Education and Circular Causation: Everything Causes Everything Else

The student will have seen in these educational essays the notion of “Husserl’s rhomboid”:

The great philosopher, Edmund Husserl, who died in 1938, would bring a matchbox to class and show his students they see parts and some surface area of the matchbox (a kind of rhomboid, hence the name “Husserl’s rhomboid”) but never all of it at the same time. Students can walk around the matchbox and see facets. They can twirl the matchbox but whatever they do, the students cannot “espy” or glimpse all of it except in their imaginations, once they have been exposed to all of it, side by side, facet by facet.

Gunnar Myrdal, the Swedish economist who won the Nobel Prize in 1974, has something a bit analogous when he speaks of “circular cumulative causation”:

Circular cumulative causation is a theory developed by Swedish economist Gunnar Myrdal in 1956. It is a multi-causal approach where the core variables and their linkages are delineated. The idea behind it is that a change in one form of an institution will lead to successive changes in other institutions. These changes are circular in that they continue in a cycle, many times in a negative way, in which there is no end, and cumulative in that they persist in each round. The change does not occur all at once, which would lead to chaos, rather the changes occur gradually.

Gunnar Myrdal developed the concept from Knut Wicksell and developed it with Nicholas Kaldor when they worked together at the United Nations Economic Commission for Europe.

In the characteristics relevant to an economy’s development process, Myrdal mentioned the availability of natural resources, the historical traditions of production activity, national cohesion, religions and ideologies, and economic, social and political leadership.

He writes:

“The notion of stable equilibrium is normally a false analogy to choose when constructing a theory to explain the changes in a social system.

What is wrong with the stable equilibrium assumption as applied to social reality is the very idea that a social process follows a direction—though it might move towards it in a circuitous way—towards a position which in some sense or other can be described as a state of equilibrium between forces. Behind this idea is another and still more basic assumption, namely that a change will regularly call forth a reaction in the system in the form of changes which on the whole go in the opposite direction to the first change. The idea I want to expound in this book is that, on the contrary, in the normal case there is no such a tendency towards automatic self-stabilisation in the social system. The system is by itself not moving towards any sort of balance between forces, but is constantly on the move away from such a situation. In the normal case a change does not call forth countervailing changes but, instead, supporting changes, which move the system in the same direction as the first change but much further. Because of such circular causation as a social process tends to become cumulative and often gather speed at an accelerating rate…”

(Gunnar Myrdal, Economic Theory and Underdeveloped Regions, Gerald Duckworth, 1957, pp. 12–13)

Myrdal developed further the circular cumulative causation concept and stated that it makes different assumptions from that of stable equilibrium on what can be considered the most important forces guiding the evolution of social processes. These forces characterize the dynamics of these processes in two diverse ways.

These essays that you are reading here are examples encouraging students to put causes in a kind of circle: history exists because economics exists because psychology exists because society exists because history exists. Everything is causing everything else. There isn’t a simple “linear parade.”

By way of contrast, in a person’s private life, he/she went to the dentist before buying the batteries and after having lunch. There’s a timeline of events.

In history, there are such linear timelines also: John Kennedy was assassinated before Donald Trump became president. You had breakfast before dinner. You slept before you got up in the morning.

However, processes (industrialism, migration, urbanization, inflation, etc.) are not analyzable as events like meals and one-time occurrences but are more like getting old or learning a language.

Multi-causal interpretations and circular causes get the student out of simple, “this happened and that happened” in favor of “this and that caused each other, going both ways and interacting with other pressures too.” Everything is causing and altering everything else in all directions.

Education and Word and Number Hidden Vagueness

These mini-essays help students of any age to re-understand education in a deeper and more connected way.

They look for “circum-spective” intelligence. (Not in the sense of prudential or cautious but in the sense of “around-looking.”)

One of the things to begin to see is that explaining things in schools is misleading “ab initio” (i.e., from the beginning).

Let’s do an example:

In basic algebra, you’re asked: what happens to (x2 – 1)/(x – 1) as x “goes to” (i.e., becomes) 1.

If you look at the numerator (thing on top), x2 is also 1 (since 1 times 1 is 1) and (1 – 1) is zero. The denominator is also (1 – 1) and zero.

