Tag Archives: geometry

18 November 1987 Personal Correspondence on Women, Myth, and Goddesses (PDF)


Ts-itstsinako, Thought Woman

is sitting in her room

and whatever she thinks about


She thought of her sisters,

Nau’ts’ityi and I’tots’ityi

and together they created the Universe

this world

and the four worlds below.

Thought Woman, the spider,

named things and

as she named them

they appeared

She is sitting in her room

thinking of a story now

I am telling you the story

she is thinking.



I will tell you something about stories (she said)

They aren’t just entertainment.

Don’t be fooled.

They are all we have, you see,

all we have to fight off

illness and death.

You don’t have anything

if you don’t have the stories.

Their evil is mighty

But it can’t stand up to our stories.

So they try to destroy the stories

let the stories be confused or forgotten.

They would like that

They would be happy

Because we would be defenseless then

She rubbed her belly

I keep them here (she said)

Here, put your hand on it

See, it is moving.

There is life here

for the people.

And in the belly of this story

the rituals and the ceremony are still growing.

[Leslie Marmon Silko: Ceremony]


Nov. 18, ’87

Dear Pam

In the poem [Ceremony], I changed (He said) to (She said). It makes more sense that way. Silko’s book was quoted by Paula Gunn Allen, and I was checking the source for the purpose of finding some illustrations for my story on Linear/Non-Linear Dynamics.

The “Belly” is Ghii Lii, but I do not know if you would like to use that or not. I am trying to make up some “intellectual model” for those academic snobs who are not enlightened enough to appreciate the sacredness of the Womb, particularly described as “Belly” — of perhaps the Mother who is old enough to tell stories —.

Like we talked about, Stories (Myths) are in the hands of Males nowadays. I think that is why Silko wrote (He said). But, that brings the question of how Women lost the status as the Myth Makers.

I forgot who wrote it in what book, but it is a standard theory in Sociology that Women lost their status when “external relations” (trade, war) invaded tribal communities. It was an almost universal reaction of tribal communities all over the world that the “external relations” were handled by “Warriors” who were, by and large, males. Paula also  says the same as to the “degradation” of women’s status in Native communities which came in contact with “outsiders”.

[There were some exceptions. In the Japanese Myth I sent a copy to you last week, the Goddess Amenouzume was a “diplomat”. Besides, ancient Japan was ruled by an Empress, and even pregnant women went to wars along with men. They were like Amazons, who supposedly lived in Northern Europe, possibly Czechoslovakia. In my father’s country in northern Japan, peasant women used to be the ones who sold and bought things, until 1945 or so. Peasant men in the country were, in general, “reclusive” and did not like to deal with strangers. They talked only when they were drunk, but then they could not count money. “Samurai” Warriors were the complete opposite, which supports the theory in Sociology.]

But, trades and wars were “external”. How did that become “internal”? Why is Myth Making lost?

I am not against the “happy myths” that women make about “A little cozy house with a white picket fence and Sunday strolls to a park with children”. It is a worthwhile Myth and I hope the Myth becomes a reality for every woman. After all, the Socialist Ideal that Rosa Luxemburg fought for, with all her intellect and passion, was for the happiness of all people in that sense. And, in that sense, European Socialist movements had at least a partial success, in terms of a compromise called “Welfare Capitalism”. That is, Rosa’s Myth becomes true, to a degree. It is rather the megalomaniac Utopia of men-socialists, such as that of Stalin, Hitler, and Big Money Men, that brought disasters.

You read Silko’s poem, with a minor substitution of “Myths” for “Stories”. The “Theory” is absolutely correct. When women make up a Myth of the New World, the New World comes. That will be, for sure, the reality sooner or later.

Women, with their “manipulative minds”, can make men do most anything. Men would not know what was happening to them. It was Women — said to have been some 200 of them — who made Jesus do what he did. It was ladies who made Galileo do science, by their show of support in terms of “popularity” and perhaps coy flatteries. Galileo was known to be a lover of wine and women.

