Research on hummingbirds (also known as nectar birds or Colibris), the smallest of the 9,800 bird species living today, has revealed remarkable facts. The world’s smallest birds are equipped with mind-blowing structures and functions that push all physiological and anatomical boundaries. The bee hummingbird (Mellisuga helenae), considered to be the smallest bird in the world, is only 1.96-inch-long and weighs 0.06 ounces.

There are around 330-340 species of hummingbird and they live only in North and South America and the nearby oceanic islands. With their colorful feathers, they are some of the most beautiful birds.

How the hummingbird flies

A hummingbird flaps its wings so fast that the motion cannot be seen by the human eye but only detected through special cameras. The wings move at an incredible speed in a seemingly complex pattern, drawing circles back and forth 50 to 80 times per second, depending on the species. Under the genus Colibri, the horned Sungem (Heliactin bilophus) species flaps its wings 90 times per second; the purple amethyst Colibri (Calliphlox amethystina) flaps its 80 times per second. This speed increases up to 200 per second during a short spike while escaping from an enemy. Moving back and forth, the wings oscillate in the form of the figure 8 in the air. While in most other birds the movement of the wings produces the power to lift up and down, Hummingbirds, like helicopters, can perform movements such as hanging in the air or standing steadily as well as flying backward or rising in a vertical direction.

Figure 8

Metabolic rate and energy consumption

Flying requires a lot of energy. The amount of energy spent is related to the bird’s body size and flapping speed. In this regard, given that a colibri flaps its wings 80 times per second, it takes a great deal of energy to maintain such a rapid movement. The colibri’s chest muscles were perfectly created for flapping quickly and take up 40% of the hummingbird’s total body mass. Therefore, a colibri consumes more energy than other birds; it’s basically a fighter jet.

In order to meet this high energy demand, the amount of nectar a colibri consumes every day has to be equal to their body weight. Living at such a high metabolic rate requires a fine adjustment of food consumptions with precise calculations.

Such a high food intake requires a high metabolism – and thus, the need for oxygen increases dramatically. When the need for oxygen increases, there can be two kinds of conditions. Those animals with very large lungs can intake a lot of air at once. And those with smaller lungs can produce the required oxygen by breathing many times a minute. Colibri or Nectar birds are the ones that can breathe the most in one minute. The lungs of the world’s smallest birds breathe 250 times per minute to transfer oxygen to their hearts weighing a mere 0.003 ounces and beating 1,200 times per minute.

Toronto University’s Kenneth C. Welch Jr. studied the metabolism of hummingbirds for more than 10 years. He discovered that there is a relationship between the size of hummingbirds, energy efficiency, and oxygen consumption, and that larger hummingbirds are more efficient energy users than smaller ones. A hummingbird can take 2.44 cubic inches of oxygen per 0.03 ounces an hour. When a small weight is added to the bird, this amount increases to 3.66 cubic inches, and their tissues use oxygen very efficiently.

Energy requirements

A hummingbird’s metabolism is the fastest among all vertebrates. It needs to eat almost constantly to get the energy it needs to produce fuel for its breathtaking metabolism, which functions like a power plant. It receives nectar from 2,000 flowers every day. If we humans could work at this bird’s energy levels, we’d have to eat about 1,300 sandwiches a day to produce energy, and our body temperature would rise to 725 °F! Also, our hearts would have to beat 1,260 times per minute. Although nectar from flowers is the main fuel source driving the bird’s metabolic engines, it also occasionally eats insects, for protein needs.

During any given 30-minute period, hummingbirds burn the sugar they had taken in an hour ago. If we apply this rapid intake of sugar and the metabolic cycle in human beings, we would have to drink a large bottle of soda and burn the sugar in it every minute.

Unlike us, hummingbirds use both glucose and fructose from nectar in their intestines, circulatory systems, and muscle cells. However, we can support our bodies at urgent needs with an intake rate of 30% of glucose. Half of the nectar that hummingbirds take is glucose and half is fructose. In this modern age, high fructose derived from corn in our diets has paved the way for metabolic diseases and obesity – that is, people cannot metabolize high fructose.

Scientists are trying to determine how hummingbirds can process fructose. It is known that there is a carrier molecule different from glucose in fructose. This carrier is very rare in human muscle cells, but it is found in abundance in hummingbird’s muscle fibers; so we believe the mystery of how they utilize fructose so fast is about to be solved.

Hummingbirds have been equipped with mechanisms to increase the rapid introduction of nutrients such as fructose and glucose – which are basically small sugar molecules – or amino acids into their metabolisms. Their hearts and blood vessels work at a high speed to carry the sugar into their tissues as well as to transfer a lot of blood. In addition, a large number of capillaries have been implemented close to the muscle cells so that the blood can reach each and every cell.

Wing design

While humanity has not yet invented a machine that can move in a figure-8 pattern 80 times per second, including forward and backward, the ultra-flexibility of a hummingbird’s unique wing strokes demonstrates the special creation of its bones, muscles, and joints. The colibri’s brain and nervous system, which control these muscles and joints by transmitting signals, require infinite knowledge and power. The flexibility of the shoulder joint in the movement of the wings, which allows them to bend to extreme positions not found in other birds, gives us an idea of the wing’s unique design and architecture. Although biomimetic engineers have spent millions of dollars applying this complex system to technology, they have so far failed in their attempts to produce a similar machine.

Cooling the feathers due to the friction of the muscles and the tremendous movement of the wings is a problem in itself. While man-made machines need advanced cooling systems, the hummingbird has been created with a such a built-in system.

Unique tongue structure

Biologists from the University of Connecticut have discovered that hummingbirds’ tongues have a very special design and work like micro pumps. Tongues about twice the length of their beaks allow them to reach deep into flowers. The nectar is then pumped into the body in less than 1/20^th of a second. This occurs thousands of times each day. Tai-Hsi Fan and Margaret A. Rubega, who for a long time examined how hummingbirds stick their tongues 15 or 20 times a second into the tubular part of a flower, said that they “could not clearly understand how they drink the nectar.” In their latest study, they showed that it was only possible for the birds to hold nectar through two channels in their tongues. It was once thought that the physical rule of the upward movement of liquids in capillary tubes, even without suction, worked in the hummingbird’s nectar intake; but when special video recordings of the movement of their tongues were examined, it became evident that the tongue first compressed the nectar in a series of movements, then sprung up very quickly and the nectar was suddenly sprayed into the channels.

It would seem that both the hummingbirds and the flowers they need for sustenance were created in perfect harmony.

Red hummingbirds migrate from Alaska to Mexico every year. They can fly 56 miles per hour. Prior to this journey, they feed for one or two weeks to fill their fuel tanks, forming a layer of fat equal to half their body weight. Since these activities cause a lot of heat loss on the body surfaces, they cannot provide enough energy to stay active for more than 12 hours at a time. To counter this, they fall into a deep sleep every night for 12 hours. The energy storage, flight endurance, long-distance migration, and returning with the young ones are each complicated factors that their coming together to make this journey possible cannot simply be explained by blind chance.

