What Counts?
John L. Waters
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What Counts?
John L. Waters
Copyright 2000 by John L. Waters.
All Rights Reserved.
What counts is what you believe is very important, at
least at the time you are counting it. For example,
maybe when you were three years old you believed burnt
paper matches were very important, so whenever you
found a burnt paper match, you picked it up eagerly,
and you put the specimen into jar number eight because
you already had seven twelve-ounce peanut butter jars
filled to the top with burnt paper matches. And you
kniew that in your collection you had four thousand,
three hundred and fifty nine. Some people said you
were precocious, but by the time you were twelve you'd
thrown all those matches into the fireplace and now
you were collecting baseball cards.
Two years later, when your Aunt Sarah counts her doll
collection, she's going through the same physical
movements you go through when you count your
collection of paper wasp nests. You both pick up one
item at a time and utter the name of a number. Each
time you tag one item with a number name you move it
from the set of "uncounted" objects to the set of
"counted" objects. When you started to count the set
of "counted" objects was empty. When you are finished
counting the set of "uncounted" objects is empty. But
all the time you are counting you really are more
interested in your wasp nests than in understanding
the counting process. Because you take as much
delight in old wasp nests as Aunt Sara takes in her
precious dolls. Your delight isn't really in numbers.
Most adults consider money to be even more important
than dolls or wasp nests, because without money a
person can't pay the rent, the utilities, and the
grocery bills. Without money a person soon starves.
Furthermore, people who have a lot of money can do
many things which poor people can't do, such as ride
on large ships and visit every large seaport in the
world. And so, even though people count their money,
they pay more attention to the money itself and to the
benefits of having money than they pay to numbers and
the process of counting numbers. It's like Aunt Sarah
and her dolls. Your money is very very important to
you. And maybe you think that mathematics stinks.
Even if you don't feel that negatively about
mathematics, a lot of people do.
Mathematics doesn't actually deal with real, physical
objects in themselves. A mathematician doesn't care
if he's counting nails, dolls, burnt matches, wasp
nests, or billions of dollars. You can see this makes
mathematicians really odd people, because most people
would much rather be surrounded by money than by
nails, matches, wasp nests or dolls. What the
mathematician counts as important is the counting
process itself, the numbers themselves, the algebra of
numbers, and all the rest of that subject which so
many people consider dull, intimidating, and quite
beyond their comprehension. But that's partly because
the subject of mathematics just isn't well presented
to young people.
For example, when Sallijane comes to algebra class,
her intense fascination with antique oil lamps isn't
relevant to what's in the algebra textbook. Moreover,
Tom's burning interest in restoring old cars isn't
satisfied by what the teacher presents in algebra
class. Then there's John. John's fascinated with bees
and beekeeping. But the applications of algebra to
these and other specialized subjects isn't covered in
the standard math textbook. And so when math class
comes around, these teenagers have to forget all about
what really counts to them, and focus on something
which doesn't count. And that's a little bit like a
young man who believes that Jesus Christ is the Son of
God being converted to a Moslem who believes that
Mohammed The Prophet is the One True Messenger of God.
In short, the naive pre-algebra student has to be
converted into a savvy young person. This takes a bit
of brain work.
It's probably more work for the brain to be converted
from one religion to another than it is for the brain
to be converted from counting antique lamps as
important to counting abstract mathematics as
important. But it still is a conversion. It takes a
lot of brain work to take a student who has no
interest in algebra and turn that person into a
dedicated algebraicist. And so each high school worth
its salt is a laboratory in conversion experiences. A
few students have an epiphany and are illuminated as
they realize they REALLY DO understand algebra! But
often the math teacher doesn't really make the point
I'm trying to make in this article.
So what is the point? The point is that children and
most older people remain intent upon physical,
tangible objects like burnt matches, dolls, nails,
silver coins, antique lamps, and wasp nests. These
are objects you can pick up in your hands and
manipulate. You can wave them about and throw them.
You can even bring your mouth close and bite them,
lick them, and taste them. You don't have to be
theoretical and abstract about them.
When you begin to listen and talk, you learn to call
the objects you love by name, and when you begin to
count out the numbers, you learn to think of your
beloved objects in terms of a collection of objects
and a number of objects. Most people nowadays arrive
at this stage even before First Grade. But
mathematical abstraction leaves the physical, tangible
world behind. The world becomes filled with invisible
entities, many of which are infinitely too numerous
even for all the human beings and all the computing
machines ever to count. For example, just the line
segments contained in a pinhead are infinitely too
numerous to count.