The only exception was Newton. Young Newton adored a daughter of a pharmacist in his town. But she did not even look at him. And we all know the dreadful result of that. If Human Race annihilates itself by Nuclear War, I shall blame women for their part in frustrating men, driving them crazy, and making them desperately suicidal. To be sure, however, before men can blame women, women of the world must be given a universal and absolute “Natural Right” to each own “a little cozy house”. You may not have noticed it, but with some 800 Billion Dollars we have been spending on armaments every year, we can do that. (No less than 40 million houses a year. And think about the employment they would create, plus the secondary effects on the economy.) The problem is, of course, the “egg and chicken”. We are in a Vicious Circle — a bad type of Non-Linear Dynamics —.

The only way to get out of the Vicious Circle is Myth Making. I do not go into mathematics here. But the same can be explained in cases like the “high jump”. Athletic coaches would tell you that the first thing one has to do is to make an Image of one jumping high. If you cannot see yourself jumping high, you cannot jump high. That is the most important “pedagogical” secret.

If you can imagine that you are doing it, then you can do it. Whatever the “it” is. If we can see what Indian Reserves look like, then that is what it shall be. We do not have Peace, simply because we do not know what Peace looks like. In dealing with Vicious Circle situations, Imagination, i.e. Myth Making is the most important thing. If we have a “Story”, we can jump. That is why I am “holding a gun to your head” — though I would prefer a better metaphor —.

OK I tell you a story. The story is about a strange man and an author. This strange man used to stand on a bridge over a river in Tokyo. There was a sand bar in the river. This strange man, on a certain weekday, every week, would go there and look at the sand bar. The author also had a habit of taking a walk and passing by the bridge on the same evenings. Eventually, the writer came to know the man and they started to talk. The man was thinking of building a beautiful town on the sand bar. I do not remember the details, but I guess it was something like Utopia. Maybe it was a Woman Town, consisting of “cozy little houses” with flower gardens and parks.

The writer did not believe a single thing this strange man was talking about. It was a crazy dream, nothing more than an “escape from reality”. But nevertheless those two kept meeting and discussed all details of the Town Plan.

Then, like any story of this kind, it came to an end. One evening, the writer came to the bridge, but the strange man was not there. The next week, the writer waited a little longer, but the dreamer did not show up. The next next week, the writer went a little earlier and waited. No show. A month passed. A season passed. A year passed. In the dusk of Tokyo, the writer kept looking at the sand bar in the River Sumida. The Utopia was no longer there. And there the story ended.

I must have been 10 years old or so when I read it. But the sad feeling is still with me. My mother did not even know that I was reading stuffs like that. My teachers, schoolmates, brothers, would not have known what the feeling was like, even if I told the story to them. Only my sister knew that I was reading, but I did not tell her about the story. And that I learned math, physics, Marxism, Christianity, etc., including digging into Bear Shit, has to do with the story too.

I am looking for the imagination lost.

You see I am the writer still looking for the man with the strange imagination. I am not holding a gun at you. I am hanging on to the imagination.

What you are talking about may be a dreaming nonsense. But it is important to me. I expect you to be a Myth Maker. You have to tell me your “Stories”.

If you cannot find words, I supply you tons of words. As long as there is a vision, in a sense of even being a feeling, there will be words for it. If not, we make up words. If you can’t get the picture right, someone will dram it for you. One thing about Myths is that they are communal properties. Don’t try to monopolize the burden like Jesus Christ — even his case was not an egoistic enterprise  as the Bible distorted it to be —. You are not even a Christian.

Back to the “Woman talk”. The difficulty of Ghii Lii is from its Femininity. C. Kerenyi open the chapter on Kore by saying “How can a man know what a woman’s life is?”

[Essays On A Science of Mythology. C.G. Jung, and C. Kerenyi. Princeton U Press 1949. BL313 J83.]

Kore, a Greek goddess, Holy Virgin, The Mother Earth, The Female Spirit of the Universe, is dated some 5,000 B.C. Her name is spelled variously, like “Car”, “Carna”, “Ker”, “Kali” and apparently worshipped all over Indo-European World, including Egypt. The Myth is the oldest, from the time before any Male Gods appeared. But the Kore Myth was destroyed. We only have fragments, and with many distortions. Probably you do not think of this, but to me it was obvious from the beginning that Ghii Lii has to do with the Female Spirit. It was “Water” that led me to it. That led me to Paula’s books, etc.

