INFINITY

 

INFINITY

I was a little bit nervous as I was preparing myself to face a whole new batch of first year Electronics and Communication engineering students. Being nervous is very common among teachers and is also a very good sign. It is a driving force for the teacher to know more and prepare accordingly before he goes to teach in a class. It builds a confidence inside the teacher to face students’ spontaneous questions. Now a day’s students just don’t believe whatever you say, thanks to their access to internet, rather they test your knowledge and they like to judge you. One cannot escape students by making a wrong statement. If you know more, then only you can give less, you know less and you won’t be able to deliver anything.

In engineering colleges students are often reluctant to learn Mathematics or any other basic science subjects, like Physics or Chemistry. They are subjected to some kind of hallucination that in the professional course like engineering, these basic science subjects are out dated. This mentality has been nurtured by the students since their school days, thanks to the sincere unrestricted guidance from their parents or due to irresponsible supervision by teachers or the students develop this attitude within them somehow, whose reason is  unknown to me. Facing such students, who are victims of such delusions, is indeed a challenging task for the teachers who teach basic science in engineering colleges. This was the reason for my concern and I was thinking of how to motivate them or what to teach them in the first class, because I believed in the saying, ‘first impression is the last impression’. At last I decided to teach ‘Real Number System’ as introductory topic to that class.  

I had three reasons in my mind for the choice of the selection of this topic to be taught in the introductory class. First, the study of real numbers was there in their syllabus, second, students know a bit of number systems since their school days and last but not the least they can attach themselves to real numbers, which is very funny though. Number systems originated with natural numbers and gradually it moved to complex numbers on the basis of steady requirements in the field of mathematics. Complex numbers, though, serve a great deal in engineering calculations; students use them without actually feeling the need of using them. But somehow they can connect to real numbers. Once a student told me, “real numbers have physical significance with real system”. I don’t want to drag one into this debate as that will diminish the crux of my story.        

The students of my class were sitting disquietly, some chatting with new friends, some texting in whatsapp, some googling, some checking their status in facebook, some were confused about what to do and in the midst of all these everyone was eager to meet with their new teacher. Not because, they were very serious kind, instead they wanted to measure me as a person. This would help them to decide future manipulation with their attendance in the class. I greeted them ‘good morning’ and they returned the same in courtesy. After an introductory speech, slowly and steadily I was trying all of us to be stitched together with the discussion on real numbers.

Infinity is an abstract topic which is part of extended real number system. Any undergraduate student is not supposed to know that. Yet even school students find heavenly pleasure in uttering the word infinity without actually knowing its meaning. That day in the class I was teaching division algorithm and when I asked my students what would be the quotient when one divided a non-zero number by zero, many students in the classroom voted for infinity. The answer was not correct though, the actual reply would have to be that zero cannot be a divisor by definition. So I started explaining this to my students.

A girl was quietly sitting in a corner and was listening to what I was lecturing. The girl was smart looking and was confident in her approach. Suddenly the girl stood and said to me, “And Sir! Some infinity is bigger than other infinities”. The statement made by the girl was strong enough and in no way was part of undergraduate syllabus. I didn’t know what other teachers would have replied if they were in my position. The girl threw this statement to me intentionally, that I was pretty sure. She was evaluating me. Either her intention was to test me that how much I knew or she was trying to show to the class how much more she knew. Had the girl succeeded in showing that she knew more, that would have been a triumph for her and would give her a ticket for not being present in the subsequent classes of mine. Why? Because she knew more than the teacher and gradually it would have paralyzed the structure of my class and I might have lost the number of students subsequently. This would have brought bad reputation for me and a negative feedback at the end of the session as well. This sort of incident is very common in engineering colleges.

Instantly, something sparked in my mind like flash of thunder. It seemed as if I heard this statement that ‘some infinity is bigger than other infinities’ somewhere very recently. No! Not in Mathematics book but somewhere …YES! I could recall.

I asked her, “How many times have you watched ‘The Fault in Our Stars’?” (This was a movie based on a book of the same name by writer John Green.)  I had never seen such paleness on the face of a living person. As if by asking this question I had drunk blood out of her veins like a vampire.

She timidly replied, “Twice”. She couldn’t have imagined that a middle aged college professor could ever know a movie on teen romance. Nevertheless, she couldn’t guess how on earth someone would track her thoughts so quick.

I asked, “Now tell me who made this mathematical statement?” And the reply she gave me made me certain about my presumption that the girl was being smart in the class by showing off.  Although she was confused with this sudden unprecedented attack yet she replied with confidence, “Hazel Grace Lancaster”- (the female lead character of the movie).

I actually wanted her to tell me the name of the mathematician who worked on infinity. I smiled and told her, “Listen dear! What I wanted to know was whether you knew the name of the mathematician who made this statement. But you are far beyond that. As for the movie is concerned, what you have replied is also incorrect. See, I have seen this movie five times and have read the book too and it was Peter Van Houten (another character), and not Hazel Lancaster, who first made this statement in the movie. I am sorry but you have not watched the movie attentively at all”.

The entire class was listening to our conversation and most of them were puzzled to see what was actually happening.  By my last fourteen years of teaching experience I have developed a sense of perception of how much today’s students can know. By seeing a student I can feel how far he or she can go.

George Cantor, a nineteenth century mathematician was the first to elaborately study the theory of infinities. He developed certain theories on infinities which he ‘did see but couldn’t believe’ as claimed by Cantor himself in a letter to his mathematician friend Richard Dedekind. Such was the impact of infinity on those days that even today the concept of infinity and moreover infinities have become a subject matter of higher mathematics. I thought, after hearing from that girl, how easily and without understanding a bit, these youngsters made comments on something so robust. They even don’t realize the impact of making these statements in public.

And this had not happened to me for the first time that day. Earlier once I asked a child of fourth standard, who very well knew the statement of division algorithm, what would be the quotient when a number is divided by zero. The child replied, “Infinity”. I was speechless, not out of appreciation, but out of audacity by which these children are supervised by their parents. Because immediately, after hearing that I asked, “What is infinity?” He replied, “Cosmos”. I asked, “Who told you that?” He said, “Daddy”. I didn’t know what to say further to that child as I knew the very moment that his mathematical career was doomed.

Anyways, I felt pity for the girl.  I put my discussion on real number on hold. I started giving lectures on Cantor and his life, briefly discussed Zeno’s paradox and how Cantor’s theory on infinity helped solve the paradox. All these were discussed briefly and lucidly. I suggested several good popular level books to the students then, such as, George Gamow’s ‘One Two Three Infinity…’, R. Curant’s ‘What is Mathematics’ and many more. I called the girl into my chamber and counseled her, told her about how much further she should study and how far she must know. I even told her that I would be there any time if she needed me in understanding some topics from the books, that I would like to discuss any time on infinity. And there comes the funniest side of my story. The girl never turned up in my class thereafter.

 

                                                            DR. SOVIK ROY (Assistant Professor, Dept. of Maths)

                                                   TECHNO MAIN SALT LAKE, (TECHNO INDIA GROUP)

                                       (SNBNCBS Alumni, Ph. D in Quantum Information Science, 2018)