While attempting to obtain a love for knowledge and willpower to think, one must not overlook reality or disregard past experiences. One must relate to the “sense of reality” under the watch of reason and control of conscience, and consider it on a par with one’s ability to taste, smell, and touch. Houses of knowledge, centers for research, and the symposiums that they hold must support and stimulate a love of knowledge. It is essential that we all support this cause.

The way of moderation is to do everything necessary in terms of causes and do it prudently and insistently; yet moderation is also full submission to God so much so that nothing can come between a person and their trust in Him. Cause-and-effect relationship must be observed at its best, yet without giving way to extreme determinism. I am not sure how much flexibility in this matter would be welcomed, but I think at the very most one can be open to a conditional, moderate type of determinism. At least this much of openness to causality and cause-and-effect relationship has existed among the circles of the faithful throughout the history, with certain varying interpretations.

If causal determinism is the name for the phenomena in which the same causes in the same circumstances bring out the same results, then it goes without saying that conditional determinism does have a place in our worldview. Cause-and-effect can be relevant to a certain extent in the social life, too, even if not as rigorous as in the physical world. This implies future consequences of our actions on the society today, and that we must have a plan according to which we can establish a social and individual life in harmony and order.

Indeed, if our society and administrations are going to exist in tomorrow’s world then we must start planning for them now. This is only possible through clear engagement with reality and when all possible alternatives and possibilities are weighed. Otherwise, unexpected internal and external events are inevitable.

We must review all the current institutions of our society and their essential dynamics according to conditions of today and tomorrow – schools and their curricula; universities and all higher education facilities; nursing homes and orphanages; congregations in houses of worship; soldiers in their barracks; police officers at police stations; public servants in government offices; workers in factories … Without a review done with a cause-and-effect analysis, it will be very difficult to guarantee a generation free from chaos, nor can we claim having raised well-rounded individuals or promise peace for the society. Under such circumstances, the place of worship fails to fulfill its mission, the school fails to reach the sanctity of a place of worship, the barracks fails to maintain its reputation, and masses will succumb to destitution.

We cannot sit and wait for surprises as though everything will be prepared in another world to be sent to our aid. The question is, are we taking an active part in life, or are we not?

There are certain thoughts that are dangerous for a society’s future. If people are only concerned with the present (like Omar Khayyam), or if they don’t believe in thinking deeply because it makes them crazy, or if they do believe in excessively indulging in material pleasures, then the society has lost its meaning and is already dead spiritually.

It is incumbent upon intellectuals and those in the administration to prevent such aberrations of thought and degradations of the soul by way of leading the society to high goals and enlightening people through knowledge. If we do not imbue people with a true love for knowledge and the spirit of thought, and choose to bemuse them with daily politics instead, we will have made society a source of daily conflict. Social problems cannot be solved by the suppression of thought, nor by a simple change in political power. Even if we solve these problems once, the changing circumstances and an ever-evolving world will constantly bring forth new problems. In the face of these obstacles waiting for us at every corner we have no other choice than to struggle against them with a love of truth, knowledge and understanding.

Existence is constantly developing; to be left on the outside of this development would mean isolation, which is no different than colliding with the wheels spinning and turning in the universe. Actually, without comprehending this dynamic of renewal and advancement throughout the universe, it will be impossible to understand existence as a whole, the mission of the human being, and the truth of humanity.

In this world, the inanimate is constantly running towards life; life travels towards consciousness and understanding. The alternation between dark and light is on a continuous cycle, and every single thing builds upon each other to form a profundity of knowledge. Yes, all the existence and events, too, run without cessation towards the infinite just as all rivers and streams flow onwards through rocks to reach the sea. Using our willpower and consciousness, we, too, must flow towards our future with diligence and effort that surpass our current power and durability. Otherwise, whilst creation and life are developing and perfecting, we will be like climbing an escalator in the opposite direction. Every attempt that fails to comply with the prevailing harmony in the universe is destined to be cast aside, and they will not be able to form, develop, and reach perfection.

While the Islamic world excelled in a blessed period of history, so did the Western world in terms of its own Renaissance. Both did so having benefited from the common knowledge accumulated along a few thousand years of human history.

Now, if we wish to once more achieve a similar development, we must evaluate the dynamics laid out above and apply them across our society.

Indeed, these essentials, and the spirit and meaning that they carry, must be infused into the soul of society, even in an unsubtle form. We must ensure that our traditions and customs turn green and take root in families, schools, and places of worship – not one single section of society should be left deprived of this spirit and meaning. The souls of children should be kneaded with this spirit and meaning. Beginning with elementary school, their souls should soar with these values, and in the periods to come, they should be nurtured with the same feelings and thoughts with gradual increase in the content.