Of course, the smallest bird in the world would have the smallest egg size: a mere 0.5 x 0.3 inches, for a total weight of 0.007 ounces. Considering that this wonderful bird’s design is embedded into this egg, which is about the size of the nail of our little finger, it can be understood how perfect a creation it is.

A planet that revolves around another star outside our solar system is called an Exoplanet or Extra solar planet. Ongoing studies involving this field are carried out via simultaneous ground and space based missions and observations. Scientists are searching a small portion of the Milky Way galaxy, approximately 3000 light years away, by using ground and space telescopes, along with various other astronomic methods (1). Despite all this technology, the observation area is too big when compared to the size of the object of interest.

It has been calculated that the Milky Way, a disc shaped galaxy, consists of 200 billion stars spread over a diameter of nearly 100,000 light years and a thickness of 1000 light years. When we consider the amount of stars in a single galaxy, and the fact that there are between a hundred billion and one trillion galaxies in the universe, the number of possible exoplanets is likely much larger than those we currently know of.

Classification of exoplanets

Exoplanets are classified according to their physical, chemical, and other characteristics, along with their diameter and mass: Jupiter like; greater than Jupiter; Earth like; greater than Earth

Classifications according to surface and atmospheric temperatures are as follows: Hotter than Jupiter; colder than Neptune; colder than Jupiter; small blue dots or twin Earths.

The presences of free-floating planets which have lost their parent stars because of different formation processes or other factors have also been discovered.

One of the common features of the exoplanets currently discovered is their short distance to the star they revolve around, which is usually less than half the distance between the Earth and the Sun. The known exoplanets are also defined by their faster revolutions in much shorter periods. Therefore, larger planets that are closer to their stars can be observed easily. When these planets are passing in front of their stars, a decrease in the brightness of the star is detected via spectrometers (Figure 1).

Figure 1. Passing of a planet in front of a star and a spectrum of this event.

Radial velocity, one of the methods used to discover exoplanets, relies on the observations of a star’s kinetic fluctuations. The proximity and size of a revolving planet leads to slight changes in location and velocity of a host star. As a result of this, the star gets closer to earth and then becomes more distant, which is observed as the Doppler shift of spectral line color waves. 75 % of all known planets have been discovered using this method (Figure 2).

Figure 2. Doppler shift – radial velocity

Earth-like planets or habitable places

In an official NASA report in December 2011, the discovery of an Earth-like planet was announced for the first time. This planet, named Kepler 22b, is 600 light years away and remains the most similar one to Earth among the known heavenly bodies. The distance of Kepler 22b to its star shows a high possibility for the presence of a habitable zone.

So what does this mean?

Earth is such a special home for us humans that everything here has been assigned to serve us with delicate calculations. Factors such as the Earth’s mass, gravity, distance to the Sun, rotational and revolution velocity, chemistry, thickness of the atmosphere, magnetic shield, hydrosphere/land ratio, ecological balances, and average temperature are all perfect for biological life.

Earth revolves in such a region and position that a majority of the planetary water is in a liquid state and is not ice or vapor.Thedistance of the habitable zone to our Sun is between 135,000,000 – 225,000,000 km. Earth revolves at a 150,000,000 km distance to the Sun. The value of a habitable zone for each planet depends on the diameter, mass, heat and radiation strength of the host star. In other words, aside from the similarity of an exoplanet to Earth, a classification of its host star with in terms of size and age is also important.

Kepler 22b owns the title as the first planet to match the criteria above with its following features:

• Has a radius 2.4 times bigger than Earth
• Revolution time is 290 days (365 for Earth)
• 15% closer to its star compared to the Earth-Sun distance
• The size and surface temperature of Kepler 22b’s host star is very similar to that of the Sun’s
• The surface temperature of the planet is 22 C
• The size of the habitable zone for Kepler 22bis 133,500,000 – 240,000,000 km (Figure 3).

Figure 3. Comparison of the solar systems of Kepler 22b and Earth.

Aside from these similarities, it is noteworthy to report the problems that scientists encountered regarding Kepler 22b:

• The unknown presence of water on the surface
• No information on the gaseous contents of the atmosphere.
• The gravitational force is 2.5 times greater than on Earth.
• Rocks constitute the surface instead of soil.

The hardest part is that Kepler 22bremains 600 light years away from us. This means it would take us 11 billions years to get there with today’s fastest spacecrafts. Who knows when we will be able to decrease this time with the advent of superior technology.

What do religious scholar say about life in outer space?

Among His manifest signs is the creation of the heavens and the earth, and that He has dispersed in both of them living creatures. And He has full power to gather them together when He wills. (Ash-Shura 42:29)

While interpreting the Qur’anic verse above, Fethullah Gülen notes the following:

“Since the earliest times, this verse has been taken as a proof for the view that there are living creatures, whether resembling human beings or not, in the places other than the earth. This view may be true. The second part of the verse, ‘He has full power to gather them together when He wills,’ has been understood that these creatures and human beings will possibly come together either in this world or in that of the other creatures. … there may be earth-like globes in the heaven where creatures resembling earthly ones live.” (Gülen 2012, 272-273)

“Perhaps people will not be able to reach those places individually or as a whole generation, but this can be achieved by mankind as a species. In other words, when the Divine Will manifests itself in that direction, humans here can encounter those other life forms.” (Gülen 2007, 232)

This commentary reflects what Bediuzzaman Said Nursi had said decades ago:

“The earth, although much smaller than other heavenly bodies, is so densely inhabited by living creatures that even its grossest and most rotten parts are full of living things, such as micro-organisms. This shows that those infinite firmaments, with their numerous stars and constellations, are inhabited by conscious, living beings …” (Nursi 2010, 530-531) 29th Word, First Aim, First Fundamental)

Nebiyev is a professor of physics in Azerbaijan.

References

• http://kepler.nasa.gov/
• http://planetquest.jpl.nasa.gov/
• http://en.wikipedia.org/wiki/Habitable_zone
• Gülen, M. Fethullah. 2007. Kendi iklimimiz, Istanbul, Nil Yayinlari.
• Gülen. M. Fethullah. 2012. Reflections on the Qur’an: Commentaries on Selected Verses, NJ: Tughra Books.
• Nursi, Bediuzzaman Said. 2010. The Words, (29th Word) NJ: The Light, Inc.
• Chris Kitchin Exoplanets: Finding, Exploring, and Understanding Alien Worlds- (www.springer.com/series/6960)-2012
• Mercy, G., P. Butler et al. 2005. “Observed Properties of Exoplanets: Masses, Orbits, and Metallicitie”.. Progress of Theoretical Physics Supplement, Vol. 158, No. 24-42.

