Numbers, Time, and the Counting Process
John L. Waters
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Numbers, Time, and the Counting Process
John L. Waters
February 25, 2001
Copyright 2001 by John L. Waters. All Rights
Reserved
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(Revision of second paper entitled "What Counts?")
In front of Wall Mart, with the hundred and ten pound
family Great Dane "Poochie" standing by, a gleeful
five year old boy is counting his hops. He's hopped
out from under the sheltering eaves of the building.
"One, two, three, four, five, six," he shrieks again
and again.
The young man is elated in his newfound mathematical
ability. He's getting soaked in the rain but his
attention's on hopping and counting. Moreover, the
boy's parents are inside shopping so they aren't aware
of his ecstatic behavior. So to the consternation of
several passersby, the lad keeps on enjoying himself
In the kitchen of an Iowa farmhouse a whistling girl
sits in a chair happily counting eggs and putting
them into egg cartons. Her right hand grasps one egg
after another and moves the food item from a wire
basket containing more than a hundred similar items.
She carefully places each oblate spheroid in a
styrofoam carton holding eleven others. Her hand
follows the same path over and over. The hours creep
by.
3. In front of his class, a grey-bearded pedant
wearing a tuxedo is meticulously counting one bean at
a time, and marking on a notepad a stroke for each
bean, to determine exactly how many beans are in
bathtub filled with beans. The man's doing this to
illustrate an important point. Furthermore, after
sitting in a chair for fifty minutes, each student
understands. The silent man's body is going through
cyclic motions reminiscent of an oil rig pumping
black gold from beneath the Arabian sands. And as the
man repeats the same body movement, a recording he's
put on the CD player repeats the nonsensical chant,
"unkachunka, unkachunka, unkachunka", and the clock
keeps on ticking off the minutes tickaclick,
tickaclick, tickaclick, like a frog chirping on a cool
night without feeling the urge to dream up any esteric
philosophy or theoretical mathematics.
A mechanical boy resting on his hands and shins is
rocking on his bed, repeating the same body movements
as he hums the same tune over and over. After forty
minutes he has hummed this theme over fifty times. At
five AM he is standing in the pantry counting the
number of rotations of a phonograph record spinning on
the turntable as he listens to the same tune for the
nineteenth time. This autistic boy is intrigued by
mechanical, repetitious activity, and he counts
objects for the sheer delight of doing so. When people
walk by he pays no attention to them.
Over a broad expanse of water shimmering in the
moonlight, a robust man is rowing a small boat.
Sitting in the bow, his lady friend counts the number
of strokes he makes. The man's body rocks forward and
back, forward and back, forward and back, and
sometimes he grunts with delight. But the woman
records only numbers. She doesn't record the man's
vocalizations. Later, when the numbers are
contemplated, no record of the vocalizations and the
body movements exist in a tangible, physical form.
On page 126 of a tattered Mother Goose book there's a
picture of a grandfather clock. One can almost see
the ticking of that large mechanical clock, with its
fourfoot long brass pendulum swinging like a liana
with a jungle boy or a monkey hanging on at the bottom
of it. But we aren't supposed to think about the law
of the pendulum. We aren't supposed to think about
Mother Goose or about what is living in the Jungle.
Instead, we are going to think about the
cyclic-repetitive process by which any counter records
the number of strokes. Each time the boy swings past,
each time the pendulum makes a stroke, the system
returns to its former position and the cycle repeats.
This goes on for days and days.
You can observe the cyclic-repetitive movement in
small clocks and in large clocks. Furthermore, when
you look in the back of an old-fashioned mechanical
clock you see a tiny wheel rocking back and forth with
an attached spring which returns the wheel to its
former position. In an electronic modern watch or
clock there's a quartz crystal with vibrating atoms in
it. It's the vibration in these atoms that the clock
uses to keep accurate time. The clock is just
counting the vibrations of these atoms.
