19 November, 2018

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Ramanujan, Hardy & The God Debate

By Kumar David

Prof. Kumar David

Where do truths lurk before they are discovered by humans?

Suppose a mathematician discovers a theorem in 1916, does it mean that this truth was invalid before then? Of course not; it existed in 1915, in 1815, in BC 1915 and before. Where then did it hide? This discourse has overtones of Platonism but lies at the heart of the long arguments between Ramanujan and G.H. Hardy. At issue was the former’s religious faith and Hardy’s atheism strengthened by his friend Bertrand Russel’s rationalism. Russel, a Wrangler (so was Hardy), was a lecturer at Cambridge before he was kicked out for pacifism, rationalism and atheism in 1916.

What got me going on today’s ruminations was that on the Colombo-Bangkok leg of my journey to Hong Kong two weeks ago I watched The Man Who Knew Infinity, an enjoyable film about the Cambridge days of Sirinivasa Ramanujan, a poor Madras Tamil Brahmin now recognised as a mathematical genius. Ramanujan had no formal training in mathematics before joining Cambridge in 1914 at the age of 27 thanks to Hardy’s efforts; but his previous untutored solo work was stunning. This adds wonder to the question: “Where do ideas come from?”

There are many sides to the film that I cannot deal with; my focus is on the dispute about god and the sources of knowledge between Ramanujan (Dev Patel) and his mentor, another brilliant mathematician Godfrey Harlod Hardy (Jeremy Irons) who was only 10 years older. A second mentor who played a role in Ramanajun’s Cambridge days was John Edensor Littlewood, a Senior Wrangler (played by Toby Jones in the film) – Jeremy Northm plays Russel.

Hardy and Ramanujan

Hardy is said to have rated Ramanujan side by side with Euler, Jacobi and even Gauss and if he meant potential, not achievement – Ramanujan died of tuberculosis at the age of 32 – it is reasonable about the first two, both algorists like Ramanujan. But to include Carl Friedrich Gauss is a considerable stretch of Ramanujan’s potential had he lived to a ripe age. A scene in the film has Hardy reading out a note from Littlewood projecting Ramanujan’s latent potential as akin to Newton. This is baloney and probably the note was concocted by the film makers. Newton, for cognoscenti and laymen alike, is supreme among scientists; he was no mere mathematician. Nothing Ramanujan is likely to have achieved had he lived long could have stood beside the impact Newtonian physics (Classical Mechanics) has had on the practical world. Not just scientists but every engineer is reminded of this every working day.

Ramanujan was elected a Fellow of the Royal Society in 1917. Trinity which had previously rejected Hardy’s proposal to allow him to trample the grass was compelled in 1918 to let Ramanujan graze on its lawns. His recognition in India is extensive including a journal and societies bearing his name, and a special postage stamp with his likeness.

The god debate

Ramanujan was deeply religious; Hardy a hardened atheist but curious about how dazzling ideas entered his protégé’s head. To put things in context we must take account of Ramanujan’s magic method. Scientific researchers and mathematicians labour long over a problem, slice and scratch and go through much drudgery before reaching a conclusion or a theorem. Even flashes of insight only cut through difficulties that have long obstructed progress. Ramanujan was the polar opposite. Call it intuition or revelation or what you will, but his mind would in a flash see a result, an equation, or a theorem, and only afterwards would he sit down to brush it up, or bother about proving it. One thing that drove Hardy to paroxysms of frustration was Ramanujan’s reluctance, sometimes his refusal, to write out a complete proof without which publication was impossible. The impatient scholar would respond: “Of course it’s correct; I know it’s correct; why waste time writing out a proof”. Many theorems that Ramanujan left dangling have been proved by others later, sometimes much later. Only a few have been found to be erroneous.

So you see the kernel of Hardy’s curiosity. “How does it come into your mind? From where do these flashes of intuition arrive? What is the process; how does it happen?”  Ramanujan was lost for an answer: “I don’t know; it just happens; it’s like a revelation; it just comes floating in”. And this is why Ramanujan came to say to Hardy “It must be God; it has to be the mind of God engaging with me, otherwise how to explain these revelations that I see in a flash?” Hardy, firm atheist that he was, did not buy the god story but he was shaken by Ramanujan’s all but miraculous gift as he admitted when he delivered a commemorative oration at Trinity when news of Ramanujan’s untimely death in 1920 came from India, a year after he had returned home.

