Featured

Journey to the Himalayas – an elevating experience

Have you ever set foot on a journey to the Himalayas – Alone? or may be with just one companion? Did you ever know that travelling can teach you much more subtle lessons of life than any other school, college or university? ‘Journey to the Himalayas – an elevating experience’ is one such journey..

A coffee table book which is not just a travelogue with lot of beautiful pictures that can tell you how to reach a particular place and what to buy and what not to buy or specifying places of visit. ‘Journey to the Himalayas’ is a book that can spiritually uplift you through the 18-day journey undertaken by two brothers in the wilderness of the Himalayas. The book promises that the reader will be tempted to make an attempt to visit, if not scale, the Himalayas at least once in his lifetime.

Take up the journey…and discover yourself.

For pre-order, contact:
Vinay Nair – vinay@sovm.org or +91 9820 509 484
Follow us on http://www.facebook.com/JourneyToTheHimalayasTheBook
Journey to the Himalayas Cover Final

Algorithm Design Workshop: Day 2 (April 2nd 2017)

images (6)

How would you feel if you were to work on one single Math problem for two hours at a stretch? Most people would never even dare to think about it. The second session of Algorithm Design Workshop saw 9-13 year old kids working on an algorithm and turning it into a flow chart for two hours. I have to admit that what they have discussed and discovered would seem to be a very challenging task for most students of Computer Science. The whole session was about the following (in the order in which the questions were discussed)
1. Why do we have leap years?
2. Why are years like 1700, 1800, 1900 not leap years but 1600 and 2000 are leap years?
3. What is the condition for a year to be a leap year?
4. Write an algorithm (for the computer) to check if the given year is a leap year or not.
5. Among the different possible Algorithms, how do we compare and decide a better Algorithm? (In the terms of Computer Science, how do we calculate the running time of the Algorithm).
6. How can we find an Optimal Algorithm (the best Algorithm)? And why is it the Optimal Algorithm?
7. How do we prove that there cannot be a better Algorithm than the Optimal Algorithm that we have got?

Any Computer Science student from India would agree that in the college curriculum, if a question on writing an algorithm is asked, they would cover at the most points 1-4 where the concept and figuring out an Algorithm would be discussed, but not points 5-7. Whereas, points 5-7 are the most important points a programmer would be (rather, should be) concerned about. It is the speed (running time) of a program that makes a program efficient. And if someone has to check if his Algorithm is the best, he needs tools from Mathematics to prove that there cannot be a better Algorithm than his.

For the readers who are not familiar with Algorithms, here’s what Algorithms are about. It is a step-by-step procedure for executing any task. When a programmer has to write a computer program, he needs to know a programming language and the logical process that will have to be taken into consideration for writing the program. This logical process is the Algorithm which turns into a Computer Program with the help of a Programming Language. Most students are taught programming languages, but rarely are they taught How to Program (how to develop the Algorithm/thought-process behind the program).

Coming back to the class. In one of two batches where we did the above topic, we completed upto point #6 and some students started to come up with answers for point #7. In the other batch, it was almost the same scenario and we discussed another question of finding day of the week for any given date. The objective was not to give out the solution for the problem but to make them think, strive and try to develop an algorithm for getting the result. Some of them got it at the first go while some struggled and still didn’t get it 100% correct. But what they learnt cannot be measured in quantifiable terms. They learnt that learning is not about getting the answer, but the attempt to arrive at getting the answer. They learnt that in the times when everyone wants a quick solution, real learning requires Time, Effort, Patience and Perseverance. And most of all, they learnt to Think.

As they finished one attempt for an Algorithm, they came up to me to check if it is correct. The others patiently waited in a line behind them. For them, the most challenging task was to understand what was wrong in their Algorithm. In fact, when it comes to questions on logic, many a times it is difficult to explain why is a process/solution wrong. But they were willing to think and make corrections in their Algorithm and come back again. This might have gone for about 3-4 times with each student in one of the batches. In the other batch, some students worked in groups and tried to solve the problem.

