The atheist debate

January 4, 2015

Debating the existence of God and the relevance of religion is the doorstep to understanding the role of imagination in reality. Imagination is a tool of dynamics of reality- Imagination, shaped by the past of reality, shapes the future of reality. It evolves reality in time.

To explain the above statement with an example, consider a chess game. The board, the pieces and the players are real. The game setup and rules are imaginary. In the imagination, the board is a war-field, each piece is a certain type of warrior, and so on. The future of reality, i.e,  the next move to be made by the players is entirely guided by this imagination.

The sense of loss or win is also determined by the imagination. Losing a pawn is a much smaller loss than losing the queen- although in reality, they are both just pieces of plastic or wood.

God is an imaginary entity. So are the rules of religion and the associated wins and losses, rights and wrongs. In what way does it impact the reality? What is the magnitude of this impact? Is it possible for a civilization to exist without religion?

A civilization without a religion is likely to collapse internally or remain primitive. We could have seen why is this true, if we had a chance to watch the formation of a civilization, and observe how they came up with God and religion.  We can do so, but such an experiment will take several thousands of years, and so, it better be a thought experiment. :D

A thought experiment

Let us choose an inhabitable, but uninhabited island, far off from the rest of the world as the site of our experiment. Let us then initiate a civilization, with young children. For a few generations, we have to silently protect them, making sure that they survive safe. Later on, we can cut off all contacts with that island. A a few generations later, the people in the island will forget about us, and it will grow just like any natural civilization; no civilization remembers a time when they didn’t have a language of communication and a system of documentation. They will eventually find us, after they invent ships and start sailing, but this will take a very long time.

We can observe how the civilization develops, from a remote sensing satellite.  Of course, this will take several generations of observation in reality, and that is the reason why this is a thought experiment.

This setting can be used to analyze many things. Our question here is of relevance of religion and God: Will the civilization in the island necessarily develop a religion and a God?  Let us refer to our history. We know of a large number of civilizations that existed sometime in the past, somewhere in the world. How many of these didn’t have a god or a religion? Turns out, most of the known civilizations have a religion and god(s), with extremely sparse exceptions. Pirahã people is one such example. They don’t believe in any deity, but they do believe in spirits. However, they are not an independently grown civilization; they are a subtribe of a bigger tribe. So, this doesn’t really tell us how to evolve the civilization in our island without a religion.

Does this mean that no civilization can exist without religion and God? There are two possibilities: One, religion is a part of the growth of a civilization, or two, all those civilizations that didn’t develop a religion collapsed too soon to leave any footprints of their existence, and so we don’t know about them. Perhaps, they collapsed because of not having a religion.

For one thing, the civilization in our island should say something about death; something nice like, dead people become stars in the sky, or they become spirits or, they go to heaven/hell. Otherwise, the civilization will collapse internally. People are glued in to a society by an emotional attachment(relation, friends,, etc). This attachment also has a bad facet – it causes anguish, particularly over death, which is certain. If it is not dissipated, it can potentially crush the civilization. So, a strong civilization needs a strong attachment and a robust way of dissipating destructive emotions. Evidently, rituals associated with death and afterlife are a big chapter in every religion.

Moving ahead, the most prominent feature of a religion is, it creates God, as a protector of all :D. Is it really necessary to have an imaginary protector? Will the civilization in our island develop such an imaginary protector?. Well, if it doesn’t, it will never explore outside the island, and so, it will make a very slow progress in science!. Let us see why:

A civilization will attach value to life of a person(and many more things), not only that a person values his own life, but also, others value his life. Any prospect of loss of life will therefore induce an emotion called fear. It prevents the civilization from exploring too far away from their safe home. An imagination of a protector, can create a counter emotion to fear and therefore make it possible to explore. Knowing that this protector is not real does not alter anything!; Imagination can create real emotions.  One example where this method of evading fear is employed is, explorations in the ocean. Sailors are known to be superstitious, in order to evade the fear due to risks in their sailing. (Sailor’s superstitions. Why aren’t there similar superstitions with today’s astronauts? This has a simple answer  :D ). Therefore, the people in our island may never find us, if they don’t imagine a protector!

