Tower of Brahma

                                                                        Tower of Brahma

The Tower of Brahma (also called the Tower of Hanoi, indeed it is more widely known by this name, I’d imagine) is a puzzle that also offers a teaching/learning moment in schools and to first year engineering students (most puzzles do, and I am taking this as an example). 

Three circular discs with a hole at the centre are stacked on a pole per increasing diameter top down (smaller at the top, if anyone has any doubts). There is also a set of three poles and the discs can slide down the poles. Let us call the pole on which the discs are stacked on the “original” pole (How original, eh?), in the figure above, the left most. 

The task is to move all the three discs from the “original” to any one of the other two poles, on the condition that at no time a larger disc can be on top of a smaller disc. What is the minimum number of moves needed to achiever the target? I am not giving the solution as it is well known.

Have our students learned anything beyond solving this puzzle? I seriously doubt that.

Just suppose one student asks herself, “OK, I have solved this puzzle, it is so simple. The answer I get cannot be any smaller, as any move at any step besides the one I made will violate the condition. Hence, I am right. Voila!” 

But, as studious as she is, “What if there are four discs?” she asks. Not one to ask for help, she follows all the rules and gets the correct sequence of the moves with the appropriate disc. In fact she sees that, after getting three discs in order, she has to move the fourth disc and go through one more stacking of three disks. That is, shifting three discs directly indicates the number of moves involving four discs. None of the three discs on the move are smaller than the fourth. “I am OK!” 

The fifth comes along, and she knows that she is on the right rack and does not do the shifting and gives the response immediately!

The student is better than smart, she is brilliant. She decides to check whether she can do the same with the reverse order of discs, with the appropriately changed condition, a smaller disc cannot be placed on a bigger disc; it has to be the other way, after all from the original puzzle. She learns one more thing: to test whether something is equivalent to some other thing, one has to accommodate ALL the rules and regulations in both the cases.

Just one puzzle enabled the student to learn so much!

Obviously Lord Brahma thought of that as after creating all the beings and their souls. He had time one hand. While Yahweh rests on the seventh day, Brahma indulges Himself playing this game/puzzle! We are so superior, of course!

Raghuram Ekambaram

How do You See Temba Bavuma?

                                                                   How do You See Temba Bavuma?

Oh, you do not see Temba Bavuma at all? There is a reason for my seeing him the way I do.

I see him as 4 cm taller than I was at my tallest (I have been through an accident in which my spinal discs got compressed; besides, just about everyone loses height as they get to 60 years in age and go beyond; I am 71 now).

But some see him as yet another token black on the South African cricket team. Bavuma’sbatting average is nothing to write home about. In the same breath I would mention he captained his nation’s cricket team to win the ICC World Test Championship. South Africa’s cricket team now onwards cannot be called “Chokers”. That has to count for something He had the nous. That too counts. A captain is a captain and a winning captain is perched a step above. That is really how I see Temba Bavuma.

Raghuram Ekambaram

P. S. The above was written before South African victory over India in the match on November 16, 2025, two days ago. I posted it at 2:20 PM. I am now reposting the material with hardly any change as I had inadvertently deleted that blog post. I retyped (as distinct from rewrote) the post from material I had in .pdf with hardly any changes, like the name of the Championship South Africa won beating Australia, and the opening two sentences.

Raghuram Ekambaram

P. S. 2 I am giving below an article profiling Bavuma two days after South Africa’s victory in The Hindu of 2025-11-18, that is two days later. Don’t tell me that I am patting myself on my back, though that is precisely what I am doing. The newspaper piece has some details that would have been available to him to which neither had I access nor was I interested in them. 

 

Raghuram Ekambaram  

Postmodernism and ‘I’

                                                                        Postmodernism and ‘I’

No, this is not going to be any highfaluting piece on who is ‘I’, whether the ‘I’ changes and do you recognize those changing ‘I’s, if not who else does and whether they have any standing in this matter.

When someone, anyone, asks you, “Who are you?” the instinctive and the almost universal response is, “I am _______,” the blank filled by your name. This name is not given to you by you yourself, you would agree. Yet, postmodernism−yes, these are the times of postmodernism−subjectivity rules and you are the subject and your name should be the most meaningful to you! So, you should name yourself. This should be your choice, and as your personality, your thoughts, indeed anything that connected with you (like how you see and perceive the others, the objects that you encounter) changes and accordingly your views of them change, you are never “YOU”, except at every instant!

Hence, your fundamental freedom must be to have no fetters if and when you wish to change your name, which after all was given to you by your parents. I do not mean to say that you ought to keep changing your name; only that you ought to have the most fundamental freedom to change your name whenever you wish. If society becomes confusing, then that is postmodernism! So be it!

One last thing: postmodernism is accused of being nothing but relativism. Yes and No. Yes, it is relativism but not relative to others but relative to oneself at different slices of time, the slicing is at your own convenience!