If there is one thing that is more important than knowledge itself then that is the understanding of knowledge and the engraving of that understanding onto the souls of a society. Instilling youth with this love of knowledge is as important to their development as water is. This love and these principles of knowledge should, without a doubt, be instilled in every individual throughout a society, from age seven to seventy. This way, any friction that develops between differences of thought and philosophy can be resolved through dialogue and understanding instead of conflict and rivalry.

The ethical dimension of this matter calls for a separate analysis on its own; so, I am passing over it for now, leaving it to another piece.

The scene depicts an ordinary day in a metropolitan city. People are crossing the streets, perhaps going to work. There are traffic lights and so on. However, it is just a simulation program; all the actions of the people and all the events in the environment were predetermined. We can imagine questions popping into Neo’s mind: “Is the universe really a kind of simulation? Does God interfere with the universe or does it operate like a machine?” and followed by “Is it possible to compute someone’s fate? Does free will exist?”

Neo would neither be the first nor the last to ask similar questions. Until the 1930s, the answers to these questions were sometimes influenced by the idea of scientific determinism which considered the universe like the one in The Matrix. A paradigm shift took place in 1930s when two brilliant scientists proposed their ground breaking studies on non-determinism. Gödel’s Incompleteness Theorem and Heisenberg’s Uncertainty Principle considered the phenomenal aspects of non-determinism in the universe. First, we will have a short journey through the idea of scientific determinism. Then, we will investigate non-determinism and its consequences.

The idea of scientific determinism

The term ‘scientific determinism’ is defined to be the computability of future states, given the current state and a computer that has sufficiently large computation capacity. Suppose we take a snapshot of the universe at a particular time, or press the pause key and freeze the universe such as the example from The Matrix. What scientific determinism says briefly in simple terms is that by looking at that entire picture of the moment, the picture of the next second can be calculated using the laws and formulas of physics. On a large scale and in the long term, this idea leads to an exact computation of a moment of the universe given the initial conditions and its governing laws at the time of its creation. This is the key point for some scientific determinists who exclude the Divine work in the universe; if God exists, He only sets the initial conditions and the physical laws of the universe. Then the universe works on its own like a machine.

The first modern idea of scientific determinism was articulated by Newton in 18th century. Newton believed that all the laws governing the universe could be deduced from formulas, and these formulas could be derived by following the scientific method. First of all, science requires consistency among all known formulas and theories. This led the German mathematician David Hilbert to tackle the problem of proving the consistency of arithmetic in 1900s. One way of showing the consistency of arithmetic was to prove or disprove infinite number of statements in arithmetic, which was practically impossible! Instead, a clever idea was to develop a methodology that will generate the proof or disproof of a given arbitrary statement in arithmetic. If that methodology existed and was shown to be correct, that would be the happy ending of the story. Motivated by this problem in 1913, Alfred Whitehead and Bertrand Russell wrote their work, Principia Mathematica, a three-volume work on the foundations of mathematics. It was an attempt to derive all mathematical truths without the requirement of human intuition. They utilized symbolic logic, since it has a profound methodology for proving statements.

Later, this work would have played a fundamental role for proving the correctness / incorrectness of any statement in the universe. As an ultimate goal, by deducing all the information that belongs to a certain time of the universe, it would have been possible to compute the exact situation of the universe at an arbitrary time, which we mentioned before.

The fall of scientific determinism

At that time, Principia Mathematica left two questions open:

• Could a contradiction be derived from the Principia’s axioms (the question of inconsistency)?

• Does a mathematical statement which could neither be proved nor disproved in the system (the question of completeness) exist?

These questions were the heart of the discussion, and they had to be both answered as ‘no’ by Principia Mathematica to be deterministic. We have already explained the necessity of consistency before. On the other hand, some states cannot be calculated in an incomplete system which violates the determinism.

In 1931, Gödel published his famous article “On formally undecidable propositions of Principia Mathematica and related systems.” This work claims to refute the claims of scientific determinists about deriving all mathematical truths from logical systems. In his article, Gödel’s first incompleteness theorem showed that sufficiently complex systems (such as the ones described in Principia Mathematica and the physical laws of the universe) could not be complete and consistent at the same time. Gödel proved his theorem using a genius idea, which was by showing that a similar statement to “This statement cannot be proved” can be expressed in any sufficiently complex logical systems. Hence, one who proves it will create an inconsistency in the formal system, or it will be considered as improvable, violating the completeness rule of the formal system.