The​ most difficult task (and the most important one) was to compare two correct Algorithms and decide which one is a better choice. And the question that would concern a Computer Scientist was How to find the best Algorithm and prove that it is the best? To give you a taste, here are a couple of Algorithms that you might want to consider comparing.

Algorithm #1:

Enter a year
Ask the question – Is the year an odd number?
If Yes, then print – Not a Leap Year
Else (if No, then), , ask the question – Is the year divisible by 400?
If Yes, then print – It is a Leap Year
Else, ask the question – Is the year divisible by 4?
If No, then print – Not a Leap Year
If Yes, then ask the question – Is the year a multiple of 100?
If Yes, then print – Not a Leap Year
Else, print – It is a Leap Year

Algorithm #2:
Enter a year
Ask the question – Is the year a multiple of 100?
If Yes, then ask the question – Is the year a multiple of 400?
If Yes, then print – It is a Leap Year
Else, print – Not a Leap Year
If No, then ask the question – Is the year a multiple of 4?
If Yes, then print – It is a Leap Year
Else, print – Not a Leap Year

The running time of an Algorithm can be said to be the number of questions that one needs to attempt ‘at the most’ to arrive at the answer. In the first Algorithm, you can see that if the year is an odd number, we get the result in just one step. But if the year is an even number, it might take three steps (because one might have to go through three questions). So the running time of the Algorithm is 3. Let’s say that the Algorithm is 1-3 where 1 refers to the minimum number of steps and 3 refers to the maximum number of steps. In the second Algorithm, it is 2-2. There were other Algorithms which were 2-3, 3-3, etc. So when it came to the question of choosing a better Algorithm, everyone unanimously agreed that 2-3 and 3-3 are poor choices. But selecting between 2-2 and 1-3 was a tough choice. How do we find out, which one is better? How do we know if there could be a better one? The participants said that an ideal scenario would be 1-1. But there cannot be one single question which can determine if the year is a Leap Year or not (they didn’t get time to prove it in the class though). Using such logic, how do we arrive at the optimal solution and how do we prove that it is the optimal solution? I leave that to you.

For me, the greatest joy was seeing their perseverance in solving one single problem for two hours and the different learning outcomes mentioned above.

Life is about making choices. If this activity might have helped them in a subtle way to decide which is a better choice, I think the objective is fulfilled.

#Mathematics
#AlgorithmDesign
#ComputationalThinking
#FlowChart
#Education
#LeapYear

Algorithm Design Workshop: Day 1 (April 1st 2017)

Algorithm Design Workshop: Day 1 (April 1st 2017)
 
It was a session for 10-13 year old kids that we did in two places – Thane and Borivali. Below is a gist of the experiences of the first day.
 
Since the objective was to get them introduced to Algorithms and Flow Charts, I asked them to make a flow chart where a robot has to check why the baby in the cradle is crying. I said, it could be crying for three reasons:
1. It is hungry
2. It has passed urine or poop
3. It is bored and wants to be taken out of the cradle.
 
The task was to write a flow chart that will enable the robot execute the task if these were the only three reasons that a baby would cry for.
 
The initial challenge was ‘how will the robot check if the baby is hungry’. On that one boy said that if a feeding bottle is kept in its mouth, it will drink from it. Another boy said that the robot will see if the stomach is full or flat.
 
Next task was to know if the baby has passed urine or poop. One participant said that the robot can touch it. I said that the robot doesn’t have a perception of touch. Someone said that the colour of the dress would have changed if urine or poop is passed. I said that that would be one way the robot would know. On that, one fellow jumped and said, the robot cannot touch and know but it can see? How could it hear the baby’s cry in the first place? Why is it that only one sensory perception isn’t working and others are working?
 
I gave some reasons for that but i was amazed by the thinking by the children.
 
In one of the batches, a participant said that the robot can find out if the child has passed or not by checking the weight of the diaper. (This was my favourite answer because weighing is something that can be practically done and checked).
 
