26 June, 2019

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The Effectiveness Of Mathematics In The Sciences: The Science-Mathematics Nexus

By Kumar David

Prof. Kumar David

The fallout from what I thought would be a simple piece (“Ramanujan, Hardy and the God debate”) which appeared on 26 March has been nuclear. Chief offender, Gamini Kulatunga, has peppered me with e-mails while Rajan Philips and a few others have been less cruel firing only a few volleys. There have been contributions in web Comments (Siri Gamage, Lester, Dr M. Gonlaskorale, AVB, and Edwin Rodrigo to name a few). I declare upfront that I cannot do justice to all for two reasons. First, I am not conversant with spiritually oriented topics such as the “Stages of Understanding in Buddhism” or “alternative non-Western knowledge systems” (sorry Edwin and Lester) and am a layman on the brain’s “100 billion axons and 100 trillion connections” and “randomness of billions of neurons and trillions of synapses arranged as tiny networks” (sorry Dr MG, Lester and AVB). These are significant topics for readers to follow up elsewhere.

Secondly, within the limits of my column, I have to be restrained and not bite off more than I can chew. It is also not possible within reasonable length to explore minds like that of Alan Turing, inventor of the computer and founder of systematic computing (see Alan Turning: The Enigma, by Andrew Hodges, Princeton University Press) or discuss 21-st Century artificial intelligence (AI).

I have now declared the limits of this essay; it will only explore the questions: Does maths in itself discovers new truths about the physical world? Can it create scientific knowledge? Does its use in a scientific thesis (Calculus and Newton’s Laws, Maxwell’s equations and Electromagnetism, Riemannian geometry and General Relativity) create knowledge not already contained in the scientific theory itself? I say NO it cannot, I am on the side of the naysayers. But I am in bad company.

Einstein is reported to have remarked: “How is it that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”

James Clerk Maxwell (1831-1879)

Eugene Wigner a Nobel Prize winner wrote a 1960 article with the title: ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’; so you get his drift.

Mario Livio described as a renowned astrophysicist and author of 400 scientific papers asks: “Is maths an invention of the brain? Or does it exist in an abstract world, humans merely discovering its truths?”

As opposed to this there was a certain contrarian chap who intoned: “The question whether objective truth can be attributed to human thinking is not a question of theory; it is a practical question. Man must prove the truth – the reality and power, the this-sidedness – of thinking in practice. The dispute over the reality and non-reality of thinking that is isolated from practice is a purely scholastic question.”

I declare I am on the side of this contrarian chap and would to go further and replace ‘purely scholastic’ with ‘utterly meaningless’. Regarding the Einstein quote above, unless it is a fabrication it is wrong or at least incomplete. A genius can sometimes be wrong; Einstein, Newton, Plato and Gautama Siddhartha are not divine; their contributions are profound, but since human they are fallible. Einstein goofed at the heart of general relativity, inserting a fudge factor politely called the cosmological constant lambda (λ), which later he shamefacedly admitted was “my greatest blunder”. David Hilbert, the leading mathematician of the day, derived the general relativity equations at the same time but separately from Einstein but did not make this blunder.

The use of maths, statistics, computing and AI to implement the marvels of modern technology belongs to a separate genre different from the scope of this essay.

Maths in Science

Let’s get to the heart of the matter: “Do the powerful effects of mathematics in science mean that the maths itself creates new knowledge absent in the scientific thesis to which it is applied?” Mario Levi (ML) asks and is agnostic. I quote from his Math: Discovered, Invented or Both in Nova, 13 April 2015.

“How is it possible that all the phenomena observed in classical electricity and magnetism can be explained by just four mathematical equations? James Clerk Maxwell showed in 1864 that the equations predicted that varying electric or magnetic fields generate certain waves – the familiar electromagnetic waves (light, radio, x-rays) – eventually detected by German physicist Heinrich Hertz in the 1880s”.

Left to right: David Hilbert, Alan Turning, Kurt Gödel, Bertrand Russell

ML confuses himself. Are Maxwell’s Equations (ME) physics or mathematics? Their beauty can banish Cleopatra from any bridal chamber but must not seduce us to forget that the body within is physics, the raiment without radiant mathematics and can be written in two forms, differential or integral.

Forgive me this one unavoidable paragraphs; I will then get back to terra firma. The first equation  says “There is no true magnetism”; meaning magnetism is a product of electric currents. The second equation says the electric field emanating from any region depends on the net charge contained therein. The famous third equation
known as Faraday’s Law of Induction, better known to schoolboys as the flux-cutting rule, is about how electricity is made in generators. The final fourth equation supplements the first one and says how much magnetism is made by a given electric current. There is no need for readers to follow the mathematics since, qualitatively, what is being said is pretty straightforward.

Next the maths is manipulated to the n-th degree to derive weird and wonderful results; radio, TV and mobile-phone reception, electrical surges and marvellous circuits and devices. But it is not the maths that underpins it all; the maths is a handmaiden to extract implications that are already there.

A resplendent garment donned by ME after 1905 is its Special Relativity extension. This version is used to say things about places (frames of reference) moving at very fast constant speeds, close to the speed of light, relative to each other. (If there is acceleration we are in deep shit and need general relativity but this would be too long-winded a digression to undertake here).

Levi backtracks and after much meandering concedes the contrarian chap’s point. “Personally, I believe that by asking whether mathematics is discovered or invented, we forget that it is an intricate combination of inventions and discoveries. I posit that humans invent mathematical concepts – numbers, shapes, sets, lines – by abstracting from the world around”. We can forgive his circumlocution, but a materialist would not have needed so much obliqueness before getting to the point.