A small-scale blueprint of the universe, the human body is a miraculous work of art that manifests the beautiful divine names and attributes of God Almighty. A human body is made up of a set of hierarchically organized components: an organ system, organs, tissues, cells, organelles, macromolecules, molecules, atoms, neutrons, protons, electrons, and subatomic particles. In this biological organization, it is striking to observe a proportionately allocated space between components on each level for their efficient functioning. The size of human body would be reduced if these spaces between organs, tissues, cells, and atoms could be removed, and the entire human body would not be bigger than a small ball.

The structure of an atom explains a lot concerning the real size of our body, which is filled with space. An atom is comprised of protons and neutrons in its nucleus, around which electrons continuously orbit. The mass of neutrons is almost equal to the mass of protons. Electrons, however, are 1,837 times smaller in mass than neutrons and protons. That is, almost 99.95% of the atom’s mass is in its nucleus. The mass of electrons is almost non-existent compared to the nucleus.

Both the universe and our body are filled with more hydrogen than any other atom. In each one billion atom in our body, six hundred thirty million are hydrogen atoms. In a hydrogen atom, electrons rotate only 0.53 nm (one billionth of a meter) away from the nucleus, which makes the atom’s volume to be around 6.10^-28m³, whereas the volume of the proton is 7.10^-45m³, i.e., the nucleus is only as big as one hundred quadrillionth (100.10¹⁵) of the atom’s total volume. In other words, while the nucleus comprises almost the entire mass of the atom, its volume is of no considerable size. The density of protons in the nucleus is 2,3.10¹⁷ kg/m^{3 (where does the period go here??)}, which means that there is around a hundred trillion tons of matter in only one cubic meter. If we could gather all neutrons and protons in one spot, a man who is 69 kg would be only 3.10^-7 mm³ in volume. That is, the volume the total substance of our body takes up is around one ten millionth of a cubic millimeter. The human body, which is constructed of atoms with electrons rotating on an orbit quite far away from the nucleus, is in a way no different than an “inflated space.” For a comparison, the space between the earth and the sun can be filled with as many as 107 suns, whereas 450 thousand protons are needed to fill up the distance between the proton and electron in a hydrogen atom.

The subatomic world is even more amazing. In subatomic particles are found six types of quarks. A quark is considered a fundamental constituent of matter. Combinations of quarks in different shapes and numbers result in subatomic particles, the further combinations of which produce atoms, molecules, and so on. Quarks are considered to be without mass; that is to say, they are nothing else but energy. Humans have mass, but this mass consists of quarks that are without mass.

This incredibly vast space between atoms that make up matter teaches us that our true value does not lie in our physical structure, but in the artworks of no comparison designed by the Divine as manifestations of His most beautiful names. Thus, we, who are so little in material substance, should seek other gateways in the depth of our souls and attain some value with proximity to the Divine.

We may never have revolted against God Almighty in our entire life; yet still our material minority should free us from all kinds of pride and conceit. Our physical structure is very much like the number “zero,” for 0 is also nothing, and it is drawn by inflating.

The miracle of life appears in the form of a baby which develops from a fertilized ovule (zygote) following millions of other events. This series of events, which is almost always the same for every fetus, can be grouped as reproduction, differentiation, and development. The zygote completes its development in the womb; postnatal growth can continue until 20 years of age. Even though every event during the baby’s development seems to take place with chaotic reactions, harmony and order are there for us to discover. One of these astonishing events is the perfectly symmetric growth of the fetus/baby. Most organs in the human body appear in pairs and are symmetric. Babies are born with 300 bones; however, some bones later fuse with other bones, leaving only 208 bones in the adult human. It is still a mystery how long bones such as the humerus, radius, ulna, femur, and tibia are able to grow on both sides of the human body in a symmetrical manner.

Mechanisms that control growth in organs

In vertebrates, both internal developmental programs and the external factors which stimulate or inhibit growth play a role in the ultimate size of an organ. But the relative effects of these two mechanisms can vary significantly in different organs. When pieces of spleen from an embryo that is at a later stage of growth are transplanted to a newly developing embryo, each new piece grows, but not to the size of the original spleen. The total weight of all the transplanted spleen pieces is equal to a normal spleen’s weight. When the spleen reaches a certain weight, growth inhibiting factors are secreted, which stimulate negative feedback mechanisms that limit growth. When a spleen reaches a certain size, the density of the inhibiting factors increases simultaneously, halting growth. Growth in the liver is controlled by extracellular factors (various substances in the blood, hormones, vitamins, minerals, etc.). When a section is cut off of the liver, the section continues growing and developing until it reaches the size of the original liver. The thymus has a growth process that is executed by a cellular genetic program. When sections of a thymus taken from the embryonic period are injected into developing mouse embryos, every section grows until it reaches the ultimate size.

More evidence of cellular growth programs was acquired via an experiment that was carried out with the salamander genus Ambystoma. When the leg bud of the larger species was injected into the smaller species, it would at first grow slowly, but then it would reach the normal size of its own species (the larger species).

Distinguishing growth and symmetry from one another

Both the arms and legs have long bones. A long bone consists of two parts (diaphysis and epiphysis). The diaphysis is the middle (core) part of the long bone. It consists of hard bone tissue, and is like a tube. The hyaline cartilage-covered joint forms the epiphysis of the long bone. In a growing bone, there is a growth plate (epiphysis plaque) made of hyaline cartilage; this is located between the diaphysis and the epiphysis. The epiphysis plaque causes the bone to grow longer; when growth is complete, the epiphysis plaque ossifies (becomes bone). In other words, growth stops. There are some clues that show the existence of positive feedback mechanisms which control the symmetric and balanced development of the arms and legs while the fetus is still growing. The arms and legs grow due to the development and growth of the plaques located at opposite ends of the long bone. The ultimate size of the arms and legs are proportional to the size of the finger bones (phalanx) and the metacarpus. According to current knowledge, growth in our arms and legs is only controlled by internal growth programs and the active growth of the plaques. We do not yet know the mechanism through which how much the bone must grow and symmetrically with the organ (the other arm or leg) on the other side of the body. But even if this is discovered in the future, we will continue to appreciate the perfect and miraculous aspect of this phenomenon.

In addition, in growth-plaque transplant experiments, the development of the transplanted growth plaque is dependent only on the age and size of the donor. Growth plaques cause the bone to grow, but the plaques themselves remain the same size for years. The cartilage cells they produce (chondrocytes) exchange places with the bone cells (osteocytes) in harmony and without destroying the length of the bone. Cells from different areas of the growth plaque act differently. Stem cells are found on the upper section, near the epiphysis. Immediately above them is an area where cells reproduce very quickly. At the bottom of the epiphysis, the cartilage cells grow up to 4 to 10 times larger than their normal size (hypertrophy). Cell reproduction here is mostly due to hypertrophic chondrocytes. The chondrocytes die and break up, then change places with the bone tissue. The dynamic process of these events in the growth plaque repels it from the bone area, and as a result, the bone grows longer.

