Infinite in All Directions Re: Fozia

Thanks for your comments.

Remarkably, your observation about renormalization is at the heart of the reason why people have been exploring options beyond Quantum Field Theories (QFT) as models of the natural world. (A mathematician`s eye quickly spots the trouble spots ... ) I was hoping to get more into the idea and method of renormalization in the second part of the article, before I described what comes next.

But here`s a preview ...

A sensible QFT should not only be solvable, but also interpretable. Consider a generic p.d.e that I wish to solve, first in the absence of a source term, DX=0 (D is the operator). The general solution is obtained by characterizing the Green`s function, DG=delta(X). In the presence of a source term, the calculation of a general solution may not be possible, even with the knowledge of the Green`s function, so one is forced to approximate methods like a perturbation expansion, with the lowest order term being the source-less system. The validity of the perturbation expansion depends on the identification of a small expansion parameter, and on the fact that successive terms in the series should be (progressively) small, in order to avoid divergence. That is usually how one goes about solving a QFT.

In QFT, however, one often finds that successive terms, are not only large compared to the leading term, but infinite. Therefore, we look at how we interpret those results, and try to find a reinterpretation that leads to finite answers for OBSERVABLE parameters. This process, renormalization, involves first making the solutions finite by imposing a cutoff parameter (i.e M), which in the limit to infinity gives the original divergent answer. Next, within the equations themselves, we have parameters that we identify with an observable, like the charge (e) or the mass (m) of a particle. In the presence of a source term, the meaning of those parameters needs to be redefined. Without a redefinition, these parameters diverge, causing the infinities.

Let me be somewhat concrete: Consider a physical theory whose Lagrangian depends on two parameters, say e0 and m0. We would interpret these as the charge and the mass respectively. Now if I calculate two physical processes from which I would measure the true charge and mass, e and m, I will find that the results would diverge. So one first makes the theory finite, by introducing the cut-off parameter M, and then considering e and m to be arbitrary parameters (c.f my earlier statement about the reinterpretation in the presence of a source) re-write them in terms of so called ``bare`` parameters e0 and m0:

m = m(m0,e0,M)

e = e(m0,e0,M)

We want to make m and e independent of M, therefore, we can choose e0 and m0 to be functions of M in such a way that dm/dM = de/dM = 0. These lead to coupled equations that describe a trajectory in parameter space. Of course, it may happen that e0 and m0 may not have enough freedom to make the answers finite in the limit M to infinity. In that case, one will need to add additional terms and parameters to the original Lagrangian to make it finite. As long as those new terms are local and finite in number, the theory is renormalizable.

What has happened is that the infinities have been swept away into the ``bare`` parameters, e0 and m0, but that is ok, since, they are not observable.

Infinite in All Directions Re: MAK

Thanks for your kind comments. I decided to follow a simple formula in my article, which (sadly) is that the number of readers falls off exponentially with the number of equations in an article. That is perhaps one reason why I did not delve into the details of any particle statistics. The other reason was that in doing so, I would have to justify my statement about the spin of a particle and its statistics ... and things would get out of hand there. However, hopefully, I will have the opportunity to write a book sometime.

I think you have pointed out a very important thing, which is the role played by one`s mentors in encouraging/discouraging the path followed subsequently. I share your interest in fundamental physics also, and hope that despite your primary occupations in applied areas, you continue to keep in touch with the developments at a more fundamental level. Hopefully, in the second part of the article, I will get into more of that.

regards

Infinite in All Directions Re: Amar Dev

Interestingly, this quote of Blake has been used by many physicists also when initially confronted by the infinities hidden in theoretical constructs. Whether they are `physical` infinities or not is a different issue ...

Infinite in All Directions SR, You`re right, orders of magnitude quickly spiral out of the empirical capacity of our senses and mind. Maybe that is not so surprising, since the world around us does not afford us ways to condition our minds to the immensely large or small, or to things that we do not experience.