Another stroke to scientific determinism came from Heisenberg in 1927 with his famous Uncertainty Principle. Heisenberg asserted that both the velocity and the position of a particle cannot be accurately measured at the same time. Measurement requires interfering with the particle in terms of position or velocity. Observation becomes a part of the outcome which is in fact not known to be the real outcome. In short, uncertainty principle implies that the particle positions can only be calculated as a probability distribution.

One can object that this effect may be a result of our lack of the knowledge needed to find out the facts about particle position and velocity. However, Copenhagen’s interpretation of Quantum mechanics is commonly accepted, and it states that the problem of uncertainty is not epistemological but ontological; i.e., the problem is not due to the limits of scientific knowledge but depends on the constitution of the universe . From a mathematical aspect, Gödel’s theorem strongly asserts the same fact.

Consequences of non-determinism

Non-determinism in the Universe brought back earlier concepts categorized as meta-physical, such as ‘fate’ and ‘free will,’ into the debate about scientific knowledge for further investigation, and made a phenomenal change in the perspectives on the existence of God.

In The Matrix, remember the scene wherein Neo says “Deja vu” after he sees the black cat for the second time at the stairs of the apartment. Then Trinity tells him that it happened due to a change in the Matrix. The free will of Neo and his friends causes the failure of the deterministic nature of the Matrix; the Matrix cannot make exact calculation of their actions and foresee the future. Instead, it alters the simulation program based on their actions. Now, the concept of fate is not a predetermined destiny in the Matrix; it involves the human free will, hence nobody knows what will happen in the future, including the Matrix itself.

Free will requires the ability to make choices independent from deterministic constraints. A friend of yours offers you to take one of two identical apples, and you take one of them. If it was possible to rewind time and get back to the moment of the offer, this time you might choose the other apple. Note that the states are precisely the same; the entire history of the events in the universe is exactly the same as the one in previous scenario. This is the key point: in two equivalent states of the universe; i.e., all conditions are exactly the same, free will allows you to choose different options in these two states. This situation contrasts with a deterministic universe however well suits to a non-deterministic one.

Another major consequence is about the Creator’s role in the universe. As mentioned before, scientific determinism can reduce the concept of ‘God’ into the following statement [4, 6]:

• If there is a God, He created the universe, set the initial conditions and the laws, and left it the way it works. He doesn’t interfere with its execution.

By non-determinism, this statement can no longer be regarded as the absolute truth. Instead of clearly determined outcomes in the future time frames, Quantum mechanics introduced the notion of probabilities. In each decision point (i.e., quantum time frames or every single moment), there are many possible outcomes. That means either there is an entire ‘randomness’ or there is a Decision Maker that decides at these decision points and controls the flow of all actions in the universe. In case of randomness, it is always possible to reach a ‘failure state’. However, the universe has never failed for billions of years. Here, the failure state is not the ending of the universe or Armageddon, because these states are internally consistent. Failure state means to get the ‘blue screen’ as in Windows; suddenly everything stops or perishes. ‘Failure’ can be described as an unexpected error that leads unrecoverable / unhandled error which crushes the operating system. At this point, the universe needs to restart in order to start everything from the beginning. The idea of randomness in the course of actions is strongly opposed by Einstein as stated in his famous saying “God doesn’t play dice.”

So the question is “how can the concepts ‘God’, ‘fate’ and ‘free will’ be related to each other?” Now, we may say the following statements about fate: it is not computable, it is not random (due to the definition of fate), and free will is possible. In this case, we have two options:

• there is no free will – God controls all the events and free will is not involved in it,

• there is free will – God incorporates free will in his creation of the upcoming states

According to the second idea, we have been given the right to choose among limited amount of options and then God creates the chosen option. For instance, I would like to move my arm and show the tendency to move it. So, God creates necessary conditions such as the pulse from the brain that orders the arm to move, and the arm moves. Of course, He always preserves the right not to create the things according to my will. In that case, the arm doesn’t move – I might have a stroke or might not have sufficient strength or something else might happen.

Consequently, in case of free will, fate becomes all the outcomes of God’s will by including free will in the universe. But “God knows everything, everything that will be in the future. Then, doesn’t that mean the universe is deterministic?” As we mentioned above, determinism requires the computation of future states. However the Creator knows the fate with His infinite knowledge by overseeing the entire system but not computing. Here, computation and knowledge are two different concepts; knowledge may not be acquired by computation. If somebody shows us the result of a multiplication of two numbers, we learn the result by seeing it but not computing it.

Non-determinism in the universe might be considered as the beginning of a re-marriage between science and meta-physics. Non-determinism implies that it is not reasonable to absolutely reject Divine work in the operation of the universe and the idea of free will. The concepts that are considered to be currently meta-physical such as fate and free will need further investigation in the physical sciences.