Sustained symmetry despite cell sequence and speed of reproduction

The rapid growth rate in the legs and arms during the embryonic period continues to increase until the child is three years of age. This growth rate slows down until the individual reaches adolescence. During the fastest growth period, which is from adolescence to the early 20s, the growth rate rapidly increases. For example, most people who grow between 30 and 37.5 cm during the first two years of life can grow between another 7.5 and 10 cm every year during adolescence. At the onset of adolescence, rapid growth due to a sudden change in the volume of cells is observed. After adolescence a sudden falling off in the speed of growth can be observed due to the effect of hormones on the growth plaques in the spine and other long bones. The growth plaque now fuses with the neighboring cells and growth stops. However, the fusing of the growth plaque is the result of the cessation of growth, not the cause. After growth stops, the growth plaques begin to disappear. When the reproduction potential of the cartilage cells in the growth plaque has been exhausted, the growth plaque begins to disappear.

Growth plaques in different bones can trigger growth at various rates; these rates can differ as much as seven times. In fact, growth plaques on different ends of a bone can have different growth rates, provided that this rate is consistent with the genetic program. The number of cells on the growth line is 40 times more than in other areas. The number of cells produced here can exceed 10,000 cells per day. For symmetric growth between the arms and legs to be sustained, the number of cells in the growth plaque must be the same or very close. Experiments carried out on rats show that eight cartilage cells leave the growth plaque to exchange places with cells above them every day. It can be said that the growth of the bone is caused by the increase of cells in the growth plaque (which sustains its size). The growth rate caused by the growth plaque can be calculated by multiplying the growth plaque’s cell production rate by the average length of all of its cells. Different growth plaques provide different growth rates. This difference can be caused by the difference in the size of the growth plaques, the difference in cell production rates, and/or the difference in the hypertrophy (growth) rate of every cell. The upper growth plaque in the tibia of mice generates 16,400 cells every day; the average life span of these cells is around 30 hours. Can such harmonious, symmetric, and equivalent growth in the arms and legs-despite the large number and variety of cells-be the work of pure coincidence, mindless nature, or unconscious molecules?

Do hormones play a role?

The main molecular players that organize longitudinal growth in bones during childhood are the growth hormone, the thyroid hormone, and corticoids. The sex hormones (androgens and estrogens) are programmed to influence growth during adolescence. Estrogen is the main determiner of characteristics related to increased height and an increase in bone quality, as well as adolescent-related physiology. These hormones are in charge of coordinating growth throughout the body. It is for this reason for women, after the menopause, the production in estrogen decreases and osteoporosis and brittle bones can occur. According to the current view, cartilage cells have a certain genetic reproduction potential, and when this potential finishes, growth stops. The growth rate during the embryonic period is 20 times higher than that of mid-childhood. The growth rate drops greatly during mid-childhood. If we exclude the noticeable increase during adolescence, the cells responsible for growth have begun to age. The bones on opposite sides of the body stay about the same size, despite all of these changes in growth rates. Circulating hormones and neuroendocrinal factors are believed to play important roles in maintaining symmetric growth. But there is no conclusive evidence to support this belief. Even though one can think of factors such as pressure, tension, and sports as helping control harmonious and symmetric growth of bones, no proof has been attained from controlled experiments. As a person ages, a gradual decrease in growth can be observed. Even if a growth plaque is placed into another organism, be it young or old, the growth rate of the bone does not change. This shows that symmetric growth in long bones is controlled by a program that is operated by internal factors, which is also compatible with the genetic program. When chemical-based medication is given to postpone growth, after the medication has been eliminated, the growth plaques grow faster for a short period to compensate for the lost time. These findings show that timing and the location and circumstances of the cell are critical parameters for reproduction. If the cartilage stem cells in the growth plaque have a certain reproduction potential, then it is clear that cartilage cell reproduction stops when growth comes to an end. If growth inhibiting factors slowly accumulate in the growth plaque, this might cause a deceleration of growth over time. Another possibility is some sort of “meter” in the unconscious and mindless stem cells, which keeps track of the number of cell divisions and thus controls aging. The estrogen in our body has a duty of closing down the growth plaques and speeding up the aging of cells. However, we should not forget that estrogen plays the special role of closing down all of the growth plaques at the same time. Estrogen is one of the visible causes of fertility, growth and development, and resilience. Estrogen also represents femininity and fertility at all levels.

When the signals from unconscious cells in the growth plaques and the quite sophisticated interactions among all the factors that influence growth, all of which require an all-encompassing knowledge to be executed, are taken into account, the impeccable genetic programs of different growth plaques on the two sides of the body that leads to the formation of the arms and legs, as if they have been molded in a factory, is absolutely amazing for anyone who reflects upon it.

References

• Wolpert L. (2010).”Unsolved Mystery: Arms and the Man: The Problem of Symmetric Growth.” PLoS Biology. 2010 Vol. 8(9). pp 1-3
• Extremity Development during the Embryonic Period (www.visembryo.com)

ENIAC had cost around $500.000 and was capable of 5000 simple operations per second. Today, basic personal computers (PC) cost around $500 with enough processing power to perform millions of operations per second. An average PC is enough in terms of computing power for everyday use like word processing, checking emails, and computer games. However, some areas in scientific research require computers at the frontline of current processing capacity, called Super Computers. Twice a year, the TOP500 project, which started in 1993, ranks and publishes details of the 500 most powerful super computers in the world. The IBM Roadrunner, located at Los Alamos National Laboratory, was announced as the fastest supercomputer in the world as of May 2008.

In computing, “flop” (Floating Point Operations Per Second) is a measure of a computer’s performance which is similar to calculations per second. The IBM Roadrunner had cost $133 million and had a peak performance of 1.7 petaflops, which is around 1.7×1015 operations per second. The Roadrunner was delivered on 21 tractor-trailer trucks to its current location. Supercomputers are an essential component of research in areas like computational biology, fluid dynamics, structural mechanics and cancer research, which requires high computing power.

While computers get faster every year, their computing power is way behind when compared to a human brain. They consume hundreds of times more energy than a brain. It is estimated that a computer will be able to simulate a human brain in seven years, yet we are decades away from expecting a computer that can think like a human and make decisions. The brain is one of the most miraculous parts of the human body, full of mysteries. It works more efficiently than any machine developed in the last 50 years of the computer history.

However, the human brain is not the only body part which has an incredible computing power. In 1994, Leonard M. Adleman, a professor at the University of Southern California, introduced the idea of using DNA (Deoxyribonucleic Acid) to solve computational problems [3]. This idea then led to a new field of science, called DNA Computing, which combines two disciplines, biology and computer science, to build the fastest and smallest computers ever. DNA is known as the blueprint of life, with unique properties such as self-assembly, molecular recognition, minute size and high information density.

Computationally challenging problems have known solutions, but enormous amounts of resources (time and/or cost) are required to find the optimum solution. Some problems, such as optimization, can be solved by generating many possible solutions, and then selecting the optimum one. Standard computing methods can generate or test a possible solution one at a time. On the other hand, parallel computing methods can carry out this process simultaneously for thousands of possible solutions.