A similar case can be made about Newtonian gravitation and classical dynamics on the science side and Calculus on the maths side, or general relativity as physics and Riemannian geometry as maths, or the relations of quantum electrodynamics as maths serving science. The wave-particle duality and Heisenberg’s uncertainty principle in no way disrupt the materialist standpoint. But I concede the jury is still out – exclusively at the quantum level – on “photon entanglement” (“quantum non-locality”, what Einstein termed “spooky action at a distance”). This has no parallel in the macro world; trying telling the judge that when you had sex with that minor you were suspended in a state of probabilistic superposition! I am also unable to accept the fad that the real world does not exist in the absence of a conscious observer.

Gödel’s incompleteness theorem

One of my interlocutors (Gamini) has suggested that I address Gödel’s Theorem. A summary of the famous theorem from Wikipedia, with small linguistic adjustments, follows. Kurt Gödel (1906-1979) was a 25 year fresh graduate of the University of Vienna when he formulated it.

  1. If a system is consistent, it cannot be complete.
  2. The consistency of its axioms cannot be proved within a system

The concepts are self-evident. Obviously the axioms of Euclid’s geometry cannot be proved within Euclid’s geometry! (Gödel’s terrain was number theory). What is the relevance of all this to our science-maths concerns? If a scientific revolution causes one maths to be thrown out and another to find favour, the former’s axioms go out of the window as well. Euclid’s axioms lost out when general relativity lent on Riemann. Unexpectedly, some branches of abstract mathematics earned handsome dividends when quantum physics blossomed; most others remain abstractions solely for the delight of mathematicians. Maths is a handmaiden to be discarded at the behest of physics, like firing a maid when she no longer satisfies the boss’s desires.

Enlightenment and Divinity

The Buddha was enlightened but human – no scholar says he is divine. This raises problems for a certain brand of Buddhists that I have encountered only in Sri Lanka. These people claim that he knew about atomic structure, that the concepts of quantum electrodynamics are contained in his philosophy and such mumbo-jumbo. These folks don’t see the pickle they are getting into. Science is changing, so if their version of Buddha is committed to current science, than in a hundred years when science has moved on, he will be out of kilter! I wish people would think before they open their mouths.

Edwin Rodrigo wants to make me a Buddhist; he is pushing at an open door. My Marxism is no way hinders an appreciation of the wisdom of the Buddha. Phew! In one essay I have taken on Einstein, Gödel and some people’s version of the Buddha; must stop before I am certified insane and locked up in a padded cell.

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Latest comments

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    Did Buddha Know Everything?

    Dear Professor, I hope that all that mathematics, formulas etc. are not a way of keeping the door closed for Putujjanas like me. But the tactic does not work. Here is Edwin again.

    Did Buddha Know Everything? The Acinta Sutta deals with 4 Imponderables and the first of these is about the Buddha’s powers. The Sutta says that the range of powers of a Buddha is an imponderable. The knowledge of Buddha may be included there.

    That well and truly seems to shut the door for us. But the good Professor and I are made of sterner stuff. Doors however strong cannot stop us.

    The Dhamma Chakka Pavattana Sutta, the first discourse of Buddha, made a few days after reaching enlightenment, relates what the truth is and how he realized the truth by himself without the help of any Guru. In this Sutta he describes the 5 stages of enlightenment. Chakku, Gnana, Panna, Vijja and finally Aloko (enlightenment). But Buddha does not declare there that he knows everything.

    Then in Abhaya Kumara Sutta, Buddha describes using a beautiful example, what sort of knowledge he possesses. The description fits inherent knowledge that comes from long hands on experience, the sort that a master craftsman possesses, that can be drawn upon whenever required, available instantaneously and effortlessly without referring to other sources.

    My opinion is that he knew all about his special subject, the problem of existence that bothered many people at that time and does even now, and how to escape from it. And that is enough for me.

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      Dear Prof. David,
      (sorry if I would not use your surname – it s just not knowing exactly what part would be the first name).
      Quote
      “Edwin Rodrigo wants to make me a Buddhist; he is pushing at an open door. My Marxism is no way hinders an appreciation of the wisdom of the Buddha. Phew! In one essay I have taken on Einstein, Gödel and some people’s version of the Buddha; must stop before I am certified insane and locked up in a padded cell.” Unquote

      Very same pseudo buddhist has been making every effort pushing us many among CT readers to be racial against lanken minorities. If you would please study the loads of comments filled with all hatreds over the few weeks, that this particular man (calling he is one of your students) added caused us only angers.

      I really dont know as an olderage-teenager, why Edwin Rodrigo is behaving so.

      If he is a buddhist, first and foremost he has to learn respect even enimies. Surprisingly, none of his comments gave me the least sign of it.

  • 1
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    Reading your article reminded me a famous Galileo Galilei quote… “Mathematics is the language in which God has written the universe”.. Now I tend to believe this is true but it really puzzles me.
    Simple Fibonacci Series which was used 1200 years back to predict trading patterns with time is still the most used model to predict current Share Market, Forex behaviour.. Isn’t this strange ? Or Galileo must be very correct about God Nature…

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    Prof. Kumar David:

    I want to put forward a certain theory, probably most know it. Lord Buddha identified four ultimate truths in this universe. According to Buddha, as per Abhidhamma, only four truths exists in this univ universe. Nirvana (it is energy and it can not be converted, modified or created, forms or Rupa which is materiality called purest octact (very similar to super strings in Physics), mind and mental factors which are componenents of the mind. What is mentioned about purest Octact in Abhidhamma can be used to explain the universe most well and that model it better than the superstring. There is lot of information to this and I don’t write all here.

