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

I have always been pretty sure that mathematics and science are the best languages to explain the natural phenomena. While for many mathematics is too abstract, for me, it is the beautiful language of the universe.

There is no upper limit to the numerical abilities of humans. First, we discovered fire, to get warm. Then, we needed light, so we invented electricity. When we needed to talk to someone 10,000 miles away, we invented the internet. Behind all these inventions, was mathematics.

Of course, the universe cannot speak or think. However, we, the people, can read the universe. There are many scientifically and mathematically inclined people who can read the universe and find answers and then describe them. We, the normal people, can also use our imagination as an apparatus to read the universe and nature. If we can read, hence, something is written. In order to write, a language is always needed. So, the universe should have a language. The letters are circles, triangles, hexagons, etc.

Everything in life has mathematical patterns. Think of the wild animals with stripes or patterns for the purposes of camouflage. But why does a leopard or cheetah or tiger have a particular design?

The Enigma codebreaker, Alan Turing, had a mathematical theory about leopard’s spots. Turing suggested in his paper “The Chemical Basis of Morphogenesis” (published in 1952) “a mathematical schema for the formation of the patterns found in animals and plants.” This was 60 years ago [1].

Stars have patterns. Astrologists have been looking at the outer space searching for patterns to better understand life. Whatever it may be that they find, it is always about mathematics.

Seasons have patterns. They come and go. And they influence nature: the climate changes, animals migrate north or south, rain comes, snow melts, the earth changes color, etc.… Of course, seasons cannot make these miracles. They can only have mathematical patterns.

Einstein had pondered for years on how mathematics works so perfectly. He knew that mathematics is the bridge or the language that connects humans with the universe. And being a connection between us and the universe makes mathematics the greatest achievement of mankind.

If you take a closer look at the patterns of our world, you will witness the language of mathematics. Let me give you some specific examples.

Fibonacci, the golden ratio, spiral, cabbage…

Our universe is filled with spiral designs. Spirals can be found in the shapes of the DNA double helix, flowers, elephant tusks, sunflowers, hurricanes, draining water, animal horns, a nautilus shell, a snail shell, a pinecone, a cabbage, a fingerprint, algae, galaxies… the list goes on and on. Tons of lifeless and living things have spiral designs. And they are not random spirals. They have something in common: the golden ratio! And surprisingly, “there is a strong case that this so-called ‘Golden Ratio’ (1.61803…) can be related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time” [2].

All these spirals in nature tell us there are numbers all around us. Let’s observe the numbers of petals on some flowers. When you count the number of petals of the flowers in your garden, you will get the numbers 3, 5, 8, 13, 21, 34, or 55. These numbers are not random numbers. These are very unique numbers; they are part of a sequence developed by Fibonacci, a 13th century mathematician, by adding up the last two numbers starting from 1:

1+1= 2, 1+2= 3, 2+3= 5, 3+5=8 …

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

F_n= F_n-1+F_n-2, F₁=1, F₂=1

But, why are those Fibonacci numbers so important? The key is, the relationship between the progression of growth and the proportion. There is a harmonic proportion hidden in the Fibonacci sequence.

A fact: If you divide one number in the sequence by the previous number, the answers result in or come closer to phi:

For example: 5/3 = 1.6666;

13/8 = 1.6250; 377/233 = 1.61802575; 317811/196418 = 1.618033399

Definition: In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities [3].

These numbers can be demonstrated with the spiral of the florets in a sunflower. The florets in a sunflower head also form two spirals. If you count the clockwise and counterclockwise spirals that reach the outer edge, you’ll usually find a pair of numbers from the sequence: 34 and 55. If it is a very large sunflower, you will get 89 and 144 [4].

These spirals are not only in sunflowers. You can see them if you look at a pine cone or a daisy. If you mark the spirals and count them, you will always get a number from the Fibonacci sequence. And if you count in the other direction, this time you will find an adjacent Fibonacci number.

The nautilus shell, the golden mean

What makes the nautilus shell so special for mathematicians? Having the Golden Mean. But how do we know that the nautilus shell has the Golden Mean?

First of all, we will start with drawing a small, one unit square. Then we will draw another square which is larger than the previous one. We need to add in a counterclockwise direction. The length of each square has a value from the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … Then we can draw spirals, starting with the smallest one, outward through the largest one. Then the Golden Mean will appear.

Flowers, plants, or objects have no idea about mathematics, yet they manifest the best of mathematical patterns. This marvelous mathematical art has been placed in their nature for us not to be fascinated only but also to explore the mysteries behind it.

Note

1. https://www.bbcearth.com/blog/?article=the-maths-behind-a-leopards-spots
2. https://www.sajs.co.za/article/view/4033
3. http://mathworld.wolfram.com/GoldenRatio.html
4. http://www.sciencemag.org/news/2016/05/sunflowers-show-complex-fibonacci-sequences

Concepts like the number zero, negative numbers, complex numbers, matrices, and spatial geometry are inventions of mathematicians which were studied earlier and presented especially for the use of physicists. When mathematicians theorized the “Group Theory,” they were reported to have said, “Finally we have developed something that physicists cannot use.” However, this theory, which stemmed from intangible algebra, was found to be useful in investigating the symmetry of physical systems and had serious applications in particle physics.

If there were no mathematical advances, would physics and other sciences have developed as far as they have? What does it mean that sciences are found in such an interrelated state, and thus support each other?

The perfect relationship between physics and mathematics, as in the expression of many physical laws via simple mathematical equations, is truly amazing. The laws that describe the physical world – from equations expressing the laws of motion (like X=V.t, V=a.t, F=m.a h= (gt2)/2), to basic electrical equations (like V=I.R, P=I.V, E=V/d), going all the way to the equations that define gravitational forces and the expansion of the universe (like F=G.m1.m2/d2, V=H.d) – can easily be expressed through mathematics. Furthermore, this simplicity and plainness in creation of the universe fascinates many scientists. Einstein expressed this fascination when he said, “The most incomprehensible thing about the universe is that it is comprehensible.”

One of the most important relations between mathematics and physics is that the independent study of intangible works of mathematics unexpectedly became one of the best tools to describe the physical world. Numbers, for example, are one of the greatest inventions of humanity. Humans have used them to quantify their properties. For thousands of years, people used numbers, but then the concept of negative numbers developed for seemingly no reason. For centuries, negative numbers were seen as nonsense. Of course there is not a square with a negative side length, a circle with a negative value area, or a classroom with negative number of students. However, negative numbers were found to be applicable in many areas of physics; they are now accepted as being as real as positive numbers. For instance, it is almost impossible to graph position-time, speed-time, acceleration-time, and the momentum-speed relation of objects without negative numbers.

Ellipses, parabolas, and hyperbolas (plane sections of cones cut in different shapes) were studied by Apollonius (BC 262-200), who was a contemporary of Archimedes. Interestingly these shapes were one day used by Kepler and Newton to describe the orbits of heavenly bodies like planets. Three dimensional pentagonal and hexagonal patterns, like those on the surface of a soccer ball, were also investigated by Archimedes. This shape has been found to be in exact configuration of a special carbon molecule composed of 60 atoms.

Likewise, the number zero, which was introduced by Muhammad bin Ahmad, in 967, led to many innovations in mathematics, as well as physics. Did al-Khwarizmi (780-850) know, when he found and utilized 1st and 2nd degree equations, that he was working on something mathematicians and physicists could one day never do without?

Imaginary numbers, as proposed against the main principles of arithmetic, also provides a very good example for this topic. We cannot think of a number whose square is negative in normal conditions. In other words, when a number is multiplied with itself, the resulting number is always a positive number. But mathematicians thought of a number that is negative when squared and continued various studies accordingly. Again, these studies have proven to be an important tool, especially in understanding electrical circuits by physicists.

Let’s finish our examples with ones from modern physics. Riemann (1826) was a mathematician who studied spatial geometry and proposed the concept of space curves. Mathematical equations designed by Riemann, pertaining to spatial geometry, were used by Einstein in 1908 to describe and formulate the concept of general relativity. Einstein also used Minkowski’s four dimensional geo-spatial continuum when developing his theory of general relativity.

There are many more examples. The famous Russian mathematician Friedman established a mathematical model that allows the expansion of the universe by improving Einstein’s model of universal geometry. This model was also later confirmed by the physicist De Sitter in discovering universal expansion and by Hubble in formulating the expansion. In addition, well before the discovery of quantum mechanics, Davit Hilbert proposed the complex vector space with a very different mathematical purpose known as “Hilbert Space.” This concept of space with an infinite number of dimensions is today used by quantum mechanics.

Sometimes physical realities can be foreseen via these invented equations. For example, Dirac proposed the existence of a particle known as the positron (or as we call it, the twin of the electron; it just differs by the charge) through his mathematical equation that he wrote in 1928. Four years later this particle was discovered by Carl D. Anderson, as predicted. To name, James Clerk Maxwell (1831-1879), a famous physicist and mathematician, predicted the presence and speed of electromagnetic waves mathematically via his own equations. Later, these waves were detected by Hertz (1886) through experiments. Again, Maxwell calculated the speed of electromagnetic waves via his equations, and by revealing that it was equal to the speed of light, it was understood that light was also a type of electromagnetic wave. Nowadays, the particle called the “graviton,” which is supposed to be in charge of gravitational forces, and the “Higgs” particle, that theoretically fills space according to quantum theory, are waiting to be discovered.

The book of nature is written in such a way that it is expressible by mathematical language. Famous physicist Sir James Jeans (d. 1946) expressed this situation as follows: “From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.” Yes, the level of knowledge that is at play in the universe encompasses both physics and mathematics. The overall interconnectedness of sciences and the interdisciplinary character physics and mathematics point to an owner of this knowledge.