Fatih Gelgi has a PhD in computer science. He is currently the computer coordinator of Accord AMSP team in Los Angeles.

References

[1] K. Devlin. “Kurt Gödel – Separating Truth from Proof in Mathematics,” Science, 298: 1899-2000, 2002.

[2] F. Gelgi. “Implications of Gödel’s Incompleteness Theorem on Artificial Intelligence vs. Mind,” The Fountain Magazine, 46, 2004.

[3] K. Gödel. “Uber formal unentscheidbare Satze der Principia Mathematica und verwandter Systeme I,” Monatshefte für Mathematik und Physik, 38: 173-98, 1931.

[4] S. Hawking. Brief History of Time, Bantam Dell Publishing, Ed. 10, 1988.

[5] E. Nagel, J. R. Newman. Gödel’s Proof, New York University Press, 2001.

[6] C. Taslaman. Kuantum Teorisi Felsefe ve Tanri, Istanbul Yayinevi, 2008.

[7] Wikipedia, “Principia Mathematica,” retrieved on Feb 27, 2010 from http://en.wikipedia.org/wiki/Principia_Mathematica.

Notes

1. Interested reader may refer to [5] for the detailed and understandable explanation of Gödel’s proof.
2. For details see “Chapter 4: Uncertainty Principle” in [4].
3. Different interpretations of Quantum physics can be found in [6] or at: http://kuantum.gen.tr.

During the academic year of 1991-92, I had the opportunity to spend a sabbatical year in Paris. During that time, my wife Adele and I were surprised to notice intense activity, in the form of books, conferences, and symposia, on the theme of “Science and Faith,” with the purpose of bringing them together after a long time of separation and antagonism. Significantly, this attempt toward reconciliation was beginning in France, the country that so much contributed to the dichotomy between the two in the first place.

Three books figure prominently in my present discussion about science and faith. The first, the best-selling God and Science,¹ consists of a dialogue between J. Guitton, a highly respected Catholic philosopher and a well-known member of the French National Academy, and Grichka and Igor Bogdanov, young scientists whose fields of research are in astrophysics. In the dialogue between Guitton and the Bogdanov brothers, the scientists answer the questions posed by the philosopher about the laws governing the natural world. Intriguing questions are addressed: “Where the universe came from? What is real? What are the relationships between conscience and matter? Why does anything exist at all?” In every instance the philosopher, who is also a believer in God and in the Bible, finds that the answers he receives from science give him comfort and strength in his faith. He finds no contradiction between the two; on the contrary, everything he hears about science strengthens his faith.

A collection of essays edited by Jean Delumeau, Le Savant et la Foi,² presents a similar theme. It consists of nineteen contributions from scientists, some of them highly reputed, who explain, in often touching terms, how they reconcile their faith with their scientific research. One of the essays is the result of a collaboration among some twenty scientists affiliated with the University of Paris-Sud (Orsay, Gif, Saclay, etc.), who hold monthly meetings to discuss issues of science and faith in relationship to their research.

A third book that attests to this renewed interest in the relationship between science and faith is another collection of essays, Can Scientists Believe?,³ written by scientists from different religious traditions and edited by Sir Neville Mott, winner of the Nobel Prize for physics in 1977. In this book, Mott himself explains how he became a Christian at the age of fifty, when, as head of the Cavendish Laboratory at Cambridge, in England, he was invited by the vicar of the university church to join other leading scientists in contributing to a lecture series there about science and religion. Being agnostic, he felt a need to do some reading before discussing something about which he knew very little, and this was the beginning of his conversion.

In January 1992, the Catholic newspaper La Croix organized its second conference on “Science and Faith,” a day-long conference which took place in a theater in Paris and was widely attended. Among the participants were scientists, theologians, historians, and philosophers, representing all the major religious traditions, and it included atheists of good will, who were open to dialogue. Some of the participants were people of high professional standing, members of the French Academy. The opening addresses were delivered by Cardinal Jean-Marie Lustiger, Archbishop of Paris, and Professor Hubert Curien, minister in the French government for scientific research.

The recurrent theme of all the contributions at the conference was “Scientism is dead.” In order to understand the significance of that pronouncement in the context of our discussion of spirituality and postmodernism, we must consider the historical development of science.

Modern science and Determinism

In the ancient and medieval worlds, science and religion were part of the same cultural heritage; one was unthinkable without the other. What happened later to cause the schism between them?

The story is well-known. Modern science developed in the sixteenth and seventeenth centuries, with Francis Bacon (1561-1626) and Galileo Galilei (1564-1642), in the aftermath of a great period, the Italian Renaissance, during which attention shifted from God to humankind, from the supernatural to the natural.