Here is a sample. Mathematician Mahalanobis put a complex puzzle to Ramanujan. He reflected and responded with a ‘continued fraction’ but this was the solution to a whole class of problems. Mahalanobis, astounded, asked how he did it. “It is simple” Ramanujan replied, “the moment I heard the problem I knew the answer was a continued fraction. Which continued fraction, I asked myself and the answer came to my mind.”

Knowledge of the material world

I started by saying mathematical truths exist a priori, meaning that they existed before the mathematician discovered them; for this reason I was careful to use the word discover, never the word invent. America existed before man discovered it some 15,000 years ago, he did not invent it. The entities of mathematics, think of numbers, are created by man and therefore a mathematical theory or relationship is the product of the human mind, though logically its truth exists prior to its discovery by a mathematician. That much is common sense. But what about the real world which exists outside and separate from man and existed prior to man?  (Such comments drive quantum scientists into a state of entanglement and encourage the likes of Gamini Kulatunga, in probable waves of particles suspended in superposition, to pile up texts for the edification of ignoramuses like this writer).

Mathematical entities are crisp and clear, they do not soil with time – think of prime numbers. Mathematical theorems are truths that do not degenerate with age and were true from before they were discovered – think of any fundamental theorem, for example the one that says any integer can be expressed as a product of primes (note, 2 is a prime) was/is forever true.

However, when we turn to the study of the real world it is collective human experiences, not mental abstractions that need to be explained and theorised. Definitions, quantities and relationships must pertain to experience and experiment, not to prima-face concepts alone. This imperative is central to science. The laws of nature and the conceptual building blocks for their expression change and evolve with the progress of observation and knowledge; their truth value is not eternal. Action at a distance in electromagnetism and gravitation is replaced by the concept of an all pervading field.

There is nothing like the pristine clarity of say a prime number or the unchanging eternity of a product-of-primes theorem in gravitation or electromagnetism. Thus the immaculate perfectness of the mind of god goes out of business. The answer to the question where does knowledge come from is different. Knowledge comes from the processing of real world material and observable information by the human mind which is endowed with rational and logical capabilities. How long before and after its discovery is knowledge true? It depends on the existential qualities of the phenomenon itself. The Ramanujan-Hardy debate, in so far as it relates to scientific knowledge, I avoid the word truth, is heavily weighted in Hardy’s favour.

[Reader Ringa Ranga Raja from London has written to complain that 14 March 1879 was Einstein’s birthday and 14 March 1883 Marx’s death. He had expected me to use the twin anniversary last week. Sorry, next year maybe].

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    It should also be observed that during the colonial times, imperialist metropolitan centres in the global North propagated the idea that scientific knowledge for which they had a monopoly was superior to other types of knowledge existed in the colonised global south. This helped to maintain unequal relations between scientists in the global North and other knowledge holders in the global south. Furthermore this hierarchy of knowledge very powerfully nurtured by the metropolitan centres marginalised other forms of knowledge in the colonised countries. Even social sciences contributed to this dogma in the way they were introduced and maintained in countries like India, Sri Lanka. An academic dependency and a captive mind were created among social scientists in the colonised countries. Read Raewyn Connell’s Southern Theory(2007) and the work of Alatas on this latter aspect. My article in the current issue of Social Affairs,Colombo also elaborate on this.

    Now the question arising from this article is whether there are other forms of knowledge that can discover truths other than scientific knowledge? To put it differently, is it only the scientific knowledge that can discover truth? If we believe it to be so, knowledge about the universe,life and death, illnesses and remedies, what causes what etc that have been generated for time immemorial by the so called non scientists become invalid. Most social scientists in the global periphery including Sri Lanka bought into the fallacy that social science methodology,ie positivist, is the only method that can generate valid knowledge. However, some critical and interpretive methodologies have emerged since that challenge this fallacy. There cannot be one truth.There are multiple truths,some constructed by humans,ie social constructivism. Conceptions about maths are also constructed thus.

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      “..forms of knowledge that can discover truths ””

      what do you mean? do you mean other ways of acquiring knowledge?

      eg. ???? sitting under a tree without eating for a fictitious length if time?

      and, do you understand the character of what is called a scientific statement or theory ?
      nothing more than that it can be formulated in a manner that can be found to be false, if it is.

      It is certainly not the exclusive property of anyone from any part of the globe – anyone who does not want to waste time in any inquiry has to stumble on this sooner or later.