Exploration is the key for scientific progress. Scientific progress is not a process carried out by scientists alone. It is carried out by the entire society. Scientists need a strong support from all sections of the society. As an example, let us consider the big revolution brought by Newton’s laws of motion(they partly caused the industrial revolution). What does it take for the civilization in our island to make this breakthrough?. It takes three things, in order of decreasing importance:

  1. A thorough documented knowledge of the objects in the sky. This is accumulated by a thousand years of night sky observers
  2.  A thorough knowledge of the surface of the earth, and how the sky looks when viewed from different locations on the earth. This is gathered by exploratory sailors.
  3.  A genius like Isaac Newton

The people in our island will never get to this without being able to explore. As paradoxical as it is, science has gained a  little from some superstitions too!. :P

So, the civilization in our island should have a method of dissipating destructive emotions, in particular, it should have something nice to say about death. And it should also have a protector(or a means to evade fear). Do these two complete a religion? I don’t think so. I have considered only those aspects that affect the stability and growth of the civilization. Religion also has another kind of value that is shared by the arts- music, dance, stories etc. In societies where religion is strong, it appears to influence the way people think(something I don’t understand). That is a subject of another blog post. I will conclude now by saying, man created God, and then God created man!. 

The Seeds of Mathematics

November 23, 2015

Mathematics is an introspective science, as opposed to experimental sciences(Physics, Chemistry etc). Unlike experimental sciences, progress in mathematics doesn’t require getting data from deep sky, probing into an atom or colliding elementary particles at high speeds. Numbers and other concepts are in our head and all open problems are in our head. This suggests a possibility, that even if we locked ourselves in a cave, cutting off all communications with the nature, we may still be able to continue our progress in mathematics. The subject of this blog post is to examine if  this is really possible.

The converse of this question has a clear answer: Halting mathematical progress would halt progress in all experimental sciences. Mathematics develops ways of thinking, that are employed in understanding the nature. It appears that mathematics is on its own; it doesn’t depend on any of the other sciences. It can continue progressing without any other sciences. This view is expressed in this xkcd comic. But I am going to contradict this view (and I am going to contradict other aspects of that cartoon in my next blog post :D).

Although it is not apparent, progress in mathematics requires us to experimentally probe into nature. The ideas involved in mathematical research are seeded by our experimental probes. Exploration of nature is a key not only to develop physical sciences, but also to develop mathematics, although it is a purely logical subject. A problem is deemed solved, only after a logically consistent solution is found. However, the question “what is an interesting problem to solve?” doesn’t quite have a logical answer.  G. H. Hardy has described  this question to be akin to asking where do poets, writers and other artists get ideas for their work. Conceiving new problems is a work of imagination. And imagination is always seeded by reality.

The classic example for an interesting problem is the one that led to Fermat’s last theorem: ‘are there integers a, b and c such that an+b= cn for some integer n?’. Surely, the complete answer to this problem was profoundly useful, only because large number of people worked on it and it developed a great deal of understanding of numbers. However, the problem was presumably seeded by the Pythagoras theorem. We have integers, like (3,4,5) such that 32+42=52, so  a curious question like ‘what if we change the exponent to a number other than 2?’, would have been the origin of Fermat’s last theorem.

Another question in mathematical research that doesn’t have a logical answer is “what set of axioms should we choose?”. Axioms, like problems, are chosen by taking a cue from previous mathematical theories. The resulting structural similarity between different mathematical theories has been capitalized in a theory called category theory.

Where do these ‘previous mathematical theories’ get their axioms and problems from? There must be a starting point, a seed for every mathematical idea. These seeds come from outside- from our interaction with nature. Cutting off interaction with nature will cut off the supply of new seeds. But that doesn’t entirely stop mathematical progress; instead, ideas for new mathematical theories will be entirely dependent on the old mathematical theories. Over a timescale of several hundred years, this is a significant setback to mathematical progress. Seeding of mathematics by interaction with nature is a slow process. In fact, we are still benefiting from the seeds of Pythagoras theorem.

The seeds of Pythagoras theorem

‘Geometry’ stands for measurement of the earth. ‘Earth’ here doesn’t mean the planet earth or the globe; it means land; real estate. Geometrical ideas were developed as a result of extensive measurement of land, during early human settlements. The most influential of these was the Pythagoras theorem. Let me go through its development, in its three chronological stages: the content, the statement and the proof, to identify its seeds.

Given two sides of a right triangle, knowing how to calculate the third side is the essential content of Pythagoras theorem. This may be done using a formula, or using tabulated data or using similarity of triangles. All these methods carry the basic wisdom– “the third side of a right triangle is not an independent variable”. Any civilization that built large planned settlements knew the content of Pythagoras theorem.