Now I have a hell of a problem. How can a man know what a woman’s life is?

It is one thing to talk of a “different culture” in terms of, say, male anthropologists interrogating male informers. As long as “Culture” is defined by Males, there is a hope in understanding. But what I am facing is something else. I try “Geometry/Field” — because that is the only thing I know —. Hopefully there is some Female Principle in Geometry/Field, enough to get to Ghii Lii. But that is tough going.

At any rate, let us see what we can get out of this mess. Like I said, Levi-Strauss could not do it. So if we fail, there is nothing to be ashamed of (in and intellectual sense). But, for the sake of the life of people under oppression, I hope someone will find a way. I remind you that many people pampered you (a pun intended), because you hold a key. In a sense, we are “mouse woman” to you as the “bad tempered, flighty, headstrong girl” in the “Bear Shit” story narrated by Bill Reid. If and when she become the noble Bear Mother is an open question at the moment.



P.S. In summer 1988, I am offering Physics 2020 “Physics And Society”. I will be talking of the Role of Scientists in the Nuclear Arms Race/Destruction of the World. Would you kindly consider talking about Native Science in the course? The summer course will likely be offered in July (in the second session). However, if we do not get enough enrollment, it will be withdrawn.

The Need of Sensitivity in Science: As the foundation of Cross-Cultural Science Education

Sensitivity and Cross Culture Science 1



—As the foundation of

Cross-Cultural Science Education—

“Science sets forth this formative process in all its detail and

necessity, exposing the mature configuration of everything which

has been reduced to a moment and property of Spirit. The goal is

Spirit’s insight into what knowing is. ”

[Hegel: Phenomenology Of Spirit. 1807.]

1. That what we usually think as “Science” is “Power Science”

and lacks Sensitivity.

The image of Powerful Science bulldozing through problems

and resistances to get things done is very strong in our mind.

And, therefore, it is hard to talk about “Sensitivity” as an

important element in Science.

Occasionally we do talk about beauty, poetry in science,

such as Fabre’s The Diary of Insects, and Einstein’s Cosmic

Vision. But, I am afraid, we tell such stories as “diversions”

from the main instructional materials. Perhaps we tell more jokes

of dubious value to entertain students more frequently than

telling about the “sensitive” tender elements in Science.

By and large we treat the sensitivity in Science as of

secondary importance. As a consequence, teaching practices of

Science tend to be that of imposing the Powerful Science on the

minds of students. We may not be conscious of us doing that. But

if we step back and look at our practices, it appears that we are

teaching Power side of Science almost exclusively and neglecting

I think it is unfortunate, for the creative thinking, the

sensitivity is essential. Even if the majority of human

population has to perform mechanical routines to make a living,

our children deserve an educational period where they are treated

with the delicacy of the Sensitive Science. For that reason, I

would try here a “scientific explanation” of

Sensitivity and Cross Culture Science 2

the Sensitivity, is a rational to stress the importance of it in

Science. I hope, my explanation is sufficiently general to

encourage Sensitivity in human life in general.

And, I have a feeling that what I meant by Sensitivity also

has some meaning to the Cross Cultural Education. Since I am not

familiar with the Cross Cultural Education that experts here are

engaged, I do not make a claim. Rather, I would like to ask you

if what I am going to discuss here has any relevance to the Cross

Cultural Education. I would be grateful if you kindly give me

back responses and reactions to what I said.

2. Where can Sensitivity be located in our Intelligence?

In order to introduce the Sensitivity, let me talk briefly

about “Science” in general. To save time, I present a simplified

archeological diagram here.

Science is a part of human intelligence to use the

faculties of our brain/mind.

(i) The first level of intelligence on the surface is Object

Recognition level. This is what Atomism does. We recognize

objects and identify them. We sometimes decide to ignore things

as well at this level.

(ii) The second level is Relation Recognition level. There we

think of relations between Objects. Statistical Correlations,

Causal linkages may be recognized and identified. Basically, the

relations recognized are of the “Linear” kind. [*See Subnote 1.]

(iii) The third level is Utility Recognition level. We sense what

we can do with the objects and relations we recognized.

