Three Hard Questions and Quest for Their Solution

Mr. Gill

As a dabbler interested in Mathematics I am really grateful to you to bring this subject up.

I find the documentary about the solution to Fermats` Theoram. I have watched this several times and always in a mesmerised awe. In my opinion there is no drama produced whcih has such rivetting drama element to it. I sometime discuss this with a friend who has a phD in Mathematics.

THe other day someone had mentioned about a hindu scientist/mathematician who has perhaps found something/something ( I am relustant to write formula because I am cannot recall) about prime numbers. I have bee looking for that name ever since. Could you please elucidate a bit on that.

Rest of your artcle seems very interesting as well and I sincerely hope it draws the attention from the right quarters especially DRUMS, Urstruly, Sameer, rsridhar, and perhaps a few others. I will read the whole article at a litle bit of leisure.

Thanks again.

While it is true that one cannot speak on the ineffable, it is just as true that we have many inneffable concepts we use to induce precision. In mathematics, the CONCEPTS of zero and infinity are also ineffable, as is true symmetry (when we compare human produced geometry with the ``perfect circle``). Thus if god is ineffable (which it is, aside from referring to it in paradox), then we have little right to speak on numbers.

We should keep in mind which PEOPLE are pursuing the ``theory of Everything`` and from where they get their foundation. Current science sees the world through the filter of the LEFT brain. This ASSUMES an innecessary premise (Proof of God`s existence must come from scientific means). Do the math, Invalid Premise = _______ conclusion. We are not told why God cannot be accessed by other means (right brained, inspiration, introspection, paranormal activities and so on), its only implied that such methods are not factual as they cannot be repeated in a lab. Well neither can a lot of physics (we still have no proof on the properties of black holes).

Left brained arguments defeat themselves simply because one is deducing laws applicable to one field (finite) and applying them to another (infinite). It is logically flawed. The raises the question of what constitutes ``proof.``

What`s provocative is that the notion of God is central to many religions, yet most religious people have likely not even thought about this stuff.... Buddha was right, it really doesnt matter.

[ ... that is, four dimensions of space and one dimension of time ... ]

I thought space has three dimensions and not four.

Gill Sahib: I read the three questions with interest. Here are some comments:
On Question 1: I enjoyed the discussion on Fermat`s last theorem where you stated clearly and simply what the theorem was and confirmed the fact that it had been solved. It would be interesting if it is possible to describe Wiles logic whereby he solved the theorem in terms that even a chowk-ignoramus like myself can understand.
On Question 2 (the God question): this is a hoary debate by now I think, and trying to put logic here is I think a chase after a wild goose that no one has ever seen. I was surprised by your omission of Kant`s famous works in this regard where he is said to have first proved, then disproved, the existence of God. I think the question will always remain one of faith, or at least until the day humanity is so far advanced scientifically that it can travel back and forth in time at will, criss-cross multiple universes, and indeed be able to shake hands with God. I dont think that day is anywhere near. So, to me this question is as relevant as trying to determine how many angels can balance on the head of a pin (as the mullahs of middle age europe used to try and do). The more relevant question, to my mind is: can we as humans live up to the values described by the 99 characteristics of God (being fair, just, merciful etc.) in our everyday life?
On Question 3: This is essentially the same question as question 2, put differently: Can man ever know everything there is to know? History shows that it is dogmatic people have repeatedly become arrogant and believed they have found some ``final`` laws of nature. And then their neat little world is shattered by new findings. Copernicus shook church dogma when he removed earth (and thereby man, and thereby the church mullahs of his day) from being the center of the universe. Einstein and Planck did this when they showed how the Newtonian edifice (which physicists of the late 19th century thought represented the final laws of nature) straddled time-space only in the same sense that an ant-hill is an entire universe (i.e. it is an entire universe only to the ants that live in that ant hill). And as we enter into the 21st century, there are rumblings of changes to come in our understanding of the workings of nature that will dwarf even the incredible achievements of Einstein.

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Gill Sahib,

The three questions you`ve considered are of quite distinct characters.

`Fermat`s Last Theorem` is a straightforward and very specific statement about numbers. It is easily the most precisely-defined and unambiguous of your questions. An utterly mind-boggling amount of new mathematics has been discovered (created, if you prefer) in the nearly four centuries since Fermat made that marginal annotation in his copy of Diophantus. New mathematical fields and sub-fields have been discovered and explored in great depth, whose very existence was utterly unsuspected or at best only dimly perceived in Fermat`s day; sub-fields have in turn sometimes reunited in unexpected and fruitful ways, etc. Fermat were he to be resurrected today would find the subject matter and technical apparatus of contemporary research mathematics unrecognizable at first glance. However, the `rules of the game` of coming up with a proof of FLT have not changed (or changed very little) in the period between Fermat`s conjecture and Wiles` proof. Given a couple of years to catch up on three-and-a-half centuries worth of mathematics, Fermat would probably agree today that Wiles proof is valid and fair, though far more sophisticated than he could have conceived.

The so-called question of the `existence of God` is at the other end of the spectrum of precise definition. It is evident that different people have a multitude of quite different, though commonly vague, imprecise, and ill-defined, notions of God, when they raise this question. More often than not the very same person who ponders and obsesses over this question has multiple notions of God in his mind and blithely conflates them without being aware of his bemuddlement.

At one extreme, one might identify God with the Universe or with Reality itself, or at a few removes of abstration, with aesthetically perceived Harmony, Symmetry, Elegance, abstract Order in the laws governing natural phenomena. This notion is something that many if not most scientists recognize and believe in. At another extreme one might conceive of a sort of ultimate ineffable, an unmoved mover, an uncaused cause, all-encompassing, infinity of infinities, etc. This notion is connected with familiar antinomies. At a third extreme one might have in mind a personal and basically anthropomorphic God, in turns jealous, beneficient, vindictive, just, merciful, omnipotent, demanding fealty and obedience, requiring worship and propitiation, laying down laws by which human beings ought to live and judging individuals by their adherence to these laws, etc; a being who supposedly cares about the lives and affairs of human beings and societies. This is the familiar Judaeo-Christian-Islamic divinity, and has clear tribal origins. I have yet to see a good reason to believe that these several distinct conceptions (and there are no doubt many others) - even if they are all well-founded - refer to one and the same entity.