Explicit statements probably came several thousand years after the content. Early statements of Pythagoras theorem were in terms of areas. There are records of statements in Babylonian scriptures(2000 BC), in the Vedas(Shulva Sutras, 800 BC) and Chinese scriptures. An explicit statement  could’t have brought any change in the applicability. Perhaps, the room/house in which the statements were written was constructed using the content of Pythagoras theorem :D. However, it brought big changes in theory. Geometrical shapes were understood by cutting them into triangles. Triangles were now understood by cutting them in to right triangles. Right triangles took precedence over other triangles, leading to a new branch- Trigonometry.

A partial proof was recorded in 800 BC(Shulva Sutras) and a complete proof in 500 BC(Pythagoras). Presumably, there were unrecorded proofs prior to this. There are some theories that Pythagoreans might have been communicating with Chinese schools of mathematics. The proof was seeded by two pieces of intuition, which were developed when planning settlements. One is that land can be measured in areas, which can be added and subtracted by joining and cutting pieces of land. The second is scaling; a big piece of land can be scaled down and represented on paper or a flat stone. All proofs of the Pythagoras theorem are based on areas of triangles or scaling of small triangles to big ones(A book, The Pythagorean Proposition lists 370 proofs). Scaling is in fact a logical implication of the properties of areas. But it is likely that it was developed independently.

The proof, of course, had no practical implications. Proofs generally store methods of thinking. Even today we feel its impact on our thinking. The proof raised the status of the mere formula, ‘a2 + b2=c2′ to a theorem, resulting in the discovery of irrational numbers. Furthermore, it redefined the whole of geometry in terms of a single quantity- the distance between two points. The more advanced forms of geometry- Riemannian geometry and even Differential geometry contain the germs of Pythagorean distance.

The Pythagoras theorem and all of its intellectual impact on Mathematics are seeded by man’s physical exploration in to measuring land. A writer, within his lifetime travels extensively to gain experiences of reality that can seed his imagination. Mathematics is also seeded by explorations of real world, but this seeding has a longer timescale, much longer than a mathematician’s lifetime.


Action and Expression

June 23, 2014

Why should I be rational?- Part III

<< Part-I, << Part -II

Imagine, there is table in front of you. You placed sugar at one end of the table, honey at the other end and an ant at the center. The ant can make its personal choice of whether to go for sugar or for honey.

Suppose, in addition, the ant has moods- three possible moods- happy, sad and neutral. It’s mood changes randomly between these three at irregular intervals. Like we have an urge to express our feelings, let us assume that this ant too has an urge to express its mood. It has no means of verbal communication to do so; but there is still a way: It is walking towards its choice, honey/sugar. When it feels happy, it stops where ever it is, and takes a few steps towards the honey. When it feels sad, it stops and takes a few steps towards the sugar. When it is neutral, it has nothing to express; it continues walking towards its choice. This is a way to using the walking as a channel of communication to express its mood- just because it has an urge to do so.

Now, as an observer, you don’t know the ants choice- sugar or honey. Neither do you know of its changing moods. There no way to find out the ant’s choice or its mood just by watching it. If at some point, the ant is moving towards the honey, it could either be an action: i.e., it has chosen to get the honey or, it could be an expression of its mood.

So far we have assumed that the ant itself knows which of its movement is an action and which is expression. If it didn’t consciously know, and it tried to judge from its own motion, it would be impossible to do so. The ant doesn’t know what it wants!.
This is an analogy I used to define action and expression. We too use every available channel to express what we feel. And, like the ant, sometimes we ourselves are unable to identify an expression or an action.

This urge to express is one reason behind non trivialities in a language- figures of speech. Many metaphors are born because the mind uses multiple channels to express itself. Abusive terminologies(that claim the untrue :P ) are an expression of anger.

However, all these are instances where we consciously know that it is an expression. There are examples where we are unaware of this. A day before every exam, we “decide” to be better prepared next time. But this “decision” never gets acted. :D. This is an instance where the mind uses the process of deciding, as a channel to express that it is repenting. This is often a case where we don’t consciously know that it was an expression and not an action. An action too, is quite common. A decision to turn left while driving, for instance, is an action. It gets enacted without any hassle.

Many of our decisions are mere expressions. Being unable to identify actions and expressions is quite common. While both action and expression are essential, it is important to know which is an action and which is an expression. Before, this, we need to understand all the differences between them.

An action is a thought that is born in the mind and flows out through the body. It can’t be stopped in between, by a purely internal force. The thought is not complete until it is acted. It is a single piece- it can’t be broken in to thinking part, and enacting part. Action belongs to the deterministic part* of the future. Like all other deterministic parts of the future, it already exists in the present as a thought, but is invisible. It becomes visible in the future. Therefore, action is a part of reality. Therefore, questioning an action or an inaction is questioning the existence/non existence of a part of reality- it is an existential question.