      The fact that some chappies meddling with some chemicals and some fragile equipment expropriated the label in post primary school should not mislead you.

      I suspect that is the only way in which even successful animals and insects also proceed.

      It is a pity that academics should also fall into this populist nastiness that should be reserved for discussions about investigations about torture and other obscenities.

      Cheers Siri.

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        Concept of God and Self Discovery

        Fatima, in response to, “..forms of knowledge that can discover truths ” you ask, “what do you mean? do you mean other ways of acquiring knowledge? sitting under a tree without eating for a fictitious length of time”? I believe that one can sit under a tree and do many good things such as contemplate, meditate, Pray to God, or just

        observe nature and learn many things. Your problem is that you have been brain washed to believe that there is only one solution to any problem. Pray to God.

        About praying, the more brave people over here (an Islamic country) have a nice story. 3 men (a Muslim, a Buddhist and an atheist), having gone on a picnic to an island in the middle of a river, found themselves marooned on it due to heavy rains. Soon a log came floating by close to the island and the Buddhists jumped in and hung on to it and was saved downstream. After a minute or so, another log came floating by and the Atheist grabbed on to it and got himself saved.

        All this time, the Muslim man was praying and did not even look up. Many logs floated by during the prayer but the man was too busy praying to make use of them. Afterwards, no more logs came and the Muslim man died on the island due to starvation. As he was a Muslim, he went to heaven and was met by God. The man asked God, “God, you saved 2 non Muslims, but never cared save me – a faithful Muslim. Why”?

        God answered, “You idiot, I sent so many logs to save you, but you were praying did not care to even look up. Now you are complaining. Ha!” and the man was sent hell for his stupidity.

        Fatima, you are also like that. You have only one solution for any problem. To Pray to God!

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      Siri Gamage,
      As you may know, Scientific knowledge is based upon “observation”.. and Scientists uses four step process to accumulate knowledge. Don’t you think “time immemorial” knowledge were also obtained from observation? Buddha spent 6 years analysing, concentrating on his observation before he started preaching his conclusive understanding, knowledge on human mind , to me this is a science of human mind. It is said that prophet Huhammad spent many nights in mountains analysing, concentrating his observations before finding the truth.. On the other hand, Buddha’s knowledge on cosmos and physics doesn’t show any validity according to present knowledge of us humans…

      However, Ramanujan’s special abilities on analysing numbers in his “unconscious” brain is not easy to explain. But average human image processing abilities is exceptional too and not easy to explain either. For example when you are in a public place facing 200~300 people, without your conscious, you discard 299 people as unknowns .. then you consciousness may notice one face as you know, ex:Prof. Kumar David’s face..Then how much of associated/linked knowledge about David would be activated in your brain before your consciousness know it is your friend/teacher Kumar DAvid!! Do you know how you, your brain does it? No you don’t.. …… Most important thing is, how much unconscious brain power is used to discard those 299 as anybody you know, not even seen in TV , or not animal, not a tree, etc…..
      If you trained 1000 average people to same levels of tennis training and couching as Serena Williams or Novak Djokovic, I believe 90% of them would NOT achieve not more than 50% of what Serena or Novak could do with their tennis racket .. Can we explain this?? anything more than pure randomness!! Or gifted people Randomness of Billions of neurons and trillions of synapses arrange as billions of tiny networks in human brain…

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    If you read Hardy’s autobiography, “A Mathematician’s Apology”, he makes several interesting observations about mathematics. It is a “young man’s game”, it creates its “own reality”, and if someone is exceptionally good at mathematics, he or she is probably poor at most other things. We physics people (and engineers) will probably agree. Pure mathematics has little relevance to the outside world. The applied aspect (which Hardy is careful to delineate) is something entirely different. The axiomatic nature of pure mathematics may be what drove Ramanujan to believe his insights were divinely inspired.