Thus you get 0 divided by 0.

You’re then told that’s a no-no and that’s because zeros and infinities lead to all kinds of arithmetic “bad behavior” or singularities.

You’re then supposed to see that x2 – 1 can be re-written as (x – 1)(x + 1) and since “like cancels like,” you cancel the x – 1 is the numerator and denominator and “get rid” of it.

This leaves simply x + 1. So, as x goes to 1, x + 1 goes to 2 and you have a “legitimate” answer and have bypassed the impasse of 0 acting badly (i.e., zero divided by zero).

If you re-understand all this more slowly you’ll see that there are endless potential confusions:

For example: you cannot say that (x2 – 1)/(x – 1) = x + 1 since looking at the two sides of the equal sign shows different expressions which are not equal.

They’re also not really equivalent.

You could say that coming up with x + 1 is a workaround or a “reduced form” or a “downstream rewrite” of (x2 – 1)/(x – 1).

This reminds us of the endless confusions in high school science: if you combine hydrogen gas (H2) with oxygen gas (O2) you don’t get water (H2O). Water is the result of a chemical reaction giving you a compound.

A mixture is not a compound. Chemistry is based on this distinction.

Math and science for that matter, are based on taking a formula or expression (like the one we saw above) and “de-cluttering” it or “shaking loose” a variant form which is not identical and not the same but functionally equivalent in a restricted way.

A lot of students who fail to follow high school or college science sense these and other “language and number” problems of hidden vagueness.
School courses punish students who “muse” to themselves about hidden vagueness. This behavior is pre-defined as “bad woolgathering” but we turn this upside down and claim it is potentially “good woolgathering” and might lead to enchantment which then underlies progress in getting past one’s fear of something like math or science or anything else.

One is surrounded by this layer of reality on all sides, what Wittgenstein calls “philosophy problems which are really language games.”

Think of daily life: you say to someone: “you can count one me.” You mean trust, rely on, depend on, where count on is a “set phrase.” (The origin of the phrase and how it became a set phrase is probably unknowable and lost in the mists of time.)

“You can count on me” does not mean you can stand on me and then count something…one, two, three.

In other words in all kinds of language (English, say, or math as a language) one is constantly “skating over” such logic-and-nuance-and-meaning issues.

The genius Kurt Gödel (Einstein’s walk around buddy at Princeton) saw this in a deep way and said that it’s deeply surprising that languages work at all (spoken, written or mathematical) since the bilateral sharing of these ambiguities would seem deadly to any clarity at all and communication itself would seem a rather unlikely outcome.

You could also say that drama giants of the twentieth century like Pinter, Ionesco and Beckett, intuit these difficulties which then underlie their plays.

All of this together gives you a more “composite” “circum-spective” view of what is really happening in knowledge acquisition.

Education and Finality Claims

Stephen Hawking kept saying he wanted to discover the ultimate world-equation. This would be the final “triumph of the rational human mind.”

This would presumably imply that if one had such a world-equation, one could infer or deduce all the formalisms in a university physics book with its thousand pages of equations, puzzles and conundrums, footnotes and names and dates.

While hypothetically imaginable, this seems very unlikely because too many phenomena are included, too many topics, too many rules and laws.

There’s another deep problem with such Hawking-type “final equation” quests. Think of the fact that a Henri Poincaré (died in 1912) suddenly appears and writes hundreds of excellent science papers. Think of Paul Erdős (died in 1996) and his hundreds of number theory papers. Since the appearance of such geniuses and powerhouses is not knowable in advance, the production of new knowledge is unpredictable and would “overwhelm” any move towards some world-equation which was formulated without the new knowledge since it was not known at the time that the world-equation was formalized.

Furthermore, if the universe is mathematical as MIT’s Professor Max Tegmark claims, then a Hawking-type “world-equation” would cover all mathematics without which parts of Tegmark’s universe would be “unaccounted for.”

