Think of yourself as a desert ant. You leave your nest to search for food early in the morning in the deserts of Tunisia, except you do not know where to find food. You, therefore, walk randomly in the desert in a circuitous outward path from your nest until you find food. If you would find food, how do you get it back to your home? How do you go back without having left for yourself any traces or signs in the wasteland, without knowing where you located, and most importantly, without ending up stranded in the scorching heat of the desert? Could you accomplish coming back each day with food? Well, desert ants can.

To find out how ants can do this, scientists observed their behavior, and surprisingly they have found that ants did not follow back on the same trail they randomly took after they left their nests. Instead, ants took a direct route as if they already knew where the nest exactly located. How do these ants find the closest way and shortest distance to their nest from their current locations? Former studies had found that red and forest ants secrete a chemical substance to mark their paths. They leave a trail of chemical scents or visual traces behind them—like leaving a trail of breadcrumbs to help you find your way home. However, the structure of desert sands and conditions are not consonant with containing chemicals that will carry an odor or leave visual cues. Even if such markings have made, it is hard to guarantee that they will remain intact long enough considering the harsh conditions of the desert. As in Hansel and Gretel fairy tale kids who could not return home for the breadcrumbs they had left on the trail eaten by birds. Therefore, these desert ants must be equipped with another cognitive mechanism so that they can return to their nests before succumbing to the midday heat.  

Black desert ants (Cataglyphis fortis) emerge from their nests in the heat of desert sand, which rises to 70 degrees with the rise of the morning sun, to search for the remains of other insects that were not as heat resistant as they are. They can only survive for one hour on the hot sand and under the blazing sun, which means that within an hour, they must find their food and bring it back home without getting lost. The journey is quite arduous and dangerous each day. If the slightest confusion occurs and they are not able to return to their nest in time, then it could cost them their lives.

Scientists conducted a series of research in the scorching deserts of Tunisia to find out how desert ants take their food to their nests in the shortest route possible. Researchers first determined an anthill and plotted the terrain around it to set up a coordinate plane. They observed that the ants left their nests very early in the morning to begin their daily search for food, and many of them eventually found grubs that had been planted by the scientists. However, researchers moved the ants to locations that they had not previously been to after the ant began carrying the food back to their nests. The attempt was to understand whether there was a “sign placement system” within the ants. This system would encourage the ant to find its last known location, in this instance where it had picked up, then find its way back home. However, the ant instead began heading directly to its nest. It was as if the ant determined its position concerning its nest and set off for it immediately. This experiment was repeated on many ants numerous times and with the same consistent results. The ants, as soon as they had placed on the ground, moved to the nest relative to there. With a wondrous intrinsic coding of some neurons in their nervous systems, they traveled the distance between their new location and the nest in the shortest way possible. In addition to this, the margin of error was very nominal; they found their nests with a ten percent error in the average distance of 500-meters and with an error of only two degrees in angle. Additionally, a fascinating discovery revealed that the ants could calculate errors in their navigation systems. As they approach their destination, they would make adjustments if they need to by moving back and forth in parallel lines to reach the nest with minimum error.

Scientists determined that desert ants have about a thousand lenses in their compound eyes (remember that a human eye has only one lens) and 80 lenses in each of their eyes that can detect polarized light that comes from different points in the sky. Polarized light occurs when sunlight enters the atmosphere of Earth, hits air molecules and other particles, and then scatters in all directions. This dispersion leads to polarization, and the light that starts to vibrate in many planes begins to vibrate in only one plane. Therefore, the strongest of them is a distinct polarization that always makes a 90-degree angle towards the sun. The lens system in the eyes of desert ants uses this polarization to form a kind of Sky Map. These ants will occasionally stop and robotically move their heads while returning to their nest. This brief period allows the ants to make this sky map by surveying the sky and making a mental note of its layout. Researchers believe that ants can then calculate the direction that they need to travel to return to their nest. They repeat this movement along the way to continually update their sky maps. If they cannot find their home, then they utilize a patterned search method with a set of circular motions. It means that each ant knows how far it is from their nest at every point of their journey.

Then, how do ants find their direction to the nest? Perhaps they were guided by the position of the sun in the sky is. To test this hypothesis, researchers placed a set of mirrors to make ants perceive the sun in a different state than where it ordinarily would be. It observed that the ants changed their directions according to the new state of the sun. However, this finding raised another question; researchers wondered how the time of day would affect the ants since the sun moves across the sky during the day. However, this finding raised another question; researchers wondered how the time of day would affect the ants since the sun moves across the sky during the day.

In another part of the experiment, the researchers caught the ants after they found the bait, closed a box over them, and kept them inside the box for several hours so that they could not see the sun and its movements. It expected that the ants would have trouble finding their way back after they were released since a long time had passed, and the sun was in a drastically different position in the sky. However, they once again returned home by using the shortest distance possible. It understood that the desert ants were aware that time was passing even though they could not see the sun.

We now understand that ants determine their direction home by using the sun, but we still do not know how they figure out the distance they must travel to return to their nest. Researchers have developed three hypotheses to explore this phenomenon. The first hypothesis was the energy hypothesis. According to this hypothesis, the ants were able to know how much energy they needed on the way back by calculating it they had spent until they reached their food. The depletion of their energy meant the end of their journey. An ant loaded with extra weights to test this hypothesis as soon as it reached its food. The scientists thought that if their body weight increased, then they would not be able to strike reach the nest since they would spend more energy on the return trip. However, in this case, it did not affect the ants, and they returned home in the shortest way possible regardless of their weight.