Toward the end of the nineteenth century, which saw such technological advances as electricity and the steam engine, which made such a deep impact in the life of the Western world, confidence in science was unlimited. There was a general feeling that science would ultimately solve all the problems of society and the human condition. Suffering, diseases, poverty-all these evils would sooner or later be eliminated by science and technology. There was no place for God. Human reason could reach the ultimate truth without the need of a supernatural power.

In philosophy these ideas culminated in schools of thought such as logical positivism, in which there was no room for a transcendent superior being. All these schools of thought are usually referred to under the general name of “scientism.” When, therefore, H. Curien, and the other participants in the 1992 conference in Paris, boldly declared the “death of scientism,” they marked the end of a whole historical development and celebrated the present, post-modern period in science.

The new science: causality and probability

In the beginning of the twenty-first century we are more ready to recognize humbly that science has its own limitations and cannot cure all the evils of our human condition. This altered perception of science has been fostered by the advent of the so-called new science, which developed during the third decade of the last century. Quantum Mechanics has revolutionized the way people think about the natural world. In the atomic and nuclear realm the deterministic model, advanced by Laplace in his System of the World, was no longer valid. Certainty had to be replaced by the notion of probability; the whole principle of causality had to be questioned and revised. For example, the notion of “orbit,” perfectly valid when describing the motion of the earth around the sun, became meaningless in the new theory, which was designed to describe the properties of a negative electron moving around a positive nucleus. A well-defined trajectory was replaced by a “probability cloud.”

As these examples indicate, our ability to grasp reality is limited. Waves and particles are different descriptions of the same reality, which we are not able to define in absolute terms, as was once claimed by the deterministic science of the nineteenth century. At this point we realize that we must give up the idea of grasping “the thing in itself.” All this does not mean that the old, deterministic science was wrong, but only that it was correct under certain approximations, which are not valid in the micro-world of atoms and nuclei.

The healthy effect of this great revolution, brought about by the advent of the new science and Quantum Mechanics, has been to shake the arrogance of those who believed that everything could be predicted, once the initial conditions of the system were known, and to introduce an element of chance. We might say, in different words, that there is a place for God in the new scheme of ideas.

Einstein’s unenthusiastic response to Quantum Mechanics shows that he clearly perceived the “place for God” at the very heart of things. In the early stage of development of the new physics, he wrote to Niels Bohr: “Quantum Mechanics is very impressive. But an inner voice tells me that it is not yet the real thing. The theory produces a good deal, but hardly brings us close to the secret of the Old One. I am at all events convinced that He does not play dice.”⁴

Einstein’s letters and essays are famous for their many references to God. Although he did not have a religious affiliation and shunned all forms of organized religion, Einstein the scientist had a firm belief in God. Forty years before the 1992 conference in Paris declared the “death of scientism,” Einstein had come to this same conclusion, as shown in a letter to his dear friend Solovine⁵:

“You find it strange that I consider the comprehensibility of the world (to the extent that we are authorized to speak of such comprehensibility) as a miracle or as an eternal mystery. Well, a priori one should expect a chaotic world which cannot be grasped by the mind in any way… There lies the weakness of positivists and professional atheists who are elated because they feel that they have not only successfully rid the world of gods, but also “bared the miracles.” Oddly enough, we must be satisfied to acknowledge the “miracle” without there being any legitimate way for us to approach it.”

As an example of the “new scientist,” Einstein rejects a science without faith, without belief in the “miracle” that remains “unapproachable” and “mysterious.” Perhaps the best description of Einstein’s attitude toward religion appears on the back of the dedication page in a recent biography: “Science without religion is lame, religion without science is blind,”⁶ as Einstein once wrote to explain his personal creed.

Given the death of scientism, the discoveries of Quantum Mechanics, and the obvious connection between faith and science in the life and work of men like Einstein, it is now possible to write a revised history of western science based not on the split between religious belief and scientific research, but on their intimate connection. We can view science and religion as two approaches, different but complementary, to the same reality. In fact, there has never been a good reason for an opposition between science and religion; they are not incompatible in their views of the natural world.