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    Is it possible that Ramanujan ‘s unusual brain was able to rapidly analyse a problem given to him withoout him being conscious of it? In other words, what he thought was divine inspiration was a product of calculations performed by his brain consisting of 100 billion axons and 100 trillion connections forming as in all of us an incomparable supercomputer..Conscious awareness of brain processing is not inevitable after all. In fact there is evidence that when we think we know a decision was made consciously by us, in fact the neursl evidence is that it was made before we became consciousy aware of it. Instances of Divine inspiration have been continually shrinking with the advance of Science. More anf more divine explanations for natural phenomena are falling by the wayside with the inexotable advance of Science. The Germ theory, genetics, the intricaies of the solar system, the theory of evolution are just a few examples, Science cannot explain everything, especially on so called spiritual and moral aspcts but whatever it has postulated is backed by sound evidence, and to me that is the only way forwards.What we know today is vastly more than what we knew a 100 years ago and what we will know in another 100 years is , well, just unthinkable! Ramanujan was unique in possessing a bfrain with amazing powers of computation, albeit somewhat selectively.

    On another apsect of the book and film, I found it fascinating to read about the prevailing atmosphere in Cambridge at the time. I agree also that Newton and Ramanujan cannot be placed on the same pedestal.

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    “I believe in intuition and inspiration. Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world, stimulating progress, giving birth to evolution. It is, strictly speaking, a real factor in scientific research.”— Albert Einstein
    That may explain Ramanujan up to a point.

    Our education system is pumping more and more information into children with no regard for consequences.

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      “Our education system is pumping more and more information into children with no regard for consequences.”

      Schools are just training people to do one job, one career. For many people, most schooling is a waste of time, since most of the information (like foreign languages) is not useful. They are better off going to a trade school from year 6 itself and learning their craft from a master. Those who wish to pursue professional careers in science, math, medicine, etc. are the ones who should be spending so many years in school. For them, there should be an entirely different kind of education, especially with the pervasiveness of today’s technology. They should have interactions with professionals or at least the professional literature, at a fairly early age. Many of the teachers at the primary and secondary levels – even if they are capable in elementary subjects – possess limited knowledge. For example, most science teachers at this level will be able to grasp “Newton’s Laws”, but almost none of them understand that Newton’s Laws can be derived from General Relativity. It is a sad fact that even today, most people’s knowledge is limited to 300 year old discoveries as opposed to the more recent discoveries that are behind our technological progress.

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    Generation of knowledge about the physical and social world occurs through various methods. Scientific method is only one. In scientific method, one tests hypothesis or experiments a proposition by using controlled samples etc. It is a rigourous method that subjects various propositions, hypothesis etc.to prolonged testing. If confirmed with high probability these propotions or hypothesis become accepted as a theory and so on.

    Social scientists such as sociologists also started to follow scientific method believing that there are ‘social facts’ out there in society that can be discovered if we follow a similar method. Thus came methods such as surveys, hypothesis testing, sampling, statistical analysis , induction-deduction -in short quantitative methods. What happened was our undergraduates and postgraduates started produing a lot of data, some questionable analyses, and conclusions on the basis of such research. They however, operated within very narrowly defined conceptual limits selecting topics that do not contribute anything original. They were highly imitative too. Research for the sake of research rather. Conclusions typically read like that on the basis of this analysis I found this, that or whatever. For example, they are unable to interpret the findings or data in a way that contributes to greater knowledge or a theorey. Just analyse data and conclude without linking with the big picture. For example, in a presentation by a junior Economics lecturer at the arts faculty research sessions held last year at Peradeniya university, he found that the contributions by male migrant workers send .1% more money home compared to female migrant workers. What is the value of this finding unless he can show its significance? Social scientists who follow so-called scientific method contribute to ’empiricism’ also ie.the belief that the truth lies out there and if you collect enough data it can reveal the truth. But one has to use the head first to conceptualise and select a topic which is theoretically sound.Then a method that corresponds to the conceptual framework.

    Qualitative research methods at least in social sciencs have the benefit of producing better insights on selected topics.

    There are socially constructed relative ‘truths’ in addition to those that operate in the universe, physical world. Between physical and social realities and human mind there are PERCEPTIONS that can either cloud our minds or shed light. Yes meditating under a tree can improve one’s mental faculties but there is a new discourse advocated by Dr. Gamini Abey which states that one has to get rid of ‘KNOWLEDGE’ if we are to achive liberation and wisdom(gnana). Listen to his talks and interviews in Y Tube. Our traditions embody knowledge and wisdom. Our literature,arts, belief systems, religions embody knowledge -not necessarily obtained via scientific method. Are they invalid?

    Sorry if I diverted the discussion from the mathametical story that Kumar David has presented. But we need to be aware about the fact that there are multiple ways of “KNOWING’ and they consist of methods other than Scientific. I know that this will be hard for hadrcore scientists and scientific demagogues to digest but it is true,,

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      Siri Gamage:

      “But we need to be aware about the fact that there are multiple ways of “KNOWING’ and they consist of methods other than Scientific.”

