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!”