As a conclusion we can deduce that physics and mathematics, just like material and non-material worlds, are in fact intertwined with each other’s various dimensions. The physical face of the universe is the place where records are kept and concepts of matter like heavy or light, big or small, and soft or hard, exist. The mathematical face of the universe (as if spiritual) is the unseen side of events or materials that are hidden and intangible. In a way, this relation between physics and mathematics is a display of the material and spiritual sides of universe.

Nuri Balta is the Head of Physics department at Samanyolu Schools in Turkey. He is also pursuing a PhD degree in Physics at Middle Eastern Technical University, Ankara, Turkey.

In this article we will review these three concepts and the relations among them by giving examples from the realms of both physical and metaphysical concepts.

Even though there is no universally accepted definition of analogy, or metaphor, or literal similarity, the purpose of their use is unanimously defined as “throwing light on an unfamiliar concept or situation using a familiar one.” The past few decades have witnessed several attempts of redefining these terms or at least extending a definition that is somewhat agreed-upon to an all-encompassing one. In so doing, researchers tended to employ mathematical structures that are by no means simple. What seems to differ from one approach to another is the method used in the process of establishing a correspondence between the familiar and the unfamiliar. Our purpose is not to give a full account of these approaches here, as there are so many of them, but rather to adapt one that is more convenient for conveying our examples.

Analogy: The word analogy is derived from the Greek word analogia. Originally, this was a mathematical (actually a musical) term before becoming a grammatical and linguistic one, meaning “proportion” (Szabo 1978, 23). An example of Aristotelian analogy is “spine is to fish as bone is to animal.” This simple analogy is generally formulated as A:B = C:D. We say, in this case, A and C are analogous. The sense in which A and C are analogous could be a property they have in common as well as the similarity between their relations to B and D, respectively. In the spine and bone example above we observe both. In the analogy “feet are to animal as wheels are to automobile,” however, feet and tires have virtually nothing in common, but they are analogous with respect to their functions within the bodies that they are part of, i.e., both are used as a means of transportation. Therefore, common relations are essential to analogy, but common objects are not. (Gentner-Markman 1997, 46).

One of the recent approaches to analogy which is widely used is the structure-mapping theory (SMT) (Dedre Gentner, 1983). It presumes a mapping between the familiar (domain or base) and the unfamiliar (target). The domain and the target consist of objects and relations among objects. SMT establishes a one-to-one correspondence between the objects of the domain and the target in a way that preserves the relations between objects (Those who are familiar with the category theory in mathematics will notice the resemblance of this mapping to a “covariant functor” between two “categories”). This is a “structural alignment” between the domain and the target (Gentner-Markman 1997, 47). In the “feet and wheels” example the mapping occurs between a body and an automobile. It maps feet to wheels and the relation TRANSPORT (feet, body) to the relation TRANSPORT (wheels, automobile). One can find more matching elements between a body and an automobile. For instance, we can match the heart of the body to the engine of the vehicle and observe that the relations RUN (heart, body) and RUN (engine, automobile) are preserved.

One might ask where do the arms get mapped? The answer is “nowhere.” We do not expect this mapping to match every object in the domain to an object in the target. The “power of the analogy” is not in the number of objects that are matched or the common attributes that the objects share. It is rather the degree of matching among relations that makes an analogy more powerful (Gentner 1982, 110).

Having introduced the concept of analogy by using some simple physical examples let’s now consider a not-so simple metaphysical situation.

In the 1920’s two mathematicians proved a very interesting but at the same time very puzzling theorem, known as the Banach-Tarski Paradox. In plain English, the theorem states that it is possible to divide a solid ball into a few pieces and reassemble those pieces together to make two balls, each of which has the same size as the original ball that was divided. A more striking consequence of their theorem is (you may want to sit down before you read this) a solid ball the size of a small pea can be cut into a number of pieces and reassembled into a new ball the size of the sun! Strange as it may sound, it is a valid mathematical argument, not a myth. (We have to note that it is not something one can do at home using a knife and a cutting board, because some of the pieces have no volume!) The analogy that we would like to establish under SMT is to map that solid ball of the theorem to a small amount of water which could quench the thirst of an army of about 30,000 in Tabuk in year 631. This was a miracle given to Prophet Muhammad, peace be upon him. A similar miracle of Prophet Jesus, peace be upon him, is described in the Bible, Matthew 14:21 (Volker Runde, in the Sky 2 (2000), 13–15).

Metaphor: The essence of metaphor is understanding and experiencing one kind of thing in terms of another. (Lakoff & Johnson 1980, 104) Simple examples are “What a sweet baby!” “Your car is a lemon, let’s take mine.” Obviously babies are not candies, nor are vehicles some sort of fruit. We use this sort of “identification” in order to communicate our ideas/feelings in a more striking way. Here are more examples of metaphors: “he is the apple of my eye,” “it’s raining cats and dogs,” “he has a golden heart,” “she cried rivers” etc. As these examples show, the distinguishing characteristic of metaphors is substitution, for example, rivers taking the place of tears in the last example. And this substitution takes place between different domains. If we say “a nightingale is a bird,” that’s not a metaphor; it’s a literal categorization, as both nightingale and bird signify the same domain (Gentner 2005, 200).

As long as the correspondence is not purely attributional, but some relations are also preserved we can also talk about structural alignment for metaphors (Gentner 88, 49). From this perspective, many metaphors are in fact analogies, but it’s the form of the language that helps us differentiate them. For example, “the engine is the heart of an automobile” is a metaphor, but it uses the same structural alignment of the analogical comparison that we mentioned above.

Nonetheless, not every metaphor is of this sort. Consider, for example, the verse (48:10) “God’s hand is over their hands” from the Qur’an; this was revealed in connection to some 1,400 believers’ pledging allegiance to Prophet Muhammad, peace be upon him, under a tree in Hudaybiyah in year 628 by giving their hands to him. Whatever “God’s hand” in this verse refers to, whether it is to His power, His victory, His protection and blessings for the believers, or His acceptance of their pledge, it is far from being a physical hand. Therefore, we can not imagine a relation between dissimilar objects (Gentner 1982, 109; Gentner 2001, 204) that is mapped to the relation (Hand, God) under a structural alignment using SMT.

Literal similarity: If there is a considerable number of common attributes that are shared by the objects of the domain and the target then the comparison is more likely to be a literal similarity (Gentner 1982, 110). For example the comparison in the following verse of the Qur’an is a literal similarity: “Indeed, the example of Jesus to God is like that of Adam. He created him from dust; then He said to him, “Be,” and he was” (3:59). In this example there are a great number of attributes that Jesus and Adam (peace be upon them) share but only one of them is the subject of the comparison here, which is that both Jesus and Adam had no father. If Jesus also had no mother this would be an “identity,” not a similarity (Gentner 1982, 110).

The statement “Jesus is like Adam” makes much more sense than “Jesus is Adam,” even if we make it clear in what sense we use this identification. Typically metaphors use the word “is” and literal similarity comparisons (similes) use either of the words “like” or “as.” Mathematically speaking, if metaphors are equalities, then similes are approximations (Casnig).

Even though metaphors are substitutions, they are not necessarily “two-way” identifications. In other words, most of the times they are asymmetric; i.e., there is a sense of direction in the “identification.” For example, we never substitute a car in the place of a lemon and say “this lemon is a car.” This is because the first and foremost requirement of any comparison is that it be informative. What information do we obtain from the statement “rose is love” or “iron is fist”? In that respect many metaphors are irreversible, like similes: “a butcher like a surgeon” is quite different than “a surgeon like a butcher.” One is a compliment but the other is not! (Gentner 2001, 224). Perhaps irreversibility can also be taken as a distinguishing character of (at least attributional) metaphors.

Mathematical and metaphysical examples: Although there is no consensus on how mathematical ideas come about, it is certain that they are introduced into our world of knowledge by symbolism. Whether we associate a symbol to something physical, such as the symbol 70 to the weight of an object or the letter g to gravitational force, or to an abstract mathematical concept, such as the letter i to √–1, we are substituting one thing to mean another thing. We even associate symbols to concepts we cannot even describe, such as the concept of infinity and the symbol ∝ that is used to represent what it signifies in mathematics. From this perspective, mathematical symbols can be viewed as metaphors (Pimm, David 1981).

On the other hand mathematical formulas preserve the relations among the objects or concepts that they represent. In that respect, it is possible to see them as analogies as well. Therefore, they can be subjects of structural alignment. In the next example we will use SMT to form an analogical comparison between infinity and human life in order to better understand a Qur’anic verse.

In verse (5:32) of the Qur’an reads: “…he who kills a soul unless it be (punishment) for murder or for causing disorder and corruption on the earth will be as if he had killed all humankind; and he who saves a life will be as if he had saved the lives of all humankind…”

In a sense this verse means “one equals many.” How can that be? How can one be equal to a million? Or a billion? Those who know something about mathematics with infinities will remember that it is a quite different thing from mathematics with ordinary numbers. For example, if we add two infinities we still get infinity, i.e., ∝+∝=.∝=∝, something that never happens with any finite number, except for 0 (0+0=2.0=0). Likewise, if we add any number of infinities together we still get infinity: ∝+∝+∝+…∝=∝.Therefore, for any positive number m if we write m.∝=∝ it would be a perfectly acceptable mathematical statement.

Now, everyone will agree that there is no value one can associate to human life. Therefore, it’s fair to say that the value of human life is infinite. Let’s map “∝” to “saving the life of one person” under a structural alignment and let counting people in the target correspond to adding infinities in the domain. Now, if m represents the total number of lives on earth then what element should we associate to saving them altogether? The answer is m infinities added together, in other words m.∝ But seeing that m.∝ is equal to ∝ we can say that saving the lives of all people on earth is no different than saving the life of one individual! That’s how one can equal many. Now, if we map “killing an innocent person” to “–∝” then we clearly see that the mathematical statement m.(-∝)=-∝translates into “killing all innocent people on earth is as grave a sin as killing one.”

