Six Sinister Oversimplifications With Math-Level Resolutions
and with some simple but subtle ways to help us out of trouble
Does not recognize:............
Ethnocentrism The legitimacy of the interests of other cultures or countries.    LOOK
Egocentrism The necessity that others have the same rights as one's self.   LOOK
Punitive Morality The positive feedback of fighting evil by doing reciprocal evil.   LOOK
Scalar Ranking The necessity of using a multidimensional space when ranking.   LOOK
Shallow Insight The deeper level of abstraction at which mathematics exists.   LOOK
Oversimplification The multiplicity of causes and effects; the fallacies of propaganda.   LOOK
Some important abstract reality lies beyond the edges of easy human comprehension
and language (or metaphor) fails us.

ethnocentrism  1 ethnocentrism

On September 12, 2001UN Secretary General  Kofi Annan tried to remind America that it was more than an attack on America; it was an attack on humanity.  Both the Bush Administration and the American media seemed not to hear that message, seemed not to see its significance, even though Annan and many others repeated the message over and over during the weeks that followed.

"Attack on America" became the very name of September 11.  The media and the Administration managed to steer America into a patriotic path that sees virtually no legitimacy—seemingly not even reality—in concerns of the non-American world.  The Non-American world grows increasingly frightened by what they see.

Social psychologists call this cultural self-centering "ethnocentrism."   There is no word in colloquial language for the concept.  A person behaving ethnocentrically will call it "patriotism," and a person victimized by ethnocentrism will call it some flavor of  "bigotry" or "prejudice," perhaps "tyranny."   But patriotism is not the same thing as ethnocentrism.  Patriotism is the growth out from solipsism and egocentrism that informs us that we are part of a greater society to which we owe an allegiance.  Ethnocentrism is failure to grow further.

Ethnocentrism has terrifying potential for destroying human society and civilization, because mutually reciprocal blindness to the concerns of "outsiders" can easily lead to mutually reciprocal destruction of both sides, perhaps of all sides.

Solipsism Simulator

egocentrism 2  egocentrism

To a newborn infant, the outside world is only a source of comfort or discomfort for the infant.  Awareness of others' discomfort comes later.  "Solipsism" is the unfamiliar name of this abstract concept.  The infant grows from solipsism to egocentrism as he starts to recognize the world as something "outside" of self, something with an existence of its own.

It's pretty easy to get stuck in egocentrism, where "human rights" is equated to "my rights," and "everybody's rights" lies beyond the edges of comprehension.  Societies that let egocentrism get a solid foothold, easily become belligerent societies of individuals, each fighting to assert his own rights, seeing only his own interests as he gazes in the directions of others...who are doing the same.  Power concentrates.  Ruthlessness can rule.  Hierarchies form naturally: upstairs and downstairs, masters and servants.  It's a comfortable home for tyrants.

Democracy is a modern, imperfect attempt to avoid tyranny — imperfect because the concepts beyond egocentrism and hierarchy are concepts beyond the edges of easy human comprehension.

We see a strange egocentric misconception in movie fist fights. Our appetite for revenge encourages movie scriptwriters to direct their movie heroes to punch movie villains on the jaw. One movie critic saw the scientific illiteracy in that scenario when he commented, "The loud cracking sound you hear when the hero punches the villain in the jaw is the sound of finger bones breaking.  Jaw bones are stronger than finger bones."  It's egocentric to sense that the jaw should break because "I hit him; he didn't hit me." or "My fist was moving; his jaw wasn't."  The force on the jaw and the force on the fingers are the same force, a concept of mutually reciprocal symmetry.  This is the abstract concept, discovered in the 17th century and learned in today's physics classes, as "Newton's law of action and reaction,"  The meaning which makes it so useful is not really understood by most of those students—including those who graduate and become movie script writers. 

punitiveness   punitiveness

"Justice" is the goal of the movie heroes when they punish villains by punching jaws.  Retribution!  Revenge!

"Justice" has another meaning, too: mutually reciprocal fairness.  Lawrence Kohlberg and others have persuasively argued that this more abstract concept of justice lies a bit beyond the edges of easy human comprehension.

Fighting evil by doing reciprocal evil is a positive feedback in the workings of society.  Positive feedback is usually confused with positive reinforcement, but positive feedback is another abstract concept at the edges of human comprehension.   It's a powerfully destructive force, not a desirable outcome.  (Foolishly trying to put a kitchen fire out by dousing it with gasoline would be positive feedback; dousing with water is negative feedback.)