(iv) The fourth level is Strategic Construction. This is often

referred to as “Problem Solving” intelligence. We take the

situation at hand as the starting point, and see the desired

state as the final point. If we find “The Means” to connect these

two points, we call it “The Solution” of the problem.

As such, the fourth level resembles the second level,

except that the “Connection” (Relation) is imposed by us. And,

often times, the task of finding the “means” to connect the two

points is accomplished by ignoring and cutting off relations that

existed. The image for this “problem

Sensitivity and Cross Culture Science 3

solving” is Alexander The Great cutting a knotted ball of string

with a sword in one blow. The sword is the imposed connection

cutting through all pre-existing relations. Unfortunately, this

happened too many times when a powerful dominant Culture met

In these 4 levels, there is no need of the Sensitivity.

Rather, we would think of the “Minimum” that is necessary for

what is desired. We deem that is “Efficient” and “Rational”

within the contexts considered.

For example, we recognize two towns on both sides of a

mountain. That is at the Object Recognition level. We see people

going back and forth between the two towns. This is the Relation

Recognition level of thinking. We see the Utility of the

exchanges. And we Bulldoze to make a Highway between them and

think that the problem is solved.

The “Science” in our ordinary sense is an organized and

formalized “knowledge” at the above 4 levels of intelligence. It

empowers people in that sense. Let me call this Power Science. It

lets us do things. But there are levels below this, if we dig

into our minds deeper.

(v) Although we seldom think any deeper than the Power Science

levels, we occasionally do “Think Twice”. We ask whether or not

the construction of the Highway was a good thing. Let me call

this 5th level intelligence as the “Reflective Level”.

We do have this intellectual capacity to “Think Twice”

about what we have done, and also sometimes what we are about to

do. That is where the Sensitivity comes in. Although we have the

Power to do and to get a certain thing that we desire, we ask

ourselves if doing so might not hurt someone. We exercise a care

to protect other’s safety, interests, wellbeing. This takes a

fair amount of imagination as to the situations that we are about

This requires thinking of the whole system of things in a

complex web of relations. It is different from the kind of

thinking of Power science which can be metaphored as that of

“Drawing a line from a point A to a point B”. For, in the complex

web of relations, there are lines from the point B to the other

point C, which in turn relates to other points. All linked in

that sense, the circle of the linkage most likely comes back to

the initial point A. That complicates the situation. A

straightforward thinking is only applicable

Sensitivity and Cross Culture Science 4

to linking nearby points. The whole circle of relation is not

“straightforward”, but rather “Non-Linear”. That makes thinking

[Linear/ Non-Linear distinction is explained in Subnote 1.]

But the strange thing is that Humans do have an intuitive

sense by which they can “Feel” the harmony or disharmony of the

whole system. Even in highly theoretical works, physicists often

came to “Feel” the whole thing and said it is a “Poetical

Beauty”, or “Poetical Unity”.

That is the “Care” that one exercises to understand the

whole of the cyclic relationships and the “Beauty” that one feels

about the whole are related.

I think it is highly desirable that children are given the

opportunity to experience the “Care” and “Beauty”. It requires

Sensitivity to experience it. But the Sensitivity cannot be

developed without experiencing it. I think this is a great

challenge of Science Education.

I would like to suggest that Science Education has to aim

at the caring level of intelligence. And I think it is possible

to lead students to that level by asking them to “Think Twice” as

often as possible. The Science Education has to contain exercises

for saying “I can do this But on the other hand…” Such exercises

are training for Sensitivity.

We might call this “The Sensitivity Science Education”, in

a contrast to the “Power Science Education” that we have been

And I hope that they enjoy seeing the “Beauty” attained

after many exercises of “Thinking Twice”.

3. The Sensitivity Science is a “Pragmatic” necessity for

Human Survival, and Cross Cultural Science Education is a

beautiful way of the Sensitivity Science Education.

In view of what we are doing nowadays to our Environment

and to our fellow Human beings, I would say that without

Sensitivity, we will not survive the 21st century. For the

sensitive eyes, the bad consequences of the Power Science are

visible almost everywhere. Even if we do not want to see them,

things such as Acid Rains descend

Sensitivity and Cross Culture Science 5

upon us. Incidences such as Chernobyl happens and force us to

know what we are doing to ourselves.