Mathematics, in this regard, is the equivalent of a tool, which just like a microscope or a telescope, brings what is beyond the experience of the senses, to within the reach of our cognitive abilities. It is not necessary that every concept be translatable into something that we experience every day.

On the contrary, I think it is wonderful that our minds are capable of imagining more than what the world around us apparently offers to us. For example, though we live in a strictly three-dimensional world, mathematically, dealing with infinite dimensional worlds is a matter of routine for many. And there exist some ``demons`` who can even visualize complicated objects in higher dimensional spaces. I personally have a prescription in my mind on how to think about four dimensional objects ... :-)

Infinite in All Directions Re: Amber

Thank you for your kind comments. You`re right, almost all concepts can be conveyed to almost all people. Some may take more work because they assume the existence of a certain level of expertise.

Eqbal Ahmed Lecture by Kofi Annan I found most of what Kofi Annan said to be quite sensible. I think he has pointed out a very important fact -the growing disparity of knowledge between the developed and the developing countries. Not only is this chasm widening, there is no process in place that can counter it. I wonder why people are not discussing this important point, and instead focussing on things which (I think) are much less important...

The Short-Circuiting of Democracy Saad, this was a thought provoking possible course of democracy in America. I enjoyed your article very much, as always. Since you have a lot of long replies to the article, I want to add only a few words of my own.

Maybe, in this process what we are witnessing is a possible flaw in the IMPLEMENTATION of democracy.

Two questions arise:

(1) Can the democratic process, in the real world, deliver the lofty goals it sets for itself?

(2) Are all of the underlying assumptions of the democratic process justified?

Not that one should reject the ideals of democracy but maybe one should reform the method through which it is implemented.

I think the problem of reduction of issues to the basest possible level arises naturally if one invests everything in the dissemination of information but not enough in the human being who has to interpret that information.

I Cheat Therefore I Am I denigrate myself, therefore I am (Desi)

:)

Infinite in All Directions Rabbani Sahib,

I hope all is well with you. Thank you for your kind comments on the article. Some of the concepts that I have tried to present are not that difficult to grasp, once they are discovered (i.e. the famous Eureka! reaction and the post-Eureka this-was-so-simple-why-didnt-I-think-of-this-before). So I feel that I need to work more on my elaboration of these concepts. If you`re interested, I could revisit some of the things that you thought were not clearly presented, hopefully in a more understandable way this time.

I agree with you, that to an outsider, some of the concepts and jargon of a science becomes as abstract as the concept of angels dancing on a needle-point. But as you pointed out, there exists the element of experimentation, which constitutes the supporting evidence. About the efficacy of the scientific method itself, there has been a lot of work during this century, prominently by Popper and later Kuhn. Whereas Popper would allow the realization of only the falsification of a theory and nothing more, post-modernist Kuhn takes away even that consolation. But surely that is a separate discussion. But in real terms, the efficacy of science lies not in its abstraction, but in being able to communicate its key concepts to everyone and attracting interested people to continue the thought process. A detached and incommunicable knowledge quickly becomes useless, to put it another way, the vitality of science lies in its constant change. The parallels to other things in this context are rather obvious.

The question about the recent announcement of the expansion rate of the universe is a very interesting one. I have not heard much about the issue since its first publication some time ago, and it is unclear what is the exact status now. Roughly speaking, one could understand the issue as follows: When one assumes a given amount of density of matter in the universe, one can calculate how the gravitational pull of that matter would slow down the expansion rate of the universe. Now what these guys did was to look at galaxies that are extremely far away, more than approx. 6 billion light years, and by looking at their spectra, inferred the velocity at which they were receding from us. That velocity in very distant galxies, they found, was larger than what one would expect if one had assumed the retarding effect of matter on the expansion of the universe. One of the explanations given for this was to hypothesize the presence of a long-range repulsive force which would be pushing stuff away.