The second hypothesis was the optical-flow hypothesis. In this hypothesis, it believed that the ants had visual memory, and this was how they remembered the way back. To prove this, scientists prevented the ants from seeing their surroundings by blindfolding the ants when they found their food source. However, the blindfold did not prevent the ants from obtaining the shortest distance back home. As a follow-up to this experiment, the researchers placed an extensive television screen in front of the ants showing an endless desert on the television screen to make the ants feel as if they had crossed the entire desert in this simulation. They used various types of simulations, but the result did not change; the ants found their way.

The last test involved the pedometer hypothesis. It surmised that ants could be counting their steps to determine how far they had traveled. To test whether they were doing so, researchers attached stilts made of hair strands to the legs of one group of ants after they found the food. As their legs now extended, they could move with longer scale steps. Another group of ants had their legs cut below the knee, thus shortened to increase the number of steps needed to walk the required distance back. They then observed the return journey of both groups of ants. The results were astounding; the ants with shorter legs had concluded their course before reaching the nest, while the ants with longer legs ended up passing the nest. Thus, it understood that the ants counted their steps according to the distance they traveled.

The findings reveal that the ants are created with an internal system that keeps track of the steps they take and re-calibrates itself on the way back. People make these complex calculations with measuring instruments and by knowing the laws of trigonometry. However, these small creatures find their way directly back without using any tools or computer applications. They do not use their perception to find direction, and they do not use any other directional methods because they all remember direction and distance as they move forward. If you look at this situation, what would be your simplest explanation? You can only have one definition: These little creatures can measure distances and angles precisely by applying mathematical calculations and trigonometry within their conditions. Since the first day of their existence, these creatures show only a few of the shreds of evidence of the divine power created them out of nothing with wondrous systems and superior abilities in their bodies.

I have put my trust in God, my Lord, and your Lord. No living creature is there, but He holds it by its forelock and keeps it under His complete control. Undoubtedly, my Lord is on a straight path (He governs all that exists and carries out His decrees rightly and with absolute justice). (Surah Hud, 56)

Dolphins produce clicking sounds to navigate, to collect information about their environment, and to locate food. Each and every dolphin has a different sound just like every human being. Distinguishing between different sounds, they have been known to instruct each other, receive instructions, and act accordingly.

Sounds for hunting and navigating

Dolphins send out clicking sounds. When those sounds hit an object, they bounce back vibrations to the dolphins. These echoes allow them to identify where objects are located. It also gives them information about the location of the object and some indication of the shape and size of it. This system is called “Echolocation” or “Sonar,” just like what a submarine uses to navigate while underwater.

How can dolphins analyze the information contained in these echoes?

Dolphins produce sounds with their larynx and a complex system of cavities connected to their blowhole. The sounds used in echolocation are a rapid series of clicks. The clicks contain a wide range of frequencies, but most of the sound energy is in the range between 50,000 to 200,000 cycles a second, or hertz. These high frequencies are necessary for echolocation in water. Because sound waves travel at about 340 meters a second (m/s) in air, and the speed of sound in water is five times greater than in air. The wavelength of a sound of a given frequency in water is five times longer than in air. Dolphins must generate frequency five times higher to achieve the same resolution.

How do dolphins use sound to gauge the distance and speed of objects around them?

The physical phenomenon of sound is defined to be a disturbance of matter that is transmitted from its source outward. Sound is a type of energy made by vibrations. Sound energy cannot be produced on its own. Sound waves move like ripples of water after a pebble has been dropped on the smooth surface of a pond. When any object vibrates, it causes movement in the air particles. This movement, called sound waves, work travel through a medium by passing vibrations from molecule to molecule until the particles run out of energy. 

Sound waves need to travel through a medium such as a solid, liquid, or gas. The molecules in gases are not packed as tightly as liquid. Therefore, the spacing of the molecules enables sound to travel much faster through a solid than a gas. Energy goes into compressing and expanding the surrounding water, occurring slightly higher and lower local pressures. These cause compressions (high pressure regions) and rarefactions (low pressure regions).

A sound wave travels approximately at 1,500 m/s in water. Another phenomenon related to the perception of time delays between two events is an echo. A person can often perceive a time delay between the production of a sound and the arrival of a reflection of that sound off a distant barrier. The time delay between the holler and the echo corresponds to the time for the holler to travel the round-trip distance to the canyon wall and back. A measurement of this time would allow a person to estimate the one-way distance to the prey. For instance, if a dolphin hears an echo in 0.2 seconds after making the holler, then the distance to the prey can be calculated as follows: distance = vxt = 1,500 m/s x 0.1 s = 150 m.

How can any dolphin analyze the information contained in these echoes?