In the line-like thinking of Power Science, we do not see

the remote consequences of our actions. But the fruits of our

deeds loop around and come back on ourselves.

In that, I am not a Romantic Idealist to advocate the

Sensitivity Science. I have a “Pragmatic” concern about the

future of the World in which our children live or die. Either we

educate ourselves and change to become Caring Beings, or we

annihilate ourselves. It is not possible to evade the choice.

Fortunately, however, we have a marvelous educational

opportunity called Cross Cultural Education.

It gives very good opportunity to Think Twice about the

Power Science that our dominant Culture has been practicing up to

The Cross Cultural Education is one way of giving our

children the opportunity, and a beautiful way of doing the

Sensitivity Science Education. Here, remarkably, we have a

consistency of the means and the aim. We have the way of studying

which cal1s for Sensitivity. And we have the aim that is the

I look upon Cross Cultural Education to be not a “Tokenism”

to satisfy disgruntled minority races, or “Window Dressing” to

soothe the “Guilt” from the colonial oppressions and the racial

discrimination in the historical past. But I consider it as a

Golden Opportunity for every one to learn the way of Survival and

at the same time the way of constructing a beautifu1 Future.

Beyond that, I would like to stress here that this is not a

subject of “social studies”, but of “Science”.

I am not saying this because I am a scientist and wanted to

externalize the power of science. You must realize that I am a

“scientist” only in the Power Science. Among other things it was

the prejudice of the “Power Science” that used to say that Euro

Americans have the Science.

And, I have to learn Cross Cultural Science for my own

sake. And people here are great help to me. I wish I could go

back to school again and experience beautiful education that you

Sensitivity and Cross Culture Science 6

– – – – – – – –

I add one, perhaps, “Bad” example for the advocacy of Cross

Cultural Science Education. It is from General Relativity.

General Relativity can be viewed as an “art” of how to

connect a small local Linear way of thinking (analogous to making

a short sentence) to the next. The connections of many small

Linear descriptions (analogous to a whole “story” made of many

sentences) make up a Global Geometry which may be “Non-linear”.

General Relativity is concerned with the Whole of the Global

Connections. Needless to say, to make a comprehensible coherent

picture is not a trivial task. Some constructions are beautiful,

The “connected whole” is a “World View”. And among many

ways to make up the “connected whole(s)”, we can study how to

compare various ways of making “connected wholes”. In this sense,

General Relativity is interesting. It resembles “Cross Cultural”

However, as I said before, General Relativity is “perhaps a

bad example”. The trouble with this example from modern physics

is that it is by and large inaccessible to the general public.

There are “popular books” such as The Turning Point by F.

Capra etc. However, ordinary Science Education does not come

anywhere near to the “Way of Thinking” contained in those modern

developments in science. Schools, perhaps unconsciously, teach

the 300 year old physics and waste time in “beating the

established mechanical routines into blank minds of children”

under the name of Science Education. It so happens that the Old

Science also carries the Authoritarian Ideology of that

It also represents the “Alienated” mentality of the 19th

century European Intellectuals. [see] M. Berman. The

Reenchantment of The World.] That Science emerged in the 17th

century as a “Liberation of Thinking” is largely forgotten and

perverted, under the disguise of “Rigorous”, “Exact”, discipline.

Psychoanalysts ought to examine why so many scientists and

science teachers today still maintain the illusion of “rigorous,

exact science” as if they have never heard of the Uncertainty

Principle or Godel’s proof of Incompleteness of Mathematics.

Their quasi-religious belief may be within the Freedom of Belief

allowed by the Constitution, but the Authoritarian posture of

scientists talking down to the

Sensitivity and Cross Culture Science 7

public, as if they are the guardians of the Absolute Truth, is a

pedagogical disaster in barring the majority population from

access to the modern science.

That I have a considerable difficulty in talking about

fruits of the modern science in terms of “Ways of Thinking”

attests to the failure in Physics Education for which we

physicists are collectively responsible. We have spent Hundreds

of Billion Dollars of tax money, but we have not helped society

with cultural developments in terms of the Ways of Thinking. The

public money is used to edify a small group of specialists and

widen the gap of thinking inequality, not mentioning the North-
South disparity in science-technology and wealth. We ought to

think, for example, why we do not use science to make rudimental

water supply systems available to the poor half of Humanity. It

could be done at a fraction of the cost of sending a school

teacher to Space and getting killed in a Show of National

Superiority. I do not think it is excusable.