As to various alleged `proofs` of EoG, these are not airtight logically impeccable proofs in the mathematical sense. They are better regarded as attempts to create faith in the mind of the True Believer, and in that sense they serve the same function as supposed `miracles` and `Signs to the Faithful`. On close examination some - such as Anselm`s ontological argument - are seen to depend for their force on the confused and imprecise uses of concepts. Others - such as the cosmological and teleological arguments - boil down in their essence to `the negation of this proposition is inconceivable, therefore it must be true`. As far as I can discern, their overall effect seems to be to befuddle, bemuddle, bedazzle, becloud, bemuse, bewilder, bewuther and in short to bludgeon, befog and benumb the believer`s baffled brain into accepting religious faith, on the grounds that something confusing and convoluted but supposedly profound must be sound. So perhaps God might be fruitfully identified with the befuddled believer`s bafflement.

Some of the more defiantly honest, if logically unsustainable, excuses for religious faith have been Tertullian`s `Certum est, quia impossible` (`It is certain, because it is impossible`) and Pascal`s `The heart has its reasons of which reason knows nothing`. Many people who proffer arguments for religious belief lack this intransigient honesty. Requests that they defend or explicate their claims are typically sought to be dismissed with an airy hand-waving ``Why, it`s obvious!``. Should the tactless questioner be persistent he can expect to encounter a smokescreen of obfuscation concealing vacuity.

Finally, the sought-after `Theory of Everything` is a theory of physical reality but probably not of all conceivable phenomena. Criteria of success of a ToE seem more vague than for FLT, and with a strong aesthetic component. Nevertheless this is probably a less futile endeavour than the searchfor a proof of EoG.

GhalibZaman

``THe other day someone had mentioned about a hindu scientist/mathematician who has perhaps found something/something ( I am relustant to write formula because I am cannot recall) about prime numbers. ``

Prime numbers were always a fascination to errr... ``Hindu mind``. I think you are talking about the recent breakthrough in the field of ``Number theory`` by a team comprising of a couple of IIT Kanpur kids Neeraj Kayal, Nitin Saxena and Dr. Manindra Agrawal. Basically they have developed an algorithm to find out quickly and definitively whether a number is prime. You can download the celebrated paper from this IIT Kanpur website that contains the media reports, paper and the photographs of the team members.

http://www.cse.iitk.ac.in/news/primality.html

For a more laymannish explanation, you can visit the New York Times report, the link to which is provided by the above site.

PS Number theory also fascinated one of the greatest Indian mathematicians of the modern era, Srinivas Ramanujam. I remember from our earlier exchange that you are well aware of his achievements.

A Birthday Greeting for Zulfikar Ali Bhutto.

He left with many questions.

With Pardons.

Ras H. Siddiqui

AlephNull #7:
[As far as I can discern, their overall effect seems to be to befuddle, bemuddle, bedazzle, becloud, bemuse, bewilder, bewuther and in short to bludgeon, befog and benumb the believer`s baffled brain into accepting religious faith, on the grounds that something confusing and convoluted but supposedly profound must be sound. So perhaps God might be fruitfully identified with the befuddled believer`s bafflement. ]

Thanks AlephNull for the best, beautiful, precise and ``concise` statement. Is this your own brainchild?

I was not going to interact at this thread but your post forced me to post the first and the last post here. The reason for boycotting was simple. It was the use of supposed finesse but sneakish in reality, of sandwiching - an antique, mediocre at best, a poor theoretical religious contruct developed by mediocre fringe elements at the periphery of Pharoah and Babylonian civilizations, forced humanity into acceptance with all possible cruel means leading today to about two third of world population into believing it - existence of god in between two perfect scientific endeavors.

There are cleat principles, explained in a number of books, for empirical methods in scientific studies. It is not about hitting darts on a huge dart board. Most of all, as you also mentioned, is the scientific understanding of mathematically explainable scientific and laws of nature. That is what Newton achieved by mathematically coming up relationship between gravity and force.

The existence of god is not a hard question at all; it is a desire for some believers to convince those remaining non-believers whose forefathers were fortunate not to succumb to the might of swords, guns and cannons and onslaught of other forms of pressure tactics or agnostics.

The so-called hard question, ``does god exist`` could have been sandwiched in between science fictions such as time machine and cold fusion. That is where this `hard` question belongs with other similar `hard` questions. Sandwiching between two perfectly scientific areas is akin to cheating or playing trick or a poor attempt to elevate the intellectual level of a silly and, at best, a mediocre figment of imagination of antiquity.

Okay here is a very simple but interesting puzzle taken directly from ``The Man who knew Infinity``.

Say the house numbers in a particular mohalla start from 50 and continue as 51, 52... and so on. The numbers can only be integers. You have to find the house number of Mr. Saxena. The only thing you know is that the sum of all house numbers before Mr. Saxena`s house is equal to the sum of all the house numbers after Mr. Saxena`s house in the row. Now try finding out Mr. Saxena`s house number and the final house number in the row. The final house number cant be greater than 500.

For instance, one such solution is (6,8), i.e. Saxena`s house number is 6 while the final house number is 8. Now 1+2+3+4+5=7+8. There are infinite solutions to the above problem. If anybody succeeds in solving the above puzzle(writing a small code is the easiest way), can you obtain a more general form of the solution so that the you can tell the solution given a range of numbers.

These are unanswerable, insoluble, quests. I haven`t read this essay. Not because I feel above it, or I have a condescending attitude towards it. Far from it.