Awe and excitement in science and religion

Many scientists, then, have been and are believers. The question then arises: what do science and religion have in common, so that realms previously thought to be mutually exclusive can now be seen as intimately linked? We may point to three elements common to both science and faith: the belief in things unseen, the awe and excitement of discovery, and the goal of service to others. First, the belief in things unseen. It is said of Einstein that he was a religious person… in the sense that he [had] no doubt of the significance of those super-personal goals which neither require nor are capable of rational foundation. His was not a life of prayer or worship. Yet he lived by a deep faith […] that there are laws of Nature to be discovered. His lifelong pursuit was to discover them. His realism and optimism are illuminated by his remark: “Subtle is the Lord, but malicious He is not.”⁷

One aspect that links science and religion, and characterizes a scientist’s spirituality, is the feeling of excitement, the thrill that both scientists and believers experience when confronted with a new facet of the truth that lies beyond the boundary presently accepted as the ultimate limit of their knowledge. As John Polkinghorne, a British professor of theoretical particle physics at Cambridge University and now an Anglican priest, one of the speakers at the 1992 conference, observes, “Part of the authentic experience of a scientist is the feeling of astonishment he or she experiences when contemplating the remarkable rational beauty of the physical world, as it unfolds in his/her research.”⁸

The eminent physicist, Isidor Isaac Rabi (1989-1991), who was honored with the Nobel Prize in 1944, bears witness to the religious dimension of this experience of astonishment: “When I discovered physics, I realized it transcended religion. It was the higher truth. It filled me with awe, put me in touch with a sense of original causes. Physics brought me close to God. That feeling stayed with me throughout my years in science. Whenever one of my students came to me with a scientific project, I asked only one question, “Will it bring you nearer to God?” They always understood what I meant.”⁹

At the time, Rabi himself had no particular religious affiliation, except for his background, which was strongly rooted in Orthodox Judaism. According to his own testimony, his upbringing in a household where the holy books of the Bible were familiar readings, gave him a definite spiritual formation that affected his attitude toward science: “To choose physics in the first place requires a certain direction of interest. In my case it was something that goes to my background, and that is religious in origin. Not religion in a secular way, but religion as the inspirer of a way of looking at things. Choosing physics means, in some way, you’re not going to choose trivialities. The whole idea of God, that’s real class… real drama. When you’re doing good physics, you are wrestling with the Champ. You have one life to do it, you don’t want to waste it.”¹⁰

Like Rabi, who moved “nearer to God” through scientific research and discovery, Xavier Le Pichon, a speaker in the 1992 conference and a professor of oceanography and geophysics at the prestigious Collège de France, speaks of his amazing encounters with the God of nature. A member of the French National Academy of Sciences, he has been exploring the bottom of the oceans for the past thirty years. Those underwater explorations have, as he says, awakened his “capacity for adoration”: “I have often experienced this capacity for adoration during my scientific explorations. I think in particular of my first descent in a submarine in the Rift Valley, in the middle of the Atlantic Ocean, at a depth of ten thousand feet… In our little boat, we are the first people to discover this scenery reminiscent of Genesis, the virgin crust, produced by the marriage between fire and earth. I had an appointment with the Earth so that I could make an offering to God.”¹¹

The same sentiments are expressed by another one of our speakers, Fr. George Coyne, Director of the Vatican Observatory in Castel Gandolfo and at the University of Arizona. I quote: “My scientific exploration and slow understanding of the universe is a prayer, and one that is drawing me into a deeper relationship with God. My understanding of the universe, with faith as a foundation of my life, is being drawn into the mystery of God. And this is why we’ll never fully understand our universe: while the scientific knowledge draws us on and on, the more we know, the less we know in many ways. The universe participates in the mystery of God.”¹²

Recently, in an article on the New York Times, the Dalai Lama, speaking about the convergence of science and spirituality, said, “Science could benefit from exploring issues usually left to the humanities. I believe that we must find a way to bear upon the direction of scientific development, especially in the life sciences. I am speaking of a secular ethics, which embraces compassion, tolerance, consideration of others, the responsible use of knowledge and power. These principles transcend the barriers between religious believers and non-believers: they belong not to one faith, but to all faiths.”

Those sentiments are echoed by Xavier Le Pichon, who said: “Science and technology are not only necessary, they are indeed the main tools needed to perfect the creation entrusted to humankind by God. To the extent we place the poor and the least ones at the center of our society, to the extent we ask them to inspire the civilization we are about to build, science and technology will appear as means offered in order to create a civilization of love.”¹³

So, perhaps, the “battle” between Science and Religious Faith is not so polarized as some of those at the extreme edges of the debate would have us to believe.

