“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

Basal ganglia subcircuits distinctively encode the parsing and concatenation of action sequences.
Jin et al. Nature Neuroscience, Jan 2014.

When we learn to play a musical instrument – say the guitar – first, we have to learn notes, scales and chords; only then we will be able to play a song. The very same rule applies to our basic functions. For example, when we learn how to read, we first learn the alphabet and the rules of grammar, and then we start making sense of sentences. Neuroscientists have been intrigued by this process for many years and they have wanted to understand how our brains efficiently perform complex cognitive functions by connecting separate elements to produce a unique meaningful sequence. A recent study shed some light on this very important question. Scientists found that a specific area of the brain, the basal ganglia, can signal the integration of individual elements into a behavioral sequence. Scientists designed an experiment where they first trained mice to perform gradually faster sequences of lever presses. This behavioral test is very similar to a person learning to play a guitar solo at an increasingly faster pace. Then, they recorded the neural activity in the basal ganglia of mice performing the task and discovered that basal ganglia neurons treat a whole sequence of actions as a single behavior. This mechanism is called “chunking,” which allows the brain to efficiently organize memories and actions by integrating individual sequences. It seems like the basal ganglia implement the “chunking.” The basal ganglia are known to include two major pathways, the direct and the indirect. Scientists found that these two pathways show similar activities during the initiation of movement, but show differential activations during the execution of behavioral sequences. Interestingly, basal ganglia circuits are implicated in Parkinson’s and Huntington’s disorders, in which learning of sequences are compromised. Further studies will reveal a more mechanistic understanding of sequence integration in the brain and potential interventions to enhance it in neurological disorders.

Single Gene Separates Queen from Workers

Ubx promotes corbicular development in Apis mellifera
Medved V. et al. Biology Letters, Jan 2014

In a hive of honey bees, the queen and worker bees have very different jobs. A new study shows that a single gene called Ultrbithrox (Ubx) separates a queen from worker bees. The Ubx gene was previously known to control leg and hindquarter development in bees. Interestingly, researchers now identified three functions for Ubx specific to worker bees. First, Ubx promotes the development of a smooth spot on the hind legs where the “pollen baskets” are located. Second, Ubx directs the formation of eleven perfectly spaced bristles on the section of the leg called the “pollen comb.” Third, Ubx mediates the formation of the “pollen press” which is a protrusion that helps pack and transport pollen back to the hive. Essentially, the Ubx gene promotes the development of three different physical structures on worker bees so that they can collect and transport pollen. Researchers confirmed these findings by silencing the Ubx gene genetically in worker bees and found that specialized leg features, including pollen combs and pollen presses, completely disappeared in the absence of the Ubx gene. Moreover, analyses of other bee species in the region revealed that the size and complexity of pollen baskets are directly correlated with the social behaviors of the particular bee species, suggesting that pollen baskets have yet-to-be-identified roles on the social behaviors of bees. Furthermore, the pollination of 35 percent of the world’s crops (with a $216 billion market value) depends on bees carrying pollen from one flower to another. This study might help us to develop new genetic approaches to make bees better, more efficient pollinators and to ultimately combat the worldwide pollination problem.

Molecular Switch in Aging Blood Cells Discovered

A canonical to non-canonical Wnt signaling switch in haematopoietic stem-cell ageing
Florian MC et al. Nature, October2013

Every single cell in our body ages over time. The aging of a cell is typically characterized by the progressive loss of physiological function and increased vulnerability to death. The aging of our cells/tissues/organs is the primary risk factor for any human diseases. One critical cell type that dramatically changes its properties during aging are blood stem cells, aka Hematopoietic Stem Cells (HSCs). Young HSCs have the capacity to differentiate into the diverse lineages of erythroid, lymphoid, and myeloid cells. Young HSCs are polarized (asymmetrical) cells, in which distinct cytoskeletal proteins (also called the “polarity complex”) are asymmetrically distributed within. However, the aged HSCs are mostly apolarized (symmetrical) cells and they differentiate only into lineages of myeloid cells (including, red blood cells, macrophages and monocytes) rather than lymphocytes (white blood cells in the immune system). The molecular changes in aging HSCs have largely been unknown. A recent study published in Nature shed some light onto the molecular identity of the ageing HSCs. Scientists showed that ageing HSCs have higher levels of a secreted protein called WNT5a, whereas the young HSCs have almost no WNT5a protein expressed in the cell. Moreover, the increased levels of WNT5a are found to attenuate the levels of the “polarity complex” proteins in HSCs and thus result in apolarized cells, which resemble the aging HSCs. Furthermore, transplantation studies revealed that increased WNT5a levels cause aging-related phenotypes and low Wnt5a levels promote a rejuvenation process in mice. These findings show that Wnt5a is the key molecule that controls the shift between young and old HSCs. Therapeutic approaches using antagonists of the Wnt5a molecule could potentially alleviate aging-related pathologies in the patients with a variety of blood diseases.