There is still plenty that isn’t known about dolphin echolocation. There are two hypotheses about how dolphins produce sound underwater. Scientists are not sure which hypothesis is correct. According to the accepted views, dolphins have a fat-filled organ in the front part of the head described as a melon. The melon acts like a lens for sound waves, focusing the sound waves into a narrow beam. Dolphins generate a wide variety of clicks. The clicks they use for echolocation are of a higher frequency than those used for other forms of communication. This improves resolution and allows smaller prey to be located. The clicks are generated in a series of interconnected passages behind the melon. When the sound strikes an object such as a prey fish, some of the sound is reflected back toward the dolphin. Another fat-filled cavity in the dolphin’s lower jaw acts as a receptor for this sound. The sound is carried from the fat-filled cavity to the middle ear and perceived by the animal’s brain. Consequently, as soon as an echo from one click is received, the dolphin generates another click. The time lapse between click and echo enables the dolphin to determine the distance between it and the object. The difference in sound intensity received by each ear allows the animal to determine the direction. By emitting a series of clicks and listening to the echoes, the dolphin is able to locate and follow its prey. Yet the dolphin’s sonar is highly advanced and can pinpoint exact information about its surroundings ranging from size, distance and even the nature of the object.

After all these findings, one cannot help but ask, “Who taught science to dolphins?”

References

1. Richmond, Elliot. “Echolocation.” Animal Sciences. 2002. Encyclopedia.com. 9 Sep. 2015<http://www.encyclopedia.com>.
2. http://www.jiscdigitalmedia.ac.uk/guide/the-physical-principles-of-sound
3. Beggs, J., & Thede, D. (2001). Chapter 2. The Science of Sound and Digital Audio in “Designing web audio” book. ” O’Reilly Media, Inc.”.

Our sun is a single star system, but using new technology, scientists are discovering double – and even triple! – star systems

The planets of the sun revolve around a single star, just like the planets in many systems. Revolving around a single star is the general principle, but scientists have recently discovered planets that revolve around two stars, without causing any irregularities. Planets that revolve around two stars are accepted as a new class of planets and according to calculations their numbers in the Milky Way galaxy are estimated to reach at least ten million.

How can this be possible? A planet traveling around two stars enters the gravitational field of each star during its motion, and its velocity and orbit constantly changes.

If stars can shade (eclipse) each other, it is possible for one planet to shade one or two stars. When this event takes place, the planet and stars orbit on the same plane. This intersection on the same orbital plane means that the planet and star have passed in front of each other; we can measure this due to a reduction in the amount of light emitted by the star. If the distance between the two stars is too long, these stars act as if they are isolated from each other. In that moment, the planet that is moving on one of the star’s orbits does not feel the effect of the other star. These are called S-type planets and dozens of them have been discovered in the last decade.

Interesting events take place when stars get close to each other. In such cases, the time required for stars to make a complete revolution around each other is described in days or weeks. The ability of a planet to move in “braided pathways”^[1] that will allow a stable orbit around two stars that are so close to each other cannot be a coincidental event without fine adjustments.

S-type systems are only one type of double-star systems. In P-type systems, the planet revolves around the two stars simultaneously. For this type of planet to travel in a stable orbit, the orbital distance from the stars must be longer than a critical distance. If it is closer than this critical distance, the planet’s orbit becomes progressively unstable, and it is either pulled towards one of the two stars and collides, or gets thrown into outer space. This critical distance is 2/3 of the star’s magnitude.

In a system of a single star and planet, the transit of the planet occurs as if the light makes a periodic movement, such as when a light house rotates around itself. These passes allow us to detect stars. Double-star planet systems are another example of this. It is not easy to estimate the movement of an object consisting of three elements. In a single-star system, the star’s movements are stable; thus, it is easy to estimate the movement of a planet. Yet in a double-star system, the distance between the two stars is much shorter than their distances to the planet; for this reason, these stars revolve at a higher speed around each other than the planet revolves around them. This means that the planet’s rotation is difficult to predict.

As a result, the planetary movement of a double-star system will not be periodical; different than that of a single-star system, the time of transit passes will vary according to the relative motion of the planet to the star. If the planet and the star it revolves around are moving in the same direction, the transit pass time will be longer; but if the star is located at the other half portion of the orbit and traveling in the opposite direction, the transit passing time will be much shorter.

The Kepler spacecraft and telescope that NASA launched in March 2009 is designed for detecting planets that cause reductions in the light of stars when they are passing in front of them. Today, more than two thousand twin star systems that display eclipses have been discovered. Two planets that revolve around stars eclipsing each other every 7.5 days were discovered and called the Kepler-47 system. Along with these double star systems, a triple-star system has been discovered through the Kepler telescope; the properties of this system are extraordinary.

Among these, planet Kepler-47b of the inner region completes its voyage around its stars in less than 50 days. In addition, this planet, which is not visible directly, is predicted to be a very hot planet. Since a foggy layer inhibiting its visualization is found to have formed as the result of methane gas combusting in its hot atmosphere. Kepler-47b, which is three times bigger than the Earth’s radius, is the smallest planet among those that have been discovered in two-star systems.

The planet Kepler-47c of the outer region completes its one full tour around its twin stars in 303 days and it moves in a region that is described as the habitable zone in the Milky Way galaxy. There can be liquid water present on the surface of a planet in the habitable zone. However, just being in this zone does not totally mean that the place is suitable for life. Kepler-47c is predicted to be slightly bigger than Neptune and to have an atmosphere composed of thin and bright water-vapor cloud.