    Anyway, Hinduism or Brahminic religions explain their wisdom only with respect to the mind, mental factors and the materiality. Christianity and Islam are for weak people who can not understand the reality and they say it is the creator. Buddhism is the only religion which covers the whole universe in its entirety and answer the question of why we are here.

    With respect to your discussion, Maths can be used to explain all the relations with respect to forms, mind and mental factors. But, nirvan has to be understood only if one follows the path. Sientists are no where in explaining anything even close to the physics or chemistry or Quarks or superstrings. Scientists also have made mistakes in classifying energy and material (e.g. they identify sub atomic particles as both energy and matter)Buddhism is explicit in differentiating energy and material.

    Maths is about probabilitis. So, you can expect that universe is random. But, it is not, because karma comes into play and universe is semirandom. Karma is quantum relations between one another and applies to everything. Even the biological systems follow mathematical relationships because, they are madeup of matter. Geometry is about about mathematical relationships. Magnetism is something different. I think it is about spining of particles and it is mathematically related.

    Scientific studies are trial and error, scientific method and mathematical relationships. But, science won’t be able to find everything only with these three strategies. Scientific thinking is mostly christianity based and based only everything is random. They have to apply Buddhist teachings if they want to explain everything.

    Mark my words. Anyway, this is a brief explanation.

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      Good example of famous Müller-Lyer illusion…….
      “Christianity and Islam are for weak people”.. Ops.. Isn’t this coming from common SB inferiority complex?

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      Dear Jimmy,
      “Nirvana (it is energy and it can not be converted, modified or created, forms or Rupa which is materiality called purest octact (very similar to super strings in Physics), mind and mental factors which are componenents of the mind. What is mentioned about purest Octact in Abhidhamma can be used”
      You are way, way out of your depth here . How come you talk about string theory and such only AFTER the scientists found it? If it was in the Buddha’s teachings for 2500 years, how is it nobody knew? As the professor says, if science changes the theory, you will be left looking stupid.(Which is not so rare really, with you)
      Please go back to Koti-bashing.

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    Here is a new mathematical equation I just discovered:

    Mahinda Rajapaksha, his family and cronies = genes of klepto-bias + friends of klepto-bias + opportunities encouraging klepto acts + voters approving kleptocracy

    Therefore it will only be possible to get out of the klepto cycle the country is engulfed with by radically transforming the minds of the component ” + voters approving kleptocracy”

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    What are mathematics, sciences, equations, languages, religions and all the knowledge humans have acquired from time immemorial?

    It is thought in essence, it is partly based on the results of observations of his environment and partly the abstractions he created based on that observation. Another fundamental fact of thought is it is never the present and rooted in pure past and therefore it is dead, gone, spent and the past manifesting itself through a bio-chemical process as knowledge and experience stored in the brain cells. Humans are caught up in an illusion that it is real, present and factual.

    These thoughts are always flawed and subjected to the physical limitations of the brain and the sensory glands and the idiosyncrasies of the one in whose minds they arise.

    All the sciences, theorems, theories, mathematics etc. are based on thoughts and therefore the said limitations of the thoughts apply to them as well. For example there are certain people who are blind to certain colours whereas other people can see those colours. How can science or math solve this difference and bring into the minds of the two parties unique reality? This is why thought is flawed, limited, relative and a tool that is very week in grasping the myriads of nuances, facets, vividness, multitudinous and combinations of nature, material, natural and man-run processes. However despite these limitations humans have done well to harness and understand the world, energies and materials around him to so that he could intervene in the nature to change it course to fulfil his personal and collective objectives.

    But what could Buddha have said so many years ago when so called industrial revolution and the advent of the sciences had not still happened and the world and its natural environment remained pristine, pure, unsullied and undistorted? Well, any layman’s or any Monk’s explanation or definition for that matter who hasn’t really grasped and factually understood and seen what he said based purely on thought would be pure imagination and useless. How then do we see what Buddha said? ………………..?

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    “Edwin Rodrigo wants to make me a Buddhist; he is pushing at an open door. My Marxism is no way hinders an appreciation of the wisdom of the Buddha.”

    Messrs KD’s or Edwin Rodrigo’s Marxism or Buddhism are relative, based on cause and effect and born out of thought. KD is now aged and will continue so until his faculties are so weak he is no more able to sustain his thought process which is happy to say he is Marxist, appreciate Buddha’s certain seemingly valid pronouncements etc. But thought being the very limited tool we have, rooted in the dead past where do we go from here while our senses can still function satisfactorily? What could have Buddha said almost 2500 years ago?

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    Frozen Nuts

    The most interesting part of AKD’s article is Div(B) = 0. But in normal style AKD makes it so unromantic by just saying “There is no true magnetism”. Even Silvestra my unromantic housekeeper, would have put it less unromantically. The problem with AKD he is that that he is so unromantic.

    It is as if Maxwell is telling me, ‘Buddy, there are no magnetic monopoles. So don’t ask your Silvestra to look for them under your bed.” Maxwell doesn’t know that even without his advice, I have made it very clear to Silvestra that the region under my bed is no man’s land (or should I say No woman’s land?). There are good reasons for that and they are not very scientific.

    As the Professor has explained, the equivalent Electrical equation is Div(D) = Rho (The charges contained in the region concerned). D here is the Electrical flux, the electrical equivalent of B (the magnetic flux).