It is so, because my mind will start from ``casual chains``, and go to ``conjunctures`` -- thereby negating my own visualization of `causation`
-- and ultimately to `X` which Huxley, you would recall, called ``God``. All right, we start all over again from this wrap-up, from this terminus!

Now, all this would be fun if lives were not measurable in months -- let`s say 480 months, average, since in the first 240 you don`t even know which end of the world is up! And the logical end of such pursuit, ag`r t`lb sadiq ho, to, will be suicide, madness, lunacy or, the m`a^iraj of quest, takhta-é dar!

I said above that I haven`t read your essay or term paper. Now, that is not entirely correct. I have in a way `thumbed through it`. After all, I didn`t wish to sound utterly ignorant. Yet, both you and I are!! You see, once you and I have ``mastered`` the nature of the problem, concept, thought, conviction, schema or import, it becomes a ``yester-day`s
solved`` riddle or puzzle; a consumer of our meagre treasure of months ``, or parts thereof``. See if the following feels worth humming.

[Yeh jama-é s`d chak b`dl lainé maiN kya thha,
Moh`lat hii na dee Faiz hamaiN bakhia-g-ree naiN]

I am familiar, after a fashion, with your academic background. We share a common universe of discourse, to a degree. But where do we go from here? Where do I go? I can`t even understand what I have just written!

The presentation of an idea [and here we can, to express our `conception` of this word, use as many synonyms from the built-in thesaurus as we wish or to the point where we physically or cerebrally tire] is always -- as a rule of rational behaviour -- constrained by the ambience, the milieu of its presentation or its birth . This is a sensitive, time-space and `available-web resources` ``hole``. I believe that the square peg of the posited question is too big to even be relevant in this milieu.

To wit, then: `` We share a common universe of discourse, to a degree. But where do we go from here? Where do //I// go? I can`t even understand what I have just written?``

P.S. At the time I wrote these lines only Ghalib Zaman`s post had appeared. He seems to have benifitted by it and I am happy for him.

At the time of posting this, a day later: Sameer, love, as we say in Pakistan, ``how`s ya doin`?`` At last I caught you. Greetings and good thoughts. Aap ham-d`m-é déreena haiN, aur aap ka milna kum nahiN, mulaqaté Masiha `O Khiz`r sé. Zinda r`haiN, aur khush!

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Question -- IF God created MAN -- WHO creaed God?

Answer -- Man created God

Question -- who came FIRST -- God or Man?

Answer -- MAN MAN -- MAN came first -- THEN and THEN only -- came GOD...

want to verify it? -- ask ur dog -- if he knows who GOD is --

Equazon solved -- folks

#13

Hasan sahab,

As someone who works with science, I`m sure you appreciate the incredible complexity of the human body (just the variety of calcium transport mechanisms in the renal nephron is enough to stagger the mind; I know, I have to memorise them!). Contrast this with the simple unicellular zygote, which is where we all started from. It`s bewildering how so much could have gone wrong so many many times and yet it didn`t.

God doesn`t need us to worship him. Actually, God doesn`t need us, period. But can we really imagine our own nothingness?

Aamir

Gill sahib, I really enjoyed this article of yours. Coming from a physical sciences background myself (though with applications in medicine) I find mathematics and the like fascinating. Simon Singh`s book on Fermat is excellent...

I also am interested in philosophy too and the arguments for/against God and also Sufism (being a murid of the Most High Naqshbandi Order)

You are right that logically (taking logic in its strict Aristotlian sense) God`s existence cannot be proven. Imam Ghazzali came to the same conclusion and suffered a nervous breakdown of sorts as he himself tells us in his autobiography al Munqidh min al Dalal...but his faith in God`s existence never left him and his faith was confirmed and proven through the spiritual path of the Sufis. Thus we can say that there IS a spiritual proof of God`s Existence which can confirm one`s blind faith; yet the path to this proof is long and ardous and full of difficulties--ie. the Sufi Path.
Becoming annihilated in God (fana) is the goal of this path and of Islam.
When one does reach it, in Ghazzali`s words one has as much certainty of the existence of God as one does of the existence of a physical object which one is holding in one`s hands. For then `God` is no longer an abstraction but a Being of which the Sufi has experience of spiritually.

``My period of retreat had lasted about ten years,148 during which I had innumerable inexhaustible revelations. It will be enough to say that the mystic Sufi follow to an uncommon degree the Way of God. Their behavior is perfect, their Way is straight, their character is virtuous. If to this were added the good sense of the reasonable, the wisdom of the wise, and the knowledge of the doctors of law, could one be sure that this would improve their behaviour or character? Surely not! Every action or state of theirs, their outward appearance and their inward conscience, is illuminated by the flame of prophecy sitting in its niche149 beyond which there is no other light on the face of the earth.

What can be said about such a Way? Its purification consists above all of cleansing the heart of everything which is not God, the Almighty. This begins, not with the state of sacralization which opens prayer,150 but by the fusion of the heart with God`s name, and is completed by the total annihilation of the self in God.151

Even this completion is only the first step with regard to one`s free will and all that one has learned. It is the first step on the Way itself. What went before152 was only the waiting room.

Once one has started on the way, one begins to receive inspirations and visions. The mystics keep vigils in which they even see angels and the spirits of the prophets. They hear their voices and have the benefit of their counselling. From these visions of images and symbols they ascend further to degrees of spirituality which cannot be described. Nobody can attempt to express these states of the soul without failing miserably.

In a word, the mystics achieve a nearness to God which for some can be a virtual in-dwelling,153 total union,154 or fusion155 with God. This is not true, as we have shown in our treatise al Maqsid al-Asna (The Greatest Goal). A person in such a state should say nothing but these lines.156 ``Whatever has happened, I shall not speak of it. Think well about this. Do not question me about it.``
http://www.muslimphilosophy.com/gz/md/IIA-02main.htm (from Deliverance from Error by al-Ghazali)

``Whereof one cannot speak, thereof one must be silent.``-Tractatus, Wittgenstein Online edition..