Similarly, enzymes can work in parallel for replicating and repairing DNA strands. They can even work on the next strand before the first one is replicated. An enzyme can replicate a DNA strand 500 times in a second, which is equal to 0.001 MIPS (million instructions per second). The computations in DNA can reach to 1014 MIPS, while a modern computer runs at an average of 1000 MIPS. DNA computing is not only faster in processing, but also much more efficient in energy consumption. The energy consumption of a DNA operation (on one strand) is about 1010 times less than the energy consumption of an operation on modern computers.

The Traveling Salesman Problem (TSP) is one of the most studied problems in computational mathematics. Here is an example of the problem: a traveling salesman needs to visit 20 cities once, with predefined starting and ending locations, and certain rules. The complexity of the TSP problems increases exponentially with the number of cities, so problems with only hundreds of cities will take thousands of years to solve by modern computers. If there are 18 factorial possible paths in this problem, it will take 2 whole years for a computer with 100 MIPS of processing power to generate the possible paths and find the correct answer. However, all possible paths can be generated in a very short time by using DNA computing. A simplified version of the Traveling Salesman problem presented by Adleman involves the following scenario:

A salesman wants to visit the cities (Figure 3) Monroe, Gainesville, and Conyers, starting from Athens, and arriving at Atlanta last. Each city should be visited only once. The cities are not fully connected. While some cities are connected to another in one direction, others are connected in both directions. Our objective is to find the shortest route to visit all cities once. The solution for this problem is a travel from Athens -> Gainesville -> Monroe -> Conyers -> Atlanta.

When we convert the problem to a molecular language, each city is coded as a single-stranded DNA molecule with 8 nucleotides. We can think of nucleotides as bytes in computer programming, which will take the value 0 or 1. Nucleotides exist as four bases: adenine (A), thymine (T), guanine (G) and cytosine (C). All cities are coded with eight nucleotides as follows:

City Code

Athens ATGC CATG

Gainesville TCAG GTCA

Monroe GACT TGAC

Conyers CGTA ACGT

Atlanta AGCT TAGC

Connections between two cities are coded with the last 4 nucleotides of the departure city and the first 4 nucleotides of the arrival city. For example, the connection between Athens (ATGCCATG) and Monroe (GACTTGAC) is coded as CATGGACT. The complementary codes for connections (the Watson-Crick complements), where every C is replaced by a G, every G by a C, every A by a T, and every T by an A, and connection codes are given below:

Connection Code Complementary Code

Athens – Gainesville CATG TCAG GTAC AGTC

Athens – Monroe CATG GACT GTAC CTGA

Gainesville – Atlanta GTCA AGCT CAGT TCGA

Gainesville – Monroe GTCA GACT CAGT CTGA

Monroe – Conyers TGAC CGTA ACTG GCAT

Conyers – Atlanta ACGT AGCT TGCA TCGA

Conyers – Monroe ACGT GACT TGCA CTGA

The mixture for performing reactions will include DNA strands and their complements for 5 cities and 7 connections between cities in our example. If an Athens molecule (ATGC CATG) encounters the complement strand of an Athens-Monroe (GTAC CTGA) connection in the mixture, a hydrogen bond will be formed between strands (Figure 4). Other strands will continue forming bonds for valid connections between cities, building a complete travel path with the help of DNA ligase. There needs to be enough copies of each DNA strand to generate all possible travel paths.

ATGC – CATG

| | | |

GTAC – CTGA

Polymerase Chain Reaction (PCR) will be used to make multiple duplicates of DNA strands containing Athens (start) and Atlanta (end) cities. The result of PCR will be the amplification of correct travel from Athens to Atlanta, which makes it easy to separate. PCR is a method by which a few strands of DNA can be copied into millions in a very short amount of time. This also makes PCR a very important method to increase small amounts of DNA found in blood or hair samples, which could be enough to carry out analysis and reveal a person’s identity in forensic science.

Electrophoresis follows the PCR process to sort the resulting paths according to their sizes. Since every city is coded with 8 nucleotides, the correct path should include exactly 40 nucleotides representing a full path for 5 cities. The gel electrophoresis process uses an electric field to separate DNA strands by size as they travel through a gel matrix. The speed of DNA molecules differs by their size, which results in the sorting of the molecules by size. After this step, DNA strands starting with the code of Athens, ending with the code of Atlanta and with a size of 40 nucleotides are separated from the mixture.

The last step will be reading the code and removing the DNA strands that didn’t contain all the cities. Adleman used a common method known as affinity purification for the separation process. Finally, the mixture has the DNA strands with the correct travel path, starting from Athens and arriving to Atlanta, and traveling through every city once. All the laboratory work looks complex for this simple problem, but as a new concept for computing, it is revolutionary. In its ability to perform parallel computations, DNA computing shows great promise over traditional computing approaches.

Data density is another unique advantage of DNA. Billions of DNA strands can be stored in a regular laboratory tube. A DNA strand is composed of bases A, T, C and G spaced evenly, 0.35 nanometers apart from each other. The data density of DNA is around 106 GB (gigabytes) per square inch, which is 100,000 times larger than the data density of today’s storage technologies (7 GB per square inches). Moreover, DNA is a durable and strong molecule; the information stored within it can be kept for thousands of years in the right conditions. In 2008, 80% of the woolly mammoth genome, several thousand years old, has been identified from tufts of frozen woolly mammoth hair [4].

DNA is also created with remarkable mechanisms such as built-in error correction. The double stranded nature of DNA provides a double check on pairing. Error repairing enzymes are always ready to search for anomalies during the DNA replication process. It results ina ratio of one error per billion replications. DNA is located and protected at the center of each cell with a perfect balance. The miraculous architecture of DNA has waited for thousands of years to be understood by humans and be used for the benefit of the world. Further studies on DNA might open new opportunities to help researchers in solving technologically challenging problems.

Acknowledgment: This article was produced at MERGEOUS [5], an online article and project development service for authors and publishers dedicated to the advancement of technologies in the merging realms of science and religion.

Halil I. Demir is a postdoctoral scholar in the area of Informatics, and lives in Iowa.

References

[1] ENIAC, Image Credit: Wikimedia, http://upload.wikimedia.org/wikipedia/commons/4/4e/Eniac.jpg

[2] IBM Roadrunner, Image Credit: Wikimedia,

http://upload.wikimedia.org/wikipedia/commons/c/c7/Roadrunner_supercomputer_HiRes.jpg

[3] Leonard M. Adleman (1994-11-11). “Molecular Computation of Solutions to Combinatorial Problems.” Science, 266 (11): 1021–1024.

[4] Miller, W (et al). 2008. “Sequencing the nuclear genome of the extinct woolly mammoth”, November, Nature.

[5] Mergeous, http://www.mergeous.com

Ancient people, considering it very important to determine Earth’shape, derived two important clues from the night skies. According to Aristotle (384-322 bce), these were lunar eclipses and the North Star. Lunar eclipses occur when the sun, Earth, and the moon line up in such a way that Earth temporarily blocks the sun’s light from reaching the moon while its circular shadow gradually crosses the moon’s face. The North Star appears lower in the sky the further south we go: at the Equator it lies directly on the horizon, at a latitude of 45 it is 45 above the horizon; and at the North Pole it is directly overhead. However, it is not visible south of the Equator.(1) As both of these indicate a spherical Earth, the scholars of that time discarded the idea of a flat Earth.