An expression is always preceded by a strong emotion, which is to be expressed. It is not a part of reality. So, an obvious way to distinguish between action and expression: if a chain logical deductions leads to visibly absurdity, it is an expression. Expression is itself absurd, but its absurdity is usually invisible. So,, many times, we don’t identify expressions as expressions(like the confused ant). This is a state of illusion. The illusion is broken by a chain of logical deductions starting from it, that reaches an absurdity. We are a part of reality, and everything that we want to call reality must be deducible from it. Expression/ surreal objects can’t replace the reality.

* “the sun will rise up tomorrow” is a deterministic part of the future to our present knowledge

We are Incomplete

June 23, 2014

Why Should I Be rational?- Part II

<< Part-I

Can man survive all by himself without even the knowledge of the existence of others somewhere? It seems, he can. He can look for food himself. He can fight for his life against predators himself. Our body has a process to fight every challenge to its survival. And such a process has a closed end within the body- it does not involve any other member of the species. In this sense, such processes are complete. We can therefore say we are individuals.

However, there are some processes that are not complete. E.g weeping. Tears are not like a digestive juice, which is produced as a part a complete process- digestion. Another example is screaming.

When a man meets with an accident, and is wounded badly, he screams uncontrollably. This screaming is an involuntary reaction to pain. It does not contribute to healing of the wound. A complete process to heal the wound is initiated separately. It may take days, or may not succeed at all. But screaming is not a part of it. It is an open ended process and not a part of a complete process. It is incomplete.

Incomplete processes are a call for help, to other members of the species who could be around. The human mind is equipped to initiate incomplete processes, which means, it knows that it is not alone. Also, we are tuned to respond, on hearing a call for help from another member of the species. The incomplete process is then completed by a second individual, who receives it. So such a process initiated in us is to be completed by others. Therefore, we are incomplete individuals.

What is the mechanism of the response? I believe, an incomplete process produces the same emotion in the second individual as that of the first, in a much weaker form. For instance, when a man dries in pain, the cry produces the same emotion- pain in a very weak form, in the listener and prompts him to attend for help. When a musician plays on stage, people enjoy by resonating with what he expresses through his music. Thinking is also a sequence of well controlled emotions. When someone lectures a proof in mathematics, he is expressing this sequence. Anyone who understands it essentially resonates with it.

Incomplete processes form a weak link between people. In short, we are wired to both seek empathy from others and to show empathy to others. Resonating with others’ emotion is the most fundamental form of communication. It is the reason why we developed languages, common beliefs, common hope, religion, and finally, civilizations. It is the origin of all surreal objects.

An incomplete process is an expression of one’s feeling to others. I have carefully chosen the term expression here. It is chosen in opposition to action, where in we execute a decision. Expression is born from the urge to communicate what we feel, and ends with communicating it. Following this urge, the human mind attempts to use every available channel of communication as a mode of expression. There are several channels of communication, other than verbal. Two people playing chess, for instance, are intensely communicating with each other through the chess board, even though they don’t speak to or even look at each other. Making a decision can also be used as a channel to communicate. Our mind, by nature, attempts to utilize every such channel to express what it feels.

Part-III >>

Why should I be rational?

June 23, 2014

Part I: Truth and logic

Trying to be rational is placing restrictions on oneself. If I don’t want to be rational, I can be sometimes rational and sometimes irrational :D. Like playing a game without observing its rules, not being rational is easier. So why should anyone try to be rational? One observation is: we are more peaceful when we are rational. This is just an observation, not an answer. Moreover, it could be that it is the other way round: we are rational when we are peaceful :P.

Being rational is a way of accepting the reality. Reality is anything that is either verified through senses, or deduced from another reality(that is verified through senses). A rational argument is a link connecting two realities. Reality is interconnected within, through logical deductions. In other words, the set of realities is closed under deductions. Therefore, no untrue statements can be deduced starting from a true statement. Also, starting from an untrue premises, some deductions will be untrue. Some of them might be visibly absurd, and this way, deduction can be used to identify untrue statements. Thus, logic is used to keep our self within reality.

Therefore, the question really is, why should I restrict myself to reality?. Is it possible to live totally in an imagination, by believing it is true?. If not, what is the role of imagination? Also, why do we feel more peaceful when rational?

