The boy named Zilch

It is the year 2020. A 4-year old boy named Zilch is waiting for his mother, Delta, who generally narrates bed-time stories to him. He is pretty upset about what happened today in the Inventor's Paradise, his school. The incident has made him mad on his parents too.

His mother finishes all her work in the kitchen. She is all tired from the day’s work. As soon as she enters her son’s room and looks at his face, she knew its going to be a long night. She settles down next to her son with all the warmth in her eyes and smile.

She puts her hand around his shoulder and asks him, “What is the matter son? You do not look well.” He does not respond and looks at her angrily. She asks again, “Did something happen at IP?” IP is the short form of his school’s name Inventor’s Paradise. For some strange reason, he finds it cool to say, “I go to IP. Today this happened and that happened at IP!”

He blurts out at her, “Why did you do this to me? Because of you, my peers at IP teased me. This is going to be a part of my life now!!” And he starts crying with big tears rolling down his eyes.

Delta makes him sit on her lap and wipes his tears using a tissue. She gives him a quizzical look and says, “Sweetie! I am so sorry I hurt you in some way. You’d feel better if you tell me what did I do?”

He wipes the remnants of the tears with his little palms and questions her, “Why did you name me Zilch? I hate my name. I cannot live with this name. I want to change my name.” Delta very sympathetically asked him, “So what name do you want for yourself? Choose a name that best describes you.” He kept his little finger on his lips, tilted his head a little and looked at the ceiling. Then he looked at his mother and said, “I don’t know but I kind of liked my name but now with all this teasing and all, I start to dislike it.”

Delta looks into his eyes and asks him, “Let us think of a name later on. Why don’t you tell me what exactly happened and we might come up with a solution?”

Then he said, “Last week our teacher gave each of us names of five of our peers and asked to find the meaning of their names. We all found it a funny exercise. It did turn out to be funny when we all shared our findings today with the rest of the class. When my name’s meaning was told by one of the peers as ‘zero’, the whole class went hysterical. And the whole time, everyone kept teasing me that am a head filled with nothing blah blah blah….”

The sobs start again.

Delta gave a smile and wiped the tears told him, “Do you know why I named you Zilch?” Zilch asks, “Why? ‘Coz I am nothing.” Delta explains to him, “No, because you are the most important part of my life as zero is the most important number in Mathematics and in almost every subject you may say. The study of science would never have reached the stage without the number zero. Zero or zilch has great mathematical and spiritual significance. That is the reason I chose the name for my little baby!”

Zilch innocently asks her, “Really? Is zero that important?”

Delta answers, “Yes, there is a huge history behind the invention of zero. Do you know how zero came into existence?”

Zilch says, “No. Can you tell me, what is the story of zero?”

Delta rubs her hand in excitement and sits upright and starts her narration.

“It was very long time ago, some time in BC, when people started feeling the need to represent nothing by a symbol. Babylonians started using space whenever they wanted to use nothing. But they did not follow decimal system as we do. Remember I explained the sexagesimal numeral system the other day?”

Zilch replied, “Yeah, it is the base-60 system. I remember that. The time represented using this system.”

Delta continued, “Very good! But they had not yet come up with the symbol. Then sometime later, the Mayans and the Indians independently came up with the symbol for nothing, which is what we use today. Zero represented as ‘0’. Indians in fact, came with arithmetic significance of zero and its great application in mathematics.”

Zilch asked, “Is there one person who invented zero or all Indians together?"

Delta chuckled and replied, “It is said the Hindus invented it. Aryabhatta and Brahmagupta have contributed to the concept of zero. Although, the earlier works of Aryabhatta reveal use of zero as a place-holder in a vague sense yet Brahmagupta actually used zero in its right sense. He also developed the basic operations, namely addition, subtraction, multiplication and division. Later on, Arabs learnt this system and the zero concept traveled to Europe through trade. Fibonacci did a lot of work based on this concept.”

Zilch narrowed his eye-brows and asked his mother, “This is interesting but I am still trying to figure out why is zero important, though?”

Delta winks at him and says, “You want to know how your name is important, right?”

Zilch takes out a sound and slowly says “hmmm…….! Ok, so what is the importance of zero?

Delta takes a pen and paper and writes 605. Now she asks him to explain the place-holders as he has learnt in IP. Zilch looks at the number and answers, “It means, in the unit’s place there is 5, in ten’s place its zero and in hundred’s place its 6.”