    We know that any magnet has two poles (North & South). So can’t we just cut a bar magnet in half and separate the poles? The answer is NO. If you do that, you get two shorter magnets with 2 (N & S) poles each.

    However, recent advances in physics such as the exotic string theory, necessitates magnetic monopoles to exist. Furthermore, about 40 years ago Paul Dirac showed that magnetic monopoles are not prohibited by Maxwell’s equations if electric charges are quantized. About 30 years back, there was a news story that a magnetic monopole had been discovered floating in the upper atmosphere. The search for them has been going on at CERN for decades.

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    Fifty years ago the efac where AKD lectured was on par with world’s best like Cambridge (so they were saying). Today it is even below the rank of 4000. So much for science, maths and engineering. It in in these hallowed institutions that the foundations were laid for the development of computer (over 200 years ago in Cambridge when they tried for difference engine to prepare astronomical tables for navigation purposes). The primary occupancy of our academics (and students) to date is how to topple governments. When will they try to do something for the country by getting the students to do innovative things. Please remember that the world has entered the fourth industrial revolution with AI.

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      That is also the reality for the cambridge and oxford today.

      They are not the leading universities in the world today for science, engineering and medicine.

      But I do know the levels that lankens unis have been fallen in to.. that has lot to do more with the standards of the local universities. Some 60 years ago, just a BA or BSc degree holder earned a high value not just within a boudaries of the country but in the world. Nigerians repeated how their school systems hired srilanken teachers. And how intelligent those teachers had been.
      Today, even MBBS holders and their levels are not professional enough to compete in other parts of the world. Most moved out of the country being unable to prove their abilities, lag without being employed in their fields. Please get your facts from Australia, UK, Canada and America.

  • 0
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    Science/Math or Religion is based on belief/faith.

    Can talk about axioms and assumptions and most will fall asleep.

    Most will agree that religion is based on faith.

    Is not science based on faith. Does anyone test and verify the basic tenets of science/math.

    Say simple Arithmetic 1+1=2

    We take it for granted. Is it really true.
    Can it be proven, maybe within statistical limits.
    Then stats assumes certain assumptions, a circular argument.

    At a molecular level is each proton absolutely equal to each other (forget about under different conditions).

    So is this absolutely true.
    1 (proton) + 1 (proton) = 2 (protons) (under equal conditions).

    So is there an absolute truth? in Religion or Science.

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      sbarrkum
      There could be an absolute truth.
      An essential difference between religion and science is that the former claims access to it and argues that all else follows from it (and it fudges when claims fail); while the latter ceaselessly searches for it (and when it thinks that it has got there, it is made to realize that there is more to it than discovered, despite attempts to fudge findings that challenge theory).

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        So

        Religion believes/has faith there is an absolute truth.

        Science is searching for the absolute truth.

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        To put it simply:
        Science is a blindfolded man in a dark room looking for a black cat.
        Religion is a blind man looking for a black cat which isn’t there, shouting “I found it!!”

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          o.c.
          Some do not stop at shouting “I found it!”, they proceed to describe it in detail.

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        “(and it fudges when claims fail)”

        SJ,

        Sorry to disappoint Sir.

        How do you explain the uncreated and revealed using the human language designed for describing/semi-experiencing the created realm only and that too a fraction of it? Yet that which is “shown and seen” is the clearest and profoundest perception and the source of unfading joy. It is like asking a dog, even of the best breed to describe a Da Vinci.

        It is the limitation of the human languages not obfuscation by the “seers.””(and it fudges when claims fail)” should be read as: “is unable to explain further)….

        He who knows understands, he who does not cannot. That is the truth about truth.

        I mean to say that language is the problems Sir, not religion.

        Philosophers and Marxists, too are stumped when it comes to “Wisdom”. Go back to Pera and sit on top of the Hantana Hills. It will dawn.

        All who studied too hard did not “Learn” there.

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          Todi
          Thanks for the lesson.
          But I do not claim to have answers to all questions: I have plenty of questions on each answer.
          If a question is relevant I seek an answer and if I succeed– to the extent that it addresses my concerns –I am glad. If I fail I try again.

          I have no issue with anyone believing what he likes to believe.
          But I have seen too much of fudging when claims fail to stand up to reality. (I will not go into specifics as you would already know enough.)

          On God, Truth and other such things, I like this one:
          “kanDavar viNdilar viNdavar kaNdilar” (The one who saw said not; the one who said saw not.”

          I have no claim to wisdom, but try– occasionally successfully –to be practical. May I improvise on the above to say: “The wise do not claim to be wise; those who claim to be are not wise.”

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            SJ

            Thank you for the quote, though the expression is known in other tongues too. Who said this please in Tamil?

            “kanDavar viNdilar..” (The one who saw said not…)

            Back to square one. Kandavar cannot say what “IT” is like (he knows one cannot describe “IT” using human communicating mechanisms). So he said not.

            Ah, words are very tiresome to the soul. Truth is always there, unchanging ever, and is arrived at when the fog of thoughts (words) subsides.

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              T
              I am not sure of its existence in many other tongues.
              It is deeply philosophical and something like it could be in an Upanishadic text. (I am no expert.)
              It sounds rather in the Siththar tradition to me. (Some have tried to attribute it to Thirumuular but without the full text.)
              I vaguely remember Gopalakrishna Bharathi touching on the idea in the song “aiyaiye meththak kadinam” (in his Nanthanaar muscical).

              I liked the quote because it puts pretenses to ‘supreme knowledge’ where they belong.