To answer these questions, we need to understand the origin and nature of all surreal objects that we can think of. I have broken my thoughts on this in to two other posts, due to its length :D.

Part -II >> , Part-III >>

Waves don’t drown the boat

March 23, 2014

I started writing this post four months back. But in between, I was stopped by an existential question associated with both the contents of this post and the act of posting it O_o. While the process of overcoming this hurdle was a struggle, it also generated content for many future blog posts :P. To begin the way I intended:

“As our boat was rowed between the two islands in the ocean, huge waves appeared to engulf it. While we screamed in fear, the locals in the boat were smiling(and laughed at us silently). The waves were much higher than our boat, but, they didn’t engulf us. They lifted the boat higher up than themselves, while they passed underneath. It was a common part of a boat ride. The boat is after all, on the water.”

This is a tourist’s(not me) experience, at the Andaman and Nicobar islands. I don’t remember who was it, but his description was crisp enough to leave a permanent picture of the waves lifting up the boat as they approached. I remember even the exact words he used to describe it. And I am able to use this picture to understand something totally unrelated to the boat and the waves. :P

One ingredient of intelligence is, a deep understanding of the world(or equivalently, the mind :D ). By deep understanding, I mean a knowledge of how different elements of the world, both physical elements and nonphysical, but thinkable elements are inter connected. The world includes three things: the bare physical world(without people), the people in it, and finally all nonphysical thinkable objects in it. An Understanding of the world would include observations on how two people interact, how many people come together to form a society, and how two societies interact. These are indeed observations on the fundamental properties of the human mind. Understanding the bare world is actually, observing how our mind reacts to it. Finally, the non physical thinkable objects form the biggest part of our world. They include all mathematical objects, games, stories, music etc. Such objects are constructed out of a language of communication between people. So much so, that they can be regarded as a part of the language. They are created out of the mind and hence bear fingerprints of the mind. In effect, exploring them is exploring the mind. So the question I want to ask is, on the whole, how does one develop such an understanding?

It is natural to assume that a man, privileged from childhood, has better opportunities to attain a deep understanding of the world. But sometimes, I felt that privilege leaves little to explore, so it is more advantageous not to be privileged. Now, I have concluded that, the deepest insights about the world are attained, neither by the one who was born privileged, nor by the one who was born in destitution, but it is the one who traveled between the two ends(either of the ways ;) ). Traveling the socioeconomic spectrum(not as a tourist!) provides the deepest insights.

Problems are like waves in the ocean; they can do both: drown a boat or rise it high up. A new insight is gained out of the experience of overcoming the problem. All non trivial insights are gained through solving a non trivial problem. There are two questions to be answered here: One, is there any value to the insight that is developed in this process? or, is the insight useful only to solve that particular problem? In that case, it would be redundant; However, a very deep insight is also very general in its applicability. It contributes significantly in enhancing the overall understanding of the world.

Secondly, what determines whether the wave drowns the boat or rises it up? This is a hard question. At this moment, I don’t have an answer more precise than saying that it depends on how many unintended observations we made in the past. Naturally, all the way, we make a lot of random irrelevant observations without intending to do so. Such observations made in the past are put together in overcoming the problem.

Obviously, one cannot intentionally make unintended observations :D. Any conscious attempt to make irrelevant observations would result the set of observation being one-sided, since they are powered by an intention. Moreover, the mind tries to put together all conscious observations to make a ‘conclusion’, and there after it systematically remembers the conclusion with most clarity.

Though this was a simple post, the process of writing it, strangely, was one such boat ride over a wave :P. I believe I went over the wave, and that, at least, generated more posts to come :D.

Hidden in the games

July 20, 2013

Few days back, I was playing a carrom game on android. My machine opponent is an expert at striking. With its accuracy, it can score a coin placed almost anywhere on the board, in a single strike. But it cannot score in a single strike when the coin is cluttered with other coins, or when its path towards the hole is obstructed by other coins. In such cases, it is theoretically impossible to score in one strike. It needs two- one to separate the clutter and one to score.

I am not perfect, unlike the machine; but I can score most well placed coins on a single strike, unless I get unlucky(only on android, not in real carrom :P). But the machine is not tactical.



Once at the climax of a game[fig-1], I was at the WHITE end, ready to play my turn. I could have finished the game in this turn, if only the two whites were separated; but they are cluttered. I cannot score them in one turn- I need two: one to separate them, and one to score.