Punitive morality is seen as sociopathic by many (probably most) social psychologists.

hierarchy 4 hierarchy

Ranking people is a favorite pastime of seekers of simplicity.  But even ranking athletes by size is a gross oversimplification if we imagine the athletes lined up.  Nevertheless, that is the almost universal way that "rank" is conceptualized:  "Put 'em in a line and see where they stand." TRY IT; SEE IT

Ranking requires that we conceptualize a space of many dimensions and not limit our thinking to the one dimension of a line.  The basketball coach is interested in who is the taller; the football coach is interested in who is the heavier; and other coaches might have little interest in either height or weight.

One truly insidious linear concept of rank is that which places people in a line according to intelligence.  Intelligence is much, much more than memory—or recall, or speed of recall, or linguistic skill at sounding "intelligent,"…  What is your favorite notion of "intelligence"?   J.P. Guilford found 17 dimensions needed for the space of ranking by intelligence as measured by tests used back in the 1950's

Ranking  people—perhaps by their wealth, perhaps by their contribution to society, perhaps by their perceived value to society—is perhaps even more insidious.  Such a ranking cannot possibly be linear.  "Value of humans" is among the most multifaceted of measures.   Should access to the needs and comforts of life be awarded according to the same ranking that distributed wealth through lucky guesses in the stock market or the lottery, or through lucky genes that produced enviable beauty in a celebrity actress?  Who deserves the bigger reward, the poet, or the middlemen who have erected ingenious toll gates between the poet and the public?  Collecting tolls can get costly when the toll taker in return gives society only his Enron-ingenuity in justifying high tolls—costliness that can deny the less fortunate the necessities.  The value of day care workers and energy manipulators lie in unrelated dimensions.  One-dimensional ranking gives simpleminded, often cruel, answers to our questions.

Justice and humaneness exist reliably only in deeper abstraction.

New Age Man
superficiality  5  superficiality

When "parameters" are discussed, the mathematically savvy will not use that term to mean "limits" or "boundary," especially when speaking math. In math, "parameter" and "perimeter" have no similarity.

Mathematics is insight into the world's patterns of patterns of patterns of… Language, and its roots, metaphor, isn't quite so deep, but it is the stuff of wonderful literature, poetry, song, and even day to day discourse.   Imagination is even less deep but it's a human skill that other animals have not evolved to anything like that of human imagination.  Imagination goes beyond the immediate reality of perception, the least deep of human information skills.  (These are the four "levels of abstraction" as defined by Keith Devlin, PBS's "The Math Guy".)

The "fourth level of abstraction," as Devlin calls mathematics, lies largely beyond the edges of easy human comprehension, but it's the insight that has brought us our unprecedentedly powerful science and technology.  It includes insight into what is relevant and what is not, to the use of ratios and proportions, to extrapolation to unattainable limits, to sensing logical relationships and contradictions that usually go unnoticed, to the realization that many causes, many effects, many parameters (defined variables and constants), are the stuff of the real world we face day in, day out.

New Age man uses much of the fruits of the fourth but too little of its insights.

The mathematically savvy know how to make the lottery work to their advantage.  The scientifically literate recognize that which is merely pseudoscience.
oversimplification   6    oversimplification

"Accentuate the positive, eliminate the negative, and don't mess around with Mr. Inbetween" was a cheerful motto of the past.  Today's most powerful persuader, advertising, constantly tempts us with wondrous delights that seem true, or at least possible, by encouraging us to stop thinking after we detect some sliver of evidence suggesting that our desires are at hand.

The shortest route to disaster is to ignore the rest of the universe once we've seen what we like.  But it's the easiest route to follow because sensing the relationships between a network of multiple causes and effects is a lot harder than assuming one is all there is — and that once we've found it we need look no further.  It's the abstractions of Devlin's "fourth level" of abstraction that give us adequate insights into multi-parameter relationships (Jean Piaget called this kind of insight "formal operational.")

We are simpleminded at birth, and the journey from infancy to the world of science-see is a joyous journey.  But it's a strenuous journey filled with puzzlement, hard work, rewards of delightful discovery, and discovery of magical things we find in places we had never before thought to look.

It might even save humanity from much mutually reciprocal destruction.    In the 60's and 70's, the journal Science published...

This page is a printable, essay version of "Seven Poison Fruits of Dumbing Down."
Web versions are on these pages:

Dumbing Down
Mystery Words
Secrets of Science
Look here for "aura-detector" words:
intelligence - parameter - rank - justice - human rights - terrrorism