One very inexpensive way of introducing New Way of Thinking

to general public is to do Cross Cultural Science. Since most of

the “Sciences” from different cultures are accessible through

non-technical expressions, they are better suited for general

Education. (I fancy that “Hopi Relativity” is just as good in

conveying the main idea as General Relativity which is accessible

only through complicated mathematical manipulations.) That is to

say, we have discovered a mountain of treasures in the Native

Science. I recommend school teachers to seriously look into

Native Science and take advantages of the treasure.

(However, I would caution the teachers to pay proper respect in

exchange, lest be accused of stealing the last and the most

precious treasures of the Natives after taking everything away

from them. One way of expressing respect is to invite Native

Scientists and let them speak, rather than giving an

“Interpretation” to students as if that is genuine Native

Science. And if possible, let students learn from the way the

Natives live with the “Science in their actual life, rather than

substituting an “intellectualized version” for it.)

– – – – – – – –

My story here was perhaps tedious and technical and it was

from the background of the Power Science. But I hope it is of

Thank you for your patient listening.

Sensitivity and Cross Culture Science 8

[Subnote 1. On Linearity.

“Linear” means “line-like”. When relations between pairs of

two quantities, such as “Input and Output” plotted on a graph

paper appear like lines, the relations are called Linear.

Most relations in Reality, however, are not Linear. Why,

then, do we favor Linearity? The most theories in science are

Linear ones. Economists use Linearized models; Political

Scientists and Politicians talk and think in Linear Language. We

usually think Linear, such as if something is good, then more of

it is better. It is not rare that sick people take more pills,

thinking that the more pills he or she takes, the faster the cure

is, then ends up with an Overdose. Or a man who makes hundred

thousand dollars a year thinking that he would be a twice bigger

man if he could make $200,000 etc.

But, the worship of Linearity is not just silly

superstition in numbers. There is a definite advantage in

Linearity. I cite an example.

Suppose a psychologist or social scientist is faced with an

unknown entity or system named, say, G. How will the scientist go

about knowing what G is?

The first principle of Science is the Principle of “Do

something and see what will happen”.

So the scientist does something, which in psychologist’s

jargon is called “Stimulus”. Sociologists might call it “Input”.

Something happens in Response (X) to the Stimulus (x), or Output

corresponding to the Input. By this, the scientist gets a data

(X) = {G} (x) or x → X

Of course this one data point is not enough for the

scientist to claim “Knowledge” on the entity. The scientists have

to try more Inputs and get Outputs. But if the entity (or system)

is Linear, it is easier to know what Response would be for any

Stimulus. For example, the Linear Entity G would produce a

Response 2X for Stimulus 2x, and 3X for 3x, and so on, i.e.;

Sensitivity and Cross Culture Science 9

What is more, provided the Entity (System) G is Linear, the

scientist can predict what the Response (Output) would be for an

arbitrary combination of various kinds of Stimulus, say like

(3X + 2Y – Z) = {G} (3x + 2y – z).

This predictability is an enormous savings in the cost of

the research to construct the Knowledge about the Entity (System)

Having this sense of Linearity in mind, one looks into

texts in Physics, Engineering, Economics, etc. One would find

that the majority of Theories are about Linear entities or linear

systems. Texts in Psychology, Sociology, Political Science,

Anthropology etc. are not explicit in what they mean by

“knowledge”. But when they do imply “knowledge”, they are usually

an implicit assumption of Linearity.

Most economic-politico-social policy recommendations from

the Power Science are of the Patch-work type which in effect says

“Granting that all other things stay constant, do x to get the

result X”. This is only justifiable on Linearity Assumption. The

characteristic of Linear Thinking is that it neglects all

complications. It only sees the starting point (the problem as

the initial state) and the desired end point, and finds the means

to connect the two points. It is like drawing a line between two

points without looking at other points around. Perhaps, it is

analogous to shooting an arrow at a target. As such, the

concentration of attention is necessary and it is not a bad thing

In real systems, however, when one thing is changed, all

others change. There would always be the second, third, fourth

order effects, like the ripples created by a stone dropped in a

lake. Linear Assumption is simple and convenient, but it is a bad

“superstition”, if it is worshiped as The Best Science. Yet the

Insensitivity of the Power Science neglects the higher order

Another trick of the Power Science is that, when the

uncertainties in the higher order effects are visible, it goes

for “Short Term” projections and makes decisions on that basis.