      Science has a very practical application, that is why it is so useful. Religion is what, just people chanting and doing some ritual. Science improves the standard of living via technology, in that sense it is a wealth generator.

      Statistical analysis is important for quality control.

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    Types of Knowledge

    Dr. Kumar David, as my teacher long ago, you know that I am not very good in Mathematics and people like Ramanujan are out of the world super beings for me. I do not know how I landed in the Engineering Faculty. It must be due to luck or karma? I know that you too were excellent in Mathematics though not exactly a Ramanujan. So was another engineer turned politician like you, Dr. Vikramabahu Karunaratne. You could both have done a better service to Sri Lanka if you had remained engineers/mathematicians instead of turning to politics. Anyway, I am glad that you have written this article, which is at a much higher intellectual level.

    Regarding the different types of knowledge that you have touched upon, the knowledge of Buddha is supreme. It was not given by any God but self achieved through extremely hard work.

    What the Tathagata knows is not established in him. In other words, he does not define himself or the awakened mind in terms of knowledge or views, even concerning the Dhamma, although the knowledge that led to his awakening is fully available for him to draw on at any time. (Thanissaro Bhikku).

    To illustrate the type of knowledge he has, we can consider the following example: A certain Prince Abhaya, an expert in chariots, asks Buddha Lord, “when people, having formulated questions on various things come and pose them to you, you always come up with answers on the spot. How do you do that? Do you prepare yourself by thinking, ‘If those who approach me ask this, I — thus asked — will answer in this way’ — or does the Tathagata come up with the answer on the spot”?

    Buddha answers this by a counter question and the dialog continues as follows:

    Buddha: In that case, prince, I will ask you a counter-question. Answer as you see fit. Are you skilled in the parts of a chariot?

    Abhaya: Yes, lord. Being a well known charioteer, I am an expert in chariots including individual parts of a chariot.

    Buddha: And what do you think: When people come & ask you, ‘What is the name of this part of the chariot? What is its purpose?’ does this line of reasoning appear to your awareness beforehand — ‘If those who approach me ask this, I — thus asked — will answer in this way’ — or do you come up with the answer on the spot?

    Abhaya: Lord, I am renowned for being skilled in the parts of a chariot. All the parts of a chariot are well-known to me. I come up with the answer on the spot.

    Buddha: In the same way, Prince, when wise nobles or Brahmins, householders or contemplatives, having formulated questions, come to the Tathagata and ask him, he comes up with the answer on the spot. Why is that? Because the property of the Dhamma is thoroughly penetrated by the Tathagata. From his thorough penetration of the property of the Dhamma, he comes up with the answer on the spot.

    In this way, Buddha continued to answer questions instantly and give discourses without reference to any notes, hesitation or prior preparation for 45 long years, covering great distances by foot, and resting only for a few hours in the night, creating and spreading an extensive body of knowledge called ‘Dhamma’. The beauty is that, there is not a single contradiction, vagueness, ambiguity or impreciseness, anywhere in this body of Dhamma.

    I think the knowledge of Buddha was inherent to him just like a part of his body.

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      Edwin
      In commenting on a recent article by HLD Mahindapala (CT 25 March) you said that you have three enemies Tamils, Tamils & Tamils in that order. I believe Prof AK D has Tamil lineage!

      You also said that HLD M is inspiring. Now I understand why.

      You revel on talking about Buddhism. Are you happy with the way it is practiced in SL?

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        My Duty and My Enemies

        Pliiai, Excellent Question that makes me happy. Why happy, because now I know that at least one person reads my comments. I will answer in two parts. First the 2nd part.

        Q: You revel on talking about Buddhism. Are you happy with the way it is practiced in SL?

        A: Who cares whether it is practiced properly or not? I don’t. Buddha gave us the job of protecting Dhamma not practicing it. In his wisdom he knew that Practice and Protection are poles apart.

        Q: Edwin In commenting on a recent article by HLD Mahindapala (CT 25 March) you said that you have three enemies Tamils, Tamils & Tamils in that order. I believe Prof AK D has Tamil lineage!

