Three Hard Questions and Quest for Their Solution

Mohammad Gill
Jan 4, 2003

Three Hard Questions and Quest for Their Solution

By Mohammad Gill, Detroit, Michigan

Paul Davies wrote in the preface of his book, The Mind of , that he used to infuriate his parents continually by asking questions. For instance, he would ask, "Why can’t I go out to play? Because it might rain. Why might it rain? Because the weatherman has said so. Why has he said so? Because there are storms coming up from France…These relentless interrogations normally ended with a desperate ‘Because made it that way, and that’s that”. In his mature and adult life, the questions didn’t leave him alone but then he pondered over them philosophically. He would muse, “Can the chain of explanation really stop somewhere, with perhaps, or with some superlaw of nature? If so, how does this supreme explanation itself escape the need to be explained? In short, can ‘that’ ever be ‘that’?”

Davies is not the only one who had mused on this endless chain of questions; there were others also who posed the question: Who created ? in response to the answer that had created every thing. Man has considered, discussed, and heatedly argued this question since immemorial time and probably would continue forever without finding a truly satisfactory answer. I will discuss this question further herein later in a little more detail.

Man has created many other questions for himself, some of which can only be formulated but not solved. One of such questions is: Can create a stone which is so heavy that even He cannot lift? Whatever way you try to answer this question, you contravene the essential attribute of ’s omnipotence. The question does not have any answer. I do not propose to consider such impossible questions herein; on the other hand, I will discuss only three questions one of which is already solved and the other two are still posing a formidable challenge to man’s analytical skills. I will discuss the question, which has been solved mainly for its fascinating history. It defied solution for more than three hundred years. This question was popularly called Fermat’s Last Theorem. Of the other two, one may be solved soon or not so soon while the other may live with the mankind forever.

One of these questions belongs to Mathematics, another to Physics, and the third is not restricted to any particular area of human knowledge; it may require application of the entire human knowledge and still remain unsolved.

Fermat’s Last Theorem

I will take the liberty of writing one algebraic equation here, if you bear with me, because it becomes so much simpler to describe the Last Theorem with the help of this equation. Most of us are familiar with the Pythagoras theorem, which we read in high school geometry. Fermat generalized this theorem and wrote it in the form of an equation as follows,

X^n + Y^n = Z^n

and stated that it has no non-zero integer solution for X, Y, and Z when n is an integer and greater than 2. In the Pythagoras equation, n =2. Fermat had written this equation in his copy of Diophantus’s Arithmetica, around 1630. His son discovered it after his . Fermat had claimed, “I have discovered a truly remarkable proof which this margin is too small to contain”. Whether he indeed had a proof, no body knows for sure, although it is generally believed that he didn’t. It took more than three hundred years to provide a general proof of this apparently innocuous but actually very complex theorem. Andrew Wiles provided the formal proof in October 1994. Asked if his proof was the same as Fermat’s, Wiles responded, “There is no chance of that. Fermat couldn’t have had this proof. It’s 150 pages long. It’s a 20th century proof. It couldn’t have been done in the 19th century, let alone the 17th century. The techniques used in this proof just weren’t around in Fermat’s time”, (Solving Fermat: Andrew Wiles, wysiwyg://50/http://www.pbs.org/nova/proof/wiles.htm). Fermat wasn’t even a mathematician by his formal ; he had studied .

Wiles was born on April 11, 1953, in Cambridge, England. He has received a number of honors. He became a Fellow of Royal Society (FRS) in 1989, won the Royal Society Royal Medal in 1996, and AMS Cole Prize in 1997. He is a Professor at Princeton University.

Fermat’s Last Theorem had the dubious distinction of being the theorem with the largest number of published false proofs. Even Wiles’ original proof had an error, which he was able to remove after working on it for several months.

Many mathematicians had devoted their lives to developing a proof of the Last Theorem but without success; they however indirectly contributed materially to the number theory while working on the elusive proof. One of such researchers was Sophie Germain (1776-1851) who was born on April1, 1776, in France. France at that time was in a political transition which in the end led to the French . Germain’s interest in mathematics was kindled when she read the following anecdote in Jean-Etienne Montucla’s book, History of Mathematics (wysiwyg://47//http:www.pbs.org/wgbh/nova/proof/germain.htm) , “Archimedes had spent his life at Syracuse studying mathematics in relative tranquility, but when he was in his late 70’s, the was shattered by the invading Roman army. Legend had it that, during the invasion, Archimedes was so engrossed in the study of a geometric figure in the sand that he failed to respond to the questioning of a Roman soldier. As a result, he was speared to ”.