Note that this “one equals many” situation is not a violation of the requirement that structure mapping be one-to-one (Gentner-Markman 1997, 47). It’s a relation that occurs between the objects of the domain and the objects of the target and that relation is preserved under a one-to-one structure mapping.

Another relation between infinities is that “∝-∝” is indeterminate. In particular “∝-∝” is not necessarily 0. Using the analogy we just constructed we can translate this as “killing one innocent person and saving the life of another does not balance out.” Then, “∝-∝” is indeterminate” translates as “we cannot know if God will forgive that person for saving a life or punish him/her for taking one; it depends on which ∝ is greater!” Indeed, those who have taken calculus will remember that “∝-∝” sometimes turns out to be a positive number and sometimes a negative number; as well as 0 or ∝ or -∝

One could ask, what about m.0=0? Isn’t this also true? Yes, indeed “the sum of m zeros is equal to zero” is another mathematically accurate statement. Then, what meaning could this equation be given? Perhaps this would be the “murderer’s” version of the Qur’anic principle that we mentioned above: “When the life of an individual has “no value” in your heart, killing one person or a million people should be equally disheartening (!)”

Another mathematical tool that would be helpful in interpreting the above-mentioned principle is a technique that is used in mathematical proofs. When proving a fact about a set of elements in mathematics one proves it for an arbitrarily chosen member of the set and it is automatically generalized to the rest of the elements in the set. For example, in order to prove the statement “the square root of every prime number is irrational” we choose a prime number, say p, arbitrarily and prove the statement for it. Once we do that it is as if we proved that √2 is irrational, √3 is irrational, √5 is irrational etc. It covers all the numbers in the form √p, where p is a prime number. In the same way, when one kills an innocent person the message that it is acceptable to kill “any” innocent person is given, as the choice of person has been made arbitrarily. Therefore, this can be likened to killing all of mankind because being able to kill one person is simply generalized to all people who could be in that person’s shoes.

Summary: In this article we have given examples of analogy, metaphor, and literal similarity and have tried to indicate some distinguishing characters that set them apart. We included some uncommon metaphysical phenomena which have been placed in analogical correspondence with mathematical quantities with the intention of showing that mathematics can be used to shed light on purely religious concepts as well.

Yusuf Ziya Gurtas is an assistant professor of mathematics in Queensborough Community College, CUNY.

References

• Casnig, John D. 1997–2009. A Language of Metaphors. Knowgramming.com. Kingston, Ontario, Canada.
• Gentner, Dedre. 1982. “Are scientific analogies metaphors?” in David S. Miall (Ed.), Metaphor, Problems and Perspectives, Brighton, England: Harvester Press, pp. 106–132.
• –. 1983. “Structure-Mapping: A Theoretical Framework for Analogy.” Cognitive Science, 7, pp. 155–170.
• –. 1988. “Metaphor as Structure Mapping: The Relational Shift.” Child Development, 59, 47–59.
• Gentner, Dedre & Markman, Arthur D. 1997. “Structure Mapping in Analogy and Similarity.” American Psychologist, 52, 45–56.
• Gentner, Dedre, Bowdle, B., Wolff, P., & Boronat, C. 2001. “Metaphor is like analogy” in D. Gentner, K. J. Holyoak, & B. Kokinov (Eds.), The Analogical Mind: Perspectives from Cognitive Science, Cambridge, MA: MIT Press, pp. 199–253.
• Gentner, Dedre & Bowdle, Brian F. 2005. “The Career of Metaphor.” Psychological Review, 112, pp. 193–216.
• Lakoff, G., & Johnson, M. 1980. Metaphors We Live By. Chicago: University of Chicago Press.
• Pimm, David. 1981. “Metaphor and Analogy in Mathematics.” For the Learning of Mathematics, 1, 47–50.
• Runde, Volker. 2000. “The Banach-Tarski Paradox or What Mathematics and Miracles Have in Common.” in the Sky, 2, 13–15.
• Szabo, A. 1978. The Beginnings of Greek Mathematics. Dordrecht, Holland: Reidel.

In this article I address four questions regarding the importance of mathematics in our lives:

1. Why is mathematical thinking significant to comprehend the universe and how it runs?

2. What are the problems in the new millennium and what solutions to these problems are expected from scientists?

3. How important a role does mathematics play in today’s world?

4. What is the relationship between defense industry and space research

In contemporary scientific research methodology, mathematics is the most objective tool which can be used to draw a general conclusion from outcomes obtained. Mathematics is considered to be an expression of the knowledge of the All-Knowing. This characteristic of mathematics recognized by Muslim scholars in the Middle Ages was emphasized by well known scholars such as Ghazali, Al-Biruni, Nasiruddin Tusi, Al-Hujandi, and Al-Khwarizmi. Following in the path of Muslim scholars and being considered one of the pioneers of modern science, Galileo stated in his second book published in 1623, Il Saggiatore, that “it is impossible to understand the universe without learning the real logic of the universe and decoding its characters. The universe was created in mathematical logic and it is impossible for us as human beings to comprehend its words without mathematics.” Galileo’s statement points towards an important truth-that even though it is possible partially to explain the intricate perfection in the universe through the mathematics that has been developed so far, we are not skilled enough to produce or comprehend any mathematical systems or formulas that can express the whole universe despite the complexity of occurrences that go on in the universe.

In the history of science, the structure and the mechanism of the universe have been explained to some extent using mathematics. Physicists have developed equations to demonstrate the structure of matter and forces in nature. An engineer who designs an artificial heart considers the equation that governs the bloodstream in a vein. An astronaut at NASA utilizes equations that describe the motion of satellites or the orbit of a spacecraft. In our contemporary world, the crucial role of mathematics is the main reason why Landon Clay, a millionaire philanthropist and the founder of the Clay Mathematics Institute, came up with a list of seven “millennium problems” and promised seven million dollars to the first person who found the solution to each of them. They have not yet been solved.

Many of us remember traditional mathematics classes as boring because they were not apparently related to real life. Only once symbols and equations become meaningful and solutions are found, does mathematics become pleasurable. Despite the stress endured, true success is hidden in the process of writing the correct equation. An equation developed to solve a specific mathematics problem becomes an invention when it is practically used in life, for example, to build a spacecraft or design a medical device.

However; in order to make an invention, the correct equation for that invention needs to be developed, or a pre-developed equation that works for the invention needs to be determined. The next step is to solve it. Even if the solution to an equation cannot be found, an approximate solution can always be discovered and used to build an invention.

The equations for two of the millennium problems come from physics. One of the problems involves finding a general solution to the Navier-Stokes equations governing fluid dynamics. These equations were first formulated in the 1820s to describe the motion of fluids and gasses. Examples include the flow of water around a boat, air over the wings of a plane, and blood pumped from the heart to the vessels. At first glance, the Navier-Stokes equations resemble equations taught at the undergraduate level in the fields of science and engineering. However, the way they look is deceptive because no one has ever come close to finding the general solution to these equations. Even though a general solution to these equations does not yet exist, the Navier-Stokes equations do help one comprehend the aforementioned problem. Therefore, they do not help naval architects to construct better marine vehicles, aerospace engineers to build better aircrafts and spacecrafts or biomedical engineers to build artificial organs.

Another millennium problem involves finding a solution to the set of equations formulated by Chen-Ning Yang and Robert Mills in 1954 that describe the fundamental forces of nature. This set of equations reveals the description of the raw material out of which everything in the universe has been created. None of these equations have been solved so far. Physicists have gained accurate results and made calculations tested in laboratories based on Yang-Mills equations that could be solved by using computers as in Navier-Stoke equations. Even though these kinds of equations provide physicists with almost all the necessary information, no one has ever been able to solve the Yang-Mills equations by known methods. What is important is not to solve equations; it is to figure out what the solution means instead. Using numbers and making calculations based upon these equations remain secondary despite their importance.

As a result of positivist and materialist approaches to knowledge and science, most people today are interested in science and technology for the sake of their own material wealth and comfort. If this degrading approach continues, worldwide degeneration cannot be prevented. However, mathematics is a universal language generated by mathematical thinking. This type of thinking is one of the qualities of the “inheritors of the earth.” In The Statue of Our Souls (2005), M. Fethullah Gulen says,

In the past the people in Central Asia and later on in the West achieved their renaissances by means of the laws of mathematical thinking. Man discovered and brought to light many uncertain and unknown things in the mysterious world of numbers. Without going to the extremes of the Hurufis,^[1] what we say is that without mathematics it is not possible to understand the relations of humanity and natural phenomena with one another. It illuminates our roads like light on the line that stretches from the universe to life; it indicates to us what is beyond the human horizon, even the depths of the world of contingencies, which is very difficult to think upon; and it makes us meet with our ideals.

On the other hand, being mathematical does not mean knowing everything related to mathematics. It is to think mathematically, to think within mathematical laws, and to be aware that it permeates everything from man’s thoughts to the depths of existence, from physics to metaphysics, from matter to energy; from body to soul, from law to Sufism. In order to comprehend existence completely, we have to accept a dual method of Sufi thinking and scientific research. The West essentially lacks essence, and has tried to compensate for this loss, as far as it can, by taking refuge in mysticism. In our world, which has been always intimate with the soul of Islam, there is no need to look for anything strange or foreign, or to take refuge in anything. We have all our sources of power within our system of thought and faith. That suffices as long as we comprehend that source and spirit with its original richness. Then we will see some of the mysterious relations in existence, how harmoniously such relations run, and reach a different knowledge of observing and taking pleasure in everything.