Reference

William F. Welsh, Laurance R. Doyle, “Worlds with Two Suns,” Scientific American, October 2013, pp. 40-47.

S- And P- type planets traveling around two stars

Kepler-47c exists in the habitable zone and liquid water is predicted to be present on its surface.

A representative image of the Kepler 16a/b based on acquired data.

^[1] The Qur’anic verse “By the heaven full of braided pathways, surely you are in contradicting views”(Adh-Dhariyat, 51:7-8) sounds like pointing to this phenomenon.

a

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 heavenly spectacle happening every 6585.32 days, lasting up to 7.5 seconds, can be seen along a track 300 kms wide but cannot be observed with the naked eye

A solar eclipse is a celestial event that takes place when the moon gets in between the earth and the sun. This event has always caught the attention of mankind since the beginning of time and has always been a matter to ponder upon. For example, why can a lunar eclipse be observed everywhere on earth under the night sky yet seeing a solar eclipse is only limited to a corridor 300 km in diameter? A solar eclipse is dependent upon two conditions: First there needs to be an intersection of a lunar orbit with the earth’s orbital plane; second the phase of the moon at the time needs to be a new moon. Because there are 12 months in a year, one would expect 12 solar eclipses, but a 5 degree difference between orbital planes makes this intersection a less frequent event. The diameter of a lunar shadow on earth during a solar eclipse is only 300 km while the shadow of the earth falls on the moon as wide as 12,000 km in diameter.

The sun and the moon, the brightest objects that are most visible to our eyes, are not hanging up there without any purpose. In addition to their many significant effects on our biological, psychological and social conditions, the sun and the moon offer us incredible reasons to be amazed not least during the eclipse when we observe from the earth their complete overlap: a star as big as almost 1.5 million km and a satellite as small as 3,500 km in diameter. The sun and the moon need to be positioned in their orbits with such a precise calculation that this enormous size difference does not get noticed during a solar eclipse by an observer on the ground. This is only possible when both the sun’s and the moon’s distances to the earth are reversely proportioned to their sizes. This fine balance is called “angular diameter” or “visual angle” by scientists. Therefore, in order for a complete solar eclipse to take place, the sun’s and the moon’s angular diameter need to be equal to each other.

If we have to explain this with mathematical expressions:

Lunar diameter / Moon-Earth distance = Solar diameter / Sun-Earth Distance

If we take numbers as below:

Lunar diameter 3,474 km, Moon-Earth distance 376,000 km, solar diameter 1,400,000 km, Sun-Earth Distance 149,000,000 km

Then we get two similar ratios:

3,474 / 376,000 = 0.009239361

1,400,000 / 149,000,000 = 0.009395973

As seen above, the ratio of the two independent and unrelated numbers turns out to be very similar to each other indicating the management of the universe through fine care, calculated fashion and wisdom. The significance of the angular diameter in this solar phenomenon is oftentimes ignored or covered not sufficiently enough in documentaries, books, and journals, whereas it offers a lot for us to ponder deeply over how the entire universe relates to our lives through many apparently irrelevant events. The sun and the moon and their eclipses are substantial reasons for awareness, appreciation and prayer, as highlighted in a Qur’anic verse:

“And the night and the day, and the sun and the moon (all the phenomena and objects you see in the universe) are among His signs (guiding to His absolute Oneness). Do not prostrate in adoration of the sun or the moon, but prostrate in adoration of God, Who has created them, if indeed it is Him that you worship.” (Fussilat 41:37)

A solar eclipse, as do all other things in our material universe, takes place in a world of causations. Yet, it takes place in such mysterious finely tuned measurements that may become a reason for divine testing, and it has been more so in the past for that matter. The Prophet Muhammad, peace be upon him, gave a warning on this issue for us not to fail this test: “The sun and the moon are two signs of God; they are not eclipsed on account of anyone’s death or on account of anyone’s birth. So when you see them, glorify and supplicate God, observe prayer, give alms.” Thus, it is important to observe the universe and use our intelligence to discover the laws operative in nature and the divine wisdom behind those seemingly supernatural events.

No matter how fast or how far a person runs, the horizon will always be beyond them. This being the case, the real distance and depth of the horizon is inside a person, it is in their mind and perception…

A race I will always remember

Not too long ago, when I was still a little boy, I found myself running from my father’s village to my mother’s, and from my mother’s to another and to another, in the hope of catching up with something that was neither a ball, some other toy, nor a bird, but rather the point, the line where the sky seemed to touch the earth. We call it the “horizon.” That line, that “place,” first presented itself to me hiding right behind the trees to the left of my father’s house. I started out that day walking rather leisurely because the distance between me and the horizon seemed so short. When I observed that the sky had moved, or rather seemed to have moved further away, I hastened my steps. Then I noticed that the sky moved further and further away. Well, being determined to reach the place where the sky certainly touched the ground, I kept walking faster and faster until I found myself running.