Factors underlying variable DNA methylation in a human community cohort. L.L. Lam et al. PNAS October 16, 2012 vol. 109

The effect of environment on genes can be very profound. Our surroundings may not directly change our DNA sequence but it can surely dictate how our genes are transcribed. Epigenetics studies heritable changes in gene expression caused by non-genetic mechanisms, i.e. mechanisms other than the changes in the DNA sequence itself. DNA methylation is one of the major epigenetic modifications to regulate the gene expression. The addition of methyl groups on DNA sequence acts like a dimmer on a light bulb switch, which will turn certain genes on or off. A recent study showed that a person’s early life experiences shape their DNA methylation patterns. The research team discovered that childhood poverty (not socioeconomic status as an adult) is highly correlated to distinct methylation marks left on genes. Although children in rich and poor households have identical sets of genes, the degree of adversity or stress at home determines which combinations of those genes are activated or silenced through differential DNA methylation. One can imagine that such epigenetic changes might cause some alterations in the gene expression program of blind people to certain environmental signals or make them even more sensitive. Perhaps such changes could make some people more adaptive to harsher life conditions, hence enhance their survival. These findings suggest that environmental conditions early in life shape our epigenomes permanently thereby influence our life experiences, health and probably many other things that we are not yet aware of.

An alien planet next door

An Earth-mass planet orbiting α Centauri B. X.Dumusque et al. Published online 17 October 2012, Nature

Astronomers have just discovered an earth-size alien planet right next to our solar system. A new earthlike planet, named Alpha Centauri, is just 4.4 light-years away. That’s 40 trillion km away from earth! Although this rocky planet’s mass is similar to Earth’s, it orbits much closer (25 times closer than the Earth) to host star Alpha Centauri B. As a result, a year lasts 3236 days and the surface temperature of the planet reaches around to 1200 °C, which makes the planet incapable of supporting any life form we know. However, solar systems with a rocky world are usually predicted to have multiple planets. One possibility is that that Alpha Centauri A, the bigger sibling of Alpha Centauri B, might host some yet to be discovered unknown planets with more habitable zones. Although this recent discovery has sparked people’s dreams to travel to another star system outside of our planetary system, such an exploration mission unfortunately seems impractical in the near future. Even a cell phone-sized probe that is accelerated to 10% of the speed of light would need to travel non-stop for 40 years to reach the target. So, what is the next best thing to do? Will it be taking photos or dropping probes on the planet’s surface to study a potentially modified atmosphere? It seems like while astronomers work hard on the identification and characterization of this new star system, scientists should focus on developing super-fast propulsion systems, which will perhaps include new concepts like nuclear rockets and antimatter fusion drives.

Bad memories, substitute or suppress

Opposing Mechanisms Support the Voluntary Forgetting of Unwanted Memories
Benolt RG et al., Neuron, Volume 76, Issue 2, 450-460, 18 October 2012

For the nervous system, forgetting a memory is almost as complicated as creating one. A recent study probed the mechanism of how the brain allows us to voluntarily forget unwanted memories. Researchers utilized functional magnetic resonance imaging (fMRI) to examine the brain activity of participants who had learned associations between pairs of words and subsequently attempted to forget these memories by either blocking them out or recalling substitute memories. The fMRI results showed that two separate forgetting strategies looked equally effective yet they seemed to use different neuronal circuits in different parts of the brain. For memory suppression, dorsolateral prefrontal cortex inhibits neural activity in the hippocampus which is a critical region for recalling past memories. On the other hand, memory substitution specifically activates caudal prefrontal cortex and midventrolateral prefrontal cortex that are known to bring specific memories into awareness in the presence of distracting memories. These findings can help us to better understand the mechanisms of memory disorders such as posttraumatic stress disorder, and may ultimately help to develop effective treatments. At a more personal level, this study may direct us to explore how we deal with our unpleasant or unwanted memories. We might be surprised to realize that one approach might be working much better for us than another one. In other words, neuronal wiring in our brain might simply favor one approach over another.