...also faith by definition is just that.
Personally I cannot imagine for a second how God (Allah) CAN NOT possibly exist...
As the Koran (and the Bible) says, ``Blessed are those who have not seen but yet believe...``

**

Also Wittgenstein himself came to the conclusion that philosophy cannot answer such a question as he says in his Tractus Logicus Philosophicus...

The ONLY way to achieve absolute certainty is via a spiritual method...

freethinker

I would like to thank all the interactors who took the time to read my paper and comment on it. There is nothing much that I could say further to elaborate my point. People have devoted their lifetime to debate the question of the existence of God but so far there is no logical proof one way or the other. It is still a matter of personal faith and belief and will probably remain so for yet a long time. That being so, my hope was that this realization might help in diminishing the interfaith tension and hatred to some extent. The logic that `my God can lick your God` is irrational. I was impressed at the calmness and objectivity with which the interactors handled this sensitive question.

In reference to tahmed32`s feedback, I must first express my heartfelt sympathy for the accident that he had. The kind of free-spirited person that he seems to be, he handled it well. He had good time at the hospital and spread his good humour and cheer all around.

The question regarding the proof of the Fermat Last Theorem (FLT) that he raised is a difficult one. I had mentioned in the paper also that Wiles` proof occupied 150 pages. To describe it simply in layman`s lingo is not easy and is beyond me. To be honest, I haven`t read the proof myself. What interested me is the fact that he has provided the proof and not the details of the proof itself. Even if I try to read it, I wouldn`t understand it anyhow. I am not a mathematician although I have used it in my research to some extent. I am out of depth in `pure mathematics`. Many people still believe that there may be a simpler proof of the FLT, the kind of proof that would need simpler mathematics that existed in Fermat`s time. Many others more knowledgable about the intricacies of the FLT however reject this kind of notion.

My objective of including this hard question in the paper was to highlight the single-minded persistence of mathematicians in taming the FLT. Wiles spent much of his productive life in this work. Not many mathematicians understood what Wiles had done. Two other mathematicians who had been working at the FLT were entrusted with the task of checking Wiles` proof before it was accepted. They found an error in it and it took Wiles another year to correct it. Simon Singh`s book on FLT to which Naqshbandi has referred is a valueable resource. I had read this book cover to cover before I wrote my paper.

Regarding GhalibZaman`s comment on prime numbers, Pankaj has given the web page address which provides information regarding an algorithm, and its proof, to detrmine if a number is prime or not. This work has been accomplished by Professor Manindra Agarwal and two of his Ph. D. students.

I appreciated the comments made by AlephNull, DRUMZ, and SameerJB. nasah`s comments are subjective and explosive. As I had said in my paper, there is no proof that a God does not/cannot exist. I do not have any problem if like many others, he does not believe in the existence of God because there is no proof of the existence of God either.

Naqshbandi`s comments are mystical and philosophical in character, as usual. There is a lot of interesting thought in Sufism which again is subjective. I`ve read a lot of Sufistic literature but I don`t find any objectivity in it. I love Rumi`s and Hafiz`s poetry though.

Regarding the Theory of Everything (TOE), although not much was said about it by the interactors, I am on the watch to see when this difficult problem would be tamed. That would not be the end of Physics though as I had clarified in one of my earlier papers on Chowk (End of Physics). The search for TOE is becoming more and more interesting as the time passes. One day, this will also be brought home.

Excellent article. The existence of God is debated eversince man became aware of it`s surrounding. Through the dark ages, and Renaissance time philosphers/mathematician have put forth several arguments. I happen to came across the one by Rene Descarte`s ``Eight Meditation``.
I personally believe that there exist a higher authority and I/muslims call it Allah.

My dear Aamir miaN -- in that brief post u have packed so many powerful statements -- I bet besides being a keen clinician -- u must be a terrific discharge summary writer..

u write --
``the incredible complexity of the human body (just the variety of calcium transport mechanisms in the renal nephron is enough to stagger the mind;......Contrast this with the simple unicellular zygote, which is where we all started from. It`s bewildering how so much could have gone wrong so many many times and yet it didn`t.``

but azeezum -- it DID -- so much DID go wrong -- and so many many times -- before the final polished product -- as a marvel of biological engineering -- became available to us

it’s all the doing of that -- Mulla’s Nightmare – the Evil EVOLUTION – and its Yajooj Majooj – Munkir Nakeer -- SPONTANOUS MUTATION -- & that SIEVE of SELECTION –

Spontaneous Mutation is the doodler/dabbler -- the mindless creator –

Selection by the environment – is the SIEVE/Chulnee --

it is the CRUEL QUALITY CONTROLLER – that determines -- will this new stuff be -- a best SELLER – ‘FIT TO SURVIVE’ – a winner -- or a loser only fit for the trash can.

so many bad mutations -- with bogus blueprints are made by -- SPONTENAOUS MUTATIONS – that if they survived -- we all will look like -- one eyed Cyclops and hydra headed monsters –

luckily most of them cannot pass the mustard of ruthless, heartless SELECTION by the Environment`s chopping blocks -– are aborted -- and perish without a whimper.

THEN -- once in a blue moon a `good` mutation occurs -- at a `right` time -- with the ‘right conditions’ in the environment --

and its gets picked up like a hot cake -- gets selected for survival and propagation -- because it gives the organism some new advantages over the cruel environment -- and over other competitors -- and it flourishes –

whereas the older organisms that cannot cope with the changed environment – are eliminated – and die.

There are many many more misses than HITS – most of the ‘good’ changes are SERENDIPITOUS -- depend on one in a million lucky CHANCE –

EXISTENCE of both the STABLE inorganic world and the stable organic world -- have come through -- Evolution propelled by -- CHANCE -- by which – a key finds its lock that fits it perfectly -- MARRIES IT -- and starts having more of the `good thing` --

example Water -- produced and propagated by -- the marriage of Oxygen with Hydrogen -- locked in neptual embrace -- in a certain way -- in cerain proportions....

after millions of blind attempts and interactions -- there is one arrow that hits the bull’s eye and -- Walla

If there is -- anything that comes closer to being GOD – it is the phenomenon of – CHANCE –

one might say God is Chance – and Chance is God – thus when we pray we pray for actually the Chance – for the success of `one hit` -- among the many failures – more or less.