Delta says, “Imagine now that you did not know the digit zero, instead, use a blank space. It would look something like ‘6 5’, isn’t it?

Zilch looks at the numbers and says, “Yes, that looks so odd. I get the significance of the symbol 0 to represent nothing.”

Delta writes two more numbers: 341 and 3041 and asks him, “Is there any difference between the two numbers?”

He immediately answers with a big nod and says, “Of course, they are different. One is three hundred and forty one and the second one is three thousand forty one.”

Delta exclaims, “Awesome! Do you observe, because of the presence of zero, the place values and the way stated in word form. In the first one, 3 is in the hundreds place while in the second one, 3 is in the thousands place and in the hundreds place there is nothing represented by 0.”

Zilch kind of starts springing on her lap and says, “Wow! That means without zero, it would have been so much difficult to write numbers. I am enjoying the fact that zero is really important. But is it only as a symbol or it has any other property?”

Delta immediately answers, “Oh no! Its not just symbolic significance, there is more to it. Remember you did number line. Now, zero actually separates the positive and the negative numbers. Can you draw the number line with 5 positive and 5 negative numbers?”

In his child-like handwriting, he draws the number line.

Delta pats on his back and praises him, “Good job son!”

Zilch excitedly asks, “What else? What else?”

Delta continues, “Tell me what comes to your mind when I write 2, 4, 6, 8, 10 and 1, 3, 5, 7?”

Zilch thinks for sometime and then replies flipping his middle finger with his thumb, “Even and odd numbers. Hmmmm……. I see that the even numbers start from 2 and odd numbers start from 1. Where is 0?”

Delta goes on, “0 is neither even nor odd!”

Zilch exclaims, “Another uniqueness! Wow!”

Delta continues, “Now a little about its arithmetic properties. Tell me the result of the following operations?

5 + 0 = ____

5 – 0 = ____”

Zilch takes the pen and writes 5 in both the blanks and looks at them again and remarks, “Oh yeah! So the number remains unchanged if 0 is added to it or subtracted from it. Since 0 means nothing, that means nothing is added to 5 so 5 + 0 = 5. Again nothing is subtracted from 5 so 5 – 0 = 5.”

Delta adds, “But 0 – 5 is not 5 but actually – 5. Remember number line!”

Zilch replies, “Yes I completely understand once I see the number line. I did get confused without it, though.”

Delta writes another statement on the paper as shown below.

5 × 0 = ____

Zilch thinks and writes 0.

Zilch remarks, “I learnt it IP but it never looked this interesting! That when we multiply any number with zero, the result is zero! Now, how about 5 divided by 0?”

Delta thinks for a moment and then writes

10 ÷ 5 = ___

Zilch writes 2.

Delta asks him, “How is the result 2?”

Zilch replies, “Let me think! Hmmm…… ok one explanation using table of 5 that 5 times 2 = 10. So reverse of multiplication is division hence 10 divided by 5 = 2. But there has to be more to this.”

Delta says, “Ok. Let us say I draw 10 circles and then ask you to form group of 5. How many groups will you get?” 

He drew two boxes to represent the groups and replied, “2 groups. Alright, I understand. If it is 6 divided by 2, then I can form 3 groups with 2 in each group. Hmmmm…. Then if it is 5 divided by 2, then, how do we explain the remainder?”

He drew five circles and did his grouping. 

He continues, “Since the last one cannot be grouped, thus, it forms the remainder. This is so much fun!!”

Delta asked him to try with 5 divided by 0 now. He again drew five circles. 

He thinks aloud, “So, I have to form groups so that each group contains zero circle. Hmm........ Now I am lost mom!”

Delta explains, “You were correct that you have to form groups of with zero circle in each. This cannot be done, hence you can have infinite such groups with nothing. But, let us not get into infinity right now, so for ease, we say that the result cannot be determined.”

Zilch has twinkles in his eyes and talks to himself, “Wow! My name is really great!! Tomorrow, I am going to teach Pat and Alpha some lesson in IP!”

Delta interrupts, “Son, careful! No harm to anyone!”

Zilch replies, “Of course not mom! I will tell them what you told me, in just a manner that they will understand, you know!!”

Delta narrows her eyes and looks at him and he gives him a naughty smile. Then he hugs her and says, “Mom! Thanks for keeping my name as Zilch and am so proud of it. You are also important to me, you know that right?”

Delta sets aside the pen and paper and tugs him in to his blanket and kisses him on his forehead and wishes him, “Good night dear!”

Zilch replies back, “Good night!”