At the end of the 1950s, Richard Feynman (1961, pp.282-96) described the possibility of building computers that were ‘sub-microscopic’. More recently, several people have advocated the realization of massively parallel computation using the techniques and chemistry of molecular biology.

At the end of 1994 Leonard Adleman published a paper on ‘Molecular Computation of Solutions of Combinatorial Problems’ (Science, vol.266, pp.1021 – 24). He explained how a problem could be set up by synthesizing DNA molecules with a particular sequence, and solved by letting the DNA molecules react in a test tube, producing a molecule whose sequence is the answer. In the same paper he recounted how he had put this theory into practice by solving a standard problem with a DNA reaction system. Adleman called his DNA computer the TT-100, for test tube filled with 100 microlitres of fluid, which is all it took for the reactions to occur.

Since then, many advances have been proposed to refine the protocol for programming a DNA computer to reduce the complexity of the operations and eliminate errors (see Lipton, n.d.; and Boneh and Lipton, nd.). Despite their respective complexities, biological and mathematical operations have some similarities:

The very complex structure of a living being is the result of applying simple operations to initial information encoded in a DNA sequence.

The result f(w) of applying a computable function to an argument can be obtained by applying a combination of basic simple functions to w.

For the same reasons that DNA was probably selected for living organisms as a genetic material, its stability and predictability in reactions, DNA strings can also be used to encode information for mathematical systems.

Conventional computers represent information in terms of 0’s and l’s, physically expressed in terms of the flow of electrons through logical circuits. Builders of DNA computers represent information in terms of the chemical units of DNA. Calculating with an ordinary computer is done with a program that instructs electrons to travel on particular paths; with a DNA computer, calculation requires synthesizing particular sequences of DNA and letting them react in a test tube. In a scheme devised by Lipton (n.d.), the logical command AND is performed by separating DNA strands according to their sequences, and the command OR is done by pouring together DNA solutions containing specific sequences.

‘It will fill a bathtub, not the universe,’ says Lipton, ‘and it will be incredibly cheap to build.’ A pound of DNA in 1,000 quarts of fluid, about three-feet square, will hold more memory than all the computers ever made. The chemicals are inexpensive; DNA runs virtually on its own power, and the soup, with a little splicing, can be re-used from one experiment to the next. Lipton estimates that a superparallel DNA computer, offering trillions of processors working simultaneously, could be built for $100,000.

The fastest supercomputers can currently perform 1000 million instructions per second (MIPS); a single DNA molecule requires approximately 1000 seconds to perform an instruction (.001 MIPS). Obviously, if you want to perform one calculation at a time (serial logic), DNA computers are not a viable option. However, if one wanted to perform many calculations simultaneously (parallel logic), a computer such as the one described above can easily perform 1014 MIPS. DNA computers also require less energy and space. While existing supercomputers operate 109 operations per joule, a DNA computer could perform 2 x 1019 operations per joule (many times more efficient). Data can be stored on DNA at a density of approximately 1 bit per cubic nm, while existing storage media require 1012 cubic nm to store 1 bit (Adleman, 1995).

Thus, the potential of molecular computation is impressive. However, it is too early for either great optimism or great pessimism. It is possible that DNA computers will become more common for solving very complex problems and DNA computers may also become automated. In addition to the direct benefits of using DNA computers for performing complex computations, some of the operations of DNA computers already have (Adleman, 1995), and more could be, used in molecular and biochemical research.

References

• Adleman,L.(1994).’Moleculer computation of solutions to combinatorial problems’,Science,vol.266,pp.1021-24.
• Adleman,L.(1995 ‘On constructing a moleculer computer’:ftp://usc.edu/pub/csinfo/papers/adleman/molecular_coputer.ps
• Boneh,D.&Lipton,R.J.’Making DNA computers error resitant’.(Unpublished manuscript.)
• Feynman,R.P. (1961)’Minaturization’,in D.H.Gilbert (ed.)Reinhold,New York.
• Lipton,R.J.(n.d.)’Speeding up computations via molecular biology’:ftp://ftp.cs.princeton.edu/pub/people/rjl/bio.ps

