “won’t meet us halfway.” Remember Ian Stewart’s warning above:

“There is no tidy geometric characterization of three-body orbits…” and you sense that this must apply to human affairs even more deeply.

## Essay 58: Machlup and Knowledge-Watching

Fritz Machlup is an underappreciated emigre economist from Vienna. His 1962 book, The Production and Distribution of Knowledge in the United States (Princeton University Press, 1962), is a “bible” of knowledge-watching and the zones where knowledge meets information, where Machlup was very prescient.

Fritz Machlup was an Austrian-American economist who was president of the International Economic Association from 1971–1974.  He was one of the first economists to examine knowledge as an economic resource, and is credited with popularizing the concept of the information/knowledge society.

Born: December 15, 1902, Wiener Neustadt, Austria
Died: January 30, 1983, Princeton, NJ

Machlup distinguishes five types of knowledge:

1. Practical knowledge
2. Intellectual knowledge
3. Small-talk and pastime knowledge
4. Spiritual knowledge
5. Unwanted knowledge

These five kinds of knowledge are discussed and analyzed in Machlup’s The Production and Distribution of Knowledge in the United States starting on page 21 (and are discussed in Daniel Bell’s The Coming of Post Industrial Society, 1976, Basic Books, page 175).

The more comfortably one can link types 1, 2, and 4 in the list above, the more “together” one’s understanding might become.  One does not have to be “dismissive” of Type 3.

Pleasant diversions are a a part of life and have their honorable place. One reason (to give a simple example) we’re drawn to poets like Wallace Stevens is that they seem to “sit comfortably” in their various (knowledge) roles: insurance salesman, poet, thinker and don’t “line up” or “array” these types of knowledge in a conflictual way but seem to “smile down” on all of them finding beauty everywhere.

Workaday knowledge might not have to “fight with” other kinds of knowledge. Insurance, say, is a form of risk-management and risk is essential to life and economics, as we have seen elsewhere.  Economics looks at cost-benefitrisk-uncertainty all together when it goes beyond the narrow confines of academe to become a fuller quest.  Cost-benefit analysis by itself is too restrictive.  Start with Machlup as a highly intelligent “backdoor” into these domains of knowledge, information, learning, social contexts.  This would help give you a handy additional “flashlight” on schooling in society including universities and campuses.