In short, being mathematical is necessary to describe the universe we live in and the principles of how it runs. This tool will be considered triumphant in as much as it can remove blockages from the individual’s eyes and exhibit the truth. Only if scientists who have attained the harmony of heart and mind penetrate into the secrets of existence, utilizing science and its fruits for the benefit of humanity, will justice be done to their profession.

Be they physical or chemical, many attributes of beings are dependent on mathematical laws and their appearances are also shaped along mathematical principles. When we observe creation from this standpoint, we can perceive the perfection as well as the spectacular beauty that is inherent in every being. As reflections of the Attributes of the Names of God Almighty, Jamil (The Owner of Beauty), Bari (The One Who Creates from nothing), Sani (The Maker of All) and Musawwir (The Designer), this beauty found in the external appearance of beings is dependent on more than one factor coinciding. The most important factor here is “symmetry,” which is described as “an exact correspondence and beautiful balance among the parts of an object.” Beings are created with various symmetrical attributes and with great artistic beauty.

The most common symmetry type is the bilateral symmetry; this creates a mirror effect which is an exact correspondence between the right and left sides. An object forms an exact symmetry with its reflection in the mirror. A perfect symmetry that is very similar to the mirror effect can be found in the human body. The left and right sides of our body are symmetrically corresponding. Imagine a dividing line that passes from the middle of the forehead, through nose, chin and down the chest, we can see a perfect symmetry on both sides of the body. Our arms, legs, eyes, ears, nose and lips are designed with a bilateral symmetry. The same symmetrical structures can also be seen in most other creatures. All mammals, reptiles and birds are symmetrically created.

Another type of symmetry is rotational (radial) symmetry. Imagine a metal object that is in the shape of an equilateral triangular placed on the sand. If we will rotate this object 120o around an axis that passes through its center, the new position of the object will fit exactly into its original mark left on the sand. The reason for this is that the radial symmetry for equilateral triangles is 120 degrees. In the same way, a square has a radial symmetry of 90^o and a regular polygon with n number of sides has a radial symmetry of 360/n degrees.

The beautiful symmetry of snow flakes, with their regular hexagonal shape are a beautiful natural phenomenon. In addition to these there are shapes in nature that have a three-dimensional radial symmetry. The most significant of these shapes are regular polyhedrons. An example of such polyhedrons is the salt crystalline elements that have cubical structures. Until recently, the fact that there is a creature in nature that has a regular polyhedral shape, consisting of twenty sides, was unknown. However, when a type of adenovirus that causes infections and hepatitis in dogs was discovered, it was found that there is a creature with twenty regular sides in nature.

One of the most beautiful samples of radial symmetry in nature is the daisy. Symmetrical structures do not only exist in the normal world and in the micro worlds, but also can be found in the macro world, like all the huge celestial objects, the Sun, the Moon, galaxies, star clusters in the sky . . . . All planets move around the Sun in a symmetrical manner, whereas galaxies have a spiral symmetry. It is interesting that the symmetrical structure of living beings is overwhelmingly apparent externally, rather than internally. For example, the internal organs in the human body, like the lungs, liver, stomach and intestines are not symmetrical and we have only one heart in one side of our chest cavity. Moreover, the lobes of the brain are not symmetrical either. However, all the metabolic processes in human body function properly. Does this mean that the mathematical beauty found in our external appearance is merely for aesthetical reasons? God does not create things for only one reason or purpose, on the contrary, He creates them to serve many motives and in relation with many functions. For example, if we did not have two eyes and if they were not symmetrically placed on our faces, we would not be able to see objects three-dimensionally. In the same way, if our ears were not symmetrically placed on our heads, then we would have great difficulty in determining the direction and source of sounds. If we did not have symmetrical feet and legs, we would not be able to walk well, and if our arms were not symmetrical, we would not be able to balance our body’s center of gravity while walking. If birds did not have symmetrical wings, they would not be able to fly, and if the fins of fishes were not symmetrical, they would not be able to swim smoothly.

Symmetry is also closely related to physical and mental robustness. According to one study, women who suffer from an infectious disease during pregnancy are more likely to have babies with asymmetrical features. The same study claims that asymmetrical babies are more susceptible to heart disease than symmetrical babies.

Another study shows that people with asymmetrical teeth are more likely to have more harmful microorganisms in their mouth than those who have symmetrical teeth. It is interesting that there tends to be a greater difference between the fingerprints on the left and right hands of schizophrenic people than on those of normal people.

Symmetry is a phenomenon that is used by animals and insects. For example, an experiment showed that bees prefer flowers that are symmetrical. Actually, flowers with perfectly symmetrical shapes produce more nectar than those that are asymmetrical. In one investigation, a symmetrical flower was made asymmetrical with a pair of scissors. The flower had been attractive to bees before its shape was changed; after made asymmetrical, the flower became unattractive to bees, even though it had just the same amount of nectar as before.

All these facts reveal that there is much wisdom and beauty hidden within the symmetry that the Almighty Designer uses to shape all beings. We take symmetry for granted. To have two eyes placed equidistance and two ears on each side of the head is the norm. Anything else strikes us as strange. But if we just take a few moments to think about why our eyes are where they are, and why our ears are placed on the sides of our heads, the answer is obvious. God’s mercy is infinite; in even the simplest example of symmetry there is a reason. We should not take this world for granted, but rather use every opportunity to dwell upon and be thankful for the wonderful world that has been created for us. 

References

• Stewart, I. & M. Golubitsky, Fearful Symmetry, Blackwell, 1992.
• Rosen, J., Symmetry Discovered, Cambridge University Press, 1975.
• Tarasov, L., This Amazingly Symmetrical World, Mir Publishers, Moscow: 1986.

For instance, those seeking scientific information limit themselves to concrete and physical knowledge. Furthermore, they have to form the mechanisms of causality from natural causes and then refine the resulting knowledge through a sieve of doubt. Likewise, those who seek religious knowledge, which mainly depends on belief, must learn the pillars of faith by searching and then using their minds and logic, rather than mere imitation, to check the information’s authenticity by consulting the primary sources. Religious knowledge is gained through belief and using the principles of reason and logic, rather than experimentation and observation, to analyze the resulting knowledge.

Human knowledge that can be known can be divided into three subgroups: that which is unknown, unknowable, and known. If we subdivide these further, the following classes emerge: the knowable that is known; the knowable that is unknown; the unknowable that can be known thorough the use of various means; and that which will never be known by humanity. This classification is based on having the means to acquire and learn information, as well as the type of information demanded.

There is other knowledge that belongs only to God, and that can acquired only via revelation (wahy), divinely inspired Prophets, and divinely revealed books. As the bulk of such knowledge has absolute meaning, its application, validity, and meaning can be acquired only after appropriate education and training. Since most religious information is like medicine, it must be applied at the appropriate place and taken in the proper dosage to give the greatest benefit. Otherwise, this information could lead people astray.

In today’s information age, useful communication is possible if we know what information we want and how to obtain it. Adherents of scientific ideologies and societies that view scientific and religious-moral information as contradictory and mutually exclusive should realize the differences and boundaries between the knowable, that which remains unknown by scientific methods, and the unknowable. We must understand that information seen as contradictory and mutually exclusive is actually complementary, for nature’s diversity reflects the principle of the “unity and entirety of differences.” Only this understanding will ensure peace and security among the different parts of society that represent the different types of information.

Scientific and religious (faith-related) information represent different types of information gained by various methods. At the same time, however, they form a “meaningful unity” in human life. The critical task is to synthesize these two types of information and then apply the results to one’s daily life.

The boundaries and characteristics of unknowable, long-time subjects in philosophy and epistemology have been (and still are) debated by philosophers for centuries. Based on this understanding, we will discuss the meanings of the unknown and the unknowable concepts of modern science.1

THE PROBLEM OF THE UNKNOWN AND THE UNKNOWABLE

In 1931, logician Kurt Godel shocked scientific circles with a new discovery: some basic mathematical propositions and premises, the common language of science, cannot be proven or refuted. He called this the Theorem of Uncertainty. In the 1980s, British mathematician Alan Turing used a digital computer (the Turing Machine) to prove that one could not give a correct answer before posing an abstract problem. Do these two discoveries tell us something about the place and grade of the unknowable in science?

Science seeks to explain and understand all of the universe’s elements and happenings. Scientific questions can be very general or very specific: Will the universe expand continuously? Will human activity engender large-scale change on the Earth? There is no prior knowledge or premise on which to base answers to such questions. Science, which uses mathematics as a means, is different from mathematics. All discoveries are made in mathematical fields by using models formed by manipulating symbols. Can we apply all appropriate mathematical findings to other sciences?

Ralph Gomery, head of the Alfred P. Sloan Foundation, states that we can understand science by dividing it into three parts: the known part of the scientific universe, the unknown, and the unknowable. The subjects taught in schools and universities form the known part of science. At the same time, exhibits in science museums and elsewhere are summaries of what has been discovered. Scientists and researchers feel the excitement of searching the unknown in order to make it known. According to Gomery, that which is now unknown will be knowable in the future, and the unknowable will remain unknown forever. The limits of science are determined by the subtle lines between what is unknown and what is unknowable. According to some, these boundaries are very rigid, predetermined, and cannot change (i.e., the boundaries of science and religion). Following are some unknown “facts” and questions that might be known and answered in the future.

Models that can forecast the Earth’s dynamic functions, and thus predict the currently unforeseeable nature of earth quakes, might be successfully developed. What negative ecologicial changes will be wrought upon the Earth through human production and consumption, and how can they be prevented or mitigated? Is there intelligent life in outer space? If so, how and by what means can we communicate with it? How does human consciousness develop? What is the relation between free will and the brain’s physico-chemical reactions? How can a national or global economy be kept stable without driving it into chaos? Can we prove which of these questions are unknowable?