I ran for quite a while until I realized that “there”, where the sky and the earth met, was still further away, that it would take me more time and effort than I had thought. I went back—I had to go back—to my father’s village, back to my usual village life because I saw that perhaps much more was involved, that maybe much more effort was called for in order to achieve what I desired, namely, to get to the point where I could touch the sky, where I could climb the sky. I went back to the ordinary, the normal life and experience of the village and of my people. But I did not tell anyone, I did not discuss the experience with anyone, even though I did not stop and could not stop thinking about it. I thought to myself that perhaps a week, a month, maybe a year would suffice for me to reach the place where the sky and the earth embraced. I was absolutely certain that right there in front of me, over there, not too far away, the sky touched the ground. And I thought that perhaps all I needed to do was keep walking, keep running, and keep racing forward, without stopping, without interruptions, without distractions in order to get to where the sky kissed the ground.

Today, thirty-five years later, I have realized that I was not wrong. I was right. The sky did touch the ground. It touches the ground all the time. You may ask “but where and how?” The sky touches the ground in our perception. Look across from your window into the distance. What do you see? Or, go outside and look in the distance. What do you see? The sky is right there, over there, touching the ground, the road, the houses, the trees, the mountains, the sea, and remaining there. But keep in mind that this is all happening in our perception. In perception, things are the way they appear, the way they seem. No rigorous, critical thinking is involved. And this happens so many times, and in fact is happening now; it happens every time that we are not thinking deeply, with attention and effort. It happens every time we fail to allow other perspectives, other possibilities and other possible interpretations to emerge.

The sky touches the earth, embraces and kisses the ground, right there in a fixed position, as long as you do not move. Once you move, it moves. And when you run after it, it too runs, not towards you though, but rather away from you. If you stand still, it stands still. If you stay where you are, it remains where it is. If you move even an inch, it will move. It will never allow you to catch up with it, to touch it; it will never allow you to possess it, to tame it; it will never allow you to take possession of it. And yet, it is always there, “putting everything into perspective.” By that I mean the horizon enables us to see, for without horizon one cannot see much of anything. Think about it! Everything presents itself in horizon. Everything dwells in the horizon, everything is within the confines of the horizon, and depends more or less on this phenomenon. And if I may borrow an expression from Saint Paul’s speech at the Areopagus (Acts 17:28) and be at liberty to use it as I see fit in this context (just as some scholars say he himself was at liberty to do with the same expression from the writing of Epimenides of Knossos (6th Century B.C.)), one can say that “that in which we live and move and have our being” is the horizon.

Standing still, remaining in one fixed position is not in the nature of the horizon. Its every stop (or what appears to be its end, its boundary) is temporary and transitory, like a pilgrim’s stop on a journey whose destination is still far away. It keeps moving, and it invites us to keep moving too, keep working, keep meeting people, keep exploring, keep digging, keep sowing, keep cultivating, keep harvesting, keep looking, keep reading, keep writing, keep thinking, keep talking, keep wondering.

We hear, not infrequently, the expression, “on the horizon/in the horizon.” What does it mean? It means in view, in the possible future, in sight. That which is in or on the horizon appears close, and seems to be approaching; it is as if it’s right there among the things that one hopes to do soon, as something squarely within one’s reach, among the things that one’s abilities can handle. What is in the horizon, then, is something that appears “present” and seems quite achievable.

What is a horizon? And what does it do?

A horizon is inseparable from a living, perceiving human being who is in the open or in the frontier of the open. There are no horizons in closed spaces, closed places. The distance between a living human being and the line where the sky and the earth meet is very wide. It is infinite. It is far, far away. You can only measure it with your eyes, your mind and your soul. You can figure out how long it is only to the extent that your eyes, your mind and your soul can go. An application of any other measuring device will only frustrate you because the moment you start going after it to measure it, it will recede. But the truth is that what you are actually seeing of the horizon is only a small part of it. The bigger part is on the other side of the horizon. Every horizon has at least two parts: a front and a back. The front of the horizon consists of the part you are seeing, and its back consists of the part hidden from you because of the hills and mountains, the earth, the road, the trees, the sea. In fact, the line where the sky seems to touch the earth is really only a perceived curve or a perceived point of contact, but the horizon really goes far and farther away, without end: it stretches into infinity.

All the things we are seeing are in fact standing in the way of the horizon. Similarly, all the things we are thinking right now, all our thoughts and ideas, everything that is presently on our minds can be an obstacle to a deeper and fuller understanding and appreciation of the horizon. We have to let go of all of these things in order to begin to have an idea of the depth and richness of the horizon.

For now, let us focus on the part of the horizon that is visible to us. It is a world, the world that we live in or would like to live in. Normally, it consists of people, people of different religions and/or of no religion at all, people of different languages and cultures, different experiences, different states and walks of life, different situations and aspirations, people driven by different desires, values and visions, people of very deep opinions, inspirations, beliefs and deep convictions other than our own, people heading in a thousand and one directions. This world, this visible side of the horizon also includes animals of many different types and habitats, which eat different kinds of food and have different spans of life. It also includes many different trees, bushes and flowers, and different types of grasses, etc. Mountains and hills and valleys too, rivers and big oceans, streams and creeks, are all part of this side of the horizon. Small and big houses, low and high buildings, shelters and palaces, mud houses and ghettoes are all part of this side of the horizon that we are seeing. But we do not actually see everything that we know is out there, that is all around us, that is over there in front of us…

How do we even know that there is anything out there, that other people are out there? A long walk, travels, meeting people, doing business with people, education, etc. confirm that there are other people out there, other lifestyles, other ways of thinking, other ways of doing things, other attractions, other things that people consider as very precious and worth dying for. We read about these things, have actually met and seen them with our own eyes, have lived with people of different orientations and values, have had some great opportunities to exchange ideas with them. But neither our reading and studying nor our investigative and explorative eyes can exhaust the visible side of the horizon because even the visible side has its own invisible aspects and invisible faces. Let us take for example persons, situations and objects.