The question that i loved the most was…’Sir, you said Computers are dumb because they cannot think on their own and that they need to be taught. So does humans because we also need to be taught. So how are we different from computers?’ I think this was a brilliant question for a 9-year old. In my reply I asked him, ‘Who taught you to talk, walk, cycle, swim?’ Promptly he replied, ‘My mother’. I asked, ‘Did you learn to talk by listening to her or was it like a classroom teaching? How did you get the ability to walk? Who gave you the cycle balance? Was it a discovery by you or were all these taught to you?’ I could see the bewilderment in his eyes and he nodded his head saying he got the answer for this question.
 
Another task was to explain to a person over the phone ‘How to draw a 5-pointed, 7-pointed and 8-pointed star? And this person who is listening doesn’t know what a star is.’ Basically, it was to write an algorithm which can be made into a program to make a star.
 
In the exercises, the children also learn to define concepts. E.g. In one of the tasks was to construct a star. While doing so, some constructed a 5-point star, some 6-pointed and some constructed very different stars which normally we do not think of. Most of them rejected that these different-looking stars to be called as stars. Thus we came to a point where one had to define what is a star. If a 6-pointed star can be constructed using two overlapping triangles, why don’t they accept two overlapping squares as a star? Once a common consensus happened on definition of a star, we came to algorithm to construct a star. Some of the started saying…Join point A to point B …but later realised that we haven’t defined the positions of points A and B. Some said, draw a line diagonally a bit longer …but then they realised that they have not defined what is a ‘diagonal’ and to which direction are they refering to and how long is ‘a bit long’? Through all this, they kept aside all their pre-conceived notion of a star and started defining terms and processes without taking anything for granted.
 
Another example that we discussed was – how to return the discounted amount when we buy something in a combo-offer? The best thing was the students themselves discovered each and everything. All i had to do was to introduce them to how a flow chart is drawn. Rest of the things followed on its own. In fact, a lot of exploration was done on star shapes and Algorithms to draw those stars. I was quite amazed to see three 9-year olds working with full enthusiasm and rigour on the problems. So was on 6-year old (a guinea pig) who was an experimental piece in the workshop.
 
My learning: No topic is boring. It is the examples that can make a topic interesting or boring.
 
While everyone celebrated the FOOL’s Day, we did something more MeaningFUL!
 
#AlgorithmDesign
#Algorithms
#Mathematics
#Education
#SummerCamps
#FlowChart17546775_1462448087119675_3769436404707352928_o

Why study the past when there is so much to do for the future?

There are three types of responses by anyone to any topic – Acceptance, Rejection or Indifference. When we ask the question ‘Why study history?’ all of us would come under either one of these three categories. I’m listing down a few areas and a few thoughts as to why I believe that history has to be dealt more seriously than how it is done today.

Bharata’s Natya Shastra:
Written by Bharata Muni around 200 BCE deals with classical performing arts. In music, percussion instruments and dance, he deals in great detail with the topic of Combinatorics (Permutations and Combinations). He discusses about the rasas (unfortunately, there is no English word for rasa) that arise in a person while watching/listening to Classical art forms and how these rasas affect the mind of a person. In case of dance, he talks in detail about how the facial muscles have to be moved to generate a particular kind of rasa in the audience. It is the best guidebook for those who wish to pursue Classical art forms. Is there a detailed guide book in modern times that goes into the subtle nuances of art forms which will enable an artist to excel in his area?

