Junior High Math

pk School Stories, Junior High Math

Euclid Alone Has Looked On Beauty Bare
posted online c. 1998

To succeed at school, you have to pass
a long series of intelligence tests …

Much of what follows here happens daily to millions:

The seventh grade brought Mr. Bell to me and my grateful classmates. The only time I’ve ever seen a number of my friends cry was when, at the end of the year, Mr. Bell explained to them that however hard they tried to get left back, he saw their ruse and would have none of it. Mr. Bell had us delirious with mere tidbits from George Gamow’s mathematics of infinity. I don’t recall his mentioning Gamow by name; he just bent our minds with a few of the concepts. Mr. Bell gave me my first sense of the nature of tautology, of axioms, of definitions …

Kids like things big: big athletes, big dinosaurs … Mr. Bell mesmerized us with big numbers. A side kick and I spent days filling notebooks with zeroes following the initial one. “Is this a googolplex yet, Mr. Bell?” we’d giggle, knowing the answer.

To succeed at school, you have to pass
very low level intelligence tests …

Why then did I go back to sleep through 9th grade algebra? Because it didn’t seem to be about anything. At no point was the concept of any communicated to me.

The following year I had to suffer geometry. The first day the teacher had us open our text books. She read us a list of axioms. Mr. Bell had gone over those axioms with us. The school text’s version was sloppy. They were neither Euclidean nor improved. I challenged them. The teacher looked blank and repeated the text.

Those who see the fallacies,
those who even might see the fallacies,
never get heard.

Meanwhile, you and the school
are failing
a long series of high level intelligence tests.
This is not just a school, he thought.
This is an institution for the production of automatons.
It is run by automatons who were produced by other automatons,
long ago, and now they have forgotten what it is to be human
and are engaged in turning us into automatons in turn.
Wilson, The Earth Will Shake


2000 08 21 By now, several modules in my Social Pathologies Directory discuss the phenomenon of human beings obediently and respectfully absorbing misinformation given in the name of authority. (Knatz.com/teach/society/survival/) Social Survival vs. Biological was the first of them. Santa (…/society/social epistemology/belief/) continues the argument.

Church, school … are institutions that our modern “belief” in Santa Claus prepares us for: what’s said is false; no one believes it; but unless you keep your (Knatz.com/teach/society/survival/integrity/) integrity bottled and private you won’t get your prettily wrapped “share” of what we stole from god, from nature, from God, from the Jews, from the Indians …

Question:
How do you turn a sphere
inside out
without
puncturing, creasing,
or ripping it?
4 stages of sphere eversion graphic from The Optiverse
computer-generated video
John M. Sullivan,
George K. Francis, & Stuart Levy

How could my “geometry” teacher teach math? She didn’t know any.

For social intelligence honesty and integrity ought to be important ingredients.
First, God created idiots.
That was just for practice.
Then He created school boards.

Mark Twain

I wove a new chrysalis around myself, cocooned from the public school enterprise’s blatant indifference to accuracy, honesty, intelligence, and truth. Having Mr. Bell had been luck; the others were the norm.

That same year we had poetry: English and American.
Euclid alone has looked on beauty bare.
What the hell was Edna St. Vincent Millay talking about? The excitements of the mind that Mr. Bell had introduced us to were dead for me as far as math was concerned. My liberal arts college required at least one math and one science for all majors. My aversion to math was such that I got them to make an exception in my case, volunteering to take extra chemistry and physics.

Unfortunately, the resulting handicap is permanent. I’ve just spent a blissful, however frustrating, couple of months laboring through what I am sure is one of the greatest books ever written: Nobel Laureate Ilya Prigogine’s The End of Certainty. I followed the translated English awestruck, but two thirds of it remained opaque to me. The core of the book is in mathematical notation. Despite having math encyclopedias and symbol dictionaries at my side, I see the signs and I go blank. I look them up.

You started practicing to fail tests of honesty at home with Santa Claus
and in church with church mythology …

Track of changes in the curve

sphere eversion

Also see Science News, 1998 10 10

I can hold on for three symbols into the expression. Then I go blank again.

I know Prigogine is right from my Gestalt of the thing, from the depth of my reading of mathless translations of physics, cosmology, and other sciences, not to mention history and philosophy. But I can’t test the tautology. I, who started with a clear talent for it.

Most damaging, I can’t think in mathematical terms. I can and do think in terms analogous to math, but I’m still thinking in English! (See my Macroinformation, for example.) One can do great work in English. I believe I have done great work in English. But the greatest work is done by Prigogine and his total literacy/numeracy. I wish Shakespeare could see it. Keats too. (Of course we’d have to fill them in on Newton, Descartes, quantum physics, chaos … And alert him to errors and doubts as well as to accomplishments.)