Raghuram Ekambaram    

 

The First Three Statements I Write on the Board in the Classes I Taught

                                     The First Three Statements I Write on the Board in the Classes I Taught

1. In this class, you’ll learn how to learn

2. In this class, you will learn by yourself.

3. In this class, you will learn by asking questions; I take the responsibility to comlpete the syllabus and there would be no hurried teaching.

Intermittently I ask the students when and how I have deviated from any in the above list; that, I consider a meaningful feedback.

The first in the list is arrogance personified, and I stand by it.

Raghuram Ekambaram

One of the Sources of the Woes of Traffic on Indian Roads

                                            One of the Sources of the Woes of Traffic on Indian Roads

There must be many, but the one that comes to my mind is what the policeman told me when I passed the driving test in Lexington, KY, USA.

“Remember, now you have a killing machine under your control.” 

What is given above is a verbatim reproduction and the reason I recall it is because I used the same statement to every single friend I helped to learn driving when he/she got their license. Tell me, how many Indian parents/friends/driving school staff instil this sense of, not fear but concern for the other users of the road, in the minds of the learners.

Zero. 

I am all in on this, if anyone wished for a wager.

Raghuram Ekambaram  

Disaster Response Now and Then

 Disaster Response Now and Then

Recently I read an opinion piece in the newspaper and annotated it extensively. I am offering it below in case you have not read it.

While I appreciated the information content in it, I definitely did not agree with the tone of a part of one sentence: “Digital dashboard, predictive analysis, drone surveillance, and GIS tools replaced traditional paperwork and panic-driven coordination,” talking about things available today and those that could not have been available 30 years ago, and “[T]raditional paperwork and panic-driven coordination” were the only ways to get the job done then. 

The above asynchronous sentence of the writer disrespects−yes that is precisely the meaning I ascribe to the phrase, “...replaced traditional paperwork and panic-driven coordination.” The writer, had he been old enough, say, 70 years plus, (I am assuming things I have no right to, but which carry much weight in this write-up), would have remembered how people survived disasters doing only “traditional paperwork” and could coordinate with one another only in a “panic-driven” mode.  

It is OK to highlight how things have improved but is NOT OK to put down how things were done in the past, in the absence of technologies available today. I wrote code in FORTRAN in the 1970s and ‘80s, and now even coders do not know what kind of an animal it was (as extinct as a dinosaur).

Raghuram Ekambaram

But, He Did Die!

                                                                         But, He Did Die!

One of the lines in Spectre has James Bond saying, “But, it did stop,” talking about a fictional meteorite Kartenhoff. Taking the above line to the next movie in the franchise, No Time to Die, I am not ashamed to admit that I did not understand the title. Did it mean that it was not the time for Bond to die, or that Bond had more life in him? To my mind, it was a contest between life and time!

When I saw the latest offering and saw it end with Bond dying, I breathed a sigh of relief. Don’t get me wrong, I enjoyed every one of the movies, maybe 26? But, maybe a year or more later I read the dispiriting news that the next Bond actor has been chosen.

I wanted James Bond dead. He shall not continue after I am dead, whenever that may be! He is dead now, before my eyes, and let him stay that way; permanently dead.

Raghuram Ekambaram

What if God Had Stopped at, “Thou Shalt Have No Gods!”

                                            What if God Had Stopped at, “Thou Shalt Have No Gods!”

That is, if Yahweh had to rush to somewhere before adding, “Before Me”. But, that did not happen and we have wars and no peace.

What this post dwells on is the counterfactual. God, Yahweh was an egoist, an egotist, and vengeful. Jupiter of Greek mythology is said to have been power mongering and wedded to exercising authority.

What would have happened had Jesus not have pleaded with God, about those who crucified Him? “Forgive them, Father, for they know not what they do.” Yahweh would have been satisfied, a la “Mugambo kush hua!” 

It is not impossible, or even improbable, that Mohammed had not raised such pleas. Yet, at least some of his followers have brushed under the carpet such pleas. The Buddha was distinctly different. He asked each in his gatherings work within himself/herself! You wish to take revenge? Go ahead! Then, see whether you can live with that thought.

What about the Hinduism, not the religion, but ostensibly promoting a way of life where violence is not to be forgone? There are only a few instances in the vast literature of Hinduism exhibiting any serious forgiveness.

If you take the whole of Hindu scriptures, including the Puranas and the Ithihasas, you would be hard pressed to locate non-violent developments. An example, King Dasharatha was forced to marry every year to escape death at the hands of Lord Parashurama, an incarnation of Lord Vishnu!  

In the very old movie Sampoorna Ramayanam,  Lord Ram lets the demon Ravan go back to his palace, recoup and come back the next day – the song “Indru poi naallai vaaraai ene” so beautifully rendered by C S Jayaraman. Only a temporary relief to the eventually vanquished. All such magnanimity is only till such time the Lord’s patience is stretched to the limit. 