“In this modern era of cosmology, evolution, and the human genome, is there still the possibility of a richly satisfying harmony between the scientific and spiritual world views?”¹⁴

Dr. Francis Collins, author of the best selling book The Language of God: A Scientist Presents Evidence for Belief, and Director of the National Genome Research Institute, responded with a resounding “Yes” to this question, in his public lecture on February 20, 2007, at Purdue University.14 To an enthusiastic crowd of more than 1,100 participants, Dr. Collins stated that “The newfound power to read our own instruction book is no obstacle to faith in the existence of God.” Dr. Collins called for a truce in the escalating war between science and spirit. “We need science if we are going to survive in a complicated world, and we need faith if we are going to keep ourselves in perspective. We must seek out the ways in which these world views can happily coexist, and the mind must find a way to embrace both realms, if we are really concerned about our own future in this world.” Everyone who questions how religious faith would be reconciled with scientific knowledge, and everyone interested in an open and sincere discussion of one of the most crucial issues of our time, will be greatly enlightened by Dr. Collins’ experience described in his book “The Language of God.”

Roberto Colella is a professor of physics at Purdue University, West Lafayette, IN.

Notes

1. Guitton, Jean, Grichka Bogdanov, and Igor Bogdanov. Dieu et la Science, Grasset. 1991.

2. Delumeau, Jean (edited by). Le Savant el La Foi, Champs-Flammarion, Paris 1989; p. 230 (translated from French by Roberto Colella).

3. Molt, Sir Nevill (edited by). Can Scientists Believe? James and James, London, 1991, p. 71.

4. Pais, Abraham. Niels Bohr’s Times, Clarendon Press, Oxford, 1991, p. 318.

5. Einstein, Albert. Letters to Solovine, New York Philosophical Library, 1987, p. 131.

6. Einstein, Albert. “Science, Philosophy and Religion: A Symposium.” 1941.

7. Pais, Abraham. Subtle is the Lord… The Science and Life of Albert Einstein, Clarendon Press, Oxford, New York, 1982, p. vi.

8. Lecture on “Science and Religious Faith,” Purdue University, February 27, 1997.

9. Ridgen, John S.. Rabi, Scientist and Citizen, Basic Books Publishers, New York, 1987, p. 82.

10. See Ref. 8, p.p. 73-79.

11. See Ref. 2, p. 166.

12. Public Lecture at Purdue University, April 2, 1998.

13. See Delumeau 1989, p. 168.

14. Collins, Francis, The Language of God: A Scientist Presents Evidence for Belief, Free Press, New York, London, 2006.

As a relatively new and exciting science, chaos science grew very slowly during its infancy. Yet in the last decade, due to active research in many areas, it has became one of the hottest topics in academia as well as the popular science press. Many books have been published, and millions of Internet pages have been designed full of fractal pictures.1 Given that chaos is associated with disorder or confusion in a system or condition, why does it continue to attract so many people?

History of chaos

To understand chaos, one first has to understand the Newtonian worldview. Sir Isaac Newton’s (1642-1727) development of the calculus and laws of classical mechanics began a scientific revolution in seventeenth-century Europe that caused all subsequent scientists to view nature from a profoundly different perspective. Now that they finally could determine the dynamics of bodies by simple equations, they believed that they had found the ultimate eternal rules that shape the universe.

French physicist Pierre-Simon Laplace (1749-1827), who based his work upon Newton’s work, is credited with the following famous quotation (often referred to as Laplace’s Demon): ‘We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes.’2

Laplace’s Demon states the idea of determinism, that the past completely determines the future. One can clearly see why determinism was so attractive to scientists at that time. However, in Laplace’s word everything was predetermined: no chance, no choice, no uncertainty. A solid, inevitable destiny had frozen the events in every corner of the past and is continuously spreading out to the future to do same there. Determinism apparently invokes the idea that whole universe is like a clock. God set it in motion at the beginning of creation and then removed Himself, for everything had been planed before. The ideas that there was no place for free will and that God could not interfere killed the belief in a soul and, consequently, in spirituality. Philosophers and scientists have discussed this for many years. Determinism affected many philosophies and triggered the major ideological movements of during eighteenth century, especially in Europe.

Toward the end of the 1800s, mathematicians and scientists began encountering some very difficult equations, some of which we know today are unsolvable. The most troublesome are various nonlinear differential equations. Even though it looks like such a simple and totally deterministic system, the problem of three bodies attracting each other with purely gravitational forces (e.g., the sun, Earth, and moon triple) turns out to be missing an exact solution. At first, such problems were cast-off as special cases and largely ignored.

One reason for this also might come from the fascinating world of quantum mechanics, which dazzled even the great physicists, and the lack of fast computers at that time. When these equations finally were studied in detail, a fundamental change that would ultimately overthrow determinism began to occur in mathematics and science. An indication of the science that would be come to be known as ‘chaos’ began to appear.

Why does chaos interest people?

In contrast to its common usage, chaos does not actually mean disorder or confusion. By definition, it should occur in well-defined orderly systems. However, most natural physical systems often can exhibit an unpredictable or intractable behavior in the long run, even though the system is defined by clear-cut orderly mechanisms. In this sense, chaos can be defined as unpredictability rather than disorder.