The more challenging question was how to determine Earth’s size. Eratosthenes of Alexandria (third century bce) had a simple yet brilliant idea: insert a gnomon (a vertical stick) into a level piece of ground. This enabled him to determine noon’s exact time (when the shadow was the shortest). It was also used as a compass, for in the Northern Hemisphere the gnomon’s shadow points north.

But can such a simple device determine Earth’s size? Aswan, located about 500 miles south of Alexandria, sits on the Tropic of Cancer. So, at noon of June 21 (the summer solstice), a gnomon inserted there has no shadow. By doing just that in Alexandria, Eratosthenes found that the angle was 1/50 of a circle’s circumference (i.e., 2p/50). In other words, the angle at Earth’s center corresponding to the arc between Aswan and Alexandria on Earth’s surface is 1/50 of a circle’s circumference. Since the distance between Alexandria and Aswan is 500 miles, Earth’s circumference should be 25,000 miles, which is its actual circumference.(2) Thus, Earth’s size and shape was pretty well established over 2,000 years ago.

This knowledge was lost to Europe when the ancient civilizations crumbled. But Islamic civilization and culture, which was rising at roughly the same time as the West was declining, produced scholars and scientists who translated and refined quite a bit of this ancient knowledge. For example, in 1424 al-Kashi used Archimedes’ method of computing to determine its values to 16 decimal places. Ulug Beg compiled the greatest star catalog known at that time. During al-Ma’mun reign (813-833), al-Khwarizmi measured one degree of latitude on Earth’s surface and obtained the result of 57 miles. This means that Earth’s circumference is 360×57 = 20,520 miles.(3) Thus, in the ninth century, Muslim scientists knew that Earth was spherical and had a good idea of its size. Most Europeans at that time, believed that Earth was flat and the universe impenetrable.

The Qur’an describes Earth’s geographical shape and change in that shape: Do they not see how We gradually shrink the land from its outlying borders? Is it then they who will be victors? (21:44).(4) The reference to shrinking could relate to the now-known fact that Earth is compressed at the poles.

At a time when people generally believed that Earth was flat and stationary, the Qur’an explicitly and implicitly revealed that it is round. More unexpectedly still, it also says that its precise shape is more like an ostrich egg than a sphere: After than He shaped Earth like an egg, whence He caused to spring forth the water thereof, and the pasture thereof (79: 30-32).

The verb daha’ means “to shape like an egg,” and its derived noun da’hia is still used to mean “an egg.” As this may have appeared incorrect to pre-modern scientists, some interpreters misunderstood the word’s meaning as “stretched out,” perhaps fearing that its literal meaning would only confuse people. Modern scientific instruments recently established that Earth is shaped more like an egg than a perfect sphere, and that there is a slight flattening around the poles and a slight curving around the Equator.

The West receives “lost” knowledge

An enduring Western myth is that Columbus had to overcome a pervasive belief that he would sail off the edge of a flat Earth by sailing west to Asia. This myth stems in part from compressing the past and conflating the early Middle Ages, when Europe’s belief in a flat Earth was widespread, with the late Middle Ages, when Europe’s knowledge had caught up with and partially surpassed that of ancient Greece and medieval Islam.

During the Renaissance, Europe came into contact with “lost” knowledge by translating Greek and Arabic works. One important book was Ptolemy’s Geography, which accepts Earth’s spherical shape. Geography once more became available in the original Greek, which was not widely known in the thirteenth century. This book was translated into Latin in the late fifteenth century and became widely known. Columbus owned a copy printed in 1479.

By the time of Columbus, the idea of a spherical Earth was widely accepted in theory. Columbus believed this and wanted to sail west to the eastern shores of Asia. Earth’s size was the real issue. Ptolemy’s estimate was as much as 20% too low. Also, he vastly overestimated Asia’s size. The resulting map depicted an Earth with oceans between Europe’s western tip and Asia’s eastern tip, which was well within range of the provisions that ships of that time could carry. Columbus’ estimate of the distance to Asia was wrong, as was his assumption that there was no land between Europe and Asia. Fortunately for him, these two “wrongs” made a “right,” with all of its attendant fame and glory.

The Shape of the Universe

So far, we have given external information (i.e., lunar eclipses and the North Star) about Earth’s spherical shape based upon its position in the universe. If we use this method to determine the universe’s shape, we must observe it in an external manner. As this is not possible, let’s reconsider the question of Earth’s shape with a slight change: Can we determine Earth’s shape by using measurements and observations done only on its surface, and thereby acquire intrinsic information that can inform us of the universe’s shape?

Karl Gauss (1777-1855) answered this question positively by inventing “curvature,” which measures a given surface’s “bumpiness” at a specific point. A flat piece of paper has no bumps and so its curvature is zero. But if we look at a sphere at each point, we see some bumpiness. Gauss called such bumpiness “positive curvature.” Another kind of bumpiness is “saddle-shaped.” We can think of positive curvature at a point as follows: If we put a piece of flat paper on a surface at that point, the surface lies totally on one side of the paper. But in negatively curved space, this cannot happen.

To describe this concept formally (minus some technicalities), assume constant curvatures on the shapes in question. In other words, the shape is totally symmetric and every point has the same amount of bumpiness. There are several ways to describe curvature. Gauss’s formulation for curvature is brilliant. But before that, let’s look at his intrinsic proof for a spherical Earth. Imagine an orchard so large that any deviation from flatness is perceptible. First plant trees on the Equator every 100 kms (the approximate distance between two meridians on the Equator). Then plant another tree 100 kms (the approximate distance between two parallels) north of each tree, and do this several times. If Earth is flat, the distance between them would be same. But since the distance between the two consecutive trees (on the same parallel) decreases, Earth is spherical.

Having seen that an intuitively positive curvature implies a spherical shape, we want to follow this method to get an idea about the universe’s shape. Georg Riemann (1826-66), trying to do just that, invented “curved space” and explained how to compute its curvature. We could launch six probes at equally spaced points along the Equator, and have each of them continually monitor the distance to the two adjacent probes. If space is flat, the distances at any point in its journey would equal the distance from the probe to Earth’s center (an equilateral triangle). For negative curvature, the distance between probes would grow faster than the distance the probe had traveled from Earth; in positively curved space, the distance between probes would grow slower than the distance covered by the probes since leaving Earth.

There are two common misconceptions about the curvature of space. The first one is that curvature is a rather vague or qualitative concept. In reality, it is quite precise and assigns to each point in space and each direction at that point an exact number determined by the shape of the space near the specific location. The second one is that to describe curved space, one must think of it as “curving” into a fourth dimension. This can be useful in visualizing curved space for people familiar with four-dimensional Euclidean space (four-dimensional coordinate space). Unfortunately, science popularizers and science fiction writers often lace this concept with mystical overtones. This is more likely to confuse average people. In other words, measurements made in ordinary three-dimensional space may disagree with the results embodied in Euclidean geometry, for curvature measures the degree and kind of deviation from the Euclidean model.