Like all things in science, the best attitude is that of a reserved caution. There are many things that could change that conclusion. Suppose they discover that there was a problem in their measurement (caused by something as mundane as a slight problem with their instruments), then the result would no longer hold. Similarly, even if the instruments were correct, but they were off in determining the distance of the galaxies, or the assumption that they had made about their structure. The details of the mathematical calculation performed to determine the expected deceleration of the universe are extremely important etc. etc. All of that will take time to precisely pin down and therefore, I would not start writing a science fiction novel based upon the presence of such a force yet :)

Talking about science fiction, I think sometimes certain preliminary observations get blown out of proportion once they get into the hands of eager journalists. All of that does not hurt the credibility of the newspaper, but only of the people who have spent years looking at something. Usually then researchers try to be very cautious in releasing their finds, and try to elucidate the preliminary nature of their findings. We have often seen cases where even a cautious attitude leads to a publishing of a result that is later discovered to be flawed or even wrong.

Is Islam Undemocratic? Your article was very thought provoking. Thank you.

You have raised an important issue which one of the respondents to your article failed to grasp. That is the issue of the ability of a democracy to realize the lofty goals it sets out to achieve. Rosseau, though a profound champion of human reason and the right to exercise self-will, declared that in the end, the definition of the aims of a democracy have to be defined by, what he termed as, people of lofty or ``divinely inspired`` intellect. The role of a ``Divinity`` or a ``spirituality`` in a society cannot be denied.

You have rightly remarked that ``modernity`s mistresses - freedom, democracy and secularism - are all ideologies of method.``

Foucault, present as a reporter during the Iraninan Revolution, was surprised to see the role played by ``spirituality`` in mobilizing people, and in defining the goals of a society. That contrasts sharply with the claims of some Western scholars who feel comfortable to dismiss the role of a religion to be merely an opiate. Upon his subsequent return to France, he was so moved by this realization, that he started to investigate the role of spirituality in this arena.

The faithful protagonists of democracy are in many ways not unlike their ``fundamentalist`` counter-parts. While they point to the pathological cases of ``theocratic-absolutist`` societies for the support of their arguments, they fail to see the equivalent morass of lack of direction and exploitation in ``atheistic-democratic`` societies.

Squeamish in the Name of Science Your poem was a lovely read. Thanks

As far as I am concerened, I do not quite count become a professional (i.e a doctor) as becoming a ``scientist``, I think a doctor has far more in common with other people like lawyers or managers, than with a scientist or an artist. A biologist or a researcher has more of a scientific spirit than just a doctor. A scientist, like an artist, deals with abstractions and not with a taught and classified application of a method. An artist or a scientist is an artist because she/he necessarily requires the presence of creativity in their work. That is not usually true of professional fields. You may, however, find rare individuals, who belong to a formulaic professional field, but still are able to contribute new ideas to society.

I think that the ``science-art`` dichotomy, as understood in our culture, is quite wrong.

Drowning in the Memory Stream Wonderful poem, beautiful. Keep on writing and hope to see your work on Chowk in the very near future...

The Impossible Fundamentalism of Doubt I am sorry for the length of my reply, and please excuse my tone at times... I am basically sitting down and typing it all in :)

Re: Faisal;

I think that the popular emphasis on the literary worth of SV is highly over-sold. I can think of at least one good reason for that: There is no ``intrinsic`` literary worth of any work, it always derives from the socio-cultural matrix that gives birth to it and sustains it. The interpretations of SV, and the hard-liners that argue for them
ardently are somehow incapable of understanding this simple thing. I have seen ``explanations`` of the imagery of SV, that grow endlessly in an incoherent weed-like fashion. It is clear that the exponents of the work are merely deluding themselves by ``discovering`` symbolism in SV
that really only stems from their own minds. That is a major problem with defining an inherent literary worth of a work.