A lot of people don't consider mathematics an
important subject for them. They appreciate that
physicists, sound engineers, and rocket scientists
need to study mathematics. But when hard-pressed,
most people wouldn't be able to explain the difference
between a real number and a rational number. And for
most people this ignorance doesn't seem to matter.
They still know how to bake bread, or they know how
to make money so they can buy bread at the market.
But why should you be really interested in
mathematics?
Suppose you wanted to understand the language which
the brain uses to think and feel in tune with nature.
That's when the brain switches from learned English or
French and uses the universal language of nature.
That natural language is the same for a Chinaman, an
Englishman and a Norwegian. But little children in
Norway aren't taught Chinese, and little children in
England aren't taught Spanish. However, little
children in every land learn to count, and mathematics
is the universal language of the universe. So it
makes sense to observe that when the brain is sensing
in nature, and seeing natural forms, and projecting
natural forms, the person is not experiencing
provincial, stylized forms. Instead the person is
perceiving universal, natural forms. The productions
of this person are not imitated, learned language.
They come straight from the deep brain, the
unconscious, the evolutionary mind.
Mathematical language is a bridge or connection by
which humans can describe natural forms accurately.
Without mathematics, the forms of nature can't be
accurately described and defined. For example, you
can say, "maple leaf" but that doesn't say how big the
leaf is, and the subtle venation isn't described
accurately. And you can say, "blue light" but you
can't say exactly what color the light is or how
intense it is. Without using the language of
mathematics your mind just can't be very well in touch
with reality. In other words, studying mathematics is
a way to become more sane and stay more sane.
"Well," you say, "I'm perfectly sane and in my right
mind, and I don't need to study mathematics. I'm
already mentally healthy the way I am."
I would answer that you are a cultured person who is
well adjusted to many other people in the same
culture, but if you were isolated from these people
and you had to live alone in the wilderness for three
months, you might not remain sane. And as you became
insane your brain would project to you certain natural
forms which would bewilder you and perplex you because
you had no idea of what the source of these images
was. You might even think these images were being
sent to you by God or the so-called supernatural
realm. In fact each year millions of cultured people
under stress become confused by their own brain
activity.
Furthermore, often when a person ingests some
mind-altering substance, the person's brain presents
images in a dazzling kaleidoscopic sequence. These
images are natural forms. Many of the images consist
of wavy lines, straight lines and curves as depicted
in books on psychopathology. Similar lines and curves
are produced by aborigines to make rock art. But
modern civilized people are so cultured in their
artificiality that they rarely get into this state of
attunement to the universe.
But why is this subject important? It's important
because nature is really all there is, and the
well-coordinated brain is using the natural language
to communicate with all the sub-intelligences inside
the brain. To function at the highest level, and
coordinate all the abilities a person has, the
person's brain is using this natural language
fluently. But if you don't produce these natural
forms often, then your consciousness is severed from
your brain's central intelligence agency or main
coordinator. Your conscious mind is blocked off from
your unconscious body-mind. In dreams you may have
some contact with your whole person or self. But much
of the time you are living entirely in the imagination
which has been cultivated by your own family, school,
and society. You are remembering stories, working
with nonmathematical language, seeing visualizations
reminiscent of some stylized art seen nowhere in
nature, or recalling one of the sacred ideologies
composed by people who had no way of understanding the
source of inspiration and higher intelligence.
Even today, people who get images directly from their
central coordinating brain are said to be showing
signs of psychopathology. This is because the modern
experts on the mind have been cultured to believe in
this incorrect way about the natural mind and the
natural forms which are projected by the natural mind
in attunement with the universe. And this happens
when the person is no longer talking or listening to
talk, or reading in a book or writing. In fact
conventional medical people would say that the person
is in an autistic trance or in a psychotic state. And
so present humanity is at this state of error and
confusion, with the cultured mind alienated from the
deeper natural mind attuned to everything which
exists. And that's a very perplexing and dangerous
way for folks to be.
With the modern error so clearly defined and
corrected, the way forward is clear. And that really
counts.
2:47PM Friday, February 9, 2001
John L. Waters
johnlwaters@yahoo.com
The information on this page represents that of John Waters and not
necessarily that of Humboldt State University. John Waters takes full
responsibility for the information presented.
This page is maintained by: John Waters