Ayurveda:
Like any other shastra that originated in India, the goal of Ayurveda too is ‘Self-Realisation’. Ayuh+Veda=Ayurveda. Ayuh is defined as shareera indriya aatma samyogah – when all the three (body, senses and soul) come together, it is called Ayuh. Again, body, senses and soul don’t even come close to the exact definitions of shareera, indriya and aatma. The knowledge (Veda) that can lead one to Self-Realisation when all the three come together is Ayurveda. Ayurveda is not just a science of medicine. Major part of Ayurveda deals with the aspects of how to stay healthy. Follow the prescriptions in it and one will stay healthy. If someone doesn’t follow it well and falls ill, then how to cure their illness is discussed in the remaining part of Ayurveda. It is based on principles like – Kapha, Pitta and Vaata; Satva, Rajas and Tamas, which cannot be defined according to modern-day science. Based on these principles, the science of Ayurveda prescribes how a person can live a healthy life so that he can live a life of righteousness, become prosperous and fulfill his desires and get liberated from sorrows (Dharma, Artha, Kaama and Moksha). Before we put all this in the garage and label it as unscientific or primitive or based on some superstitions, let us look into the work of people like Prof. Thelma who are taking efforts to do experiments based on Ayurveda to see if we can find genes that cause disorders which the modern-day science have been trying to figure out and success seems to be a far away dream. A couple of links for a short read are:
http://genetics.du.ac.in/index.php?page=prof-b-k-thelma
http://www.theindiapost.com/education/gndu/ayurveda-indian-system-medicine-specialty-diagnosis-diseases-prof-thelma/
It would be interesting to compare the definition of health given by WHO recently and Ayurveda millenniums ago.
1. World Health Organization: – “Health is a state of complete physical, mental and social well-being and not merely the absence of disease or infirmity.”
2. Ayurveda – ‘Health is a state where in the Tridosha, Digestive fire, all the body tissues & components, all the physiological processes are in perfect unison and the soul, the sense organs and mind are in a state of total satisfaction (prasanna) & content”

Pedagogy:
Being a Mathematics teacher, I will talk about the issues with Mathematics education. Today, a topic like Combinatorics is dreaded by most students. If we teach them the topic using Music and Poetry as given in texts like Natya shastra, Sangitaratnakara, it will make a lot more sense and make the subject very beautiful (I have tried and tested this since past 4 years). Texts like Lilavati by Bhaskaracharya II give very good pedagogical aspects of how a topic can be taught to students. Learning ancient Indian texts not just give the knowledge but also subtler aspects like pedagogy, ethics, etc.

Logical and Rational Thinking:
One can afford to be illiterate but by being illogical one might have to pay a heavy price. How to use different ways of proving/disproving things? How to evaluate if the given information is correct or not? These are things that people of any profession has to do. Today, there is hardly any course that enables a person to enhance his logical thinking. The millennium old philosophies like Vaisheshika, Nyaya, Vedanta, etc. develop a rational thinking. How? Because all these philosophies have evolved over a period of time through discussions, debates and dialogues. They are not dogmas that were given by one single person for the whole of humanity. This way of learning also allows a person to be liberal in the true sense because he is open to new ideas and ready to change his stance if needed. The fact that there were very many different philosophies that co-existed in India in the past, that itself proves that it has to do something with the religious teachings which allowed them to accept/tolerate/respect people from other belief systems and not try to wipe them off.

Sanskrit:
When we talk about Sanskrit, what is generally missed in the Grammar structure of Sanskrit that Panini gave. Generally people think it is just about the language Sanskrit. But what is fascinating is the robust structure of Sanskrit grammar that Panini gave which can be applied to any language. Panini’s Ashtadhyayi gives the grammar rules that can make any language strong and not just Sanskrit. He uses iterations, recursions, formulae that can generate different words and much much more in a precise text which will not run into more than 50 pages. It for these reasons that it is been studied today by Computer Scientists and Linguists to see how Computer Science can benefit from Sanskrit in creating a better Machine Language.
Above all the other advantages of Sanskrit, what is most important is that the treasure box of knowledge that our ancestors possessed can be unlocked only with Sanskrit. We need to learn Sanskrit for the sake of unlocking the treasure box and taking out the pearls.

To conclude, these are just few areas where India stood in glory in the past. The list is very long and probably endless. It cannot be completed, but this writing has to conclude. Hence resting with only a few subjects where India contributed. There are lot of other areas like Yoga, Meditation, Mathematics, Pure Sciences, Philosophy, Music, Martial arts, Architecture, Engineering, Statecraft, Ethics, where India has contributed to the world.