If I separate them this turn, the machine finishes the game in the next turn- just the red and the black left, both positioned conveniently. I need to do something before the machine gets its turn, to prevent it from winning. I can score the red and retain my turn, but next, I have to separate the whites, so I cant retain my turn further. So the machine gets its turn with the board in almost same sate- red back on the board at the center and black at the same location, and it wins if I do so.

But, it is not yet check-mate. There was still a way out. I used the machine’s turn to separate my white coins!. I pushed the red towards the whites, cluttering it along with them :P [fig-2].



The machine can’t finish the game in one turn now- red can’t be scored in one turn. So, being un tactical, it used its turn to separate the red from the whites, as it has been programmed. In the process, invariably, the two whites also got separated. I got my turn with the red and the two whites uncluttered, all wide apart :P. I scored these three, one after the other, and won the game.

The red coin played a key role in above strategy. Red is the only link between me and the machine- both of us can strike it directly. Look at the rules of the game- there is a red coin, no player can win the game while it is still on the board. But, successfully capturing it doesn’t still guarantee victory. If you capture it well before the climax of the game, it adds no credit to you, instead, it clears one obstacle towards the victory of your opponent!. With these rules, the value of red lies in such strategies.

Why is there even a red coin? Why are the rules constructed in a way so that it ought to be used in strategies like the one above?. The rules facilitate a tactical game over a purely skilled game.

If the game were a strike out(like a T20 bowl out :D), i.e., a direct contest of who scores better, with just one or a fixed number of strikes for both of us, there would be no way to beat the machine. But the rules of the game make it a play of tactics rather than skill. So, although I cannot beat the machine in a strike-out, I can beat it in a complete game. The game, as a whole is different from an individual strike. It comprises of several individual strikes, but they are not to be perceived as independent strikes; there is a longer process connecting them all. The machine’s skill at individual strikes remains underutilized, since it treats them independent.

The strike out is the most plausible ancestor of the game in today’s form. It would have started as a fun-game, involving skills of striking alone. Later, gradually it would have grown in to a mind game, with the rules designed to consistently depart the game from a skill-game to a tactical game.

Look at the very pattern of arranging the coins to start a game- all the coins are cluttered in a hexagon at the center, alternating whites and blacks. If I separate my coins, or score a lot of them, in the process, I will have inevitably separated out my opponents coins too!, spreading them out over the board. This makes it easy for him to score in a rally. This is why we often see our opponent scoring a rally right after we do so. Therefore, it is a prudent practice to avoid clearing the center and to strike on particular coins. The game would have been different if the pattern of arrangement was to cluster whites and blacks separately, in two halves of the hexagon, with the red at the center.

You get to retain your turn after scoring a coin. Even if you are left with all 9 of your coins and your opponent is left with just one, it is still possible for you to win the game. So, you can afford to make mistakes in scoring. If it were a one-chance to you and one-chance to your opponent game, mistakes in scoring would have
been expensive. A rule common to carrom and other related games(snooker, billiards, pool) is, there are two types of coins, and each player is assigned one. Your opponent cannot gain from scoring your coins which you brought near the hole. A slight imperfection or a misfortune can leave a coin you struck just before the hole, making it an easy score in the next turn. This rule ensures that such a coin is not credited to your opponent in the next turn. These two rules significantly reduce the emphasis on perfection of a single stroke and fortune.

Evolution of the rules of a game over time tells us about what is adorable and enjoyable to the human mind!. It seems, ultimately, every game is played in the mind :).

Does every game, over time, mature into a mind game? Do the rules develop over years to make it so?. Cricket is now a mind game. Most games are mind games or tactical games, built upon a basic fun game. Learning how to use a striker is learning just the language in which the carrom game is played; likewise, learning how to bat/bowl, is learning just the language of playing the cricket. The real game is always a mind game.

While learning, all of us believe, carrom is about aim, bowling is about line and length, batting is about timing and footwork. Yet, we accept the rules, which facilitate a mind game over all these skills, as the supreme rules. Understanding the rationale behind these rules requires a certain level of expertise in the game, but we accept them nevertheless.

Conceiving and convincing

May 30, 2012

Imagine, we are given a task to fill up as many pages as possible on word, in a given time, with the letter ‘A’. One way is to copy ‘A’ into the clip board and keep pressing Ctrl V. This is the AP(Arithmetic Progression) way. There is another way; we can copy ‘A’ and keep pressing ctrl C, Ctrl A, ctrl V in sequence. This is the GP way. Mathematics tells us that although Ctrl V appears once in three buttons, the GP method is faster. This is not obvious for a common man at the first sight. And most of the public, are insensitive to logical arguments. Nevertheless, one can convince anyone of this fact, simply by demonstrating it.