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                It is the teachings of the Christian desert fathers 2nd century AD down. It is in Coptic and Greek also.

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      In Boolean Algebra we ave 1 + 1 = 1. It all depends on the intital assumptions and definitions.

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        Also the domain of operation.
        1 and 0 are just symbols here for true and false.
        They hove nothing to do with binary numbers either.

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          Yes you are right. Logic values. practically logic gates, on off switches etc.

          In Binary numbers, 1 + 1 = 10, right?

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            E.R.
            YES

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      sbarrkum

      Science/Math or Religion is based on belief/faith.

      Religion is based on faith. but, buddhims is not based on faith. Lord Buddha asked people to question the dhamma every way possible and if it understandble your mind, then accept it.

      It is a very democratic doctrine and does not force people to believe it.

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        J
        Buddhism I agree is the most open minded.
        But there are weak spots.
        The place of women is something not to be very proud of.

        Studying the views of Buddha is not a matter of faith.
        Claims to following the Buddha involve an element of faith. That is where a cult of the Buddha and practices of worship creep in.

        The big question is whether it is practiced at all, except by a very tiny minority.

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    IDAPPACCAYATA – The Heart of PATICCASAMUPPADA (Dependent Origination)

    The Author says near the end of his article, “The concepts are self-evident. Obviously the axioms of Euclid’s geometry cannot be proved within Euclid’s geometry! Great! That is like an invitation for me to open the Idapaccayata door.

    *Imasmim sati idam hoti (When this exists, this exists);
    *Imassuppada idam uppajjati (Due to the arising of this, this arises);
    *Imasmim asati idam na hoti (When this does not exist, this does not exist);
    *Imassa nirodha idam nirujjhati (Due to the ceasing of this, this ceases); (Source: A Dhamma Website)

    Paticcasamuppada, is the heart of the Dhamma. Buddha said that, one who sees the Dhamma, sees the Paticcasamuppada and vice versa. The 4 sentences above contained in Idappaccayata may be considered as the 4 principles that govern the working of Paticcasamuppada. With them, Buddha is laying down the nature and definition of what is meant by a Cause-Effect pair.

    A set of axioms is any set of initial assumptions from which other statements are logically and systematically derived. As AKD says, Axioms cannot be derived from principles of deduction nor can they be proved in the formal way because they are the starting point and there is nothing else they logically follow from.

    This shows that, 2600 years ago when introducing Dhamma, Buddha introduced the concept known as axioms today. Thus he followed an ‘axiomatic approach’ to the subject, which was independently developed by Greeks such as Aristotle, Archimedes and Euclid about 3 centuries after Buddha introduced the concept.

    Modern logicians and mathematicians say that a good set of axioms (postulates) should possess several characteristics to be considered so. These are.

    *Simplicity
    *Conciseness
    *Completeness
    *Consistency
    *Non Redundancy

    On analysis, we find that Idapaccatata meets all these conditions.
    (Contd.)

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    The point that most of you are missing is this – to understand Science, Religion etc we use the brain. But we don’t really know how the brain works! We are using an instrument which we don’t understand and which may be faulty. That’s not very scientific is it?

    The Buddha’s discovery of a way out of Dukkha is based on gradual awakening through awareness, rather than thought. Whether it works or not can only be determined individually by trying it. All else is idle speculation, what he called ‘the all-embracing net of views and opinions’.

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    Maxwell’s Equations and Ant Holes

    As summer approaches, black ants (Kadi) come out of their cold underground lair in my garden searching for food. Watching them, I realized that the patterns of movements of ants symbolize the meaning of Divergence (inverted triangle) found in Maxwell’s Equations. The author says: “The second equation says the electric flux emanating from any region depends on the net charge contained therein”. (i.e.) Div(D) = q (the electric charge inside that region).

    Imagine my ant lairs having 2 holes. One for entry (A) and the other for exit (B) exclusively. Ants are highly disciplined and never break traffic rules, which can hardly be said about humans. The ants disappear underground through A. If you draw a circle around that hole, the divergence of ants in this region is negative (- by convention) because they disappear.

    The ant movements can be given as small arrows called vectors. Each ant has a speed and a direction. At A, this large collection of small arrows go inside the hole. But no arrows come out of it. The situation at the exit (B) is exactly the opposite. Little arrows, again forming vectors, come out of it. Thus, it has a positive divergence.

    If you take any other region away from A and B, we have ants moving around forming small vectors. If you mark out any region, you will find that some arrows will be moving in to this region and some moving out. The region is in constant flux but no ants disappear. The divergence there is zero.

    What I have described here is the 2 Dimensional model. Arrows do not go up down and remain on the surface, if you are willing to ignore the vertical movement at the holes.

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    Discussion is about effectiveness of mathematics. But comments are every where and mostly out of point.

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      Jim, though the Kalaveddah invariably starts off with the phrase, “Jimsofty, dimwit”, I have been following up your writing with a lot of interest and I can tell that you that you are certainly not dimwitted `and that you hold a lot of promise.

      So, why don’t you try to correct the situation by writing a model comment relevant to the discussion about the “effectiveness of mathematics”, to the point, not exceeding 300 words. We shall all be grateful to you for that.

      Go ahead buddy we all are watching you.

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        Yes,Jimmy, we shall watch your career with interest.

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        EDWIN RODRIGO

        Read my comment. I wrote which parts of the universe obey mathematics or can be explained with mathematical models or equations. Mathematicians can develop models for every part of the system except when it comes to purest octacts (superstrings) they should fail at least partially. for Nirvana, the only scientific method is
        meditation.