Because of their biochemical importance, the nucleic acids receive much more attention than the others. DNA was first isolated in 1869 by F. Miescher from cell nuclei. Nearly 80 years of research have been carried out to identify the major building block units and the basic structure of nucleic acids. DNA molecules from different cells and viruses vary in ratio of the four major types of nucleotide monomers, in their nucleotide sequence, and in their molecular weight. Four major bases (adenine, guanine, thiamine, and cytosine) are found in all DNA. The DNA isolated from different organisms and viruses normally has two strands in complementary double-helical arrangement, and it is the basic compound of genetic material (chromosomes). In its double-helical structure it has a 20 A (1 A=10-8 cm) diameter width and the nucleotides are repeated in every 3.4 A.

This polymeric molecule, DNA, is the chemical basis of heredity and is organized into genes, the fundamental units of genetic information. It was first demonstrated in 1944 in a series of experiments that genetic determination of the character (type) of the capsule of a specific pneumococcus could be transmitted to another of a distinctly different capsular type by introducing purified DNA from the former coccus into the latter. This agent (later shown to be DNA) was called ‘transforming factor’. Subsequently ,this type of genetic manipulation has become commonplace. Similar experiments have recently been performed utilizing yeast, cultured mammalian cells, and insects and rodents as recipients, and cloned DNA as the donor of genetic information.

DNA has the ability to replicate itself. It is this property that holds the genetic material in the same type and number sequence during the cell divisions. In prokaryotic cells, which contain only a single chromosome, essentially all the DNA is present as a single double-helical, two-stranded macromolecule exceeding 2 x 10- 9 in molecular weight. In eukaryotic cells, which contain either several or many chromosomes, there ate either several or many DNA molecules. 

The double-stranded structure of DNA can he melted in solution by increasing the temperature or decreasing the salt concentration. The denaturation of DNA is used to analyze its structure. Not only do the two stacks of bases pull apart but the bases themselves unstack while still connected in the polymer by phosphodiester backbone.

Careful examination of the model reveals a major groove and a minor groove winding along the molecule parallel to the phosphodiester backbone. In these grooves,proteins can interact specifically with exposed atoms of the nucleotides (usually H bonds) and thereby recognize and hind to specific nucleotide sequences without disrupting the base pairing of the double-helical DNA molecule. As easily seen, regulatory proteins can control the expression of specific genes via such interactions.

The genetic information stored in the nucleotide sequences of DNA serves two purposes. It is the source of information for the synthesis of all proteins of the cell and organism, and it provides the information inherited. Both these functions require that the DNA molecule serve as template – in the first case for the transcription of the information into RNA and in the second ease for the replication of the information into daughter DNA molecules.

DNA is likely to survive for millions of years in some conditions. Amber can provide some of the right conditions to preserve DNA. The most reliable report of DNA to date from amber is that of termite-like sequences from around 30 million year-old Dominican amber. The earlier recovery of DNA from a 20 million year-old magnolia leaf, near Moscow, was more remarkable because the leaf was preserved in a sequence of easily split soft clays and silts, interbedded with layers of volcanic ash.

Recent developments in genetics are providing very powerful new techniques for the analysis of DNA from remains of ancient organisms. The young field of ancient DNA research is less than a decade old but is growing exponentially. In spite of some serious technical difficulties, the study of ancient DNA promises to become a revolutionary research tool in archaeology; anthropology and molecular biology.The earliest report of retrieval of informative DNA sequences from extinct animals – in this case from the desiccated skin of a quagga, a member of the horse family which became extinct more than one hundred years ago – was that by A. Wilson and his colleagues in 1984. Shortly after this, DNA was isolated by S. Pbo from the skin of a pre-dynastic Egyptian mummy; it was shown by DNA hybridization that a small amount of recognizable human DNA was left in the ancient tissue. In 1988, the first report of an amplified ancient DNA sequence was made by S. Pbo and colleagues who retrieved it from a 7,000 year-old skull found in a peat bog.

It seems likely that studies of this kind will become even more popular in the near future. With the ancient DNA sequence studies, one of the most controversial problems in biology – evolution – will possibly be enlightened. No there is a drive to gather genetic information from indigenous groups to increase our understanding of human origins, history and migrations. Ancient DNA studies will play a very important role by providing a direct source of objective evidence on past populations, and perhaps the only reliable insight into the genetic characteristics of vanished peoples.