In Germain’s day, study of mathematics was not only gauche for ; they were not allowed admission in the institute of higher learning for mathematics and sciences. The Ecole Polytechnique had opened in 1794, in Paris. Germain managed to sneak in pretending she was a man by impersonating an older student, Monsieur Antoine-August Le Blanc, who had already left the Polytechnique but the school was not aware of it. Every thing went along fine until, one day, the course supervisor, the famous Joseph-Louis Lagrange (1736-1813), wanted to see his brilliant student, Le Blanc. Germain had no recourse but to reveal her . Lagrange was astonished and pleased to meet the young woman and became her mentor and friend. Germain was so preoccupied with her work that she never married. There were numerous others who contributed significantly to mathematics even by their failure to prove the Last Theorem.

Now we come to the next question. Can the existence of be proved logically?

Existence of ?

Man had debated this question ever since he was capable of thinking rationally. No satisfactory logical proof exists to prove or disprove the existence of . But before one could discuss the existence of , it is appropriate to consider what is. How is defined? is generally defined by His attributes. The attributes of Christian are, according to The National Catholic Almanac: almighty, eternal, holy, immortal, immense, immutable, incomprehensible, ineffable, infinite, invisible, just, loving, merciful, most high, most wise, omnipotent, omniscient, omnipresent, perfect, provident, supreme, true.

The problem with these attributes is that they over-define and over-specify . According to George H. Smith (: The Case Against , 1989), “..included in this catalogue of characteristics is ‘incomprehensible’. One must wonder how it is possible to declare ’s incomprehensibility and simultaneously list twenty-two additional attributes. If cannot be comprehended, how can the Christian offer us a string of attributes whose function, presumably, is to enable us to understand the nature of ”? For another, if is infinite, He cannot be comprehended by human mind anyhow because human mind is finite. The finite cannot comprehend infinite. It is therefore pointless to talk about because our knowledge of Him is not certain. Also according to another attribute, He is ineffable which means indescribable. So all descriptions of lack certainty. The Holy Quran has assigned ninety-nine attributes to Allah.

While it is not my intention to go into any detailed discussion about the logical arguments generally offered one way or the other about , I will briefly describe Iqbal’s criticism of the three oft-quoted historical arguments, e.g., Cosmological, Teleological, and Ontological Arguments, and then mention the others only nominally.

Cosmological Argument

According to Iqbal (The Reconstruction of Religious Thought in , reprinted 1999, pp. 28-29), “The cosmological argument views the world as a finite effect, and passing through a series of dependent sequences, stops at an uncaused first cause of the unthinkability of an infinite regress….To finish the series at a certain point, and to elevate one member of the series to the dignity of an uncaused first cause, is to set at naught the very of causation on which the whole argument proceeds…Logically speaking, then, the movement from the finite to the infinite as embodied in the cosmological argument is quite illegitimate; and the argument fails in toto”. If we believe in cause and effect then the question, “Who created ?”, is not meaningless and is quite legitimate.

Teleological Argument

This argument is based on the premise that a supremely intelligent designer (architect, if you will) is responsible for the creation of the universe and that being is . Iqbal discusses it as, “From the traces of foresight, purpose, and adaptation in nature, it (Teleological Argument) infers the existence of a self-conscious being of infinite intelligence and power. At best, it gives us a skillful external contriver working on a pre-existing dead and intractable material incapable of orderly structures and combinations. The argument gives us a contriver only and not a creator; and even if we suppose him to be also the creator of the material, it does no credit to his wisdom to create his own difficulties by first creating intractable material, and then overcoming its by the application of methods alien to its original nature… The truth is that the analogy on which the argument proceeds is of no value at all.”

Ontological Argument

Ontological Argument was originally propounded by St. Anslem (1033-1109) and soon afterwards, refuted by Gaunilo. The argument is quite convoluted; according to one version, is defined as the being in which none greater is possible and it is true that the notion of exists in the human mind. Therefore who is the greatest being exists in reality. Iqbal comments on this argument as follows: "But whatever may be the form of the argument, it is clear that the conception of existence is no proof of objective existence. As in Kant’s criticism of this argument the notion of 300 dollars in my mind cannot prove that I have them in my pocket….Between idea of a perfect being in my mind and the objective reality of that being there is a gulf which cannot be bridged over by a transcendental act of thought”.

There are other arguments also which, have been discussed by various authors; Smith has classified them in two broad categories. The above three arguments are also included in them.

 The Cosmological Arguments which include The First Cause, The Sustaining First Cause, The Contingency Argument, and The Entropy Argument.
 The Design Arguments which include The Teleological Argument, The Analogical Argument, and The Argument for Life.

Different other scholars have used different nomenclature for some of these arguments. For instance, I had referred to a recent debate on the question: Does Exist? between Imran Aijaz and Bill Cooke in one of my articles published at (Intellectual of Human Thought, , November 8, 2002). Aijaz had presented his arguments for the existence of under The Prima Causa, The Personal Creator, and An Intelligent .