The above is an example of what I call as an operationally testable statement. However there are statements which are not operationally testable. The man on the platform, says “the train is moving”; while, the man in the train says “the platform is moving”. Usually, a common man assumes that the man on the train is wrong; he knows the ‘truth’- the train is moving. The profound realisation is that, neither of them are wrong. But there is no way to demonstrate it! This concept of relative motion is operationally un-testable. So much so, that this un-testability was responsible for the Galileo affair. (besides religious concerns)

In fact, most of the statements with profound reasoning are operationally un-testable. For instance, the counter intuitive results of cantor, like the number of points on a side of a cube, the number of points on a face and the number of points inside its volume, are all equal; it is impossible to trisect an angle using a straight edge and a compass. A common man certainly has problems with accepting it. And unfortunately, there is no operational way to convince him of this fact; i.e, a person who assumes the contrary will not be punished for being wrong. :D Hence it is apparent that there is no way to convince the public of these facts.

To digress a bit, I often say utilising an object is to do something with it, which cannot be done without using it :D. By that token, reasoning should be used to conceive (currently)un-testable facts. Because, operationally testable facts can be conceived even without reasoning. Hence, real utilisation of reasoning is to conceive operationally un-testable facts.

How do I convince a common man of such facts? In the first place, should one care to convince someone who is not sensitive to logic? To answer these questions, I shall consider examples from the history where the task of convincing the public has been accomplished.

The earth is not flat, but spherical, and further, it is not at rest, it is rotating and revolving. These two are among the most profound, but operationally un testable realisations. However, they are widely accepted by the public!. Let us examine how were the public convinced of these. Aristotle conceived that the earth is spherical. At that time this would have been counter intuitive and operationally un testable; So, he would have had a great trouble in convincing people about it. It is clear that he did care about convincing people about it; why else would he list down the common fallacies in logic committed by people :D (see ‘Aristotle’s 13 fallacies’). And the way he did it, was to impose it as a belief. This is clear from how people believed everything that Aristotle said.

Most of the public today, believe that the earth is in a complicated motion. They just believe– they don’t really know the reasoning which led to this fact!. In fact, to really go through the reasoning, one has to understand relative motion. This was the major trouble with accepting Galileo’s arguments; he was asked to prove that the earth is moving (for which he gave a wrong argument :P). And it is apparent that most of the public don’t really appreciate relative motion. So, it is clear that they have been convinced of the heliocentric theory, just by imposing it as a belief. This, is not very different from religion!. Isn’t it unjustified for an intellectual to impose a belief?

Majority of people are insensitive to logical reasoning; ie, if the result of a logical reasoning is against their intuition or religious or any other concerns, they cease to accept it. Therefore, it is impossible to propagate the picture of moving earth, through reasoning. If it was not propagated as a belief, the public would have accepted a different picture of the earth, still as a belief!. Hence it is not unjustified, to propagate a belief, if it is necessary to convince them of these facts.

It is clear that whether or not a statement gets propagated as a belief among the public doesn’t depend on whether the statement is based on a sound reasoning or not!. It depends on the ability to impose a belief among the public, of the person who conceived it. This means, almost anything can be propagated as a belief!. That is a little disturbing :D. There ought to be a fundamental difference between conceiving a statement out of rigorous logical reasoning, and claiming without a strong logical background. I guess this difference is brought out in the confidence: the confidence attained by conceiving a fact through thorough reasoning is stronger. I guess(hope :P) this difference can be utilised to beat the propagation of unsupported claims.

Finally, I come to the question I postponed to the end. Is it necessary to care about convincing others? Again let’s ask (old)people :D.Usually, mathematicians don’t care about the public; after conceiving a result, they wouldn’t worry about convincing. Kepler, who went a long way ahead of Galileo, at the same time, didn’t care to convince everyone; that is why he doesn’t have an affair attached to his name, unlike Galileo :D. Apparently, he was able to go that far simply because he didn’t care about convincing people. It is clear that Galileo and Aristotle cared about convincing people. If none of the physicists and mathematicians care about convincing others, their next generation to be physicists and mathematicians will find it hard to see the facts amidst misconceptions. Avoiding this is the only possible motivation for a physicist/mathematician to get in to the job of convincing, as far as I can see right now. This post is the longest one so far, and has crossed 1K words :D and so I stop here :D :D

The Car

March 23, 2012

Ever since one of our profs said ‘most of the beautiful things are useless’, I was disturbed by the fact that in mathematics and physics, most of the intellectually deeper works don’t have practical value. This means, there is no value associated with the ability to do such a deep work. Also many of my friends keep asking me what is the point of all the hard core theory in physics, and why do I study them? The best way to analyse it is to look at the history.