Synchronization is a problem in many areas of science, notably in electrical and electronics engineering. In synchronization, there must be at least two events, one of which serves as the reference for the other. Synchronized events always follow each other in a regular manner. In electrical engineering at the instant of synchronization of two busbar voltages, both voltages must be equal in magnitude and period and they must be in phase so that they can be switched in parallel if desired.

In my research I was synchronizing output voltage with line voltage; more recently I was trying to add certain further features into my program like time delay. At this stage while trying to generate synchronized outputs with a delay I failed to allow a few microseconds to the related registers (necessary because of some time delay caused by a few instructions) and also (as I later realized) I was putting some instructions in the wrong sequence. Maybe the beauty of the micro controller design is that it does not allow you to generate (actually you command the microcontroller to generate at the related outputs what you want it to generate) just anything you may happen to have in mind. The input has to be correctly ordered. If you give the right instructions in the right order, it generates (of course, within its limitations) the correct result, otherwise it generates the wrong result or just rubbish.

I spent a whole week looking for the reason for the problem which I have very roughly described. The program ought to have worked correctly because every instruction looked to be all right. But I didn’t see far enough into just how important a few microseconds and the sequences of instructions are. So, I got very frustrated and annoyed at not being able to find the reason for the failure of what ought to have been a simple program.

At night, while thinking about the problem, I realized some of the reasons for the problem, with the help of God. It was only a matter of a few microseconds in every cycle. I did not think that the program could be affected that much by that little. The outputs appeared quite stable for a time but then, after a while, the program would suddenly crash.

Ordinarily we might think: What can a few microseconds matter or the sequence of instructions? When we ask such questions, actually we are starting to think about the complexity of the universe.

The cause of the problem I was having was a few microseconds in every cycle (one cycle is 20,000 microsecond). A few microseconds in one cycle may seem nothing, but in fact the few microseconds are out in a continuous system, every cycle is affected. As a result, the program was causing the wrong outputs to be generated.

If, at this juncture, we think about the magnificence and/or complexity of the universe or for that matter of human beings, we begin to appreciate the greatness of God. In reality, it seems to me, it is impossible to imagine fully or to realize exactly the greatness of God since we cannot even grasp fully how complex the organization of the universe is. Take my problem as an example: it was a simple system with single input and single output, and yet neglecting to compensate a few microsecond of delays caused my output to crash. In the universe, every action and event in every bodily process in every plant and animal, must take place with the most minute exactness in real time, and not in the microsecond range but maybe in many times more or less than that range. Any oversight, be it ever so small, any error of sequence, any delay however small in any event in the universe, will affect all the other events in a chain of effects causing the system to crash suddenly, locally or, maybe, entirely. In short, the existence of the universe depends upon the correct instructions being minutely programmed in the correct sequence.

When we look at either the universe or at an individual creature in it, a human.being or plant or animal, we see that each operates as a large, separate system. We cannot even imagine how many inputs and outputs these systems have, we cannot imagine the complexity of the innumerable problems that are solved in such a way that life has been going on for millions of years. Whenever we look with open mind at any living organism within the universe or at the universe as a single, whole system, our sight returns to us, dazzled and overwhelmed-exactly as is described in the beautiful words of sura al-Mulk:

Then look again and yet again, your sight will return to you weakened and made dim. (67.4)

We see in the sky billions of stars turning in synchronization with each other according to some extraordinary law of harmony. And this harmony has been operative for millions of years, so effectively that its continuance is not in doubt. The same extraordinary miracle of harmony can be studied at the microscopic level: Within a single atom huge numbers of particles whizz past each other around the nucleous at unimaginable speeds in a continually renewed and vital process of creation.

Our understanding cannot fathom, nor our researches exhaust, the wonder in which we live and which we behold. And when we realize the complexity of the innumerable systems which compose the universe and whose inter-related functions have been managed not for seconds or hours, but for hundreds of millions of years, can we do otherwise than humbly acknowledge the wisdom and power of God? Equally, when we accept, as logically we must, that in the universe as a whole, everything is organized in the right way for its continued operation, are we not bound to conclude that every event, seemingly good or bad, has occurred at its own time and place, precisely, as pre-ordained (or ‘programmed’ we might say) by God? Thus, we are led to acknowledge the Creator, to marvel in humility at His grandeur, and His greatness.