According to Joseph Traub, Godel’s theorem only limits the power of mathematics; it has nothing to do with whether or not a scientific question is answerable. Traub believes that there are causes in science that make some questions unanswerable. Examples are insufficient archeological and historical data, as well as the first appearance of language; the fact of coincidental events and simultaneous discoveries, which make these events indistinguishable and hence their explanation harder (e.g., we cannot distinguish the cause-and-effect relations between events that took place isochronally in the first appearance of life); and insufficient sources, methods, and experimental designs to test the correctness and validity of today’s prevalent theories.

We must be careful when claiming that something is unknowable, for doing so without exposing the reasons may hinder scientific progress and development. On the other hand, many scientists accept the presence of that which is unknowable and unanswerable by science, and view science as trying to solve and understand the knowable universe.

DIFFERENT ASPECTS OF SCIENTIFIC REALITY

In America, scientists from various branches gather in periodical meetings at the Santa Fe Institute in an attempt to model a prototype university of the 21st century by drawing lines between the unknown and the unknowable. They emphasize that scientific truth and reality have five different aspects: the reality of the physical and concrete universe, the reality based on the mathematical modeling of the preceding reality, the reality produced and interpreted based on the depictions and descriptions of the preceding models, the virtual (cyber, imaginary) reality produced in a computer environment, and the reality produced by simulations in computerized environments. Thus, “reality” and “models of reality” are not identical.

Some researchers claim that there are only two worlds of reality: the physical universe (or nature) and computers. They also state that these two different worlds should be modeled differently. From this aspect, which reality or model is of interest becomes an important issue when scientists try to classify what is unknown and unknowable.

Let’s concretize these distinctions. Every living organism consists of proteins, which should be folded in a specific three-dimensional form to become functional. One or several of these possible foldings are functional; the rest are meaningless. The formation of folding in a living organism takes a few milliseconds. But scientists, even if they use the best supercomputers in existence, cannot simulate this process. Since the theories and algorithms of the computer environment are insufficient, there is no conformity between the model and reality, for the living system folds the amino acids properly. We do not have enough knowledge to model this amino acid structure in a computer environment, because there is no one-to-one correspondence between reality and the perception and visualization of the reality in the mind.

Niels Bohr summarized what could be done: “I cannot grasp reality, but [I can] produce a mathematical model that can predict reality.” This opened new doors to philosophy. Albert Einstein believed that there is a reality that can be defined by mathematical models. Today, a similar debate continues in scientific circles between Stephen Hawking (who defends Bohr) and Roger Penrose (who defends Einstein).

THE END OF SCIENCE?

The main argument of those who state that science has come to an end is as follows: The basic discoveries about the physical reality of the universe have been made. All that remains is to fill in its content. For example, subatomic particles have been discovered. Molecules that code life have been discovered, and hence new genes are being produced. The basic theories that enabled space technology have been developed. Perhaps future technological innovations will be limited to improving existing ones, rather than making new discoveries. Besides, science alone could not solve humanity’s problems or prevent bloodshed, although it received a considerable amount of financial support. Thus from now on, these sources should be used to discover the real nature of humanity and the sciences (e.g., social, religious, and moral) that ensure human welfare and well-being, for solely scientific information is not everything. It seems that we need religious and moral knowledge to use our scientific findings in the best interests of humanity. Today, ethics is a compulsory course in Western universities, and some scientists believe that research should focus on more concrete, answerable, and functional topics.

On the other hand, others believe that science has not ended and that many things remain to be discovered. They point out that scientific discoveries are not so numerous, and that new research areas appear by intermingling physical sciences with themselves and the social sciences. They stress that until now, scientific findings have been reached by deduction. Now, however, the dominant scientific paradigm is being transformed into systematic thinking, and the interaction of all things will be studied in database networks. This will engender new views of science and the universe. They also claim that those sciences that focused on the information of the particles will begin to focus on systems and understanding the nature of their interactions.

FOOTNOTES

1. “Modern science” signifies scientific information about the universe that is gathered by one’s five senses, observation, experimentation, and mathematical modeling and explanations. It does not include religious studies and knowledge.

REFERENCES

• Horgan, John. The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age. New York: Helix Books, 1996.
• Traub, Joseph. “The Unknown and the Unknowable.” The Third Culture. Interview. 1998.
• http://www.edge.org/documents/brockman.html.
• —. Information and Complexity. N.p: Cambridge University Press, 1998.

These words attempt to pierce the veil of habit that develops in our minds from not looking into the reason for things. The perfection of the order operative in the universe is of such a degree that it prevents us from being aware of it. In the same way, we only become aware of the faultless operation of the watches we have worn on our wrists for years when they stop working.

In the world-view developed upon the foundation of Newton’s laws of motion, the universe was likened to a flawlessly operating watch. Events were tied to one another in a cause-effect relationship and our knowing the laws of this relationship allowed us to predict events with great accuracy. It was possible to determine with mathematical exactness a wide range of phenomena, from the times of eclipses of sun and moon to the amount of fuel and the speed needed to put an object into orbit around the earth. The success of these ‘natural laws’ led many people to believe that they completely expressed and ‘ruled’ the whole order of the universe.

Because God creates and sustains all things and events from behind the veil of universal general laws, because certain events (causes) are followed reliably by similar events (effects) each time they (the causes) occur, it begins to be supposed that the causes are responsible for or ‘create’ the effects. This is, of course, a gross error, as no number of causes suffices to create even a little effect; for every event even the tiniest, the whole universe must be presupposed first, including the laws operative within it. Moment by moment, all things and all events are created and sustained by God, Who wills from an infinite range of alternative possibilities a particular actuality.

The clockwork model of the universe derived from Newtonian or classical physics is not a complete account of the phenomena which we observe in the universe. Already in the late 19th century, scientists had been bewildered by the lines that turned up in the light spectra emitted by heated gases: the steady, stable clockwork model predicted did not happen. Also, there were problems explaining the behaviour of light: sometimes it made more sense as a beam of particles, sometimes as a wave.

Today our understanding of the universe is very far from the ‘clockwork’ model. The shift in understanding occurred in the first quarter of the 20th century, beginning in 1900 with the publication of Max Planck’s work on radiation. The problem Planck worked on for six years was that the actually measured radiation from hot bodies did not conform to the values predicted by the classical theory. He put forward the suggestion that bodies radiating energy did so, not evenly and continuously, but unevenly and discontinuously in tiny packets or ‘quanta’. So startling was this suggestion that, despite confirmation by experiment, Planck himself thought of his theory as solving the problem of radiation by a sort of trick.

But then, in 1905, Albert Einstein published an article using the notion of packets of energy of definite sizes to explain how electrons are ejected from metal when light (radiation) falls on it. Whereas classical theory had predicted that the voltage (measure of the energy of the electrons ejected) would be proportional to the intensity of the light (radiation), Einstein showed that it was proportional instead to the frequency of the radiation. The conformity of this explanation with experimentally observed results gained Einstein the Nobel Prize. (Einstein didn’t receive the prize for his famous theory of relativity.) The significance of these findings and theories was not fully appreciated at the time.

A few years later in 1910, Ernest Rutherford did a ground-breaking experiment. He bombarded a thin layer made up of gold atoms with high energy particles and showed that the atom contained an extremely small positively-charged nucleus with negatively-charged electrons moving around it. Following the classical physics model, these electrons should have been small particles orbiting the nucleus in the same way as the planets orbit the sun, steadily losing energy until they fell on to the nucleus-in other words, the atom should have been unstable. Again it was a rejection of the classical model, three years later, by Niels Bohr, that helped solve the problem. Bohr argued that the electrons must move in fixed orbits until deflected by the absorption or emission of a unit of energy.

Atoms emit radiation after various external signals and only at specific wave lengths. As Einstein said, every different color of light is composed of energy packets inversely proportional to its wave-length (frequency). Because the Planck constant (h) is very small, the energy of these packets is also very, very small. For example, a normal light bulb emits 1020 light packets (photons) a second. Each of these photons is created when an activated atom or molecule passes to its normal or ‘basic state.’ Thus light, which allows us to see and which is a basic building block of life, develops as a result of the motions (in wave form) of electrons. The concepts of classical physics could successfully explain many of the events of daily life, but it couldn’t explain events on the subatomic level.

During those years (1910-1925) physics fell into a state of

confusion because of the many measurements that conflicted with general theory and could not be explained by it. This situation was to lead W. Pauli (later to discover the principle fundamental to the understanding of the structure and characteristics of elements) to say he would rather have been a singer or gambler than a physicist. Actually in order to explain the observations being made, the whole way in which physical events had been understood required fundamental revision by wholly new methods. This was achieved by Werner Heisenberg, a 24 year-old physicist described by his teachers as a person who dealt with the essence of a subject rather than getting bogged down in detail, a person with powerful concentration and ambition. Perhaps the success of this young mind can be explained by the critical perspective he developed through reading the works of great men such as Kant and Plato, which was later supported with sound knowledge he got from great physicists. Heisenberg, who relaxed from work by climbing rocks and reading poetry, said: ‘It was around three in the morning when the calculations were completed and the solution to the problem appeared in front of me. First I experienced a great shock. I was so excited that I didn’t even think about sleeping. I left the house and, sitting on a rock, I waited for the sunrise.’

Like the other scientists who established quantum physics, Heisenberg was a philosopher-physicist. The philosophy he accepted and advocated that allowed him to interpret atomic events is as follows: ‘Even though it is successful with classical physics, the language we use to explain physical events in the atom or its surroundings is insufficient. For this reason, after making a specific measurement in a quantum system (for example, an atom), using that knowledge we can get a theory that will tell us what kind of results we can find in the next measurement. But it’s not possible to say anything about what takes place between the two measurements.’