From time to time, a person whom I have known for many years, not only surprises me, but also seems to be a surprise to herself/himself whenever s/he says something or does something I could never have thought or imagined her or him doing. And people of this nature are not uncommon.

How about situations? They are similar. Even the most familiar situations often have aspects that are new and different, which we can see if and when we look with more attention and care. And the moment we become used to these, even newer different aspects of the same situation emerge. The same goes for things such as books, clocks, chairs, doors, and so on. A book often presents us with information that we did not see the first time we read it. And if you read it again, you will again see something you missed the second time you read it. If you wish, you can read it again and again, and you will see something new every time. The book will never fail to make you see something new and/or think something new.

Can a chair or a door do something similar? That is, can a chair or a door make you see something new or think something new every time you encounter them? Let us see. A chair, unlike a book, seems to have no generative power. It seems mute and sterile. But can a chair speak and make us think? The answer is yes, it can speak and make us think. No one would disagree that the chair of Pontius Pilate, the chair of a Court Judge, the chair of Saint Peter, and so forth do have a powerful message. Although these chairs I have cited are special, every chair can say something to us and really make us think. For example, chairs for children and for adults make us think different thoughts, which by the way, make us give children appropriate chairs and to adults what is suitable for them. If we did not think differently of these chairs, chances are we would give adults the chairs meant for children and vice-versa, or give the same kind of chairs to everybody, children and adults alike, seriously compromising comfort. And some chairs would even fall apart (that is, if children’s chairs are given to heavy people like me to sit on).

Doors too make us think. For example, the Door of No Return in Goree Island in Dakar, Senegal, and the Door of Hope in Johannesburg, South Africa, makes every visitor think. But again, although these specific references are special, every door, including those that may seem unimposing and insignificant, can really make us think. Every door has a message.

The bottom line is that even the most visible side of the horizon can have aspects that may not be totally obvious and immediately accessible. Therefore, the visible, that which seems completely clear can still make us think because it often has layers, folds, dimensions, messages that lie beneath its surface. There are always other meanings, other messages behind the obvious. And the moment we finish harvesting one message, the moment we finish reading one meaning, the horizon presents us another one, and yet another, and so on and so forth. Inexhaustible indeed, this horizon can constantly give new meaning, hope, color, shape, style, texture, depth, taste and strength to our lives for endless joy and delight, even under very difficult circumstances. Why? Because the horizon has power to liberate us from the present, the immediate, the obvious. As it draws back, so to speak, that is, when we attempt to respond to its invitation into the open, when we dare to go after it, go with it into the deep, when we allow ourselves to move with it and flow with it, then it can open new doors, generate new ideas, launch new beginnings, reveal inroads, illuminate new bridges, disclose exits, uncover new faces, make terrains of other possibilities visible, make cooperation and collaboration possible, make teamwork possible, bring along other solutions, other fertile soils. With the horizon, there are no closed doors, no human being is a finished project, no done deal, no finished once-and-for-all discussions, no insurmountable barriers. The horizon’s open field stretches into infinity.

All of this is but an invitation to read between the lines, i.e., “to resist simplistic interpretations that dogmatically ascribe fixed significations to [things]” (G. Weiss, Refiguring the Ordinary, Indiana University, Bloomington, 2008, p.58).

It is about the need to go on researching other possible meanings and interpretations of a text, to go on searching for other possible answers to certain problems, to appreciate the expanding limits, and to devote more time and energy to the lifelong project of exploration of self and of the world (and of God) (see P. Okogie’s “Horizon: the birthing world” in the Journal of Horizons of Horizons, Vol. 1, no. 1, Duquesne University, Pittsburgh, 2012, p.10).

Rev. Dr. Okogie is Assistant Professor of Philosophy and Bioethics, University of Saint Anselm, Rome, Italy.

Above all, it should be said that this saying is weak in regard to the hadith criteria. However, there is a verse in the Quran that expresses the same idea: “In the creation of the heavens and the earth, and the alternation of night and day, there are indeed signs for the people of discernment” (Al Imran 3:190). In one hadith the Messenger of God emphasizes the importance of contemplation: “Whoever reads this verse and does not contemplate on it, shame on him.” In addition, it was reported by Umm Salama and-according to another narration-Aisha, that the Prophet cried when this verse was revealed or when he was reading it.

Contemplation has a very important place in the life of a believer. However, for this to be the case we must understand what contemplation means. First of all, contemplation is based on prior knowledge. Blind and ignorant contemplation is dry imagination and in time it will lead to frustration. Later, a person will begin to see such a practice as meaningless. For this reason, a person must first be familiar with the subject they are going to contemplate or, in other words, they must have some prior information.

Understanding the orbit of the moon and stars, their relation to humanity, the revolution of atoms which make up human beings, and their movement is a step towards contemplation, but looking at the movement of the moon and sun and becoming overwhelmed with poetic inspiration about the mind-boggling beauty of the universe is not contemplation. There are a number of lonely, strange, handicapped naturalist poets who think like this and plunge into their imagination. They are not contemplators; rather they are fanciful people who have lost their hearts to Mephistopheles.