Lord Krishna waited for repeated insults by Sisubalan before the threshold was crossed. In Vamana Avtar where the vanquished enjoys repeated, annually, but limited relief. Of course, Lord Shiva is vengeance itself! Yes, in citing from the traditions of Hinduism, none can stop at one instance.

Sikhism began with the lofty ideal of eliminating irrationality in the spiritual life−which, by itself, is irrational; but let that pass−of people. Yet, it descended rapidly towards war against the Muslim invasions during Mughal rule. Of course, Muslims themselves became violent. 

Mohammed’s body might not have even gotten cold, when Islam split into two sects (less than half-a-century, if I remember my history lessons right), warring against each other. 

If you go back to the Book of Genesis of the Old Testament, you would realize how the House of Jacob, also known as Israel, came about. Indeed, the whole of the Old Testament is a series of violence.

In Srilanka, Buddhism is the religion of the state. The Buddha eschewed violence and never preached to settle issues through fights. Yet, Srilanka is a nation of internal violence of a very high order. The government and the rebels engaged only in violence. The irony cannot be any more vivid. Violence by the settlers in America against the natives takes one’s breath away. It is very easy to go on and on as there are nearly 200 nations. The permutations and combinations are so vast that military power cannot but go on increasing; the Military-Industrial Complex that the American President Dwight Eisenhower lamented.  

Therefore, if you went through history, you would not find any instance in which religion had not played a critical part in peaceful settlement of disagreements, however intense they may have been, and against negotiating peace. Violence is useful to religion and vice versa.

One should look at killing two birds with one stone.

Raghuram Ekambaram

P. S. This write-up was more than half finished before I limited myself to short posts. 

Imported Ideas – Unsuitable for India

                                                             Imported Ideas – Unsuitable for India

The following post is a criticism of a particular statement a judge of the Supreme Court of India as reported in a newspaper item (see the news item below).

‘[M]any environmental law principles imported from the West such as “inter-generational equity” are anthropocentric ...” 

My question to the learned judge is whethernon-environmental/non-ecological laws and ideas imported from Bharat of the remote past (if they indeed have any!) that did not treat humanity as a whole are applicable to humanity and other living beings of India of the present?

Secular aspects of Varnashrama Dharma.

Raghuram Ekambaram

Differences in Sanskrit Pronunciation

                                                                Differences in Sanskrit Pronunciation

There was a time when I could locate wherefrom, at least from which state and/or what her mother tongue is, like Marathi, Thamizh, Bengali, Telugu, from the way they spoke in English. I am not going to give examples as the time I am talking about is nearly five decades ago.

If English pronunciation gave us such a clue shouldn’t Sanskrit do likewise as, some say, the language is at least 11,000 years old.

Something for the others to think about.

Raghuram Ekambaram  

Do the Sun, the Moon and the Planets Know the Day of the Week it is on the Earth?

Do the Sun, the Moon and the Planets Know the Day of the Week it is on the Earth?

Christians take the day off on Sundays; Jews do the same on Satur[n]days; Muslims, on Fri[Venus]day; some sects of Hindus, also on the same day, not off, but special rituals for Goddess Lakshmi, and also on Mo[o]nday for Lord Shiva, Thurs[Guru]/Thor/Jupiter]day, Tues[Lord Hanuman]day, Wednes[Lord Vishnu]day, Satur[Lord Saneeswaran]day, Sun[thestar, leading them all]day.

There is one more non-planets, Rahu that dominates, for 90 minutes, everyday.  The other non-planet Ketu works with Rahu to bring about solar and lunar eclipses some years at certain regions of the earth.

Do the star Sun, satellite of the earth, the Moon, and five other planets, along with the non-planets, know that they are doing so?

Raghuram Ekambaram  

A Wolf in Tiruchanur and on Our TV in Our House!

 A Wolf in Tiruchanur and onOur TV in Our House!

The above TV video grab may look like a any other animal, including a dog of a particular breed (perhas the closest cousin of a wolf) but to me, this was a wolf, pure and simple!

Raghuram Ekambaram

Did Arjuna Understand Bhagawad Gita?

Did Arjuna Understand Bhagawad Gita?

I contend that Arjuna could not have learnt Sanskrit as he is of the warrior caste (Kshatriya). Sanskrit is the language of the Devas and only Brahmins can have access to it. Anyone else who even hears Sanskrit verses is to be subjected to unspeakable torture, as spoken in Manusmriti. 

Hence, Arjuna could not have known Sanskrit, and he could not have understood what Lord Krishna told him, as given in the Bhagwad Gita.  Q.E.D

Raghuram Ekambaram

 

Indian Mathematicians of Centuries Ago

Indian Mathematicians of Centuries Ago

 As continuation of, "We've done this, that and that too before anyone else," I wonder where the forerunner of calculus is hiding? I am hoping that someone will direct me to the source of calculus in Vedic Mathematics.

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Raghuram Ekambaram