‘His’ story
When he(mentioning who ‘he’ is, is irrelevant :P ) was on his way back from his work, his car broke down. He went to a mechanic, got it repaired, and reached home. At home, relaxing on a chair, he was thinking about his car’s history. Half an hour ago, it was at the mechanic shop. The mechanic is an important person in the car’s and its owner’s immediate history. If he hadn’t done his job, the man wouldn’t be home by now. His work has had immediate effects on the car and it’s owner. However, the job wasn’t a high skill-demanding one; in fact, with a little experience, anyone could have done that job. Also, the guy is not remembered; the man paid him and forgot about him. That completes the first layer of the car’s history.

Where was the car before this? The next interesting part in it’s history is when it’s model was designed. At this stage, it is not just it’s history, it is the history of all cars of it’s model. This was about a decade ago. The car was on paper, on the desk of the man who designed it. This man, is another person who influenced the car’s future. His job, unlike the mechanic’s, didn’t have an immediate impact. If he hadn’t done his job, that would have probably gone un noticed after all! The effect of his effort would have taken a couple of years to come out. But this guy is actually skilled; any arbitrary person cannot be trained to do this work. One needs to be a little talented to be able to learn to do such a job. And, at least people in his company will remember him for designing that model. So That’s the second layer.

The third layer is over 250 years ago.(that’s exponential in time! 30 mins-10yrs-200yrs). This car and several other machines had their common point in history, on the notebooks of the guys who discovered the laws of thermodynamics. Now there is a trend!. This piece of work takes 100s of years to yield its value!. At the time they did it, no one could have imagined that someone will make an auto-mobile out of it, 200 years later!. Coming to the skill required, even a considerably talented person cannot be trained to do such a job. It requires a rare capability. And after 200 years, we still remember them for their work!

I have spoken about three quantities-the time scale in which the work will be utilised, the skill levels required and the reward in terms of people remembering the man who did it. And, the trend is clear :D. That summarises all I have to say about the value of hard core theory.

However everything that looks deep and, useless at the moment is not necessarily going to be useful some 100 years later :D. In fact, most of them are so, which is to be understood from G H Hardy’s A Mathematician’s apology, where he justifies the work of a mathematician saying they are harmless, rather than useful :D. To foresee what could be useful in the long run is unimaginably non trivial!. It is possible that a great mind can foresee it; but they usually work for the fun of it, rather than its impact on the society in the long run. It seems to me, that Newton might have foreseen the impact of his laws of motion-the industrial revolution, although this impact was none of the reasons why he did all this work. But I believe he did not foresee the giant impact(we are able to watch TV today!) of his law of gravitation.

Mystery is a guide to hope

January 14, 2012

Once, I was walking down along with my prof, discussing a result I had just managed to prove. He said “well, you have managed to prove it, but you should also understand your result”. We generally believe we certainly understand something that we developed ourselves. For the first time, I was talking to someone who had, in his mind, a genuine definition of understanding. I knew how I arrived at the result, but it was counter intuitive. That means, there is a flaw in our mental picture of the subject. So, reconstructing our intuition, based on this result is a more important part of understanding it. In fact, this is the value attached to the result.

The above instance speaks also about the value hidden behind a mystery. A mystery points at something that we don’t understand. A counter intuitive result is also a mystery. The moment we encounter a mystery, we can hope for something radical, coming out of resolving the mystery. In fact, look at almost any radical change in human thinking, there would have been a mystery out of which it emerged! Quantum mechanics was itself found hidden behind a mystery. Also, the theory of relativity was born out of a mystery!. Another classic example is quantum computation. This example is too technical to be written in a blog, but I prefer to mention it because, I myself solidified the thoughts behind this post using this example. It all started with Einstein pointing out an apparent contradiction in quantum mechanics, and Bell clarifying that this was no contradiction, but it was only a mystery. They called this mystery ‘entanglement’. It took a while for people to understand it; but a revolutionary looking idea did emerge out of it. That was quantum computing.

The examples I gave are of a huge magnitude :D, and very specific(to physics). One may not expect to encounter mysteries of this magnitude, but the idea works at all scales. A big mystery leads to a big revolution; a small one to a small one :D. So when we confront a mystery, we can expect something new coming out of resolving it. However, every mystery need not lead to something fruitful, but we can hope!.


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