        I have written it in brief. I will also be passing my best before date soon. So, don’t expect anything much from me.

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          Jim, I said a model comment. I hope no one will take it as a model. It is like one of those comments in Yiddish that Malle Urine makes. I have to say that your comment is not purely in Yiddish, only about 80% of it. The rest of it is drivel.

          Examples:

          “What is mentioned about purest Octact in Abhidhamma can be used to explain the universe most well and that model it better than the superstring”.

          “Buddhism is explicit in differentiating energy and material”. Differentiating? That is what everybody was doing until E=mc2 integrated it. Now you want to go back?

          Abidhamma Pitaka is not purely Buddha’s word. If you want pure Buddhism please go to the Sutra Pitaka only. After Buddha, Pandithayas like Nagarjuna have played havoc with Dhamma in Abidhamma. Anyway can you give us the references from Abidhamma?.

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            Bāhiya Sutta – English Translation (Ref. ‘Clearing the Path’ Rev Gnanavira:)

            This is the best I could find.

            Then Bahiya, you should train thus: In the seen there shall be only the seen; in the heard there shall be only the heard; in the sensed there shall be only the sensed; in the cognized there shall be only the cognized. In this way you should train yourself.

            When, Bahiya, for you, in the seen there is only the seen.(and so on).. in the cognized there is only the cognized, then, Bahiya, you will not be that by which. When, Bahiya, you are not that by which (tvam na tena), then, Bahiya, you will not be ‘in that place (tvan na tatta).’ When, Bahiya, you are not ‘in that place’ then, Bahiya, you will be neither here nor yonder nor in between the two. Just this is the end of suffering.

            Rev. Gnanvira says that this is a highly condensed statement but as tough as you will in Satre (Jean Paul Satre) Nobel Laureate and well known philosopher.

            Edwin’s comments: The above translation is the best the Rev, could do. Pali is a highly complex language and PhD’s have been awarded, just for research on one Pali word. For example, (tvam na tena) and (tvan na tatta) are very difficult to understand, leave alone translate. A good knowledge of Pali is essential if you want to study Dhamma.

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              Sorry, please read the Pali version first and the Translation second.

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              EDWIN RODRIGO:

              What you have written is totally unrelated to the discussion here.

              What buddha taught here was to achievement enlightenment in the shortest way. In other words how to give up attachment to the desires within a short time. Bahia was very intelligent and was matured to be enlightened. Buddha knew he did not have much life left and he was about to be killed. That is why buddha taught him these four short versus.

              I don’t know why you think, it is relevant here.

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                Well Jim, as the Keralites Indians here say “Dafren Dafren people have dafren dafren ideas”.

                Cheers!

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                Abhidhamma

                Jim, we have to take our own paths we see as correct to realize the truth. I took Buddhism as a subject for my GCE(OL) and scored a Distinction pass, the only one to do so in our school (Ananda) in that year. I studied Abhidhamma at that time with diligence and was wondering how one could spend time on such detailed things if one were to strive like a man whose head is on fire to escape from Dukkha.

                Then when I was introduced to Rev Gnanavira’s ‘Clearing the Path’ I found that he mentions the components of Suttapitaka and Vinayapitaka as Buddha’s teachings. He says no other Pali books whatsoever (this of course includes the complete Abhidhamma Pitaka) should be taken as authoritative; and ignorance of them may be considered as a positive advantage, leaving less to be unlearned.

                I agree with him.

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                AKD and Bahiya

                Jim, you say that Bahiya Sutta is not relevant to the discussion here, I disagree. Please refer to the last section of the Author’s article entitled, “Enlightenment and Divinity.” As mentioned therein AKD knows that I am working on him for quite sometime. Being a highly intelligent man, I know that he can be a modern day Bahiya, something that I can never be in this life. Hope that covers the relevance once and for all because I want to delve deep in to Bahiya Sutta together with you.

                This part of the Sutta is like a riddle.

                When, Bahiya, for you, in the seen there is only the seen.(and so on).. in the cognized there is only the cognized, then, Bahiya, you will not be that by which. When, Bahiya, you are not that by which (tvam na tena), then, Bahiya, you will not be ‘in that place (tvan na tatta).’ When, Bahiya, you are not ‘in that place’ then, Bahiya, you will be neither here nor yonder nor in between the two. Just this is the end of suffering.

                Please help me to understand the parts in italics.

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            Edwin rodrigo:

            All the information is in the internet. Read Abhidhamma.pdf (Abhidhamma mulika Karunu by Ven NArada), chapter 6 – analysis of Matter. If you read Abhidhamma, you understand Buddha taught Arahant Sariputta the summary. After that, different arahant monks described it. Nalanda University which desecnding pupils of Arahant Sariputhha explained it and what we read is from that school because, all those students educated Nalanda university came to Sri lanka.

            that is not the only reference. there is one more by Ven. Rerukane chandaWilama and more by Myanmar monks. There are more explanations such as those by tibetan monks. Palica non, I heard there are five different versions based on the language.

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            Edwin rodrigo:

            Another mistake. Sutta pitaka explains things in macro scale. that is skandha, ayathana etc., but, Abhidhamma explains things in it’s minute form which is the ruupastaka or sataha maha bhutha. Unlike science, it is not theory or concepts, but it is the reality.

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              Abhidhamma

              jimsofty, you are not dim witted at all as the Kalaveddah claims. Thanks for all the references.

              Here are some of the important sayings of Buddha.