Also, in my opinion, the political aspect of the novel is not separable from its contents. SV is known because it came in the political limelight at a time when the West faced an intractable enemy
in the ``rogue state`` of Iran. Why is it, that we do not know of any modern work that describes the Western civilization in unfavorable terms? After all, statistically speaking, the Western civilization has caused more harm to humanity than any other previous civilization in human history. Why is it that the entire propoganda apparatus of the Western world, aided and abetted by its economic and political might, is rallied to the defense of Rushdie, who happens to be saying
precisely what one would like to hear?

It is this political dimension of this affair that also answers why we don`t focus so much on earlier Orientalist works, some of which are much more offensive to Muslims. Those works are not viewed today as entirely ``objective`` studies of Islam or Muslims, but as biased accounts that focussed more on sustaining the popular myths about a foreign adversary civilization than on an effort to gain insight about a people and their ways. Once the motivations are realized and understood, one can have a measured and deliberate response. And that
is the case with the Orientalist works, which have receded to oblivion within the ranks of Islamic institutions of learning. I think that SV
is bound to the same dustbin of history where other such works currently reside.

Am I also allowed to suggest that maybe, just maybe, by giving too much credit to SV and the apologetic discourse that surrounds it, we are
ourselves falling victim to the well-tested and tried political adage: ``A lie told a thousand times, becomes a truth``?

best,
Wasiq

Re: Rad and Saima

I wish to say again that I do not intend to discuss whether the death sentence on Rushdie is justified. The reason is that most people
approach this issue in a very simplistic manner and insist on a resolution one way or another. Such things are not possible within the
human domain, no matter how much we wish them to be.

Coming to the issue of freedom of expression: To me the absolute sanctity of freedom of expression is as dubious as the sanctity of religious dogmatism it wishes to challenge. An unequivocal insistence on freedom of expression, regardless of its contents, purpose and effects, is as dogmatic, absurd and infantile as the belief systems of
a cult.

You mention humanism, and I hasten to add that I myself would wish that the myth of humanism is achievable, but let me ask you the following:

(1) Isn`t humanism as much of a fantasy as the sanctity of a God, Prophet or a Divinity? By fantasy here I mean something that cannot be
absolutely proven. Can you give me historical proof that the myth of humanism has actually produced less carnage than in the past? We
believed in humanism while people were killed in tens of thousands across the globe, in most cases by the dubious prophets of humanism themselves.

Let me mention to you another such ``ism``: Nationalism, the supposed panacea for all ailments. Nationalism, the new material substitute for all that was sacred, gave us colonialism, two world wars, countless smaller wars and endless oppression that continues to this day. Isn`t
there a stark contrast between the reality and actuality of nationalism?

(2) Do you agree that different civilizations may have different symbols that represent the same concept? Humanism is, thank God, not a
Western invention. All civilizations are humanistic. The savagery starts when one civilization insists that its interpretations and
symbols of humanism are more valid that those of another.

By saying that ``this is a century of Humanism`` you are guilty of that age-old mistake, i.e of defining humanism to be something that you
perceive it to be and discounting all other possible variations of it. I am sure that the Conquistadors believed in humanism too while
they decimated the ``savages``, and the French believed in Humanism too when they killed a million Algerians, the list is practically
endless.

I think that, regardless of what the ceaseless incantations of popular media and its pundits say, there is more to the issue of SV than we
would like to handle.

I think it would be worthwhile to step back for a day from what people on either side say, and view this issue in terms of a civilizational conflict and not as a Western allegory of conflict between a dogmatic Church and a ``heretic``. Symbolism is very hard to transfer cross-culturally, but a person of sufficient intelligence can, with
effort, appreciate the importance certain symbols play in the lives of people.

Maybe you should ask yourself the question: How must the faithful Muslims regard the Prophet for them to espouse a death penalty for Rushdie following what he has written in Satanic Verses? If you can appreciate why that would happen, then you would have come closer to understanding the importance of the Prophet as a unifying core of the Muslim communities.