        A: Yes I said that. The reason is that for thousands of years you Tamils have been acting like the Taliban, recently, even attacking the Temple of the Tooth. Yes I know AKD is a Tamil. But a good Tamil. He is so good that you guys wanted to bump him off. Instead, your RPG (Round Prabha God) got bumped off by us. (Ha! Ha!)

        Wait and see. Under my influence AKD will soon be a good Buddhist too. Right now, he is Clearing The Path under my guidance.

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          A saying of Edwin: “…….. Buddha gave us the job of protecting Dhamma not practicing it. ………”

          Practicing Dhamma is the best way of protecting Buddhism from bigots.

          Thanks for confirming that Prof AK D is Tamil and a good one too.

          If and when you convert AK D to Buddhism please let us know.

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            Bahiya Sutta: The Most Intriguing Sutta in Tripitaka

            This is the story of a wanderer named Bahiya, an extremely intelligent man like AKD who was searching for the ultimate truth. One day Bahiya stopped the Buddha on the street in Savatthi and said, “Venerable Sir, you are the Samana Gotama. Your Dharma is famous throughout the land. Please teach me that I may understand the truth.”

            The Buddha replied, “We’re on our almsround, Bahiya. This is not the right time.”

            “Life is uncertain, Venerable Sir. We never know when we are going to die; please teach me the Dharma.”

            This dialogue repeats itself three times. Three times over, the Buddha says the same thing, and Bahiya responds in the same way. Finally, the Buddha says, “When a Tathagata is pressed three times, he has to answer. Listen carefully, Bahiya, and attend to what I say:

            Upon hearing these words, Bahiya was immediately enlightened. Moments later he was killed by a runaway cow. So he was right: life is uncertain. Later Bahiya was awarded the title of“The Disciple Who Understood the Teaching Most Quickly.”

            In the seen, there is only the seen,
            in the heard, there is only the heard,
            in the sensed, there is only the sensed,
            in the cognized, there is only the cognized.
            Thus you should see that indeed there is no thing here;
            this, Bahiya, is how you should train yourself.

            When, Bahiya, for you
            in the seen, only the seen,
            in the heard, only the heard,
            in the sensed, only the sensed,
            in the cognized, only the cognized,
            and you see that there is no thing here, (Pali: Tvam Na tena}

            you will therefore see that
            indeed there is no thing there.(Pali: Tvam Na tatta}
            As you see that there is no thing there,
            you will see that
            you are therefore located neither in the world of this,
            nor in the world of that,
            nor in any place betwixt the two.
            This alone is the end of suffering.” (ud. 1.10)

            Upon hearing these words, Bahiya was immediately enlightened. Moments later he was killed by a runaway cow. So he was
            right: life is uncertain. Later Bahiya was awarded the title of
            “The Disciple Who Understood the Teaching Most Quickly.”

            My comment: Perhaps this intriguing stanza is a short cut to enlightenment for extremely intelligent people like Professor Kumar David, as it was to Bahiya of the Bark Cloth.

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            Bahiya, Jean Paul Satre and Heidegger

            As my favorite Guru Rev. Gnanavira says in his book ‘Clearing the
            Path’, It is quite as tough a passage as anything you will find in Satre. I am there means, I am in this world in the form of senses.

            Heidegger tells us that the ‘here’ (senses) is always understood in relation to yonder ready-to-hand, for some purpose of mine. This is more or less what Ananda Thera meant when he said, “The eye and other senses, are the things by which one is the perceiver and conceiver of the world”. In other words, not only am I in this world, but I am also, as my senses, that by which there is a wold in which i am. ‘I am there’ because ‘I am that by which there is an I-am-there’; and consequently, when ‘I shall not be there by which’, then ‘I shall not be there’. And when’I shall not be there’, then ‘I shall neither be here nor yonder nor in between the two’.

            And when shall we ‘not be that by which’? Heidegger, who did his work about 100 years ago and with all his reputation for handling complex philosophical matters is not able to tell us. But Buddha (who lived 2600 years ago) tells us: It is when, for us, in the seen there shall be just the seen, and so on for heard, sensed, cognized.

            Now we come to the Grand Finale! And when in the seen is there just the seen? That is when the seen is no longer seen as ‘mine’ (etam mama) or as ‘I’ (eso’ham asmi) or as ‘my self’ (eso me atta’): in brief when there is no longer, in connection with the senses, the conceit, ‘I am’, by which ‘I am the conceiver of the world’.