The trouble with these arguments is that they can be refuted as easily and with equal force with which they are made in favor of ’s existence.

T.H. Huxley (1825-1895) had come to the conclusion that ’s existence can neither be proved logically nor disproved; he therefore coined the term ‘’ for a person who neither believes in the existence of nor does he disbelieve it. Bertrand Russell tended towards although he admitted he was and that ’s existence cannot be logically disproved.

So this remains an open question and man will continually engage in discussing and debating it. This also is an issue to decide whether created man in His own image or, on the other hand, man created in his own image.

Belief in the existence of is largely a matter of personal . Those who can believe in it, nothing seems simpler to them than their in ; it comes to them naturally.

Lastly, I would like to describe if the fundamental forces of nature can be unified. Physicists have been working on this problem for the last eight or nine decades.

Unification of Fundamental Forces of Nature?

In April 1919, Einstein received a letter that left him speechless. It was from an unknown mathematician, Theodor (Franz Eduard) Kaluza, at the University of Konigsberg in Germany….In a short article, only a few pages long, this obscure mathematician was proposing a solution to one of the greatest problem of the century. In just a few lines, Kaluza was uniting Einstein’s theory of gravity with Maxwell’s theory of light by introducing the fifth dimension (that is, four dimensions of space and one dimension of time). (Hyperspace, Michio Kaku, pp. 99-100)

Kaluza’s theory was a remarkable achievement but the fifth dimension that was needed for unification dampened the general enthusiasm. Einstein kept the paper with him for two years before he submitted it for publication; the paper had the title ‘On the Unity Problem of Physics’. Kaluza’s theory was later (in 1926) integrated into Kaluza-Klein field theory (named after the mathematician Oskar Klein), which involved field equations in five-dimensional space. Emergence of Quantum Mechanics opened up such wide vistas of research that scientists lost interest in Kaluza-Klein theory. But this theory is still alive and may play a role in the final unification.

Although Kaluza’s theory unified the electro-magnetic force with the force of gravity, complete unification with strong and weak nuclear forces could not be achieved. Einstein spent his lifetime in this endeavor but could not succeed. Weinberg and Salam succeeded in unifying the electromagnetic force with the weak force in the late 1960’s for which they were honored with the award of Nobel Prize. The strong force could also be combined with the electro-weak force; such theories are called the Grand Unified Theories, but gravity failed to unify. There was a great deal of euphoric excitement in the 1990’s when it was hoped that the Superstring Theory will do the trick of unifying all the fundamental forces of nature into one theory called Theory of Everything (TOE). Steve Hawkings had made a daring prediction that Theory of Everything will be developed before the end of the last millennium, but it didn’t happen and the effort is still continuing.

It has also been realized that unification may not be achieved by the Superstring theory alone; something more is required for this purpose. The Particle Physicists are working together with the Relativists to develop what is called the Quantum Gravity Theory, which holds the promise of unifying all the forces. Einstein’s theory of gravity and the superstring theory are, so to say, two asymptotes, which the Quantum Gravity theory is seeking to combine. Very complex mathematics is involved in the theoretical work and it is not easy to break it down into simple description. Abhay Ashtekar, a Physics Professor at the Pennsylvania University, who is ethnically Indian, has contributed in this effort significantly building on the previous work of Sen Amitaba, another Indian Physicist. He (Ashtekar), in 1986, “found a way to reformulate Einstein’s equations of gravity in terms of new variables. Soon afterwards a way was discovered to find solutions to the equations (Wheeler-DeWitt equations). This is now known as the loop representation of quantum gravity”, (http://adela.mff.cuni.cz/~motl/Gibbs/qugrav.htm).

According to Lee Smolin, a leading Quantum Gravity physicist, “I personally have little that in the end loop quantum gravity and string theory will be seen as two parts of a single theory. Whether it will take a Newton to find this theory, or whether it is something we mortals can do, is something that only time will tell”, (Three Roads to Quantum Gravity, 2001, p. 193).

In spite of these recent advances, it is not yet clear when the efforts of unifying all the forces completely will bear fruit. I will close this paper with a perceptive quote from Phil Gibbs: “According to conventional wisdom among physicists, the process of unification will continue until all physics is unified into one neat and tidy theory. There is no a priori reason to be so sure of this. It is quite possible that physicists will always be discovering new forces, or finding new layers of structure in particles, without ever arriving at a final theory. It is quite simply the nature of laws of physics as we currently know them that inspires the belief that we are getting closer to the end”, (http://adela.mff.cuni.cz/~motl/Gibbs/qugrav.htm).