They also can sometimes think and talk about the beauty of the universe. Worldly beauty can be made to be legendary with words, inspiring people to feel and hear the beauties of Heaven. Sometimes poets can write such epics about the splashing of water, the tapping of raindrops, the rustling of trees and the chirping of birds that a person feels as if they are in the middle of the heavens. However, this is not contemplation; moreover, it promises nothing for the life of the heart and spirit. In this way no advances are made and one has not passed behind the veils. There is no benefit from such contemplation. Regardless of how deep the dreams are, such contemplation gains nothing for a person.

As mentioned above, before contemplation it is necessary that there first be some information. In respect to the knowledge humanity has now attained, people will make new syntheses and analyses with the previous knowledge, probing deeper and arriving at different conclusions. Using these conclusions as an introductory basis for future conclusions, new results will be produced. These new results will be contemplated more deeply; one-dimensional thinking will become multi-dimensional and multiple-contemplation will be achieved. All of this is dependent on there being information. It is impossible for people to contemplate without information.

For this reason, it is necessary to do a lot of reading. Later, it is necessary to study the path and method of contemplation and finally the rules that are operative in nature and the signs of creation therein should be studied so that we can create the possibility of steady and sound thinking.

If a person contemplates soundly for one hour, the fundamental principles of faith will develop in that person. Later, that person will love God and a profound love for the divine will appear in their heart. Meanwhile, they will attain spiritual pleasure and take flight towards the beyond. Sometimes with this kind of contemplation a person can reach a horizon that another person has not reached with a thousand years of worship. If one with such an understanding and consciousness does not turn towards their Lord, then even after thinking superficially for a thousand years, the distance they will cover will not equal the distance covered by one hour of contemplation. However, this should not be understood to mean that this one thousand years of worship was in vain. For in God’s presence neither a bow or prostration or standing or a short rest between movements can be lost. In accordance with the verses, “whoever does an atom’s weight of good will see it, and whoever does an atom’s weight of evil will see it” (Zilzal 99:7–9), everyone will gain something in accordance with their actions. A person who performs worship will have fulfilled their devotion to God. However, they will not have gained the depth that is derived from contemplation. In this sense, contemplation is worth a thousand years of worship.

Everyone can broaden their ability to contemplate with portions of the scripture and remembrance, and they can strengthen their relationship with God. Who knows, maybe because of the enthusiasm that this contemplation will give us we can succeed in renewing ourselves. May God reform us inside and out!

Finally, it is also asked: “Do verses that direct one to contemplation and silent prayer count as contemplation?” If the meaning of these is not understood, then, although one will receive merit for them, they are not contemplation. For contemplation stems from reflection and means bringing together events from yesterday and today, making a synthesis, and establishing a connection between the causes and effects. Strengthening our relationship with God is the most important fruit of this. Any remembrance or verse or, in fact, even listening to the scripture from the mouth of Gabriel himself would be merit, but it is not contemplation. To be considered as contemplation there must be a concentration, focus, a serious investigation and a deepening and strengthening of our relationship with our Lord.

What is most lacking today is contemplation. In this respect, it is not an exaggeration to say that in general believers are deficient in contemplation.

A being that covers half the remaining distance with every step can reach its destination only if it can walk for infinity. When the ability to walk is limited, irrespective of the length of the steps taken, one will only be able to cover half the remaining distance, not the entire distance. In other words, there will always be a distance that remains to be covered. To cover more than half would be nothing less than attempting the impossible, because no being lives long enough to do this. With every step that the being moves forward it can only cover half the distance between the location and the destination.

In the light of this mathematical perspective, we can analyze the deeds we carry out and the steps that we have already taken, and those that we will take in our journey through life that is to be carried out towards God. I wonder if the steps we have already taken are enough to acquire His love and consent at the end of the journey. Answering this question in a conclusive way is difficult, because in the end this situation depends on God’s will. Moreover, God informed us of what needs to be done when he sent the Prophets and Books. Prophet Muhammad, peace be upon him, encouraged us to increase our steps in one of his hadith: “He whose two days are equal is at a loss.” As life passes by, we may be satisfied with our performance so far and we may be sure that we will reach our goal, but if our steps which we make for the sake of God are abating, then we are deceiving ourselves. After some time, our steps become so small as to disappear and it becomes impossible to attain our goals. There is no doubt that such a break in our actions creates a lack of progress, and this in turn induces us to take no further steps. In this saying the Prophet, peace be upon him, highlights this danger and advises us to take more steps than the day before.