The study of history is not (and should not) be just confined to taking the pride of a great ancestry but to see how it can be used today to make ourselves as better human beings resulting in a better world. Today the people who accept that Indic studies should be taken more seriously, they themselves should take efforts to study and learn more about Indian history before commenting about something so that they don’t fall prey to false claims. We should also not forget that by learning Indic traditions and culture one can make the future bright.
For those who don’t believe that Indic studies should not be glorified/studied, need to first take an effort to study before they comment. Man is an emotional being that has the capability to think rationally. But by nature, man is not a rational being. Even after we watch a movie that has enthralled us, we would be tempted to share and glorify about the movie. It is very natural. Some of us are not feeling the thrill in the scriptures probably because we have just went through it superficially and the arrogance of a modern-day educated man is not allowing us to accept the fact that we haven’t understood it well. It is not just one philosophy that we have to fit into, there are many which can appeal to our thoughts and we can find a place there.
For those who are indifferent, make an attempt to study Indian scriptures. Try.

#IndicStudies
#WhyStudyIndianScriptures
#WhyStudyHistory
#History

~ Notes from Seminar and Tutorials on Science and Technology in Indic Studies at IISc Bangalore Feb 3-6, 2017

Who discovered Zero?

Who discovered Zero? It is generally believed that Aryabhatta discovered Zero. But truly speaking, he did not. It is a wrong information that has been spread during the course of time for reasons unknown. One may ask how we can say that. It is because in the treatises written by him which is available today, there is no mention of discovery of Zero. Who then discovered Zero?

When we talk about discovery of Zero, we need to think what type of Zero are we referring to. For a layman, he would not be thinking beyond the meaning of Zero as ‘nothing’. But Zero degree Celsius doesn’t mean there is no temperature. Here, Zero is a place holder between positive and negative numbers. This notion of Zero must have come while negative numbers were first discussed by Brahmagupta (7th century Indian Mathematician) who was the first one to discuss about rules for operations with negative integers (12 centuries before the West started discussing about negative integers).

The Babylonians and Greeks had some notion of Zero but that was not the kind of Zero that we use today (refer the two links given at the end of this article). It was Pingala (300 BCE) the author of Chandass Shastra (one of the 6 Vedangas) who used Zero as a symbol for the first time in History. Pingala was also the originator of Binary Mathematics (Ref: ‘History of Mathematics in India from Vedic Period to Modern Times‘ online course on NPTEL, lecture on Pingala by Prof. M.D.Srinivas, Institute of Policy Studies). Pingala also dealt with Permutations and Combinations (2 millenniums before it was discussed in the West). It is very clear that for discussing such areas of Mathematics the knowledge of Zero is very important.

In other civilisations during the period of Pingala, Mathematics was not that advanced and they could manage without Zero. In fact, due to the lack of knowledge of Zero, they lagged behind in Mathematics.

So who discovered Zero? The answer is ‘we don’t know’. Looking at the kind of Mathematics that was dealt in India during the BCE period, it can be said that the use of Zero as not just a symbol, but as place holder and a symbol for nothing should have happened in India. But as Indians weren’t interested in accrediting their names to discoveries, it is not known who discovered Zero. As a matter of historical evidence, all that can be said is that it is in Pingala’s Chandass Shastra that we find the appearance of Zero as a symbol (as a digit) for the first time. In other civilisations, till that time zero was used only for absence of something. The development of decimal place value system should have developed somewhere between the period of Pingala (300 BCE) and Aryabhatta -1 (5th Cent CE) because by the time of Aryabhatta the decimal place value system was very much in use.

(Some interesting reads can be http://yaleglobal.yale.edu/about/zero.jsp

https://en.m.wikipedia.org/wiki/0_(number)

NPTEL Course on History of Indian Mathematics https://www.youtube.com/watch?v=p2WankcGP3Q&list=PLbMVogVj5nJThf31TNSQzuN7zqxe7HdRN)

6 different means of knowledge explained in Vedanta

6 different means of knowledge explained in Vedanta

~ (Understandings from the Webinar series of Chinmaya International Foundation on Panchadasi)

Vedanta gives 6 different means by which knowledge is gained.

