My Study - Part
I
By:
Aadel M Al-Mahdy
After
dinner, Hamzah helped his mother in the kitchen washing the dishes, and Khaled
and I sat in the living room watching the TV. Nothing was interesting. So to
kill boredom, I challenged Khaled to solve a simple mathematical addition
problem.
“I’ll
be in my study. When you’re finished, meet me there!” I said and just as I
entered the room, Khaled came running.
“I
can’t solve this mathematical problem, dad” my son Khaled said. “Why?” I asked
him. “I can’t add the unlikes” he answered. “Why not? I asked him. “Because
math doesn’t allow us to do that” he said. “Who is that Mr. Math who allows and
not allow?” I asked. “Mathematics, dad, numbers, additions and subtractions”
Khaled said. “But math is not a sentient being to allow or otherwise” I said.
“I know that, dad, but this thing called math has inherent rules and because of
those rules we can’t add the unlikes” Khaled said, almost running out of his
patience.“Who
told you that? I asked. “Ms. Caroline, my school Math Teacher” he said. “I think
you misunderstood her” I said. “No, dad, I didn’t. It is the rule and it is
simple. Apples are essentially different from lemons” Khaled explained. “I’m
sure they’re, but still you can mathematically add apples to lemons to tomatoes
to potatoes without breaching Ms. Caroline’s mathematical rule” I said. “How
can that be?” Khaled wondered. “You do it everyday. So does your mother” I
said. “Ok, explain it to me” Khaled said ina challenging tone of voice. “That’s
what I wanted to hear from you” I said, and looking him in the eye, I asked him,
“How much was the population of Canada
in 2006?” he said, “Approximately 26 million” I asked, “26 million what?” I
asked. “26 million people” he said. “Good! Are they entirely of the same
ethnic race?” I asked. “Of course not! They’re from different races; European,
Asian, Middle Eastern. African” he said. “Good! So we can say mathematically: 5
European + 3 Asian + 2 Middle Eastern + 2 African are equal to…” and awaited him
to add up. He said “12 people”. I asked, “Why can’t we then mathematically add:
3 oranges + 2 lemons + 1 pear in the same way?” He argued, “Because these are
not people, dad. They are unlikes” I said, “Yes they are likes” he asked, “How,
for God sake?” Isaid, “They are, if you use the correct semantics, if you free
yourself from the olden rules and semantically approach math from a different
angle” I said. “How much is the total then?” he asked defiantly. “Simple. They
are 6 pieces of fruit” Khaled’s mouth gaped. Linguistically, there is nothing
wrong with the phrase, 6 pieces of fruits. The concept started to sink in
Khaled’s mind. He hit himself on the side of his head. “Doesn’t your mother do
the same when she prepares her grocery list, calling all the different items on
the list groceries?” I asked. “Yes she does. What was the problem with me
before? Why did I not notice that?” he asked, wondering. “The old concepts are
so deeply rooted in our brain as they have been received through a process of
brain-washing, though we call it education, and therefore we feel threatened
when a new concept or approach arises to slam us in the face” I explained.
“What to do then” Khaled asked. “Not to be scared, embrace the innovation and
spend time studying it. If it is worthy of acceptance, then why not accept it.
In our mathematical case, semantics is the major thing. If you marry it to
mathematics, you open a door to infinity and become able to solve problems that
seem unsolvable. When your mind is stuck in the traditional way which is not
necessarily true all the times…oh, without language, mathematics is for birds”
he said, “My God, in this way, I can add up the whole universe” I said, “Oh, hold
your horses…not until you become able to grasp the concept of nothingness!” Khaled
then asked, “What on earth is that, Dad? You’re full of surprises. How can you
grasp what is not there? I asked, “Well, son, mathematics is a science full of
wonders. Can you count up to 3?” Surprised by a question that seemed dummy,
Khaled controlled himself as he knew I was not a dummy or mean person and then
slowly counted, “One, two, three” ─ “Wrong!”
I said; the word came out of my mouth in a way that startled him. He looked at
me with the severest signs of confusion on his face, but I said, putting an end
to his torture, “You should have said, “Zero, one, two, three” Khaled
interjected, “I never heard anyone counting from Zero” “Traditional! If nobody
counts from Zero, It doesn’t mean, though, that Zero doesn’t exist. Isn’t it a
number? Khaled argued, “Yes, it is, but it is a representation of nothingness
which means it is nothing, therefore I did not count it” I said, “Nice
argument! Nice Euclidian mathematics. The Greek thought of the Zero in the same
way long time ago. To sense perceptions of foreground objects, the Greek tied
numbers to bounded finite things. They did not think in terms of empty extended
space. They thought in terms of shape and location. They concentrated on the
observable, the small, the unvarying. And so they were stuck” Khaled asked, “And
how to avoid that?” I said, “By becoming mathematically concerned with functional
relationship. Thus our math becomes dynamic, not a whole punch of statistics.
Discovery of Zero by the Hindus and the introduction thereof to the West by the
Arabs has led to positional numbers, simpler arithmetic calculations, negative
numbers, Algebra with symbolic notation, the idea of infinitesimals, infinity,
fractions, and irrational numbers” I paused for a short while and then added, “Sound
familiar, Khaled?” Khaled confirmed, “Mmmm, yes it does. But why did the Greek
miss on the Zero’s potential for development” I explained, “Overzealous logical
rigor, that is why. The Greek elevated logic to the highest intellectual
status. That led to a crucial argument by the philosopher, Parmenides ─ Being
only IS and nothing is altogether NOT. Hence, because non-being was impossible,
change was impossible. To the Greek this is sound logic and therefore, they
rejected both change and non-being” Khaled then asked curiously, “How did the
Hindus and the Buddhists think of Zero, then?” I sais, “Well, for both of them, the notion of
non-being was a state that they actively sought in their attempt to achieve
Nirvana or oneness with the whole cosmos. None-being was something ─ a state
that could be discussed.
Hamzah
intruded on us and Khaled asked him, “Hamzah, can you count up to 3?” Hamzah
answered, “Are you retarded or something, of course I can” Khaled said, “Count,
then!” Hamzah quickly counted, “One,
two, three” Khaled and I said in one high-pitched voice, “Wrong! You forgot the zero. It’s a number,
too” ─ “Mother, can you count up to three?” Unbelieving his own ears, Hamzah
yelled talking to his mother. “What!” my wife’s voice was heard coming from the
kitchen. Hamzah asked her the same question again. Standing in the door of the
study room wiping her arms with a towel, my wife, said, “What’s wrong with you
people? One, two, three” we all laughed and said in one voice, “Wrong, you
should say zero, one two, three” my wife’s lower jaw dropped.
“Khaled,
since you succeeded in grasping the nothingness, could you round up 0.098 to
its nearest whole number?” I said and then added, “Hamzah, help him out if you
want” Both of them gave me two different answers, 0.01 was Khaled’s answer and
0.1 Hamzah’s answer. I shook my head and said, “You are still hesitant in
accepting nothingness, otherwise your answer would have been Zero. I do not blame
you. Even Euclid himself would have not been able to come up with the right
answer. For him being only IS and nothing is altogether NOT.
Khaled
and Hamzah stood up yawning and excused themselves to go to sleep. I asked both
of them, “Are you bored?” Hamzah said, No, nothing can bore me” Khaled then
laughed and said, “Oh, Hamzah, you just admitted that nothingness is something”
I laughed and said, “boys, go to bed!”
The
End