Other clocks work off sixty-cycle electric current.
When you stand near an electric clock you hear the
low pitched hum. The clock is filling the air with a
musical monotone. If you could slow down the number
of beats per second from sixty to forty to twenty to
five to four to three, you would certainly see how
counting is actually just naming musical beats as they
pass by.
The person who is counting beans in a jar or musical
beats in a symphony is just beating out time, counting
time, and reckoning time. The man rowing his boat
across the lake is just counting time, and reckoning
time. The autistic boy rocking for hours on his bed
is enjoying the pleasures of being mechanical,
mechanistic, mathematical, and perfectly in tune with
the physical universe.
The foregoing examples and illustrations help us
understand what we do as we become more aware of time
and counting time. As we are counting numbers and
counting time we are using the same process. As young
mathematicians and clock-obsessed timekeepers, we also
are nascent band leaders. However in dwelling upon
abstractions, we may miss a lot of the joy in our
bodies, and we may become deaf to the music of
existence.
Being true to the dominant cultural ideology of their
times, the ancient theoretical mathematicians
abstracted the idea of counting numbers away from the
actual process of counting and keeping time. The
first mathematical theorists disassociated the idea of
counting numbers and the idea of reckoning time away
from the working physical body. The ancients theorized
about the idea of number and the idea of time without
considering the naked facts about how children
actually learn to count numbers and how clocks
actually count the many small durations of time. This
traditional dissociation of the imaginative "mind"
from the actual physical brain and body has led to the
conventional modern idea that numbers are only "in the
mind" or "in the imagination." This cleavage occurred
because the ancient theoretical philosophers failed to
focus on the actual mechanical action that truly does
the counting both in clocks and in persons.
Counting durations of space is the same as counting
durations of time. Look at people counting the number
of steps they take, and the number of units of
distance they must travel. Automatic speedometers
count the number of rotations in a wheel whose exact
circumference is known. Practically speaking, we
reckon times and distances using the same counting
process. Either we count numbers mechanically or we
use a mechanical device which counts numbers.
If we use the same counting process to reckon both
distance and time, then a general theory of counting
numbers and numbering is precicely a theory about what
exists "beyond space and time." This theory is about
what young school children are taught to do in order
to become conscious of both time and space, but with
the school's increasing emphasis on abstractions
removed from tangible physical reality, the child is
never made conscious of what clocks and other
mechanical counters are actually doing!
One consequence of this error is that years later,
when a person studies under an Oriental Master and the
Master teaches the adult to forget about the intellect
and the reasoning, verbal mind, the disciple gradually
comes to focus upon doing that very same thing and
devotes his or her attention to just that, then the
person who succeeds loses all his or her customary
focus upon what is in time and in space.
Without understanding what has been going on inside
his or her brain, the person has become focused on the
purely physical non-verbal "somatic" realm, not the
abstract, mental, intellectual, rational-verbal realm
of traditional Western culture. This physical and
somatic realm is governed by purely mathematical laws,
not by wordiness and reasoned, sequential thinking.
But the philosophers are still not able to explain
what the mystics perceive, in terms of what is
observable in real life. The reason for all this
confusion is the refusal of the ancient theorists to
pay careful attention to the workings of real objects
in the tangible and physical world.
When we go back and read the writings of Aristotle,
this habit of the ancients doesn't surprise us.
Genius that he was, Aristotle preferred to review
academic knowledge and catalog it than actually step
out into the physical world and record events fresh
from the world. We note, also, that modern children
are expected to pay attention to words, and to
persons' ideas, conversations, and thoughts, rather
than focus upon physical objects and body movements.
As a consequence a child who fails to pay attention to
words and to people is said to be disturbed,
psychopathological, autistic or braindamaged. This
child is even likely to be forced to take mind-numbing
and brain damaging medication.
The antiquated cultural traditions live on and on and
on and on and on.
2:38PM Saturday, February 24, 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.
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