  1. Pratyaksha – Direct perception. Things that we directly perceive come under pratyaksha. E.g. Things we see, hear, taste, touch, feel or even the thoughts because we directly perceive them in our mind.
  2. Anumaana – Inference. Even though we might not see fire, from smoke we infer that there is fire. This type of gaining knowledge through inference is called Anumaana.
  3. Upamaana – Knowledge gained through similarity. E.g. A person is going to a forest. His friend warns him that there are bisons in the forest. If you see one, immediately run away. But this person has not seen a bison. So his friend explains to him that it is huge and looks like a cow. Now when the person goes to the forest and he see a similar creature, he understands that it’s a bison. Even though he has not seen a bison before (pratyaksha) nor has he inferred this knowledge (through anumaana), he has gained the knowledge through similarity, and this process is called Upamaana.
  4. Arthaapatti – Postulation. E.g. Devadatta is a fat healthy person. But no one has seen Devadatta eating during day time. So one can infer that he would be eating at night definitely otherwise he cannot stay so healthy without eating at all. Here, one postulates to explain what one has cognised. This method of knowledge is called Arthaapatti.
  5. Anupalabdhi – Non-comprehension. E.g. Someone asks a person to checck if Devadatta is there in the hall. He goes, checks and finds outs that Devadatta is not there. He comes back to say that Devadatta is not there. In this case, he has not seen Devadatta, but he has gained the knowledge that Devadatta is not there because of the absence. This process is called Anupalabdhi.
  6. Shabda – a trustworthy word/source. We know that the Alps and Andes exist even though all of us have not gone to there. That is because we have learnt about it through our geography textbooks. Such type of gaining knowledge through a trustworthy source is called Shabda.

There is nothing in this world that cannot be cognised by any of the above six. Any type of knowledge gained will come under one or more of the above categories.

How to argue and win?

An interesting profound discussion between a Vedantin and a Naiyyayika (follower of Nyaya philosophy).

Caution: Read only if you are willing to rattle your brains on logic.

In the 50th verse of Panchadasi, a Naiyyayika (follower of Nyaya philosophy) asks the propounder of the text who is a Vedantin (follower of Vedanta philosophy), that how can words (Mahavakyas like ‘Tat Tvam Asi’) indicate the Supreme Reality (as the Vedantin is claiming), because words have properties (JAti, GuNa, desha, KAla) and properties cannot indicate the Supreme Reality (as claimed by the Naiyyayika) for two reasons:

1. The Vedantin is saying that Supreme Reality is beyond name, forms and any other property. How can words (which always have properties) indicate something which does not have a property?
2. Because of point #1 one would be forced to conclude that the wordings of the Mahavakyas can only indicate something which does have a property. This means that the Supreme Reality is something which does have a property. This is again contradictory to what the Vedantin had earlier proposed (that the Supreme Reality is beyond name, form and other property).
Hence the Naiyyayika tries to establish that the words of the Mahavakyas cannot indicate the Supreme Reality.

This question is countered by the Vedantin. Since the question comes under the Vitanda way of argument (refer to my earlier post on three types of arguments), the Vedantin chooses to apply the ‘UShTra laguda nyAya’ which is to beat the opponent using the points from his own argument.

The Vedantin says, “Oh opponent, you say about properties and since you are a specialist in properties, before we discuss whether Mahavakyas can indicate the Supreme Reality or not, let us discuss what is the substratum of these ‘properties’…on what do they stand?” He continues, “There are two possibilities. Either the properties can come from something which has does not have a property or from something which has a property. Let us discuss on that case by case.”