              1) Monks I teach one and only one thing. Dukkha. (I believe dukkha here means that things do not go the way you want. This makes your existence a big problem for you. The problem of why we exist, bothered existentialists like Sartre, Kierkegaard and Nietzsche) and my favorite Guru rev Gnanavira (a British monk).

              2) Buddha said Dhamma is not for settling arguments, having debates etc. It is for practicing and for practicing only. Additionally, I think it is good for setting exam questions on Buddhism, to do research and get PhD’s and such academic pursuits.

              I do not want to waste my time on Abhidhamma because it goes in to unnecessary details. Many Buddhist scholars shun Abhidhamma for that reason as well as the evidence that it has been doctored by people like Nagrajuna, Boddhghosha et al several centuries after the Parinirvana.

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        Bāhiya Sutta

        Jim, Here is what many consider as the most Intriguing Sutta in the Tripitaka. Buddha gave this short discourse to Bahiya of Bark cloth, a shipwrecked wanderer, who had never heard anything about Dhamma up to that time. On hearing this, Bahiya realized the truth and became an Arahat. This means that this must contain the very essence of Buddhism if one is intelligent enough to understand it. Bahiya was a man of great intelligence, and Buddha knew that he was.

        Jim, perhaps with all the intelligence you have shown you should be able to understand it. I have tried to do so for the past 10 years, but I can only understand it partially.

        Bāhiya Sutta in Pali:

        Tasmātiha te Bāhiya, evam sikkhitabbam:

        “ditthe ditthamattam bhavissati,
        sute sutamattam bhavissati,
        mute mutamattam bhavissati,
        vinnāte vinnātamattam bhavissati”-ti.

        Evam hi te Bāhiya, sikkhitabbam.

        Yato kho te Bāhiya,
        ditthe ditthamattam bhavissati,
        sute sutamattam bhavissati,
        mute mutamattam bhavissati,
        vinnāte vinnātamattam bhavissati,

        tato tvam Bāhiya na tena, yato tvam Bāhiya na tena, tato tvam Bāhiya na tattha, yato tvam Bāhiya na tattha, tato tvam Bāhiya nevidha, na huram, na ubhayam-antare, esevanto dukkhassā”-ti.

        Translation will be posted next.

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    Mathematics Mafia and Flux Cutting

    The problem with the Author Prof. Kumar David is that, despite his innocent looks, he belongs to the Mafia – the mathematics mafia, which is as harmful to the Putujjana as the drug mafia. Therefore, we have to be careful about articles such as these, whose main objective is to perpetuate the class privileges of the likes of AKD. They want to keep the electic baases as electic baases, engineers like us as engineers so that Professors like him will remain as Professors.

    Take his treatment of Maxwell’s equations for example. Here AKD is elevating Maxwell to the level of a deity while making short shrift of Michael Faraday (who did all the spade work) by saying that the ‘famous 3rd equation’ is known as Faraday’s Law of Induction. Then he cleverly kicks it down by claiming that it is better known to schoolboys as the flux-cutting rule. In other words Faraday’s work is schoolboy stuff, like slicing bread. Then he goes on to contradict himself by saying it is about how electricity is made in generators.

    That explains why we have so many power cuts, tariff rises and breakdowns. CEB does not know how to cut flux. Of course they know how to get cuts. But to cut flux so that the Putujjana children can do their homework at night, Oh No! That is a different kettle of fish. You have to wait until our engineering faculties produce graduates who know how to cut flux. Then we will have lights. Aloko Udapadi!

    Why is AKD doing this? Faraday did not have any formal schooling and was a bookbinder’s assistant. In other words Faraday was a Putujjana like us, who should be kept in their proper place.

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    If we want to find a famous scientist in the World most probably you have to go to a cemetery,because most famous scientists were from the past.In the present scientific community there is a physicist who has acquired a legendary status through his research and popular science writing.He is none other than the British Physicist Stephen Hawking.Still amongst the living he is completely paralysed[Motor Neurone disease].
    Hawking was elected a fellow of the Royal Society in 1974 and received its Copley Award in 2006.This reminds me of the previous essay of Prof;Kumar David on the Man who knew infinity[Srinivasan Ramanujan].
    Hawking is presently working on the TOE theory[Theory of Everything].When this is typed you would see a film about him as told by his wife Jane Wilde.

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    “Can it create scientific knowledge? Does its use in a scientific thesis… create knowledge not already contained in the scientific theory itself?”

    As Hardy did, we can separate mathematics into the “pure” and “applied” streams. Pure mathematics is entirely self-contained, based on various underlying objects & structures, none of which rely on any physical phenomena in the real world. For example, you will not find an actual “vector space” in the real world. These structures and objects are defined in mathematical terms; whether or not a physical counterpart exists is a matter of coincidence.

    While mathematics defines its own structures and objects independent of any physical reality, the opposite is true of science. In science, the central objective is to perform an experiment and attempt to deduce some pattern in the physical world. Mathematics can provide the tools to refine such an experiment, whereby calculations become more precise, but the mathematics does not replace the experiment in its entirety. As an extreme case, one might consider String Theory. Here you have very nice mathematical insights and (arguably) some interesting insights into the physical world, but zero experimental proof. With general relativity, one could design a GPS system. With quantum mechanics, a solid-state electronic device. With String Theory, however, one never goes beyond the realm of mathematics, so there is a great debate in the physics world as to its value.

    Can you deduce electromagnetics from 4 equations? Yes, but in some sense, electromagnetics exists apart from those 4 equations. Certainly, Edison and Faraday only had the faintest idea of the underlying mathematics.

