Education and Spontaneous Learning

We give you examples of being receptive to the world around you and learning to see and hear as a form of education:

There is a show on PBS called Stories from the Stage. People come forward to a microphone on a stage and tell personal stories from their past, stories that they consider important, informative, educational (in the widest sense), and usable by the listener. One of the early “people at the mic” on stage is a teenage girl who says something, in a plaintive sorrowful voice, like: “I have been waiting far too long…to wait for someone…to see me.”

This perplexed girl is unwittingly raising the question of a deep human hunger: the hunger for “personhood.” At a young age, this primordial hunger expresses itself as somebody befriending me (i.e., the speaker needs a real friend) so that the befriended person comes into clearer focus to themselves, achieving personhood.

Very intelligent philosophers like Emmanuel Levinas of France have spent their entire lives trying to understand the connections between countenances (how a person “wears a face”), personhood, interactive life, etc.

In his book, The Face of the Other (the girl wants somebody to notice her and her face and like her and “smile upon her”) Levinas has a deep analysis of all these human yearnings and self-definitional journeys and quests:

“The Face of the Other” is an evocative phrase used by Emmanuel Levinas, an important twentieth-century philosopher.

  • “Other” (sometimes capitalized, sometimes not) usually translates the French word autrui, which means “the other person” or “someone else” (other than oneself). It is thus the personal other, the other person, whoever it is, that each of us encounters directly, or experiences the traces of, every day. Of course, we encounter a multiplicity of others, but Levinas more often uses the singular “other” to emphasize that we encounter others one at a time, face to face.
  • By “face,” Levinas means the human face (or in French, visage), but not thought of or experienced as a physical or aesthetic object. Rather, the first, usual, unreflective encounter with the face is the living presence of another person.

Thus, when we come “face to face” with another person, the experience is a social and ethical one (rather than intellectual, aesthetic, or merely physical). “Living presence,” for Levinas, would imply that the other person (as someone genuinely other than myself) is exposed to me—that is, is vulnerably present—and expresses him or herself simply by being there as an undeniable reality that I cannot reduce to images or ideas in my head.

This impossibility of capturing the other conceptually or otherwise reveals the other’s “infinity” (i.e., irreducibility to a finite [bounded] entity over which I can have power).

The other person is, of course, exposed and expressive in other ways than through the literal face (e.g., through speech, gesture, action, and bodily presence generally), but the face is the most exposed, most vulnerable, and most expressive aspect of the other’s presence.

Thus, a student could be channel surfing on TV, observe this young girl saying these things on Stories from the Stage, and expand one’s understanding of this entire set of hungers and self-identity efforts and go (say) from the moment of TV watching to reading Levinas.

This is a simple example from the current world of TV where a certain particular “cri de coeur” (French: “cry from the heart”) of a girl you don’t know at all could deepen and widen your understanding by following the thread to Levinas and other profound people. The girl’s plaint where she’s “waiting for someone to see me” becomes much deeper and can be understood on a larger canvas which is exactly what we want.

Many experiences from daily life, from walking around, from moments on TV, from tiny incidents, can be pathways to higher understanding and learning if you can see and hear “with the third eye and the third ear.” (Theodore Reik talks about “listening with the third ear.”)

Education is a kind of “applied awareness.”

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.

Essay 45: Then and Now Thinking: Facile Comparisons Lead to “Concept-Fraud”

The economist Arthur Laffer recently received an award from President Trump. Laffer wants to deceptively “cartoonize” reality by arguing that as taxes “go to 100%” (i.e., confiscation), output will go to zero and conversely as taxes “go to zero” output will go to “infinity.”

This is an example of playing with “bad infinities.”

This Laffer argument has been naively compared to David Hume’s economics:

“Back in the eighteenth century, the wise Scot David Hume anticipated David Hume in these 1756 words of sooth:

“‘Exorbitant taxes, like extreme necessity, destroy industry by producing despair; and even before they reach this pitch, they raise raise the wages of the laborer and manufacturer, and heighten the price of all commodities. An attentive disinterested legislature will observe the point where the emolument ceases and the prejudice begins.’”

(David Hume, Writings on Economics, ed. Eugene Rotwein, Edinburgh, Thomas Nelson and Sons, 1955, page 87)

(quoted in Greed is Not Enough: Reaganomics, Robert Lekachman, Pantheon Books, 1982, page 49)

Reaganomics and Laffer-nomics have nothing to do with David Hume and facile “then-and-now” comparisons, all of which are false since the “anarcho-capitalism” of Reagan/Thatcher views has noting to do with Hume

Thatcher said: “properly speaking, there is no such thing as society. There are only individuals.”

But Hume believes the exact opposite as a socially conscious brand of conservative:

Hume cherished the structures that sustain our social life. He was in this respect deeply conservative, in the good sense of the conservationist of the shapes and forms which these institutions have taken.

“And of course he was deeply mistrustful of any scatterbrained project of doing better, by promoting anarchism or society without government or law, or dismantling the institutions of contract or private property. 

“He would have had absolutely no patience whatsoever with the contemporary takeover of social ideals by monetary and market values.

“When free-marketeers say that there is no such thing as society, they are denying the very arches needed to sustain contracts, law, government, and markets in the first place, and then knavery loses its stigma, and we may well expect the worst, as their practice becomes ‘answerable’  to their ‘speculation.’”

(quoted in How to Read Hume, Simon Blackburn, Granta, 2008, page 70)

Deceivers make duplicitous linkages between hallowed names and ideas of the past and the dangerously “tricky” present.

Thus, Hume-to-Laffer linkages and trajectories makes no sense whatsoever. This is an example of “then-and-now thinking” used for “concept-fraud.”

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.