Iqbal in his famous couplet -- has put this -- Chance-dependent Rarity of -- Evolutionary Success – most succinctly – if I may take some liberties:

- hazaaroN saal Fitrut/Nature apni NAKAMEE/BEY NOORI pe rotee hai
- kaheeN tub jaa ke hotaa hai chaman mein deedawar paida


ur post was quite a stimulating potion –- Aamir miaN –– thanks and please write more often -- matters scientific besides ur great poetry!


shub bukhair

Regarding Question #2; Does God exist?
The key is to define `exists` .

Anything that `exists` cannot possibly be God. It will fall under the limitations of existence . God cannot be made to fit into the category of existence. He is ultimately Trancendant.
The attributes of God are a symbolic way of speaking of our experience of the Transcendant Reality. They do not define the Real, only our relationship to it. Even the ``Supreme Being`` is such a symbol and not a `thing that exists` .

Hasan sahab,

Thank you for your reply. You`ve taken me to a discussion I`m ill-prepared for right now. Will try to respond as best I can. :o)

Leaving aside evolutionary mechanics and the fortuitous strokes of pure dumb luck that are said to have produced us, what about us seemingly complete (for we can never be complete with evolution, that perennial tyrant with nimble fingers, replacing a gene here, removing a centromere there) human beings now; how do we explain the moral discipline needed to govern our lives? Were evolution, pure chaos, to rule us we would still be lost in tribal isolation, locked in perpetual conflict for resources and the right to survival, a cancerous instinct that saw the world only through the selfish need to perpetuate itself. Is the world around us like this?. . . . .On second thoughts, maybe you`re right. Maybe we`re not ready to believe yet. Maybe we need to evolve some more. :o)

Seriously though, the world is not an accident, beautiful though it may be. The beauty and our ability to respond to it are the result of some deeper truth embedded within us that science cannot overtake. It seems futile to reduce life`s origins to a series of convenient biochemical circumstances and I can`t find myself endorsing this monocular view, not with the depth of vision, and understanding, that my two eyes (faith and reason) afford me.

Muhammad Asad has written an excellent essay on the relationship between science and religion (The Spirit of Islam from his book, Islam at the Crossraods). If you leave me your mailing address (pediatrishun@yahoo.com), I`d be glad to post it to you.

This has been a rewarding dialogue, Hasan sahab. Thank you.

Khuda hafiz,

Aamir

Mr. Gill

``Khudaa agar dil-e fitrat shanaas dey tujhh ko
sukoot-e lalaa O gul sey kalaam paidaa ker``..............ALLAMA Iqbal.

From ``Javed kay naam``
upon receiving Javaid`s first letter from London.

tr:(for others` sake)

``If Allah has bestowed His blessings ( talent, aptitude, desire etc) upon you to study fitrat (observe nature) then unlock it lingo and do have a dialogue with the, apparently mute, flower.``

____________________________________________________________
``Sunee hikayat-e hastee tO darmayaN sey sunee
Naa ibtida kee khabar hai naa intihaa maaloom``
-------------------------------------------------Pundit Brij Narayan Chikbusst.

The very fact that not everyone has the yen for pure sciences, especially mathematics, it seems clear that one is definitely bestowed with it. Yes a way to explain it away could be `at the right place at the right time, in the evolution-cycle. But then who bought the ticket for us that we won this lottery? Just questions, just musings , just wondering in awe. Just humbling & prostrating myself in awe of the Unknowable. The little remnant ofa scientist in me admonishes me to always be a bit skeptic and according to its own rules instructs me never say never. By its own tenets Science cannot be an absolutist in its dispensation. The crowning glory of absolute belief shall always be that in the realm of religion. Even an atheist says the kalima, albeit half....La Ilaha (There is no god..). The listener always waits for him to at least pronounce the supermacy of Man (which incidentally also includes the believers who always are in overwhelming majority) :)

Hazrat Ali in his Nahjul-Balagha ( a most awesome compilation of his writings & speeches and a masterpiece of arabic literature---still taught in die-hard sunni AND shia SECULAR curriculum in the entire arab-world. Available evrywhere in most languages) has pondered and expositioned on this subject and few ,since him, been able to surpass that anywhere anytime.

Please peruse of it.
____________________________________________________________
No matter how much one wants to put a spin, it would always boil down to either a `scientific` belief or a `religious` belief.

In my very own way to understand this , in a fusion kind of way--among others, is that Allah is the unknown constant K which the scientists always use to balance out the unknowable. I am aware that this technique or tool has to be applied to work within a closed system to contrain oneself within the unknowable quantas of Space & Time.

As I have mentioned many-a-times I am a simply a dabbler but an avid pupil. Only if someone can explain things to me at my very primary-level.
____________________________________________________________
``Baichaara Pyaada tO hai ik mohraa-e naa cheez
FarzeeN sey bhee posheeda hai Shatir kaa irada``
-----------------------------------------------------------ALLAMA Iqbal.

PS: I sincerely hope that you will continue to expound upon such subjects. CHOWK become very plebian without such material.

freethinker #18 After reading your reply, I searched in vain on google for a general description of the Wiles` solution. I found a transcript of an interview with him on Nova where he talked about how the stepping stone to the solution was a solution he found to a ``conjecture`` posed by two other mathematicians (the ``Taniyama-Shimura conjecture``). And that he found this stepping stone after some other mathematician brought to his attention a link between the T-S conjecture and FLT. I still dont know what the Wiles` solution is, but the process through which he found the solution does seem to confirm the wise saying of one of the greatest mathematicians, Isaac Newton, who said that ``we stand on the shoulders of those who came before us``.
PS: Thanks for the sympathy and appreciative words about the quadricep problem I described in my article on chowk.