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      Maxwell’s Equations

      To Prof. David & Lester

      Lester you ask, “Can you deduce electromagnetics from 4 equations?”.

      I have problem, that is quite different. Why are the equations for Electricity and Magnetism not symmetrical? For Ex. the first two equations are (1) Div(D) = ρ (electricity) and (2) Div(B) = 0 (Magnetism). A much worse difference exists in 3 & 4 with the so called ‘displacement cuttent’ included in one. There seems to be something wrong here. With so much interchangeability between electricity, why do this differences exist in the equations?

      Nature (or God) is generally democratic. Having created electricity and magnetism, why has nature (or God) be so discriminative of magnetism? Even engineering and science curricula teach much less about magnetism than electricity.

      I have a feeling that it would be one day possible to combine all 4 equations to form one super equation.

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        Edwin Rodrigo:

        “Why are the equations for Electricity and Magnetism not symmetrical?”

        They are indeed symmetrical in curved spacetime, as Einstein deduced in General Relativity. Given an an inertial frame of reference in curved spacetime (Riemannian space), then the laws of electromagnetics are equally valid for two different observers.

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          Thanks. I did not know that. I hope you we both are referring to the same thing.

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    Prof David

    Science of ancient times.
    From one minute audio is in English. Formula for Electricity
    https://www.youtube.com/watch?v=u8EIbuDiokE

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    Mathematician’s Tricks

    Mathematicians like AKD are magicians. They resort to illusions, diversions of attentions and mathematical gadgetry to delude the ‘Putujjana.’ The idea is to keep the putujjana away from their domain and lead them lemming like, as they do in the left movement, sometimes to their death. Therefore, what the Leftist Leader AKD and what Professor AKD are doing are essentially the same thing, (i.e.) Pull wool over eyes.

    Faraday also had to face the same type of opposition. Faraday was from a poor family and the lowly assistant of a book binder. But like Bahiya, he had a very keen and inquisitive mind. He was fascinated by electricity and paid to go and listen to Sir Humphrey Davy who like AKD was an expert of his time. Faraday did not know any Mathematics and had to do all his thinking in terms of non mathematical notions such as lines of force.

    A big mystery at the time was how the current in a conductor affected a compass needle placed close to it without any apparent physical contact. The experts at that time laughed at the idea of lines of force that Faraday came out with. Even when Faraday constructed the first rudimentary motor they were skeptical and tried to ignore him.

    Finally, anyway, the putujjana lost because Maxwell managed to dress up the whole thing with mathematical tools such Divergence operators, curls etc. Not satisfied with that he added another layer of mystification using combinations of Greek mathematical symbols. The high sounding Divergence Operator (ϭ/ϭx + ϭ/ϭy + ϭ/ϭz) is one such devil, that Faraday could never have understood.

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      You too should be a magician not even seeing that you abuse web space if same comment is uploaded twice.

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    Adding Insult to Injury

    After having bamboozled, mystified and fooled the Putujjana, all of which was done to take away the admiration the Putujjana had for one of their kind, the final act in the campaign came with the adoption of the so called SI units by all countries.

    Look at the 1st equation. We have Div(D) = ρ. Thus an electrical charge of 1 unit is emanating ‘one line of force’. Is that not silly? Of course it is silly. Even a monkey can understand that there is something wrong here. “There is only one line of force”? The monkey is going to ask. So if the charge is an isolated one, “in which direction is this line going? A very legitimate question for even a putujjana. With that, the final nail was driven in to the coffin of the easily understood and vividly imaginative concept of lines of force developed by the insightful Faraday.

    To see the evilness of this, we have to go back to the previous system of units called the CGS units. Maxwell’s 1st equation with those units was Div(D) = 4πkρ. The problem of a unit one charge emanating one line of force is not there. 4π is the solid angle around a point. Thus it gives a good physical insight to a non mathematical person. One can also deduce intuitively that D decreases as we go away from the charge.

    These are the machinations that the mathematicians used to drive away creative people like Faraday from their field.

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      Physics models nature to make sense of it. Mathematics enables us to analyse natural phenomena using the models.
      There should be no serious contradiction as both are based on reality. Abstractions too return to reality at unexpected moments.

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    Buddhism and Science

    In the last section entitled “Enlightenment and Divinity” the Author says: “The Buddha was enlightened but human – no scholar says he is divine. This raises problems for a certain brand of Buddhists that I have encountered only in Sri Lanka. These people claim that he knew about atomic structure, that the concepts of quantum electrodynamics are contained in his philosophy and such mumbo-jumbo. These folks don’t see the pickle they are getting into. Science is changing, so if their version of Buddha is committed to current science, than in a hundred years when science has moved on, he will be out of kilter! I wish people would think before they open their mouths”. I agree with the Author completely there.

    What Rev. Gnanavira says about the same subject adds another dimension to it, “It is a fashion nowadays to hail modern science as the vindication of Buddha’s ‘anatta’ doctrine. Here is an example from a book: ‘the voidness of selfhood in Teachings of Buddha, is in full accordance with the scientific thinking’. The implication is that Buddha solved the problem of self and the world by adopting the impersonal attitude of scientific objectivity.

    This is pure rubbish because the scholar’s idea was to take an objective view of the problem ignoring the individual. The fallacy of this method became more evident with quantum theory that matured after the death of Rev. Gnanavira. Scholars prefer an impersonal horizontal look at the problem. What is required however is to take vertical look at the abyss, that is existence, understand the problem and then consider solutions.

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