Justice Katju, for your kind attention…

This was published on CRI.

It so happens that Justice Markandey Katju is very much interested in Science, History apart from of course law. This we know by his own admission. In today’s op-ed in The Hindu, Justice Katju laments about the horrible state of Indian education system. We definitely share his sorrow. We too are disgusted about the state of affairs. Unlike the honorable Katju, we feel there is much to blame the populist policies adopted by the past Governments of India with respect to Education starting from the primary level. However, this article is not about the education system. This article is more to do with Justice Katju’s unnecessary ramblings on topic of his interest, but the one he is not really a master at – Science Education.

Justice Katju did the same thing in his recent op-ed as he did before – prove that he is interested in Science but not really as knowledgeable. Not very long ago, he cried out at all India – apparently 90% of us[1] are fools – that Water is as good as burnt Hydrogen and we cannot harvest Hydrogen from Water[2]. In his recent op-ed, he seems to indicate that he decided a judicial verdict based on his answer to a fundamental question in Mathematics – how much is 1 divided by 0?[3] Unfortunately, whether he knows or not, he is wrong in both the cases. In the second case, since he is wrong and wrong by a light year, we seek to question whether or not, Judges across India ought to be more careful when delivering judicial verdicts based on their knowledge in areas which they are interested in but not really experts at.

We do extract Hydrogen from Water Justice Katju

One can of course take Hydrogen out of water. The process using electrical circuit to do so is called Electrolysis. Almost 5% of the industrial Hydrogen is produced in this process. Thermolysis is the process where Hydrogen is generated by raising temperature to 2500 degrees Centigrade. There are so many other ways of Water Splitting including biological means. This is basic physics, not even advanced. What Justice Katju claimed recently is total bunk. He could ask a school kid in his nearest school next time about electrolysis if he likes. We doubt if every kid could answer this – thanks to crappy education system in our country.

But what irked yours faithfully is the second case mentioned above. According to Justice Katju, 1 divided by 0 is indeterminate. Even more alarming is the fact that he asks this question, rejects the right answer from the plaintiff as wrong, based on his own weak fundamentals and delivers a judgement. This is a serious issue. More serious than his claim that “90% Indians are fools” just because he thinks one cannot extract Hydrogen from Water.

For the kind attention of Mr. Katju

Yes, Justice Katju is absolutely wrong. He couldnt be more wrong. 1 divided by zero is not indeterminate. It is not indeterminate, it is either undefined or infinity. The poor Mathematics lecturer was given a whip in the face by Justice Katju not because he was wrong but because the honorable judge thought what he was wrong.

Since Justice Katju is such a great Science enthusiast, here goes a very basic, secondary school level explanation. How do you divide any number? Say 6 by 3. 6 pieces can be divided into 3 parts so that each part gets 2 pieces. There is no other way to do it. This is a determinate division. This means when you take all 3 parts and count total number of pieces, you will get 6.

6/3 = 2 because 2 *3 = 6. When these two statements hold together, the division is defined.

This is the basis for quintessential division definition – Dividend = (Divisor*quotient) + Remainder

So, what happens when dividend is 1 and divisor is 0? When dividend is 1 and divisor is zero, remainder becomes 1 and quotient could be any number in the available range. This means, 1/0 is not really indeterminate. It is therefore considered undefined. Calculus, however, shows that it is in fact infinity, at least formally.

From fundamental calculus, a clear explanation exists[4]. Formal Mathematics proclaims that 1 divided by 0 is infinity but a two sided limit doesn’t exist for the expression a/b as b tends to zero, in which case the limit is undefined. However, in either case it cannot be called indeterminate. This is actually one of the very big topics of discussions in many mathematics lecturer/teacher circles while discussing text book updates etc**. This point is also a very important topic in science education. How does a teacher explain a student what fundamentally an undefined division is? It is absolutely necessary to add here that 0 divided by 0 is indeterminate. We won’t go into the mathematical reasoning.

We do hope Justice Katju understands all this. After all, he is a self declared genius in Science, apart from being a celebrated Judge. We do not know if the poor lecturer knew the reasoning mentioned above. Even if he knew, we wouldn’t expect him to scream at the judge that he was right – lest he be held in contempt of court. This is paradox with the judiciary system we have adopted –

You have to swallow what you are given to swallow because the judge is considered an all knowing genius. Of course you can appeal but that means you have to spend time, energy and money because of the eerie sanctimoniousness of the judge.

What rights do Judiciary have to cross the line?

It is most gratifying and welcome that Justice Katju has such deep interest in Science. It is in fact a great motivation for aam admi like yours faithfully that a judge demands proper scientific reasoning. As CJI Kapadia also noted in a recent talk, if Judges learn some of the fundamentals in other branches like accounting etc., they could ask relevant questions in the process of hearing. However, how can judges cross the line like this?

At this point, we would like to inform the reader that Justice Katju is not formally trained in Sciences beyond the primary, secondary, higher secondary and probably under-graduate education. Justice Katju is a doctorate in philosophy and he is also formally trained in Indian Law. Justice Katju by his own admission asked a question and his answer was wrong. Given the honorable position that he was in at the time of questioning, was he morally right to ask such a question? Can we now say in retrospection that his judgement could have been influenced by his wrong understanding of a topic where he didn’t do any formal study?

Judiciary in India must be careful when following Katju’s example. While it would be good if Judges get relevant knowledge, it is of equal importance that Judges do not go overboard about their “areas of interests where they didn’t receive formal training”.

And of course for Justice Katju’s kind attention, 1 divided by 0 is definitely infinity according to formal mathematics. It is however, undefined in many other branches of mathematics. In any case, it is not indeterminate. If it were indeterminate, Calculus would be as different as Mars is compared to the Earth.

**The author’s father is a Mathematics lecturer in an intermediate college in a small town in AP. The author has accounts of several instances of questions like the one Katju posed. In fact, several hours of debate, discussion, referencing in various books, happens at many district level text-book updates generally funded by private publishing agencies. Several questions that come up are not even answered by many foreign educators, in a formal mathematical way. Many times, the educators run for cover and find geometric ways to answer these questions which could only be called temporary solution.

[1] http://www.indianexpress.com/news/the-90/934145/0 “When I said that 90 per cent Indians are fools I spoke an unpleasant truth. The truth is that the minds of 90 per cent Indians are full of casteism, communalism, superstition.”

[2] http://www.indianexpress.com/news/ten-ways-of-being-foolish/940095/0 “Water (H2O) is really burnt hydrogen, it is like ash. You can convert wood into ash by burning it, but how can you convert ash into wood?”

[3] http://www.thehindu.com/todays-paper/tp-opinion/article3852614.ece ” To give an example, when I was a judge of Allahabad High Court I had a case relating to a service matter of a mathematics lecturer in a university in Uttar Pradesh. Since the teacher was present in court I asked him how much one divided by zero is equal to. He replied, “Infinity.” I told him that his answer was incorrect, and it was evident that he was not even fit to be a teacher in an intermediate college. I wondered how had he become a university lecturer (In mathematics it is impermissible to divide by zero. Hence anything divided by zero is known as an indeterminate number, not infinity).”

[4] It is a known fact that “limiting value of any expression a/b, as b tends to zero, when a is not equal to 0, would diverge to infinity since a range of quotients exist for the division”. This is a formal mathematical definition. But of course, this could be proved wrong in Calculus itself. When you take one sided limit, this expression would diverge to infinity on right side where as the it would diverge to “minus infinity” on the left side of the limit. For a two sided limit, this limit doesn’t exist. Therefore, again the expression would be undefined.


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