M Gill -
Great piece. Sorry the Heisenburg Uncertainty was left out of the quandary since it tells us in no uncertain terms, perception of scientific fact remains a psychological matter. That huge/tiny gap between momentum and trajectory, houses the fascinating science of quantum logic, which seems to infer that T.O.E. is a pipe dream. Any thoughts?

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re #22 Ansari Sahab
You ask :

Were evolution, pure chaos, to rule us we would still be lost in tribal isolation, locked in perpetual conflict for resources and the right to survival, a cancerous instinct that saw the world only through the selfish need to perpetuate itself. Is the world around us like this?. . . . .

Answer can be found in The Origin Of Virtues by Matt Ridley.

You ask :

Seriously though, the world is not an accident, beautiful though it may be. The beauty and our ability to respond to it are the result of some deeper truth embedded within us that science cannot overtake....

Answer to a related question can be found in The Blind Watchmaker by Richard Dawkins.

```` Maybe we need to evolve some more.```` (dr ansari)

no kidding -- we definitely need to evolve some more -- a few bad mutations -- and a few bad mutants like bush junior with his demented star war toys -- and we will be extinct -- sooner than later --

or do u think we are an eternal species -- more successful than the dumb dinosaurs? -- ( 2 hundred million years!) -

may be we could survive that long -- if we were as linguistically dumb -- as the dinosaurs --

but certainly NOT -- with the crooked intelligence that we possess today -- that allowed us to -- FIRST -- build the weapons of SELF-DESTRUCTION -- before developig the means of SELF-PRESERVATION a little more -- within the span of only ONE HUNDRED years of -- `PROGRESS` --

what a `PROGRESS`!

do we know that right now we have accumulated -- between the the `developed` nations -- and the not-so developed laggards -- so many nuclear weapons -- -- that we can KILL every man, woman and child of the world -- ten times over?

and this is just at -- the dawn of our -- crummy -- 6 thousand year old civilization --

may be we ARE genetically predisposed to self destruct --

it doesn`t look like -- the Ashraful Makhlooqaat that we delude ourselves about -- the `chosen` one --

it looks more like -- Ahmaqul makhlooqaat -- chosen to die a premature death -- like the lemmings...

````Seriously though, the world is not an accident, beautiful though it may be. The beauty and our ability to respond to it are the result of some deeper truth embedded within us that science cannot overtake. It seems futile to reduce life`s origins to a series of convenient biochemical circumstances and I can`t find myself endorsing this monocular view, not with the depth of vision, and understanding, that my two eyes (faith and reason) afford me````(dr ansari)

Seriously -- ansari mian -- the world IS an accident -- the universe is an accident -- it was not meant to exist -- between the matter and the anti matter -- it was supposed to be totally anihilated at its very inception -- by the interaction of matter with the anti matter -- but it did not due to a slight unexplainable excess of matter over antimatter.
The creation of Earth was an accident -- the creation of life on this planet is an accident -

- all precious things are an accident -- u r an accident -- hamidm is an accident -- sameerjb is an accident -- i am sure chowk is an accident:-)

as a scientistist, as a biologist, as a medical doctor, and as a clinician par excellence --

Ansari miaN -- you must have FAITH in your REASON...

Shah sahab; thank you for referring me to those books. I`ve been meaning to read the Origins of Virtue for some time now; strangely enough was referred to it through a talk by Prince Hassan of Jordan when he came to speak at our school a while ago. I`ve read a few chromosomes out of Matt Ridley`s Genome and if it`s anything like that, it should be a good read.

Hasan sahab; ahmaq-ul-makhlooqat; yes it certainly seems that way doesn`t it. :o(

``you must have FAITH in your REASON... `` I do, and reason enough to know that there are many things I do not yet know. And faith to keep on learning, to Read (Iqra)!
I see we are on opposite sides of a fairly aged dialogue. You cannot believe that which I do and neither can I subscribe completely to your set of views. To you your way then and to me mine. I can only hope that time, ours preferably, serves to resolve the incongruities between our two viewpoints.

Sincerely,

Aamir

ps. ``as a scientistist, as a biologist, as a medical doctor, and as a clinician par excellence. . .`` itni taareef mut karein Hasan sahab; kahin mujhe aap se recommendation letter na maangna parhe apni residency ke liye! ;)

``kahin mujhe aap se recommendation letter na maangna parhe apni residency ke liye! ;) ````
(dr ansari)

any time Aamir miaN -- u r most welcome..

``You cannot believe that which I do and neither can I subscribe completely to your set of views.````(AA)

of course

btw -- I used to believe what u do -- when I was ur age -- before I discovered a unique substance in the white blood cells (polymorponuclear leukocytes/ PMN) that kills the invading bacteria -- isolated the chemical -- characterized it and published it -- as First of my three papers -- in Science, November 23, 1963 -- am I ancient or what:-)

when I dissected a unicellular whit blood cell -- I was thunderstruck -- by the awesome complexity of a unicellular organism -- what to talk about us -- the multicelluar ones --

it convinced me for all times to come that -- no GOD anywhere in this Universe or beyond other universes -- could EVER have built such an intricate -- interconnected machinery -- at such a microscopic level -- in ONE stroke --

without learning the ropes Himself -- without training -- and without making -- trillions of mistakes -- and rejecting them... in `bits and pieces` -- by `trial and error` -- over billions of years.