What pushed Heisenberg to make such a statement was that the mathematical tools he used to develop a theory that could explain the observed discontinuity of energy in light and atoms were abstract concepts that had not been used before. In classical physics the numbers we know were used to give value to matter’s position, speed, size, etc. In Heisenberg’s quantum mechanics, these sizes were expressed with infinite dimensional n x n matrices which enabled physicists to calculate the properties attributed to electrons (energy, position, momentum, angular momentum) in an approximate way. Because these abstract mathematical expressions didn’t have an equivalent in everyday spoken language, it wasn’t possible to approach them with a classical understanding. It was observed that in order to measure the position of an electron, the experimenter necessarily altered its velocity. This problem was formally expressed in 1927 in Heisenberg’s famous Uncertainty Principle.

Independently of Heisenberg, Erwin Schrodinger made another significant breakthrough in mathematical description of electrons. Inspired by the hypothesis put forward two years earlier by De Broglie about the wave properties of matter particles, Schrodinger developed a ‘wave mechanics’ by which the movement of particles could be calculated. (figure: 1) But the fundamental question remained as to what these strange and original ‘waves of matter particles’ or ‘waves accompanying matter particles’ were.

The mathematical formulations devised by Heisenberg and Schrodinger are complementary in the sense that physicists use whichever best resolves the particular calculations they are trying to make. There is no formally distinct space between the scientists and the phenomena they are seeking to understand and manipulate: their means of observation and manipulation (the mathematics) in some sense ‘posit’, put in place, the very phenomena whose place (among other properties) they are trying to determine. Alongside the notion of an infinite array of rows and points, as invented by Heisenberg, to plot the position or motion of a sub-atomic particle, physicists and philosophers of physics have begun to speak of arrays of events or ‘stories’ to try to explain, in something resembling ordinary language, the ideas they are handling. This cannot be described as a world-view in the way that the Newtonian physics confirmed and sustained a world-view, but it is nevertheless a clear and distinct disposition which, instead of excluding God as the Force Who wound up the clockwork and then retired from His creation, admits the in-completeness and uncertainty of human knowledge as a structural element of reality-in other words, the uncertainty is not a function of our present ignorance (to be relieved by future knowledge), but an actual constituent of the way reality is.

Quantum physics, at least figuratively and metaphorically, has became a vehicle for the interpretation of such concepts as matter, beyond-matter, energy, existence and non-existence in a way nearer to Divine sources; and led to many physicists settling accounts with their conscience and turning towards God Who is understood to be simultaneously transcendent and immanent, there and here.

There are two major theories about the origin or essence of mathematics. One of these theories is attributed to Plato, and the other to the so-called Formalist school. According to Plato, mathematics exists independently of man. What man does is to discover its objective reality, just as other ‘laws of nature’, which we tend to call ‘Divine laws of nature’, are discovered. The Formalist school by contrast asserts that mathematics is a product of human thinking. In order to understand the difference between these two schools, we may cite as an example their view of prime numbers (that is, numbers like 7, 17, 41 which can only be divided exactly by themselves and the number 1). Platonists argue that the prime numbers exist independently of us: before we discovered their existence, they existed in infinite number. Whereas, Formalists are of the opinion that the prime numbers exist because we have defined them as such, and it is meaningless to think about whether they are of infinite number or not.

The language of numbers

Formalists assert that numbers came into existence when human beings began to count. A well-known account of how this happened is that of a shepherd who used to put a stone in his bag for each of his sheep and by matching a stone with a sheep could find out whether any of his sheep had been lost or not. Later on, people began to call numbers each by a different name and since there were two fingers in the two hands, they found it easier to make calculations by the decimal system. This was followed by the operations of addition and subtraction.

According to the Formalists, even the simplest mathematical operations like the four basic ones consist in some logical rules based on certain axioms. They say that we do mathematics by expressing certain rules with certain symbols. That is, we take, say, 5 and 7, a couple of signs whose meaning in the physical world we do not know, and put between them the plus sign, a third sign whose meaning in the physical world we do not know, followed by an equals sign. And we know we must write 12 after the equals sign because that is a requirement of the axioms and rules of logic we are using. This is just what a calculating machine does, that is, it goes through the operation required of it without knowing what it is doing.

Let us suppose that an adding operation consists only in applying axioms or certain logical rules, and has nothing essential to do with the physical world. If we were to take our number signs and apply them to physical objects like stones and sheep, we should be surprised, amazed even, as if by a miracle, that 5 and 7 stones or sheep added together (according to the same rules as 5+7) make 12 stones or 12 sheep. We would come to know that the abstract, conceptual realities in our mind correspond to physical realities in the outer world. According to Paul Davies, the renowned physicist, if we lived in a universe where different physical realities prevailed, in a space where, for example, there were not any countable things, we would not be able to make most of the calculations we make today. David Deutsch claims that counting emerged as the result of experiences. According to him, we can do arithmetic because physical laws allow the existence of physical models convenient for arithmetics.

Richard Feynman, regarded as the greatest physicist after Einstein, says about mathematics that the problem of existence is a very interesting and difficult problem. When you take the third power of certain numbers and then add them with each other, you obtain interesting results. For example, the third power of I is 1, of 2 is 8, and of 3 is 27. The addition of these numbers gives the result of 36. The addition of 1, 2 and 3 is 6 and the second power of 6 is also 36. When you add to this the third power of 4, which is 64, the result is 100. The addition of 6 and 4 is 10 and the second power of 10 is also 100. Added to this the third number of 5, which is 125, the result is 225. 225 is the second number of 10 plus 5, i.e. 15. And so on. According to Feynman, we may not have known this typical characteristic of numbers before but when we do come to know such characteristics of numbers, we feel that they exist independently of us, and that they existed before we discovered them. However, we cannot determine a certain space for their existence. We feel their existence as conceptions only.

Let us take another example. Ibrahim Haqqi of Erzurum, a Turkish Sufi, religious scholar and scientist of the 18th century, discovered a way of checking the correctness of an operation of addition which may still be unknown to modern mathematicians. In order to check or prove the addition, we first add up the digits of each of the two numbers we are going to add up. Let us say, we are going to add 154 to 275, for which we get the answer 429. Adding the digits of each of the first two numbers, we get 1+5+4 = 10 and 2+7+5 = 14. The next step is to subtract 9 from each of these two sums, giving us 1 and 5 respectively. The third step is to add these two results together, 1+5 = 6. Now we do the same thing with the digits of the answer we are wanting to check, namely 429, and again subtract 9: 4+2+9 = 15, 15-9 = 6. The fact that we end up with the same number (i.e.6) means that our addition was correct. This way of checking an addition exists independently of us. We did not create it, we discovered it.

As water had the force of lifting objects of certain weight before Archimedes discovered it and, again, objects thrown into air or a fruit disconnected from its branch fell before Newton discovered the law of gravity so also numbers have many characteristics only some of which have been discovered.

Heinrich Herzt, a physicist, says that we cannot help but feel that the mathematical formulas discovered so far exist out there independently of us. We know that these formulas existed before we discovered them but we cannot determine a space for them. Rudy Rucker, a mathematician, is of the opinion that there is, besides the physical space, a space of mind, which he calls ‘mindspace’ and it is that that mathematician study.

Most of the distinguished mathematicians follow the view of Plato. Kurt Godel is one of them. Before Godel, it was almost a generally accepted view that mathematics is a function of the working of mans brain consisting in the collection of the logical rules which we establish between the symbols of two sets. Godel persuasively argued that there have always been correct mathematical expressions even though their correctness cannot always been proved. Another Platonist mathematician, Roger Penrose, believes that beyond the thoughts of mathematicians there are profound truths or realities in mathematical conceptions. Human thought is directed to extend into these eternal realities and they are there to be discovered as mathematical facts by any one of us. Penrose mentions complex numbers as an example for his argument. According to him, there is a profound, timeless truth in complex numbers. Penrose cites the set of Mandelbrot as another example to prove his argument. The reality this set reveals is the fact that even the lines, twists and shapes of mountains and clouds were or are formed according to certain mathematical formulas. 

What flowers reveal

Almost everyone has heard of the series of Fibonacci. This series, named after the famous mathematician, Leonardo Fibonacci, progresses as 1,1, 2,3,5,8,13,21,34,55,89,144, and so on, each term being equal to the addition of the previous two. That is, I and I make 2, and I and 2 make 3, and 2 and 3 make 5, and 3 and 5 make 8, and so on. This is the series found in nature. For example, when we count the spirals formed of the seeds in a sunflower, we find that those arranged clockwise are 55 and the others arranged anti-clockwise are 89. Both of these figures are among the consecutive terms in the Fibonacci series. These figures may vary according to the size of the sunflower: we may find the figures of 34 and 55 in a relatively small flower, and 55 and 89 in a normal sized one, but the arrangement is always as consecutive numbers in the Fibonacci series. The spirals are arranged in pine cones in 5 to 8. We may encounter the same figures in the arrangement of tobacco leaves. Another extremely interesting characteristic is found in the numbers of petals of flowers. A lily has 3 petals, while a buttercup has 5, a velvet 13, a dahlia 21, and a daisy 34 or 55 or 89, varying according to its family. It is impossible to attribute this miraculous arrangement to chance or ignorant nature. If the DNA of a sunflower or a pine cone determines random numbers for its petals or spirals, how can you explain their correspondence with the terms of the series of Fibonacci? The ratio between the consecutive terms in the series of Fibonacci is quite near what is called the golden ratio’ and known in classical art as the ratio most pleasing to human eye. In order to explain the origin of this miraculous reality, you have to either accept that flowers know what is most pleasing to human eye or that the ‘Hand’ of One, the All- Knowing, the All-Wise and the All-Beautiful, is working in nature.

In short, what Fibonacci did is to discover this characteristic in nature. This means that the universe has a mathematical order or mathematics is the branch of science studying the miraculous order of the universe, the order which the Absolute Orderer and Determiner, One Who determines a certain measure for everything, has established.