            Note: That is what Rev, Gnavira has to say about Bahiya Sutta, with slight modifications from me. Perhaps this could be an eye opener for people who consider Buddhism as a pessimistic religion.

            Do we see some similarity between what is said above and certain aspects of Quantum Theory? According to quantum theory the observer is tightly bound with the world he is trying to observe. Scrodinger’s cat is an example where the status of the cat could be anything between alive and dead. it is decided only when the observer does his observation.

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    Five Stages of the Understanding of a Natural Phenomenon

    This idea was mooted by my friend Mr. K K Gunawardene (Former Director of Telecom) and further followed up by me. In the Dhamma Chakka Pavattana Sutta, the first discourse that was delivered by Buddha after enlightenment, which was for the benefit of to his 5 fellow ascetics, explains, how the 4 noble truths (Dukkha, Dukkha Samudaya, Dukkkha Nirodha, Dukkha Nirodha Gamini Patipada) was realized by him. In the Sutta Buddha mentions 5 stages of realization of each truth. The Pali word and its English meaning are given below.

    Chakku, Gnana, Panna, Vijja, Aloko (Observation, Initial Awareness, Initial Understanding, Complete understanding (Formation of a Theory) and Finally Enlightenment with the Formation of a Law. With that the knowledge landscape gets brightly illuminated, revealing every detail, as if the rays of a strong flood light have been thrown on.

    According to KKG the Scientific Method also has 5 similar stages. The actual descriptions are from me and I hope it is similar to KKG’s.

    Stage 1: Observation of the Phenomenon. (Ex: Humans as well as animals can see a solar eclipse when it occurs)

    Stage 2 (Initial awareness): Becoming aware that there is such and such a phenomenon characterized by what one has observed. Taking the previous example, A solar eclipse is observed by humans as well as other lower animals. The animals react to it instinctively, being controlled by neural networks (modules) that have developed naturally over millennia thorough evolution and natural selection.

    Stage 3 (Initial Understanding): This applies to humans only. The human starts asking questions and wants to know how and what caused the event. He starts making further observations or starts to seriously evaluate the observed data and forms an initial theory of what happened.

    Stage 4 (Complete Understanding and Formation of generalized Theorem and its application in a wider field): The phenomenon become clear as the Avijja (lack of knowledge or wrong knowledge) disappears like the morning mist.

    Stage 5 (The Theorem becomes a Law): A good example is Sir Isaac Newton who observed an apple falling from a tree and finally came up with Law of Gravitation, which governs the motion of bodies such as planets.

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    Thank you Prof: I saw the film -The man who knew infinity on-line.
    You made my Day. This was fascinating even for an imbecile like me.
    What is the square root of 58,639?
    Ramanujam answers from his head instantly to seven decimal places!

    Qui genus humanum ingenio superavit is the inscription on the statue of Isaac Newton located @ The Trinity college Chapel[Cambridge].
    A loose translation is given as -The one who surpassed the human race in Intellect….

    Some of the greatest men have been Jews: Newton,Einstein,Jesus Christ, and of-course your Karl Marx!

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      Plato: (1) Newton was not a Jew. (2) Professor AK D does not own Karl Marx

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        K.Pillai

        “Newton was not a Jew”

        Then was he a Tamil/Sinhalese?

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    Yes indeed Newton was not a Jew but for reasons too complex to discuss here the Jews have been a very intellectually inclined people. We can make up for the deficit of Newton by loading Freud, Spinoza, Jacobi, Max Born and John von Newman on to the list. I guess each of them is worth about 200 milli-Newtons so it works out ok.

    AKD does not own Marx? You don’t say! He behaves as if he does.

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      Bahiya and AKD

      AKD is not even a follower of Marx anymore. After Clearing the Path he may become a modern day Bahiya. (All Buddhists know about Bahiya Daruchariya – Bahiya who used to dress up in tree barks).

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    K.Pillai.
    Thanks; I stand corrected. I went on the basis that he was Issac Newton.Issac has Jewish overtones.
    I am afraid Karl Marx owns AKD!

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    AVB!
    “On the other hand, Buddha’s knowledge on cosmos and physics doesn’t show any validity according to present knowledge of us humans…”
    Can you elaborate please. Are you well-versed on Buddha’s teaching to make such a conclusive pronouncement? Thanks.

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    Plato
    Some of the greatest humans have been Jews. Only according to other Jews.
    You are a moron to believe that intelligence is determined by belief in a fables.