The Impossible Fundamentalism of Doubt Without getting knee-deep into the morass of whether the Fatwa on Rushdie is justified or not, (i.e parroting the ``standard`` stances of the two sides) I would like to make the following observation:

To me the absolute sanctity of freedom of expression is as dubious as the sanctity of religious dogmatism it wishes to challenge. An unequivocal insistence on freedom of expression, regardless of its contents, purpose and effects, is as dogmatic, absurd and puerile as the belief systems of a myopic cult.

The Fatwa, cannot, and should not, be divorced from its ideological context. And `Satanic Verses` should not be elevated to more than what it is. The dynamics of this pro-Fatwa and pro-Rushdie yo-yo should be understood in the context of two civilizations which are not entirely conversant with each other`s language and symbolism, and carry a mutual air of distrust. A Westernly schooled mind, regardless of its race, still views an Islamic, or for that matter any other, mind as foreign, and the same holds true conversely. It is highly unlikely that the effects of decades of schooling are completely reversed.

In the scenario of a civilizational clash, words are as potent a weapon as any bomb. Could it be that we are focussing too much on the pawns?

Where in the Brain is the Mind I would say that the human mind, with all of its complexities and features, is entirely understandable within the context of a correct physical theory of matter. We may not have a fundamental understanding at the moment, but once we have it, my first statement would become a tautology! (Because, by definition, the correct description of the material universe should contain within itself the answer to why the process of evolution of matter should lead to consciousness.)

About super-naturalism, my point of view would be the following: Most people need to have some answers, and in the absence of understandable ones, are willing to invent any that will momentarily pacify their need. All super-natural explanations fall within this context.

Why should one need answers? Perhaps the answer is rooted in the function served by the brain and consciousness in the survival of an animal. A curious brain will actively seek out information, and a conscious brain will continuously process it to determine the best strategies for survival. Consciousness and curiosity would then be traits determined by evolution, and perhaps are no more than a particular choice of data-handling processes within a neural network. Consciousness would then be not a domain of humans only, but would be possessed in various degrees by all living beings.

The need to understand, create, write poems etc. is in my view just an extension and a by-product of a evolutionarily favorable trait of curiosity and consciousness. After all, a computational device (our brain) configured to analyse the world around it (i.e determining the causality and eventuality of objects arounds it), and having constant access to its own information content, would inevitably ask the same questions about its own origin. In the absence of concrete answers, it would try to provide any satisfactory ones at its disposal.

All the ``mystery`` surrounding consciousness will hopefully disappear once the basis for the study of consciousness is correctly formulated. We have already seen it happen within the domain of physics, all the ``supernatural`` and ``mystical`` aspects of celestial and physical objects dissolved before our eyes once the problems were correctly formulated. Neuroscience is in a state of infancy at the moment, and is awaiting that reformulation.

The presence of a specific universe around us is an indisputable evidence that there are concrete, though yet undiscovered laws that govern it. (I personally think that we have already discovered a few of these fundamental laws). I think that we will not only completely understand consciousness, but also implement it in some of our creations. And perhaps, not very far in the future, we will actually have not only understood the physical basis of consciousness and but also would be experimenting with augmenting and improving it. That is when matter would break free of sheer probability to chart its future evolution.

Chowkwalas Interview Pak. Law Minister Respected Minister of Law,

There is an epidemic of crime in the country that is intimately linked to the economic situation of the people and to the low efficiency of the law enforcement agencies in Pakistan. I would like to ask you what concrete steps are being considered by the government to improve the situation.

I have an additional question about sectarian violence in Pakistan. There have been multiple investigations about the identity of the perpetrators, and about their organizations. Since sectarian violence threatens to undermine the very fabric of our society, the government needs to take stern and just measures against curbing this epidemic. What plan does the government have to address this problem?

Thank you.