For example, meteorologists use 12 sets of well-defined equations to forecast the weather. They relate such atmospheric parameters as pressure, temperature, flow speed, and time to each other. One can make a computer program that calculates the parameters’ final values by taking any initial conditions as the run’s starting point. In principle, therefore, if we know the initial temperature, pressure, and time values that describe today’s weather conditions, it is possible to derive tomorrow’s weather conditions by running a computer program, which is nothing more than a chain reaction of numerical iterations.

However, in practice, initial conditions cannot be measured exactly and so contain a degree of uncertainty. But since the system’s governing laws are known, one may estimate the effect of errors on future results. Hence, instead of giving the exact results, one can provide an approximate range of possibilities. This range can still be very useful, provided that the deviations do not stray too far from the actual values. In addition, knowing how the error grows in the system might help us understand and control the systems. But if we apply these error estimates to weather forecast equations, we will encounter a large problem, for errors grow exponentially in such systems. Even a tiny deviation at the beginning can create huge deviations from the actual values. It also can provide unrelated or nonsensical results.

An example of chaotic systems

This numerical behavior was first observed by the meteorologist Edward Lorenz, a pioneer in modern chaos work. Fascinated by the results he obtained, in the early 1960s he gave an interesting metaphor to explain the situation of high sensitivity to initial conditions: A butterfly’s slight wing movement (i.e., a little deviation from the initial conditions) can change the future in a way that causes some chain reaction that ultimately result in a hurricane.

Such systems that exhibit a very high sensitivity to initial conditions are called chaotic systems. Chaos comes from the mathematical properties hidden in the equations defining the system, and such unpredictability cannot be removed. Even if the measurements’ quality could be improved by minimizing errors, chaos never disappears from a chaotic system.

One may suppose that chaos occurs in complicated systems, such as weather forecast systems having 12 sets of equations. But even much simpler systems, such as billiards, can exhibit a very high degree chaos. A usual billiard system consists of many balls and a rectangular shaped table. I challenge master billiard players by requesting them to play the game in a stadium-shaped table. I am sure that they will find it difficult to do so, because such billiard tables would be chaotic systems.

If a system is defined as chaotic, this does not necessarily mean that its behavior is totally undefined all the time. As in stadium billiards, a ball has to be inside the billiards, so it should be somewhere on the table, even though sometimes we cannot foretell its exact position because of chaos. Besides, if you send the ball with a velocity perpendicular to a straight side, it will bounce back and forth between the two sides forever. Therefore, depending on which initial conditions are taken, chaotic systems also can show characteristics of regular motion.

A 3-body problem (in general n-body problems) such as the sun, Earth, and moon system, is a chaotic system. But since we can predict the motions of these celestial objects with great precision for many years in the future, why do we call this system chaotic? This triple system possesses a very special set of conditions: distance between bodies, their masses, and their velocities. These parameters cause it to exhibit near-regular behavior. It is analogous to the example of stadium billiards given above, for this triple system bounces back and forth between the table’s sides.

Conditions for chaos

Chaos also can be caused by other factors than just uncertainties measured in the initial conditions. Scientists generally define hypothetical systems by isolating them from the outside world in order to simplify them as much as possible. However, as even objects in the real world that are far apart interact with each other, no system in the real world can be isolated. Given this, a closed (isolated) system might be defined as a fluctuating approximation to its real counterpart, which is changing in an unpredictable manner all the time. In short, even though we would know the exact initial conditions, the actual system could be chaotic due to changes in the approximate system. In this sense, many physical systems have an inclination toward being chaotic.

Due to its maximum complexity, the universe is the largest chaotic system. Observable regular patterns in special parts of that system repeat themselves in time. While the rest of the flows are unpredictable, they are not totally irregular, abrupt, or disordered. Just like whirls in a flowing river, they are in a kind of free motion searching for convenient conditions in which to give birth to organized structures.

The future of chaos

Chaos gives today’s scientist a new worldview, for Newton’s concrete, cold, and deterministic one has been shaken by the uncertainty principle of quantum mechanics. No one ever thought that the Newtonian worldview could be replaced. However, now scientists are more likely to be open to chance and choice than their predecessors. The question is whether chaos theory will cause large revolutions in how we understand the universe. However, the existing excitement, expanding research and growing number of articles, and its numerous applications from economy to biology, seem to indicate that a surprise improvement might not be so far off. ‘

Footnotes

1. Fractal: A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature.
2. ‘Chaos and Fractals: Laplace’s Demon.’ Online at: www.pha.jhu.edu/ ldb/seminar/laplace.html.