In other words, history and the historical experience, cast doubt on the Stephen Hawking “finality” project. It’s not just that parts of physics don’t fit together. (General relativity and quantum mechanics, gravity and the other three fundamental forces.) Finality would also imply that there would be no new Stephen Hawking who would refute the world-equation as it stands at a certain point in time. In other words, if you choose, as scientists like Freeman Dyson claim that the universe is a “vast evolutionary” process, then the mathematical thinking about it is also evolving or co-evolving and there’s no end.

There are no final works in poetry, novels, jokes, language, movies or songs and there’s perhaps also no end to science.

Thus a Hawking-type quest for the final world-equation seems enchanting but quixotic.

Education and the Pursuit of Improved Overviews

Professor Sherman Stein was a prominent mathematician and popularizer, and his book, Mathematics: The Man-Made Universe, is a modern classic. The subtitle “The Man-made Universe” already tells you that you’re looking at a clear exposition of “humans made math” in contrast to the “mathematics fundamentalism,” à la Professor Max Tegmark of MIT, whose tone seems to say mathematics allowed for reality and us.

This is of course a perfect “argument without end.” This is the kind of argument that should help a student to rethink their assumptions and not obsess about some once-and-for-all final understanding which can become an “idée fixe” (i.e., fixed idea in French, indicating being overly rigid or stuck).

In the preface to Professor Stein’s mathematics survey classic, he writes:

“We all find ourselves in a world we never made. Though we become used to the kitchen sink, we do not understand the atoms that compose it. The kitchen sink, like all the objects surrounding us, is a convenient abstraction.

Mathematics, on the other hand is completely the work of man.

Each theorem, each proof, is the product of the human mind. In mathematics all the cards can be put on the table.

In this sense, mathematics is concrete whereas the world is abstract.”

(Sherman Stein, Mathematics The Man-Made Universe, Dover Publications, “Preface” Third Edition, page XIII, 1999)

Meta-intelligence tells you if views of what is real, what is concrete, what is abstract, what is man-made, what is mathematical, are so radically different depending on the interpreter or analyst, it makes prudent sense to keep various views in one’s mind and modify them or juggle them as you go along. Our ability as a species to nail down for eternity what the nature of mathematics, humans and kitchen sinks are and how they all interrelate, is elusive and tangled up in language, as Wittgenstein keeps saying.

Education: Linguistic and Arithmetic Elusiveness

We wish to sensitize the student to the obvious-but-hard-to-see truth that both language and arithmetic have slippery natures built into them and seeing this clearly is a part of deeper education, our mission here.

Take four simple statements and see that they’re entwined and “confusing.”

  1. You can count (i.e., numeracy).
  2. You can count (depend) on me.
  3. You don’t count (i.e., importance).
  4. Count (include) me in.

When a person says, “you can count on me” do they mean that you will be standing on me and then go, “one apple, two apples, three apples” (i.e., count in the everyday sense). No, obviously not. “On” in this context is not physical or locational, but figurative. Ask yourself: how is it that you know the difference and nuances of all these meanings given that the word count and the preposition “on” seem straightforward but are really “polyvalent.”

Wittgenstein tells us that philosophy and its conundrums are ultimately based on “language games.”

When Gadamer (Heidegger’s student) tells us that “man is a linguistic creature” he means, among other things, that man “swims” in this ambiguity ocean every moment and puns and jokes aside, handles these ambiguities automatically, somehow. How does a child acquiring language get the sense of all this? It’s difficult to understand and explain. Language is both our nature and somehow beyond our grasp.

The same slipperiness, in a different way, holds for arithmetic and numbers. You can immediately see that the square root of 16 is 4 (plus or minus) but if you are asked, “what is the square root of seventeen?” you’d be “at sea” without a calculator. If you’re now asked, what is the square root of -17 (negative seventeen), you would probably be lost.

These would seem to be very basic “operations” and yet are baffling in their way and parallel the “sudden difficulties” in language use and orientation and clarity.

Deep and “meta-intelligent” education, which we promote here, begins by seeing, among other things, that both our ability to function while “swimming” among words and numbers is puzzling if you look at them “freshly.”

It’s also not so easy to define exactly what reading and writing are in the first place or why exactly the smile in Leonardo da Vinci’s Mona Lisa painting is enigmatic.