Case #1: Assuming that properties come from something that does not have a property – This is would be self contradictory because something cannot come from nothing.
Case #2: Assuming that properties come from something that does have a property. Here we come across four different contradictions (doShAs)

Case #2.1: Contradiction of Self-dependence: – If the substratum of property A is dependent on property B, then there are two possibilities. Either A and B are same or A and B are different.
Case #2.1.1: If A and B are same, then it means B is the substratum of A and A is the substratum of B. How can B be the locus of A if A is the locus of B? How can A stand on something (B) where that (B) itself is standing on A? E.g. If we say, what is the substratum of an apple (A). The substratum would be some base (B). How can the base (B) be the substratum (on which it stands) be the same as the apple (A)? So this is contradictory. Hence there is a contradiction of Self-Dependence. Hence we are forced to assume that A and B should be different which leads to Case #2.2.
Case #2.2: Contradiction of Mutual-dependence: – If A and B are different, and if the substratum of property A is dependent on property B, and the substratum of property of B is dependent on property C, then there are two possibilities. Either C and A are same or C and A are different.
Case #2.2.1: If C and A are same, then it means that the substratum of B is A because in #2.2 we have assumed that the substratum of B is C and here we are considering C=A. In this case, it would mean that A is the substratum of B and B is the substratum of A which is contradictory by mutual-dependence because we cannot say that the substratum of the Apple is the Base and the substratum of the Base is the apple. Hence we are forced to believe that C and A are different which leads to Case #2.2.2
Case #2.2.2: Contradiction by Cyclic-dependence: – If we assume that C and A are different, and that the substratum of A is B and substratum of B is C, then the substratum of C should be something like D. Here again we have two possibilities. Either D and A are same or D and A are different.
Case #2.2.2.1: If D and A are same, then it means that C=A because in Case #2.2.2 we considered B as the substratum of A, C as the substratum of B, and D as the substratum of C which is contradictory because the dependence of A, B & C will be cyclic. How can the substratum of an Apple be a Base whose substratum is (let us say) a Chair whose substratum is again the Apple? This we are forced to believe that the D and A are different which would lead to Case #2.2.2.2.
Case #2.2.2.2: If D and A are different and the substratum of A is B, substratum of B is C, substratum of C is D, then the substratum of D should be some property E. Again there can be two possibilities. Either E and A are same or E and A are different. If E and A would be same, then it would mean that D=A (by the logic of cyclic-dependence). Else, E and A would be different. If they are different, then the substratum of E should be property F. This will go on infinitely. Hence we have a case of the fourth contradiction – Contradiction by Infinite Regression.

The Vedantin now asks, “Oh opponent Naiyyayika, please tell me, what is the substratum of a property? We have proved that the substratum cannot be something which does not have a property nor can it be something that does have a property. So before you argue that Mahavakyas cannot indicate the Supreme Reality because It is property-less, first tell me where does your ‘property’ come from? What is its substratum?”

Thus, using UShTra laguda nyAya, the Vedantin has muted the opponent.

This depth of this entire argument is covered in just one verse. One can only be left with awe on how deep and subtle the philosophical arguments explained in our scriptures like Panchadasi are!

‪#‎Panchadasi‬

Three types of arguments

There are three types of arguments explained in Hindu philosophy – Vaada, Jalpa, Vitanda

1. Vaada – When two or more people are arguing about a topic and the objective of the argument is to get clarity over the topic and arrive at a proper conclusion, it is called Vaada. A person engaged in Vaada doesn’t have a pre-conceived notion. For the same reason, the argument is not to prove his point right, but to arrive at the Truth.

2. Jalpa – When two or more people are arguing to prove their point is right and that the other person(s) is/are wrong, it is called Jalpa. Here, the person is already convinced that he is correct and the other person is wrong. So the whole argument is an attempt to win by proving the other person(s) wrong. Needless to say, there is a pre-conceived notion in the mind.

3. Vitanda – When the purpose of argument is only to prove that the other person is wrong and the opponent who places the argument doesn’t have any specific stand of his own, it is called Vitanda. If we ask a person whose argument is like Vitanda on his opinion is about the right thing, he would say that he doesn’t have an opinion (or rather, he is not bothered about it) but he knows that the other person is wrong.

These are some understanding from our weekly Webinar sessions on Panchadasi conducted by Chinmaya International Foundation.

During any argument if we are not in the state of Vaada, it is better not to argue.

‪#‎panchadasi‬