Riemann also proposed a radically different (non-Euclidian) model for the universe: “spherical space.” This would be the case if space had a constant positive curvature. Based on this, he said that the universe should be a hypersphere (a three-dimensional sphere). The usual sphere is two-dimensional and lives in three-dimensional Euclidean space. In general, n-dimensional sphere is described as in the (n+1)-dimensional Euclidean space, and the set of points whose distance from origin (the point 0) is 1.

The more intuitive way to describe hypersphere comes from the usual sphere. Starting from a point in the sphere called the South Pole, and as we go in a direction in the sphere, we see concentric circles becoming larger until we reach the Equator, after which they become smaller and we finally reach North Pole. The situation is similar in hypersphere. Start from a point in the sphere called the South Pole, and as we go in a direction in the sphere, the concentric “spheres” become larger until we reach the Equator, after which they become smaller until we reach the North Pole. We can generalize this concept for any sphere of any dimension.

Earlier philosophers speculated that the universe was infinite in extent; others (e.g., Plato, Aristotle, Newton, and Leibniz) rejected this as implausible. But the alternative seemed equally dubious: If it did not go on forever, then “like the flat Earth” it had to end somewhere. And, what was beyond that? This model solved the Euclidean paradox of the universe’s “edge,” for if the universe is positively curved, it can be finite in extent and still not have any “edge.” In Riemann’s model, every part of the universe looks just like every other part, as far as shapes and measurements go.

Qur’an 51:47-48 mentions the universe’s spreading out or expansion in space: And the firmament: We constructed it with power and skill, and We are spreading it. This verse reveals that the distance between celestial bodies is increasing, which means that the universe is expanding.

Hubbel’s law

The most surprising discovery of the twentieth century was made by Edwin Hubble in 1929: The universe is not static, but is in a state of rapid expansion. Based upon his observations, he stated Hubble’s Law: Other galaxies are receding from us, the rate at which they recede depends upon their distance, and there is a constant ratio (the Hubble constant) between their velocity and their distance from us.

This law’s most dramatic consequence is what it tells about how we got to where we are now. If distances between galaxies increase as we look toward the future, they must decrease as we go back in time. Each ring of galaxies must have been closer to us in the past; the further away (or back in time) we go, the closer they would have been, and the faster they appear to be moving toward us.

Hubbel’s evidence was limited to a few relatively nearby galaxies. Over the years, however, thousands of observations extended and refined the measurements, and confirmed the general correctness of the velocity-distance relation. Current best estimates are that those galaxies are a billion light-years away (a light-year is roughly 6 trillion miles). Assuming that light always travels at the same speed, those galaxies must have been 1/20 of a light-year closer to us each year in the past. To have ended up a billion light years away, they must have started at exactly the same point as we did “the Big Bang” some 20 billion years ago.

Let’s start by using concentric rings of galaxies at intervals of a billion light-years. Then there are 20 rings, because five rings from us represents galaxies 5 billion light-years distant from us. To see them, we need to see their light that has been traveling for 5 billion years. Thus, we now see their position 5 billion years ago. As there was nothing 20 billion years ago, the outmost ring must the twentieth ring. This might sound paradoxical, as the circles of galaxies seem to grow larger as they move further away from us. However, the paradox is only apparent. Assuming Earth is in the South Pole and that the rings are a sphere’s latitudes, the rings become larger by the Equator and then become smaller until, in the twentieth ring, we reach the North Pole. This time, the rings are spheres and thus fit in the hypersphere. So Hubble’s Law supports our model of hypersphere for the universe.

But how can an expanding universe fit into our picture? In the sphere, the whole surface is expanding, just like inflating a balloon. So the distance from us (at Earth) to the Big Bang is increasing in all directions. In other words, any two points in the universe recede from each other, just as any two points on the balloon recede from each other during inflation.

The issue of time

So far, we have considered the universe’s shape at a fixed time. But, in physics, it is useful to consider space and time together. After Einstein’s brilliant publications about special relativity, Hermann Minkowski (1864-1909) proposed a very useful four-dimensional space-time model as the fabric of the physical universe. In a global picture, each fixed time represents a thin slice of space-time. Like an onion, each layer (assuming there are infinite very thin layers) corresponds to the universe at different fixed times. Given that each fixed time is a hypersphere, the layers are hyperspheres. According to Hubble’s Law, the hypersphere becomes larger as time passes. Just like an onion, the inner layers are smaller and the outer layers are larger.

In an ordinary onion, the layers are usually spheres; in the universe, the layers are hyperspheres. Assuming that the outer-most slice represents the universe at this time, the space-time “so far” is a four-dimensional onion, with layers of the universe at different times. The center of this “onion” corresponds to the Big Bang. We receive the picture of space-time until “this time.” Now, let mathematics predict the future of the space-time, just as Newton’s laws allowed a detailed description of the solar system’s future course. As time evolves, the universe expands, distances between galaxies grow, and gravity weakens. Thus, the space-time curvature diminishes and successive hyperspheres grow at a slower rate.

Two possibilities emerge: The hyperspheres continue to grow indefinitely, although at an ever-decreasing rate, or reach a maximum size and start to contract, in exactly the same fashion as the parallels of latitude on Earth: starting at the North Pole, growing until they reach their maximum size at the Equator, and then begin contracting toward the South Pole. If the universe contracts, distances between galaxies would decrease, gravity and curvature would increase, and the successive hyperspheres would shrink ever faster, eventually contracting into a single point: the “Big Crunch.”

We could then draw a map of the universe as a succession of hyperspheres growing in size for during the first half of its life and contracting during the second half. All space-time would then form a kind of super-hypersphere a four-dimensional object known as a “four-dimensional sphere.”

Conclusion

At a fixed time, the universe should be a hypersphere. When the time dimension is added, space-time should be super-hypersphere, with a “Big Bang” like the South Pole, each fixed time of the universe corresponding to the parallels, and finally a “Big Crunch” corresponding to the North Pole in our space-time model.

Almost everybody has heard that time is the fourth dimension. Even though this concept is easy to imagine, people find it hard to understand because of its mystification by science popularizers. We live in three-dimensional space. This means that I can parameterize the universe such that I can describe any point in it by using just three letters (a, b, c).

Footnotes

1. All of these statements are only approximately true. They would be exactly true if the North Star was precisely overhead at the North Pole, instead of being off center by about 1.
2. The real estimate might not be 25,000 miles, as we do not know the exact correspondence between ancient and current measurements. However, this was a very good estimate for that time.
3. Despite the potential errors mentioned in footnote 2, this also was a good estimate for that time.

In this article, we will delve a little deeper into this magnificent miracle of God: the mathematics of nature.