When one glimpses the truth that we are surrounded by obvious things that are never really obvious, one pauses and thinks. This is where (self) “re-education” begins, especially if “enchantment” (genuine magical fascination) accompanies the thinking.

Essay 37: The Language Phenomenon in Education

Wittgenstein (1889–1951) identifies language as the principal “confusion-machine” within philosophy:

“Philosophy is a battle against the bewitchment of our intelligence by means of language.”

The philosopher’s treatment of a question is like the treatment of an illness.

“What is your aim in philosophy?—To show the fly the way out of the fly-bottle.”

Education if deep and meaningful would put language itself in front of a student to understand the “bewitchment” and to perhaps “escape from the fly-bottle.” The fly-bottle is roughly “the captive mind syndrome” described by Czesław Miłosz, the Polish poet-thinker.

There are various aspects of this language-watching:

Hans-Georg Gadamer (Heidegger’s successor, who died in 2002) writes:

“It is not that scientific methods are mistaken, but ‘this does not mean that people would be able to solve the problems that face us, peaceful coexistence of peoples and the preservation of the balance of nature, with science as such. It is obvious that not mathematics but the linguistic nature of people is the basis of civilization.’”

(German Philosophy, Oxford University Press, 2000, pages 122/123)

This is readily seeable. Imagine Einstein and Kurt Gödel walking near the Princeton campus. They speak to each other in German, their native tongue which they both “inhabit.” Gödel communicates the limits to logic and Einstein the limits to modern physics such as quantum mechanics. They bring in Bohr and Heisenberg and the “Copenhagen Interpretation” as a counter-view. They refer to equations and experiments and conjectures and puzzles, current papers and conferences.

They take “communicative action” by use of speech using German as a means.

There are two levels here that are always confused: the ontological (i.e., all the why-questions people ask using language) and the ontic level, all the how-questions people pose using mathematics and laboratory results (e.g., Higgs boson).

Gödel once made the observation that if you look at language as a kind of logical system, it’s absolutely puzzling that people can communicate at all since language is so utterly ambiguous and “polyvalent.”

Take the sentence: “Men now count.” Out of context, does it mean count as in the sense of numeracy, one, two, three apples in front of me or do you mean perhaps that men in a certain country were given the right to vote and now “count” politically. Without the context and the ability to contextualize, no sentence by itself makes certain sense at all.

This is partly why Wittgenstein sees philosophy problems as “language games.”

Heidegger coming from “being-in-the-world” as foundational, and calls language “the house of being.”

You inhabit a native language the way you “inhabit” a family home or a home town. You flow through.

When a child of ten plays marbles (as analyzed by Piaget) and his native language (say French) comes pouring out of him in a spontaneous gusher, how can we really explain it since the child doesn’t look up syntactical rules and grammatical definitions when he speaks. The words flow.

Heidegger retorts that language speaks you in other words, you’re channeling the language in a way a songwriter explains how a song comes to him. In the end, it’s something spontaneous and not propositional like grammar is.

A moment’s reflection shows you how “slippery” language is: 

A man driving to New York says to you, “the car died on me halfway there.”  He does not mean the car was “on” him physically. To die on doesn’t really mean perish forever, it means, on average, stopped to function in a way that usually can be fixed in the garage.  It means this reparable conking out of the car gave him a big headache and aggravation as he waited for the Triple A people to get there and do the paperwork. You visualize all these layers and twists.

Again, without a human context, the sentence “the car died on me” makes little sense. Without a human context, “the sky is blue” makes incomplete sense too. Does a camel or cricket see a blue sky?

A full education would explore these dimensions of language and this has nothing to do with bringing back Latin or Greek or studying a foreign language to meet a Ph.D. requirement.  Formal linguistics à la Chomsky, Fodor, Katz, etc. is not what’s being discussed, as interesting as all that might be.

It also is not about language genes such as FAP-2 or how vocal cords work since these questions are ontic (i.e., how does it work?) and not ontological (i.e., what does something mean or imply?). Thinking about language in an engineering sense with the human mouth as a “buccal cavity” is quite legitimate and a voice coach might do well to do that.  We are talking about something else:  the centrality of language in human self-understanding, functioning and the making of meaning.