A few further words on school math, including feedback to this module, I move to a note: and simultaneously transfer most such notes from this file to their own individual files: a practice that may spread throughout Knatz.com.)

The institutions that rehearse you have never not practiced them


pk School Stories 2 Math: Notes

Wilson’s Automata:
2004 02 02 I hope the visitor realizes that Robert Anton Wilson’s character’s reference is not to Central Watts High or to Corrugated Podunk Middle School but to Eton! It was delicious to me to read that last night as I’d just been characterizing the English public school system of recent centuries to my beloved Catherine: Eton and Harrow in particular.

Other notes spun off from this module at Knatz.com. Recreating the series here I put the Prigogine piece separately: see the soon-to- follow notes but for Prigogine, see the next post.

Extra Chemistry (note added c. 1995):
Now you can’t do physics without mathematics. And not much chemistry either. But then I didn’t do either of them very well. Those classes had my body a few hours a week, but my mind was little violated. I don’t doubt that my lack of involvement was connected to my Sunday School teacher’s concerns. I sat through the sciences bored to distraction, not distracted by conflict. The default setting for American culture is pro-engineering but anti-science. We want the television sets but not the knowledge and theory by which they were conceived. (And certainly not the wisdom they imply.) My pragmatism was insufficient to block my prejudices for the sake of career.


I’ll never understand why the demi for the qualitative chemistry lab gave me an A. I don’t recall doing anything but having anxiety attacks while staring out the window. Perhaps it had something to do with his shattering a large bottle of 6 molar sulfuric acid on the floor in my path. We both jumped back as the floor dissolved in a fury of chemical smoke.

“Get under the shower,” he kept shouting as he scrambled back and forth between the supply room and the disaster, smashing gallon jug after gallon jug of bicarb into the boil.

“It didn’t get on me. I’m OK.”

Ah, but the next time I tried to put those pants back on, they evaporated as I stripped them from the hanger. I laced up my shoes and stepped right off the soles, the uppers hanging ridiculously around my ankles.

In the end, Frankenstein’s monster gets a piece even of the bystanders.


By the way, the deans may have accepted my twelve of so points of chemistry and twelve more of physics in place of six of either with another six of math because I started pre-med. Columbia wouldn’t have been likely to find my real ambition intelligible. Deceptions are coached by the parents as well as by the secondary school. Like dressing the bride in white regardless.

My claim was to want to be a psychiatrist. The income and respectability would be approved by all. I half meant it. I regarded myself as a good listener. Therefore, I’d be OK at it. If God didn’t endorse that path, he’d have to speak up. (I used to joke that a bartender would be as good a choice and a deal less pretentious.)


The lab to me was like a prison. I’d find myself staring in as deep a catatonia as was my norm in grade school. The same demi introduced above said he’d never seen such an aversion. He advised me to correct my course toward the arts (the only area outside my religion I’d ever paid any real attention to anyway). Finally, I had the superficial external authority I needed to defy my parents officially as well as actually.

I may return here to tell a story about physics as well.


My thesis (Meta-Oxymoron) that Shakespeare’s sonnets dramatize the neurosis we inherit from the major intellectual conflict of the first half of this millennium is apposite here. Scholastic Realism held that only God was real. The heretical nominalists argued that the things we can weigh and measure are real. They called into question the reality of the familiar “spiritual” abstractions of supposedly “eternal” Being.

The next section of this narrative will recount how it was only years after I’d developed my thesis to my own satisfaction that I began to realize that I had gradually and largely unconsiously been converting from Realism to nominalism.

We change our ideas like an animal sheds its coat,
in patches, not all at once.

Umberto Eco

Chemistry and physics, science, hadn’t been about reality; I thought science a form of Black Magic. I bet the majority still thinks so. (See also my piece on Mechanism: once I uncensor it.)

This entire site may be seen as being about that conversion. As the Motives section of my biographical narrative explains, I don’t believe mankind can survive without that conversion becoming general. And if we don’t survive, what kind of world will we leave behind? What kind of scouts are we? Who could seriously imagine that we’re leaving the world a “better” place?

(The above are among the sorts of things I’d originally intended to write for the Discovery & Conversion section of my biographical narrative. To the degree that this is a logical “web” more than a logical “tree,” it shouldn’t matter much.)

Math & Math Feedback: (note from 1998 June)
I report an instance of false teaching from my geometry class. I can’t know what you’ll make of it.
So what?
What business does a tenth grader have telling the teacher anything?
Screw it all: go make money?

I offer it, assuming that if you care about the truth, you’ll resonate sympathetically with at least a couple of experiences of your own. Of course you could send me your own examples. I’ll make a list.
It was only last week that I got my first taker: Star mathematician John M. Sullivan, chief creator of the instantly celebrated Optiverse!

from The Optiverse

I’d asked his permission, of course, to duplicate his graphics. Apparently he decided to inspect my usage.