It is hoped that the higher order effects would not manifest in a

short time scale taken as the reference frame of the thinking.

Unfortunately, the neglected higher order effects do not

disappear; they “disappear” only in the short-term thinking.

People have to pay for them eventually. A funny thing about this

Sensitivity and Cross Culture Science 10

is “scientific”. That is the Power Science; it provides an

edifying cover not only for the negligence, arrogance, and

insensitivity, but for the stupidity. I would think that the

Native Science which thinks on a long-term scale would be good

“medicine” for the Power Science.

Non-linear entities or systems are that which cannot be

treated by Linear Theory. That is the definition. Non-linear

entities and systems are nasty, for they defy the simple

“predictability” of the kind illustrated above.

Non-linear systems are “Unpredictable”, which means there

is no possibility of doing the “science” which usually means

“predicting power”. Of course, we can do a modified sense of

“science”. In fact, non-linear physics is now getting

fashionable, where things like “Catastrophe Phenomena” are

What is so-called “Ecology” in biology and geology is

largely confined to Linear cases. Some Biologists and Geologists

are aware that Nature is Non-linear and Catastrophic Instability

— such as mass extinction — is expected. But the prejudice

(or rather “superstition”) of majority of the scientists

demanding “Predictability” for “science” on some emotional ground

does not make the study of Non-Linearity in Nature popular.

As to knowledge in social and Humane areas, their implicit

Linear “Rhetoric” are yet to be recognized. “Causal Relation” is

often nothing more than a Linearized Expression. As a

consequence, people do not know they are assuming Linearity.

Hence, Linear Thinking is prevalent.

I do not think the “Linguistic Philosophers” are even aware

of Non-linearity, except perhaps in Logical Paradoxes. (The

“Paradox of Self-Reference” has a “loop structure” and as such it

is Non-linear. “Circular Argument” is also Non-linear. They

reject it. But interestingly the most “definitions” in sciences

are “circular”. Newton’s Laws of Motion and Darwin’s famous

statement “Survival of the Fittest” are well known examples.

Perhaps, because of these bad cases, philosophers do not like

Non-Linearity, But, their dislike prevents them from serious

studies of Non-Linearity. This is unfortunate.)

However, the Philosophy of Dialectics is a Non-linear one. [See

Thorn cited below] But I doubt Dialecticians themselves such as

Marx — are aware of the Non-linearity.

Sensitivity and Cross Culture Science

As to Mathematics of Non-Linearity, see Rene Thom: Structural

Stability and Morphogenesis. Benjamin. 1972. (Thom also had an

interesting thing to say about Math Education, Science 1972.)

Also, there are several texts on Non-Linear Physics. What

is called “Solution” is an unusually stable wave produced by Non-
Linearity. It is to be noted that “Stability” can be a

manifestation of Non-linearity. Non-linearity is not always

unstable and catastrophic. I suspect almost all biological and

social systems (such as human life) is “stable” because of Non-
linearity. They “die”, however, because of the Non-linearity that

maintained them to be stable for a while (quasi-stable).

The escalation of Nuclear Arms race which goes in a

“vicious circle” is an example of bad Non-linear Dynamics. On the

other hand, the “positive enforcement” effects in Education etc.

are also Non-linear Dynamics.

These examples show that Non-Linearity is important and

interesting. But here again, it is too technical to be taught

directly in schools. I would appreciate very much if you could

suggest to me some ways of bringing “awareness” of Non-Linearity

into school science education. Interestingly “Sensitivity” is a

highly Non-Linear Phenomenon. I wish some psychologists would

write about “Non-Linear Dynamics of Mind”. Hegel came close to

doing that, but his intellectual snobbism is too much for popular

reading. Perhaps, Native Science might have good stories to tell

Oct.18, ’87. S. Kounosu Phys. Dept. U. of L.