The Quran calls the attention of human beings to the Divine manifestations on creatures such as the honeybee, ant, gnat and spider and invites them to reflect on and study phenomena like the movements of air, the alternation of day and night and the seasons, and the movements of heavenly bodies. The importance the Qur’an gives to the study of natural events inspired Muslim scientists to undertake investigations using observation and the experimental method – long before these came into use in Europe.

Science passed to Europe through the two centuries of the Crusades, through the universities in al-Andalus and Sicily and the translations made there from Arabic. This was the main factor behind the Renaissance in Europe. Building on (without ever openly acknowledging) the works of Muslim scientists, Western scientists led the way to the birth of modern science. Until correct conclusions were reached about phenomena through observation and experimental methods, the assertions of the ancient Greek philosophers had been accepted as the basic laws of nature. For example, it had been asserted as true without question from the time of Aristotle that the speed of an object’s falling is proportionate to its weight. However, the experiments done by Galileo and Newton proved this to be false. Those experiments showed that- so long as the resistance of air is negligible in proportion to the weight of the object and its vertical cross sectional area – the unhindered movement of an object on the earth is not dependent on its mass. This means that objects of different weight dropped from the same point reach earth at the same time. Such developments in physics led scientists to app rove observation and experiment as a basic rule in establishing natural facts. It was the job of scientists to try to discover the laws and basic truths prevalent in the universe through observation and experiment – empirical methods – while it was the task of philosophers to reflect on and comment on them, in other words, in order to have true conclusions about the universe and the events taking place in it we had to discard all of our preconceptions about them and study nature through empirical methods and then comment on the natural events and the relations between them.

In order to have a clearer understanding of modern science and what it can give us of truth about the universe, let us consider the law of general gravity, which is an undeniably established scientific fact:

Various observations and experiments have shown that any two objects attract each other or exert force upon each other proportionately to their masses and in inverse proportion to the square of the distance between them.

The force of attraction or gravity is the force which is in effect in events such as the falling of an object and the revolving of the earth around the sun. Science presents gravity as if it were the cause of such events. However, what we call the force of gravitation is only a notion which we use to explain those events. That is, there is an attraction observed between objects. In order to explain this attraction, we give it a name like the law or force of gravitation and then think that we have explained the event of attraction.

Science does not know the nature of what it calls the force of gravitation but, starting from the assertion that we have already successfully explained many events whose causes were unknown in the past, claims that it will be explained in the future. Nevertheless, science is unable to explain the real cause of all the events in the universe. What science in fact does is, starting from the recurrence of an event under the same conditions, to make a generalization and call it a law. Then it proceeds to assert that the same event will take place again and again under the same conditions. For example, after observing the falling of objects thrown into the air, it makes a generalization that all objects thrown into the air fall, and expresses this event of falling by a mathematical formula.

It can serve as a simple example to see how science works to calculate and state beforehand how long it takes for an object thrown into the air with a certain force and at a certain angle to fall and at what distance it falls. Since events take place in a cause-and- effect series, knowing what effect or event will take place in the next step does not require understanding why it takes place in that way. Therefore, although we suppose that the law of gravity will be understood as, say, dependent on an exchange between certain particles or the obliquity of spatial time, it will nevertheless remain unexplained through scientific methods why such an exchange takes place or why the spatial time becomes oblique and why that exchange or obliquity occurs according to certain mathematical formulations and thereby objects attract each other. In addition to the fact that why objects attract each other remains unknown, it is also a mystery (and a wonder) that this event of attraction takes place according to a mathematical formula. Because of our familiarity with the events taking place in nature, we ignore the important fact that every thing, every event in nature is a miracle. In order to see why the event of gravitation is a dazzling miracle, we should consider it more closely:

As an example to understand the law of gravity, let us consider the falling of a stone dropped (and then allowed to fall unhindered) from a certain high point. Left unhindered, that stone will realize a certain trajectory as the result of gravity affecting it. It will move faster and faster and finally hit the ground. How the stone will accelerate, how long it will take it to reach the ground and how it will move at every second of its trajectory depends on the stones distance from the centre of the earth, the mass of the earth and the constant of gravity. This means that the stone does not move at random, rather each of its movements during its fall is determined through mathematical formulas. This is an extremely regular movement. From this we inevitably conclude that if the stone does this movement of falling by itself, without an agent directing or determining its trajectory, then the stone must know accurately the constant of gravity, the mass of the earth and its distance from the centre of the earth at each moment of its trajectory, and then move in conformity with that knowledge. Whoever has a bit of intelligence will not attribute to the stone itself such a trajectory, simple in appearance but extremely complex in reality. Indeed, the falling of a stone is so complex a movement that during it all the objects in the universe, every thing with a certain mass, exerts on it certain force of attraction and the stone moves under the influence of all those forces. (Here we do not consider other essential forces such as the electro-magnetic and nuclear ones, which have determining effect on the movement of things. Expressed, again, with certain mathematical formulas, these forces make the movements in the universe even more complex.) That is, in order to determine its trajectory, the stone must know the exact distance between itself and each of about 1080 particles in the universe, calculate accurately at each moment of its trajectory the force of the attraction exerted on it by each of those particles according to the mathematical formula of gravity – a force which changes every moment – and focus all those forces to a single point in consideration of the direction of each. Let alone a stone, even the most advanced computer the size of the universe could not accomplish that. For the position of each of the particles with respect to the stone changes at every moment during its fall. Thus, the simplest-seeming movement in the universe like the falling of a stone requires comprehensive knowledge and mastery of an infinite number of interrelated processes.

Since any event taking place in any part of the universe has connection with each of the particles in the universe and the whole of the universe itself, only one who has perfect knowledge of each of those particles and the universe as a whole, one who sees the whole of the universe with each particle in it, can determine and direct all the movements in the universe. Also, since the law of gravity and all the other physical laws are the same and have the same uniformity throughout the whole of the universe, the one who makes these laws operative in the whole of the universe must be an absolutely powerful one, who dominates each and every thing in the universe. Otherwise, each atom in the universe must have an eye seeing the whole of the universe at the same time, know the position, mass, electrical charge, in short, all the physical features, of each particle in the universe, be aware of all the physical laws and obey the laws itself originated.

Every event and every thing in the universe is interrelated to every other and whatever takes place in the universe takes place according to certain laws. Therefore, it is impossible for even the smallest, most insignificant-seeming event to take place without one with an absolute, perfect knowledge of the universe with all its particles and an absolute power governing it. Said Nursi expresses this fact as follows:

If the existence and operation of the universe is not attributed to God Almighty, then it requires admitting that each particle has the attributes of the Necessarily Existent Being, and that each particle should both dominate and be dominated by all other particles. Again, each particle should have an all-encompassing will and knowledge, for the existence of a single thing is dependent on all things and one who does not own the universe cannot rule a single particle.

After explaining how complex a phenomenon gravitation is, we can go a little further to see the real cause of that phenomenon. The relation sensed between the fall of a stone and the rotation of the moon around the world in a fixed orbit led Newton to discover the law of gravity. Ever since this law received a general welcome, the cause of the falling down of an object thrown into the air has unquestionably been accepted as gravity. However, it is not necessary that the real cause of this movement is the force of the attraction of the earth or the existence of another material cause.

Consider this:

Let us imagine some animate beings living on a two- dimensional table. These living beings are aware of only the table on which they live and completely unaware of the three- dimensional world around them. Someone from the three- dimensional world fires at the table in equal frequencies and makes holes at equal distance from each other. Seeing the holes at equal distances, the animate beings living completely unaware of the three-dimensional world will inevitably conclude that each hole causes another one to be made. Whereas it is some other firing from the outside world who made the holes.

This is how the scientists attributing every thing and event in the universe to the law of causality think about the working of the universe. It is questionable whether the attraction of an object toward another near it (for example, the attraction of a falling stone toward the ground) is because of the objects themselves or there is some other source forcing the objects to such a movement. (The event of attraction is the simplest of the events occurring in the universe. You may consider how a honeybee makes honey or a cow gives milk, events which contain a much greater number of physical interactions, chemical reactions and cause and effect.) In short, since the movement of an object according to the law of gravity is one each moment of which is mathematically described and requires as many masses and distances as the articles in the universe and the distances among them to be known in their mutual, complex relations, there must be One Who is the All-Knowing. This One must also have an absolute will to choose and assign for each event a law out of innumerable ones. The uniformity of the law, that is, all the laws being prevalent throughout the universe calls for the unity of that All-Knowing and All-Willing One, and the obedience of all things, small or great, to those laws demonstrate that that One is also the All- Powerful. Again, the unchangeability or stability of the laws and the magnificent, unchanging order and harmony of the universe show that that One is Self- Subsistent and the All-Subsisting. That means it is that All-Knowing, All-Willing, All-Powerful, Self-Subsistent and All-Subsisting, Single One Who causes a stone to fall. For no one and nothing in the universe has the knowledge, will and power absolutely necessary for the falling of a stone. Every thing and event in the universe is too complex and magnificent for any material cause to bring it about. There is then no way for man other than to admit and recognize the Existence and Unity of God.

We give it life and We bring forth from it grain, so from it they eat.(36.33)

There are a number of points in this verse which can bear explication from a scientific view-point.

1-Use of the expression dead ‘earth’ (rather than dead ‘soil’), indicates that the soil of the whole earth is implied.

2- One meaning of ‘for them is a sign’ is Divine portent. The occurrence of the phrase at the outset of the verse alerts us to the fact that the verse will encourage us to understand a very important family of natural phenomena.

3-We are informed that in its initial state, the earth was devoid of life. In this way, the lifelines of the earth when it was first created is expressed as a geological fact.