I’ll tail this off with a bit more of the hash my piece on secular indoctrination has progressed through:

Here’s another example of false education which has bothered me for decades. For millennia mathematicians presented their subject as though it were the truth. Math has long been nearly everyone’s metaphor for something certain. Philosophers became leaders in the ongoing campaign.Isn’t it the case that this is still how math is presented in schools?

(Please tell me if your education was an exception.)

Godel
It is definitely the case that in 1931 Kurt Godel demonstrated mathematically that any formal logical system adequate for number theory must contain propositions not provable in that system! Were you taught Godel in school? In college?

PS: I’ll add some other comments on Godel to my Paradox module at Macroinformation.org (once I can revive my most important science domain.)

Mathematics may be defined as the subject
where we do not know what we are talking about,
neither do we know if what we are saying is true.

Bertrand Russell

Shouldn’t faulty education be recalled like a bad steering system in a model of automobile?
Shouldn’t we be able to sue, like some are now doing with the tobacco companies?
One huge world-wide class action suit!


On a philosophy final at Columbia I wrote, “I came to college to learn the truth. All I’ve been taught is the history of error.”Did I mean that literally? Hardly. My intention was to be pithy. To pull the professor and TA’s collective tail. To protest the passive-consumer nature of education.

Read The Illiad.
Read Moby Dick.
Read these hundred other books.
Now that ought to keep you from performing or writing any sequels. (See my note on Creative vs. Custodial Cultures.)

Those words on my exam were further disingenuous in that I didn’t go to college to learn the truth. I still believed I had already learned it: from ages six to twelve. The Sunday School had given it to us fast, simple, and cheap. The rest was bullshit. Oh, fascinating, great fun. I loved Columbia. Four years of adult freedom from the adult world. Brilliant companions. Unending bull sessions. And no real competition. Any of us could parade as the next Hemingway or Picasso. We didn’t have to show anything. We were kept too busy.
My Christianity had merely picked up a mask of secular cynicism, a mask I elaborated on during military service.If kindergarden was a rape, and high school was a kindergarden, Columbia had been a liberation. My high school friends had increasingly shunned me. They held me down at a party to scream the reason into my face: “Because you love jazz too damn much.” (A little truck with the n-s [Bowdlerizing K., 2016 08 03 Offensive terms go dosido in fashion.] is one thing …) But at Columbia I met others who not only knew and loved what I loved, but they could play too!
Of course I couldn’t know how realtively mild the rape of kindergarden was until I was drafted into the military. Fortunately there after basic training I was dumped into a situation akin to an ugly little prison that nevertheless had some of the qualities I’d found at Columbia: Whitehall Street Induction Station wanted only degreed English majors, preferably Ivy League, for its typing pool of drafted privates.
My great friend there said, “Why don’t you and I find some hip little college and spend the rest of our lives teaching there? Of couse,” he added, “we’ll need that fucking union card.” So while helplessly helping to draft others, I started graduate school. NYU. Supposed to be strong in English. Another kindergarden.

Keep You From: Creative vs. Custodial Cultures

With regard to technology, military technology in particular, we are a creative society. With regard to culture — religion, manners, the arts … — we are far more a custodial society. My favorite story illustrating the difference and starring El Greco is told in my piece on the Classics.

As a school boy I showed talent in writing. That meant I was to study the writings of others. My musician friends were funneled into musicology: not what music do you have to offer us? or How can we help you to do it well? But rather Study Gregorian Chants, Hayden, Mozart …
For me it was Study Chaucer, Shakespeare, Swift …

Columbia offered a “creative writing” course. I wouldn’t have touched it with a ten foot pole. It was taught by an eighteenth-century man. Had it been taught by William Faulkner, what would that have had to do with my writing?

Miles Davis got a scholarship to Julliard. The first thing he did was run downtown to 52nd Street! Found Bird! Bird put him on the stand, put him on a record!

Did you ever notice? Elvis Presley didn’t come from any college. The Beetles were out playing! What musicology did Billie Holiday study? Twelve years old, she was better than any Julliard product. See? Even with creativity repressed, we still have more geniuses than we deserve. But I’ll bet we’re not aware of more than a small percentage of them. The culture is too busy shoving cretins at us, billed as “the best and brightest.”

But even if any of the things we brag about ourselves were true, if we were a free society, if we had a “level playing field,” would we therefore have a true reckoning of our resources? I doubt it seriously. As Staislaw Lem wrote, a thousand Shakespeares, a million Beethovens, would be cacophany. Our attention is spotty at best. And even were that not so, there’s always Homeostasis …

This note was eventually promoted to a module: Creative vs. Custodial Cultures.

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About pk

Seems to me that some modicum of honesty is requisite to intelligence. If we look in the mirror and see not kleptocrats but Christians, we’re still in the same old trouble.
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