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    Max walker

    “You are a moron to believe that intelligence is determined by belief in a fables.”

    I take it that you don’t believe in Mahawamsa fables and origin stories.

    You too don’t believe in Buddha was a Sinhala/Buddhist and Ravana was a Tamil/Saivaite.

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    The Kalaveddah is here among us. This type of article is not its usual habitat although he has been seen associated with articles of the mundane genre in CT.

    Out of the 5 stages of enlightenment, Chakku, Gnana, Panna, Vijja, Aloko, only the first 2 (Chakku, Gnana) applies to him. He sees and then reacts instinctively, controlled by those neural modules honed over millions of years. But that is it. He So far and no more.

    However the dangerous thing is that we have no idea how he will react. Obviously the animal is good for navigating from branch to branch, those neural modules coming in to action perfectly and in quick succession. He may be a Ramanujan of the Kalavedi class in his own right, but do not expect miracles like understanding what we are talking about here.

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    Prof:Kumar David.

    Bertrand Russel too was there when Ramanujam met Hardy for the first time.
    What a great film! Thanks again!

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      Homer, as Plato has pointed out, all of us here, including yourself, are grazers. Some have long tethers and some short. But you seem to be blessed with the longest tether and as a result, you must be consuming the largest amount of grass.

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        Edwin appu, long time no see.. I am not interested in the topic, but your previous comments added few weeks ago. So thought of sending my greetings from Berlin today.

        The weather is becoming better- with the spring dawned to us. I ve been planning my summer trip back to home country – in July.. in case you would be in the country, we can plann a get together in Mathugama area – so that we could finally enjoy karancocu or the like local curries.. as you once added. just let me know.. what your plans are.

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          Thanks Sam. My plans are still not made up. Will you be there from July to some date in August? I am asking because my 12 year old grand daughter wants to travel alone to SL in August to be with her grandma.

          I want really to meet you and take you to Matugama. Let me know exactly when you will be there in SL and I will make a special trip for one week.

          Perhaps AKD will join us again. Also think of passing through Bahrain.

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    Prof Kumar David

    One should really be aware of all aspects of the question before one begins inquiry. As an example “From where do these flashes of intuition arrive?”; the flashes of intuition happen in the void of thought and to inquire where it arrives from, it has be in the realm of thought hence cannot be answered ( from where, does it arrive or does it exist/reside). All thought is tethered to Memory/Knowledge ( Memory/Knowledge is necessary condition for thought) and hence one is limited always by the length of one’s tether and all new knowledge is from addition from collective knowledge or through intuition when one breaks the tether ( ie. cessation of thought – Arthur Koestler in his “Act of Creation” explains this through the process of two different trains of thought meeting to create Humour, Art, Invention ). One would in terms of rational process, will be at a loss to understand why both Hardy and Ramanujan brought “God” into the reasoning to understand intuition unless one takes their belief into consideration and then Rationalizing their reasoning is mute considering one is reasoning devoid of belief (Either theist , Atheist or agnostic ) otherwise one would arrive at a conclusion according to one’s tether.
    Of course as to Ramanujan’s Intuitions one should be aware of the fact that one will always be ignorant of the genetic memory Ramanujan had carried with him

    “The entities of mathematics, think of numbers, are created by man and therefore a mathematical theory or relationship is the product of the human mind, though logically its truth exists prior to its discovery by a mathematician.”

    Speaking of knowledge one need also to take into account ignorance. There is Knowledge and Ignorance, Awareness of one’s ignorance (Intelligence) and Ignorance of one’s Ignorance ( it is impertinent to name it) and all this is interpretation of the reality and the tools of these interpretation are Language, mathematics, Science etc which is agreed upon as to standard, meaning etc. Truth hence is only the “Now” for the past and future are interpretation of the “Now”. Truth exists in the “Now” and it is the only thing that escapes being caught as experience as it always is experiencing ( The difference is in the process where one has no identifying, defining, interpreting etc where as the other is the identity, definition, interpretation etc ). The Intelligence of humanity that created the Tools of interpretation created them independent of time hence as you say “they do not soil with time”

    As a Student of yours in the early 70s I feel completely dejected most of comments. Those who commented to your article were Ignorant of one’s Ignorance and were off the topic and were naturally grazing within their tethered circle

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    Homer.

    Prof:G.H.Hardy and Ramanujam were also grazing within their tethered circle of Mathematics!

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