That is -- without EVOLUTON --

that is -- a Knowledgeable God -- CANNOT exist without EVOLUTION -- He must (successfully) EVOLVE over the billions of years -- with the evolution of the Universe -- or must PERISH -- as one of the billions of failed experiments of nature....

and pleeze nobody tell me that – God is ALL Knowledgeable – that is just a collection English words – it doesn’t necessarily prove -- He is…

I know this is strong stuff for u at ur age -- and u don`t have to agree with anything I say -- but do continue to read and keep an open mind -- and by all means if u can find an opportunity -- do some basic cellular research in your fellowship years -- besides the clinical stuff ...

best wishes for ur residency

hasan

``kahin mujhe aap se recommendation letter na maangna parhe apni residency ke liye! ;) ````
(dr ansari)

any time Aamir miaN -- u r most welcome..

``You cannot believe that which I do and neither can I subscribe completely to your set of views.````(AA)

of course.

btw -- I used to believe what u do -- when I was ur age -- before I discovered a unique substance in the white blood cells (polymorponuclear leukocytes/ PMN) that kills the invading bacteria -- isolated the chemical -- characterized it and published it -- as First of my three papers -- in Science, November 23, 1963 -- am I ancient or what:-)

when I dissected a unicellular whit blood cell -- I was thunderstruck -- by the awesome complexity of a unicellular organism -- what to talk about us -- the multicultural ones --

it convinced me for all times to come that -- no GOD anywhere in this Universe or beyond other universes -- could EVER have built such an intricate -- interconnected machinery -- at such a microscopic level -- in ONE stroke --

without learning the ropes Himself -- without training -- and without making -- trillions of mistakes -- and rejecting them... in `bits and pieces` -- by `trial and error` -- over billions of years.

That is -- without EVOLUTON --

that is -- a Knowledgeable God -- CANNOT exist without EVOLUTION --

He must (successfully) EVOLVE over the billions of years -- with the evolution of the Universe -- or must PERISH -- as one of the billions of failed experiments of nature....

and pleeze nobody tell me that – God is ALL Knowledgeable – that is just a jumble of words – it doesn’t necessarily prove -- He is… because someone says so...

I know this is strong stuff for u at ur age -- and u don`t have to agree with anything I say -- but do continue to read and keep an open mind -- and by all means if u can find an opportunity -- do some basic cellular research in your fellowship years -- besides the clinical stuff ...

best wishes for ur residency

hasan

Hasan sahab,

A pleasure reading your post. Insha-Allah will look your papers up tomorrow.

``when I dissected a unicellular whit blood cell -- I was thunderstruck -- by the awesome complexity of a unicellular organism -- what to talk about us -- the multicelluar ones --``

That`s exactly what I love about it; the beguiling intricacies of life at the cellular level; sometimes it`s almost poetry (apoptosis, for example). If I didn`t love patient interaction so much, I would have gone into pure science, pathology or immunology. As it is, I`ve found a satisfying compromise with Hematology and Oncology; insha-Allah hope I get into a fellowship program that allows me to pursue the pure science aspect of it.

It`s been a pleasure, Hasan sahab. Thank you.

Respectfully,

Aamir

now chowk don`t chicken out -- publish it :------)
:-) -- :-) -- :-)

tahmed:

Regarding Wiles’ proof, you can look up the following web page.

http://www.gotmath.com/fit/

I got this address from Charles Daney who has posted several links on FLT. The proof may not be included in one book or one web. I’ve not opened it myself.

Trillium:

Surely, there are many more questions which are occupying the attention of the scientists and mathematicians. Niels Bohr and Einstein had engaged in discussion (EPR thought experiment) regarding the probabilistic character of Quantum Mechanics without reaching any agreement. Both of them died sticking to their respective guns. This discussion lasted over a period of some thirty years.

Einstein was a determinist (believer of cause –effect paradigm) and believed that if sufficient information were available at the sub-atomic level, Quantum Mechanics should also reduce to deterministic science. This gave birth to the idea of ‘missing variables’ which was exploited by David Bohm but no prominent scientist believed his theory. So far there is nothing to support Einstein’s thesis.

TOE is not a pipe dream although it is still hard to predict when it will come to fruition. In the last decade of the twentieth century, there was a lot of optimism and euphoria about the superstrings theory; it was believed to unify the fundamental forces of nature. Now it appears that the superstrings theory by itself cannot do the trick; Quantum Loop Theory combined with the Superstrings theory is considered to complete the unification task. Let us see what happens next.

The evolutionary history of the FLT illustrates that many more new steps and new branches of knowledge might be needed to tame this problem. One has to continue taking these steps to reach the final destination.

Einsteinwallah:

Unification of fundamental forces is being sought using mathematical manipulations. Mathematicians can deal with space of numerous dimensions. The fifth dimension was a mathematical necessity. One of the models that seems promising for unification requires a universe of ten dimensions. Physicists have explained it away saying that the six extra dimensions had existed at the time of the Big bang but soon afterwards, they rolled up into an infinitesimally small manifold. Better physical comprehension will come later after the mathematicians have done their part.

Many physicists have objected to the mathematical unification that is being tried for the simple reason that it cannot be verified experimentally. And a theory which cannot be verified experimentally is not credible. Be that as it may. Unifications is one of the very big challenges for the human analytical skills and theoretical physicists and mathematicians are attracted to it like iron filings to a magnet.

Was`salam

JBSameer #9

Sameer Sahib, I`m flattered you liked that paragraph of mine. The words were my own. However, the idea of identifying God with baffled ignorance seems too obvious to be new.

The long-term trend in advancing scientific knowledge has been to show that natural phenomena both large-scale and microscopic that appear marvelous in their complexity and apparent perfection, actually obey simple elegant laws that operate uniformly, inflexibly and without exception. From a universe that required moment-to-moment intervention by an omnipresent, omnipotent being, one progresses to a universe whose complex structure and governing simple laws required design in the minutest detail by a creating Architect, and then to a universe whose complex structures are shown to consistent, both in their behaviour and their historical evolution, with the impartial, remorseless operation of those simple laws.

Thus the Governing God who at one time was thought to be present ready to intervene at every point in spacetime, was first demoted to the Architect who could be pushed out to an indefinite point in the past at which he created the clockwork and set it in motion, and then shown up to be an Unnecessary Hypothesis.