4-We learn that the soil, which appears dead is actually alive. Even this one observation affirms the miracle of wisdom contained in the verse. For it is only a hundred years since it was discovered that there are organisms in the soil, while it is scarcely forty years since the discovery that 80% of soil consists of bacteria, and thus is a community of living organisms.

5-‘We quickened it and brought forth from it habba.’ According to the latter part of the verse, habba signifies seeds of a vegetable nature or, specifically in this context, grain. However, habba in general denotes small, uniform particles, and we shall discuss the verse’s inner meaning also from this angle.

6-The verse declares that life is transferred via the soil to plants and thence to us, a chain of events singularly important from the standpoint of biochemistry. While the verse uses the word habba in the general sense, particularly mentioned is what is eaten from it in the form of vegetable food.

In order to comprehend this verse in all its subtleties, one needs first an up-dated grasp of the concepts of life and vitality as scientists now understand them. For the concept of vitality has changed greatly in recent years, and come closer to its inner truth. The biological knowledge of the past has been left far behind.

Life is a mathematical programme encoded in a giant chemical molecule. The Qur’an indicated this reality, discovered only in recent years, fourteen centuries ago in the statement (80.19): We created him from a drop of liquid; we shaped and programmed him.

Allah first created bacteria which fix nitrogen in the soil. In chemical terms, these bacteria are laboratories of ‘synthesizers’; that is, they take nitrogen from the air and prepare compounds with negative valences. They reduce nitrogen by a method that we still cannot fathom, and convert it into a form in which it can combine with hydrogen. They require water and rain for this purpose–which is why we observe that life springs from the soil when it rains.

A second type of bacteria in the soil is what might be called the ‘analyzers’ after their particular role in the Divine programme. They break down whatever falls to the ground and so prepare the way for the ‘synthesizers’. Excluding water, the greatest part of any quantity of soil is found to be composed of microbes.

In botanic terms, soil is regarded as a totally living structure, and so it has been since the origin of life on earth, which is to say, in a modern scientific idiom, a truth that is directly expressed in the Qur’an.

It is in order to sow confusion in people’s minds that atheists distort the established facts about the emergence of various organisms on this planet. They maintain that all organisms have evolved in a gradual process (with some abrupt leaps) from a single cell, randomly becoming the various plant and animal species we see around us or discover in fossil records. This is the so-called ‘theory of evolution’. But the secret of ‘the Living’, giving life to the soil, as also to plants forming from seeds after the soil has come to life, is diametrically opposed to this theory. What is expressed in the Qur’an can only be the truth while any notion opposing it can only be falsehood.

The theory of evolution was propounded toward the end of the 19th century. As I have just explained, organisms were thought at that time to embody different chemical structures, the smaller organisms having a simpler chemical composition, while a more complex organism had a more complex composition. The mathematical programme within cells was wholly unknown.

An evolution of the most primitive structures could, of course, be conceived but as soon as we wish to understand organisms, distinct living entities, however simple, the assumptions of evolution simply break down. For, as we now know, the differences in the emergence of different organisms resides in the mathematical programming to which they operate. The perfection of these very diverse programmes is not open to question; nor is it possible to speak of evolution among them, as one being somehow ‘later’ than another. Compare, for example, a bile-producing cell in the body and a nitrogen-fixing bacterium of simpler countenance in the soil. Which of them performs the more difficult task? It is not hard to decide the question: chemically, binding nitrogen to hydrogen is undoubtedly the harder task. Again, bacteria are thought to be the most developed sorts of cell, not those which carry and enable human intelligence. While DDT, the notorious insecticide, was wreaking havoc with the environment, the common house-fly, a somewhat despised and lowly creature, developed such a prescription in the fluid of its nerve cells that it proved impossible to exterminate another fly thereafter using DDT. A neuron in the human brain could not produce this prescription and preventative if it were to labor at the task for a thousand years.

Well, now, which cell is the later development? Which is the primitive form and which the more evolved? Of course, man is the most perfect of organisms, but he cannot do anything outside of the programme within which all his life is contained, and, as the Qur’an says, can be defeated even by a fly.

Thus, once the concept of life is examined in depth, it can easily be seen that the theory of evolution is a human fiction. Fish with luminous organs were swimming at the bottom of the ocean millions of years ago, just as, at that time, bats equipped with radar were flying in the dark, whereas we are only now discovering these facts and starting to put them to use.

A most important question concerning life in modern biology is how skills are handed down. Grant that an organism inherits its entire constitution from its parents, how does it acquire the special skills it needs in order to continue its life? How does it learn, for example how to build nests or defend itself against other creatures? If a living organism may be likened to a mathematical computer programme, how is the learnt part of that programme transferred from generation to generation without slip-ups or distortions?

In seeking an answer to this question, biology has accepted that a certain programme called the genetic code is passed on. This explanation is for coarse, external similarities between cells, but not for embryonic cells or cells of the bone marrow.

Allah has said (41:47): Without divine science no woman conceives, no fruit separates from its rind. In scientific idiom, the meaning of this verse is: Every cell is given its mathematical programme in a continuous fashion.

Taking all the verses quoted above together, we begin to understand that vitality has two district aspects: the molecules that form the organism are its physical components, while the mathematical programme imposed on this structure is akin to the programming of a computer. This programme is, in a sense the individual organism’s individual destiny of fate. Ya Sin, verse 12 tells us that each creature is recorded In the Guarded Tablet in terms of its most minutely individual qualities (36.12) This declaration is an invariant law for life in general. Every living entity–a weed or a flower cell or a gall bladder cell will each perform what encoded is (inscribed) in its cellular computer, within the compass of Divine Omniscience, by the Divine Will.

The principle of life’s continuation is stated in the second part of the verse we are trying to interpret. After initiating life in the soil, and introducing to it organic materials indispensable for life, Allah created plants from it which in turn carry the basic structural materials necessary for other organisms.

The ‘grain’ mentioned in the verse can refer to the seeds of the plant but also to the constituents of a complete cell. All the organic nutrients for sustaining the life of organisms exist in grain. This fact was not accepted in earlier times: it was not known or accepted that, grain contains carbohydrates, protein, fats, vitamins and minerals all at the same time; on the contrary, it was thought that food derived from wheat and similar plants could not provide sufficient nutrition. But the habba (grain) actually represents all of the basic materials necessary for life.

That fact underlines another, namely that plant and animal cells have common building blocks. The difference lies in their programme or destines. One of the most important inner meanings of the verse is that the soil vitalized by Allah also serves as an incubator for organisms. This secret is imparted especially in the second part of the verse.

A fertilized egg develops in three basic ways: 1. beneath the earth (all plants); 2. inside an egg shell (most animals); or 3. in the mother’s womb (mammals).

From the scientific point of view, all three kinds of development serve the same purpose of instilling life into the organism. The fertilized egg needs a period of incubation and development in order to form the new organism. Biologically, this process is one in which the cells of the new organism form. The seed needs protection during this period, and must draw particular chemicals and ions (as yet unidentified) from its environment. In this way, it will be born into life as programmed. In this verse, Allah has emphasized that it is He who has given this characteristic to the soil. Taking only this property of the soil as an example, the vivification of grain is demonstrated.

Actually, this feature of the soil also provides an important insight into the nature of Judgement Day. When the command for resurrection is issued on the Day of Judgement– and this, too, is a mathematical programme–the secret of the verse will be revealed once again, and the dead will be restored to life in that instant.

The enlivening of the soil by Allah is no ordinary event, but a most profound wonder of biology; what is more extraordinary is the way that all different sorts of fruits and vegetables are presented to us from the same soil

This verse may also be regarded as bearing in two respects on the wisdom of Adam’s creation from soil. The Qur’an declares that Adam was created from soil with the texture of mud. We shall investigate that verse in detail in the future. In the meantime, the important thing to note is that Allah does give to the soil something from the secret of His Divine Name, the Living. It can be clearly seen from the expression comprising the two sentences of the verse that Allah has bestowed both life and vitality on the soil, and has made it the vehicle for propagation of other life forms (the secret of bringing forth grain).

Since verse 32 of the same chapter tells of the resurrection on Judgement Day, the verse we are considering points to a connection between the resurrection at the Judgement and the secret of life in the soil.

We have learned many things about soil biology in recent years. I would like to summarize this information also from the standpoint of the resurrection.

As mentioned earlier, all the preconditions necessary for the formation of an organism from a seed are present in soil. That is, the soil conveys a fertilized organism to life, just like the mother’s womb. Both the fertilized egg and the seed are quite similar in that they both represent a genetic code ready to reproduce. This genetic code is the life and character programme of the organism to be formed. (These genetic codes are a millionth of one centimeter in size–if, for curiosity’s sake, you were able to amass the genetic codes of all the human beings who have ever lived, they would not fill a drinking glass.)

It should not be doubted that, had Allah willed, He would have developed the human seed in the soil as we sell. Indeed, when Allah declares in the verse that the way in which We quicken the dead earth is a sign, He enables an understanding of an issue that science is hardly beginning to catch up with. The verse stresses how deeply the resurrections promised at the Judgement conforms with the logic of biology. The scientific conclusions to be drawn from the biological facts given in the verse may be summarized in three points:

1-The enlivening of the soil by Allah is no ordinary event, but a most profound wonder of biology. The chain of happenings we call life stems from the secret of the Living in the soil.

2-The Day of Judgement is also closely related to the secret of the Living. Whoever doubts the Judgement will find that his doubts are baseless if he contemplates the wisdom of Allah’s bestowing life on the soil together with the secret of living.

3-Life is, first and foremost, a preordained mathematical programme. The division of organisms into ‘primitive’ or ‘developed’ is based on quite arbitrary judgements. Every organism is the representative of a perfect programme. For this, as well as for other reasons, the theory of evolution should be regarded as fundamentally flawed, if not radically false.