FLOWERS:

For example, look at the pictures given below. For 1-petalled flowers, we offer white calla lilies; for 2-petalled flowers, we offer the very rare euphorbia; and for 3-petalled flowers trilliums, lilies, and irises.

<cellpadding=”15″ cellspacing=”15″>White Calla Lilly

Trilliums

Did you ever wonder why 4-petalled flowers are so rare, and why everyone gets excited when they find a 4-leaf clover? The reason for this is because such flowers are very rare, for 4 is not a Fibonacci number. Some violets and bluets also have 4 petals.

Flowers with 5 petals are rather common. Among them are buttercups, wild roses, larkspurs, and columbines.

Examples of 8-petalled flowers are bloodroots and delphiniums. Examples of 13-petalled flowers are ragworts, corn marigolds, and cinerarias; those with 21 petals are daisies, asters, and chicories; and those with 34 petals are oxeye daisies, sunflowers, plantains, and pyrethrums.

Some families of daisies, such as the michaelmas daisies from the asteraceae family, have 55 and 89 petals.

Seed and flower heads

The echinacea purpura is a member of the daisy family native to the Illinois prairie. You can see in Figure 1 that the orange œpetals seem to form spirals curving both to the left and to the right. At the edge of the picture, if you count those spiraling to the right as you go outwards, you will notice that there are 55 spirals (a Fibonacci number). A little further toward the center, you can count 34 spirals (another Fibonacci number). If you count the spirals going the other way, you will see that the pair of numbers (counting the spirals curving toward the left and toward the right) are neighbors in the Fibonacci number series.

The same happens in many seeds and flower heads, among them sunflower seeds, daisies, pineapples, and pine cones. The reason for this is that such an arrangement packs the optimal number of seeds so that no matter how large the seed head is, the seeds are always packed uniformly at any stage. As they are the same size in any given area, there is no crowding in the center and no scarcity at the edges.

The spirals form a pattern: The œcurvier ones

appear near the center, while the flatter ones, which are more numerous, appear the further out you go. Thus the number of spirals we see in either direction differs according to the size of the flower’s head. On a large flower head, we see more spirals further out than we do near the center. The numbers of spirals in each direction are (almost always) neighboring Fibonacci numbers!

Let’s observe the spirals in these beautiful arts of the Infinite Artist. Consider the daisy. In the close-packed arrangement of tiny florets in the daisy blossom’s core, you can see the phenomenon in an almost two-dimensional form. As shown in Figure 2 there are 21 (a Fibonacci number) counterclockwise spirals and 34 (another Fibonacci number) logarithmic or equiangular spirals. In any daisy, the combination of counterclockwise and clockwise spirals generally consists of successive terms in the Fibonacci sequence.

The Math Behind It

Botanists have shown that plants grow from a single tiny group of cells right at the tip of any branch or twig belonging to a growing plant or tree. This tip is called the meristem. They grow in size after their formation, but new cells are formed only at such growing points. Cells further down the stem expand, and thus cause the growing point to rise. This means that a growing plant produces seeds at the flower’s center, and that those seeds then push the other seeds outward. Each seed settles into a location that turns out to have a specific constant angle of rotation relative to the previous seed. This constant rotation forms the spirals.

Consider the following case. There are n seeds in the arrangement. The nearest seed is seed 1, the next one is seed 2, and so on. If each seed has an area of 1, we have a total area of n and a circle with a radius of from the area formula (Area= ). Given this, the distance from the center to each seed is proportional to the square root of its seed number. If we call this angle alpha, the angle of seed k will be alpha*k. So we can easily describe the location of any seed in polar coordinates with and theta=k*alpha.

If we chose an angle of 0.15 (54A) the result will be far better. But we will be done again after 20 seeds, for 20*0.15=3, so after 3 complete turns we will be back on the same line. If we choose 0.48, which is a little bit better than 0.15, we will come back to the original line in 25 rotations.

Therefore, speaking logically, if we choose an irrational number we will not return to the original line. Of course we will get close to it, since every irrational number has some kind of rational approximation. In nature, we mostly observe the so-called golden ratio, an irrational (1.618 = ), which is the root of the equation , which is the limit of the ratio of two consecutive Fibonacci numbers.

With this angle of rotation, each seed is rotated approximately 1.618 revolutions from the previous seed (i.e., 0.618 revolutions or 0.618*360=222.5A). Notice how well distributed the seeds appear; for there is no clumping and very little wasted space. Although the pattern grows quite large, the distances between neighboring seeds appear to stay constant. In nature, you can see that plants grow their seeds simply where there is the most room.

It is really amazing that a single fixed angle can produce the optimal design no matter how large the plant becomes. For example, once a leaf’s angle is fixed, that leaf will œdo its best not to obscure the leaves below and œdo its best not to be obscured by any leaves that will grow above it. Similarly, once a seed is positioned on a seed head, the new seeds continue to push the older ones out in a straight line. However, it retains the seed head’s original angle. The seeds will always be packed uniformly on the seed head regardless of the head’s size. The principle that a single angle produces uniform packing no matter how much growth appears thereafter was proved mathematically only in 1993 by the French mathematicians Douady and Couder.

We frequently observe the golden ration in nature. In addition, we can try flowers and flowers, at least mathematically and as models.

Conclusion

We look at nature and see God’s creation. Most people just look at the general design, but others also study the seeds and their designs. As the Qur’an’s first verse tells us to œRead, in the sense of reading the signs in nature (the Qur’an was revealed to a largely illiterate people who had no significant body of written literature), we should understand this as an indication to analyze nature.

As a mathematician, I see that God has arranged everything in nature according to a mathematical order. He puts the maximum number of seeds in a minimum area. Bees use hexagons to store the maximum amount of honey in a minimal space. This fact is even mentioned in Qur’an 16:68: Your Lord revealed to the bee. Those who believe in evolution say that the picture is very clear. But there is a great art in front of us, one which is very well balanced and in perfect accord with mathematical harmony. This shows that there is no luck or chance in the world, and that everything is based on the rules that God has laid down for His creation.

Footnote

1. Fibonacci (Leonardo da Pisa, c1175-1250): The son of a Pisan merchant who also served as a customs officer in North Africa. He travelled widely in Barbary (Algeria) and was later sent on business trips to Egypt, Syria, Greece, Sicily and Provence. In 1200 he returned to Pisa and used the knowledge that he had gained on his travels to write Liber abaci, in which he introduced the Latin-speaking world to the decimal number system. Fibonacci numbers begin with 1,1 and the next term is the sum of the two previous terms. The first ones in the series are 1,1,2,3,5,8,13,21,34,55,89,

References

Mathematics Magazine 75:3 (June 2002): 163-73.

http://ccins.camosun.bc.ca/~jbritton/fibslide/jbfibslide.htm.

G. J. Mitchison, œPhyllotaxis and the Fibonacci Series, Science 1965, 270-75.

P. Stevens, Patterns in Nature (New York: Little Brown and Co.,1974).