In other words the boundary between understanding, systematic knowledge (Science) and ignorant awe (God, if you prefer) has been pushed back further and further. The actual size of the boundary may have increased somewhat because of our more detailed and in-depth awareness of the current limits of our knowledge. It is unclear to me whether it will keep expanding indefinitely or actually shrink at some time in the future.

------------------------

Re. time travel, cold fusion and such, you were probably being unfair to these fields in putting them at the same level as `Proof of the existence of God`.

One can at least objectively, empirically evaluate specific claims that cold fusion has been achieved.

As for time travel, one can likewise at least try to show how time travel might be consistent with some commonly accepted description of physical reality. One extremely famous and distinguished 20th century mathematician did actually do this.

Whereas those who obsess over the so-called question of existence of God never clarify exactly what they`re looking for. A claim that by its nature and definition is so vague that it cannot be refuted either empirically or deductively has no connection with either empirical or logical truth; considering it is a simple waste of time.

freethinker #35 Thanks for the link. Unfortunately, that page is no longer available on the web. Seems like Wiles` solution is as elusive as Fermats` problem.

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nasah

You must have done some real good work to get a paper in Science !!! Accept my belated congratulations.

tahmed:

Okay, here is the title of a book which contains the proof. I haven`t read it though; I scanned its table of contents. Try to borrow it from a library; a university library is the best shot. The title of the book is as follows:

Modular Forms and Fermat`s Last Theorem, by Joseph H. Silverman
and Glenn Stevens

The book is available through Amazon. com and Powell Books; the price range is $21.47 (for old) and $41.42 (for new). There may be other books also.

Wish you best of luck.

World on path to disaster: scientist

By David Hearst

LONDON: President George Bush, hijacked by hardliners in his administration, is setting the world on a course towards nuclear disaster, a founder of the nuclear deterrence policy said.

The 1995 Nobel peace laureate, Professor Sir Joseph Rotblat, accused the US of developing a policy which regarded nuclear weapons as bad, if in the possession of some states or groups, but good if they were kept by the US for the sake of world security.

The fact that it had signed the non-proliferation treaty and was legally bound to the elimination of nuclear weapons was ignored, he told a London non-proliferation conference, sponsored by the London-based Guardian newspaper and jointly-hosted by the Royal United Services Institute for Defence Studies and Physicians for Social Responsibility.

``Nuclear arsenals will have to be retained indefinitely, not just as a weapon of last resort, or as a deterrent against a nuclear attack, but as an ordinary tool in the military armoury, to be used in the resolution of conflicts, and even in pre-emptive strikes, should political contingencies demand it. ``

This is in essence the current US nuclear policy, and I see it as a very dangerous policy.``

Sir Joseph said that Mr Bush had already authorised the development of a new nuclear warhead of low yield but with a shape that would give it a high power to penetrate concrete, the so-called ``bunker-busting mini-nuke``.

This would have to be tested.

If the US resumed nuclear testing, it would give a signal to China to do the same. Other new arrivals to the nuclear club, such as India and Pakistan would use the window of opportunity created by Washington to do the same.

``The danger of a new nuclear arms race is real,`` Sir Joseph said.

India`s declared policy was not to use nuclear weapons first, but if the US make pre-emptive attacks part of its own doctrine, it would give India the legitimacy to carry out a pre-emptive strike against Pakistan.

Taiwan represented another potential trigger for pre-emptive nuclear strikes by the United States and now so too did North Korea, which might already be in possession of two nuclear warheads.

Israel, which kept nuclear weapons and would not allow their acquisition by other countries in the Middle East, had destroyed the Iraqi Osiraq reactor, the first case of a pre-emptive strike on a nuclear installation.

The glaring asymmetry of the US in its relations with Israel and the Palestinians was being exploited by radical groups in the Arab world.

He said: ``By utilising the tremendous advances in technology for military purposes, the United States has built up an overwhelming military superiority, exceeding many-fold the combined military strength of all other nations.

``It is claimed that this is necessary for world security, but act-ually what such a policy amounts to is to rest the security of the world on a balance of terror.``

Arms control, he said, was as good as dead. The only way out of the disaster that lay ahead was to put the goal of total nuclear disarmament back on the agenda.

``We have to convince the public that the continuation of current policies, in which the security of the world is maintained by the indefinite retention of nuclear weapons, is not realistic in the long run, because it is bound eventually to result in a nuclear holocaust in which the future of the human race would be at stake. ``We must convince public opinion that the only alternative is the total elimination of nuclear weapons.`` Gaurdian/Dawn)

Dear Pankaj -- thanks – yes – to be published in Science was and still is a privilege –

Ah -- those good old heady days of unfettered research –

yes -- that work was an original trail blazer – Science was very kind to me – they published two more papers of mine later on – it was all about discovering a unique group of very electropositive proteins from the white blood cells -- called the granulocytes or PMN – the highly positively charged proteins killed various bacteria like crazy – by combng with the negatively charged membranes of the infecting organsms.

I named them cationic proteins of the leukocyte granules – they were later found to be widely distributed in the white cells of most species -- and turned out to be one of the major biochemical determinants of innate immunity -- in humans and animals –

btw -- the joy of my first paper being published in Science was totally marred by the murder of JFK the same week --

nasah:

Any new discovery contributing to the development of scientific knowledge is a thing of beauty. And ``a thing of beauty is joy forever.``

Let this be incentive for others.

nasah jee

Unfortunately I do not have any understanding of medical research because my area of research is chemical engineering. But I am aware of the prominence of the journals like Science, Nature, Physics Review Letters, Langmuir, Journal of Fluid Mechanics etc in their respective fields.

any way like the third quantum logic this cannot be said with surety that fermat did not have the proof so in the case of GOD why do we need to discuss and boggle our ``bright`` minds in search for an answer to the very basic question .it is told in the Quran ``for you your belief and for me mine`` so forget about it and do some purposeful work