In another hadith qudsi (a saying uttered by the Prophet but the meaning of which belongs to God) related to the subject, the Prophet describes how to acquire God’s love in the following manner:

“My servant draws not near to Me with anything more loved by Me than the religious duties I have enjoined upon him, and My servant continues to draw near to Me with supererogatory works so that I shall love him. When I love him I am his hearing with which he hears, his seeing with which he sees, his hand with which he strikes and his foot with which he walks. (I protect her/him from hearing, looking at, touching forbidden things and walking on the wrong path.” (Bukhari, Tawhid, 15)

Certainly, there are occasions when we become so enthusiastic that we lose ourselves in the desire to gain the consent of God and to be reunited with God. On special days and nights and at holy times, we push ourselves; at such times we might perform supererogatory prayers. We hope that God the Almighty accepts these prayers; but if this worship is short-lived, it will not be enough to help us reach our goal. As we can understand from the above hadith, what is important is that prayers are constant. In another hadith, the narrator Abdullah bin Amr bin As reports that our Prophet, peace be upon him, told him “O Abdullah! Do not be like such and such a person who used to pray during the nights but gave up later” (Bukhari-Muslim). Again, according to a narration by Aisha, the Messenger of God, peace be upon him, carried out twelve cycles of prayer to compensate a night in which he had been unable to pray because of pain or some other reason (Muslim).

All of this shows us how important it is to be steadfast in prayer. Taking control of one’s carnal self, the believer should walk toward God with constant steps. To attain the prosperity of the servant described in the above hadith qudsi, a person should make obligatory and supererogatory prayers a habit. Although sometimes the carnal self, nafs, and the Devil try to imprison one in hopelessness, the believer should do whatever they can in order not to lose their zeal and enthusiasm. Even if, from time to time, they stumble or fall, they should never fall into a whirlpool of despair and should not be overcome by pessimism. Thoughts about the brevity of their steps or the inadequacy of their worship should never slow the servant down nor should they be a reason for the servant turning back on the road to which they have devoted their lives. We should not forget that “our Lords’ most beloved worship is the one that is consistent, even if it is small.”

Physicists study on the biggest and smallest physical measures, on the strongest and weakest forces, and they have calculated the ratio between some of them and attained results close to 1040 several times. For example, it has been proven that “strong nuclear force,” which keeps protons and neutrons in the atomic nucleus together, is 1040 times stronger than the force of gravity. Although some consider this situation a result of coincidence, there are also some people who have shown the courage to question the accuracy of this result and open it to discussion. Since then, obtaining the same number several times has inevitably led to the belief that the number was determined and calculated before. This situation resembles the situation of a chess player who hears somebody telling him the opponent’s next move, or the situation of a composer who hears a melody from upstairs that perfectly fits his lyrics while he is trying to write the melody for his lyrics. Is it not amazing when somebody says what is going to be especially at a time when you least expect such a vision? Questions emerge: Have all actions and incidents in the universe and the values corresponding to them been determined in advance? Is there a certain logic behind the behavior of materials without intellect or consciousness?

Perhaps when Comte de Buffon (1707–1788) started to do research into probability calculations concerning falling matches and needles three centuries ago, he did not think that he would make such an astonishing discovery. According to his calculations, the probability of dropped needles hitting a pair of parallel lines that are drawn a certain distance apart is proportional to the number pi (&#960;) (Figure 1–2). When the distance between the parallel lines are drawn the length of a match, this probability becomes exactly 2/&#960;. This was a theoretical result that was calculated on paper, but trying it out would raise interesting results. In other words, when a certain number of tests were conducted, it could be expected that a number of matches equal to the number that was found through the theoretical calculations would hit the lines; and, indeed, that was what happened. In addition, mathematicians found another way to calculate pi by using this method since the ratio of the number of matches or needles that hits the lines to the total number of matches or needles should give a pi-proportioned number. In 1901, Mario Lazzarini threw one needle 3,408 times and, as a result, got the ratio 355/133 or 3.1415929; the difference between this value and the real value is only 0.0000003.

The experimental proof of this fact is not difficult. When the experiment, which has been conducted thousands of times up to today, was first tried by a group of mathematicians dropping 3,000 needles, the number of the needles that touched the lines was close to 1,900, which was the desired result, and the result was amazingly found to be proportionate to pi.

Although the real relation is like the equation given in Figure 3, when the length of the needles and the distance between the lines are equalized, the desired ratio becomes 2/&#960;. What does this mean? Does the number pi, which was created with the universe and which we meet in different fields, play a role in showing the manifestation of the Majestic Will about where an object will fall-through having a result that can not be explained by coincidence? Is falling not an ordinary incident?

While this reality makes even falling an extraordinary incident, it opens a perspective on understanding the reality behind the verse: “…it was not you (O Messenger) who threw but God threw,” which was revealed about the Battle of Badr in the Qur’an. Actually, it is impossible even for a leaf to fall without the knowledge and the calculation of Our Lord, who is closer to us than our jugular vein.

Let us think about a group of creatures that lives with different physical laws in a different universe. Assume that they live on a flat, circular world (Figure 4) and their steps get longer when they come close to the center. For this kind of creature, the shortest distance between two points is not a straight line as it is for us (A–B). Since their steps get longer as they get closer to the center, they travel close to the center. Yet, since they make the way a little longer in this way, the shortest distance would be an oblique line that takes these two variables into account and that passes by partially approaching the center. So, what would we think if we saw these creatures walking in this way all the time? Or if we knew that the creatures acting in this way were inanimate beings? In these circumstances, we might wonder whether these beings are very intelligent or whether One who knows and sees everything, and is present in every place at every time, directs them.

For a soccer forward to find the best time to attack when he is facing the goal keeper or for a tennis player to choose the best timing and position to hit the ball requires a fine calculation. In tennis, the player sometimes approaches very close to the net to meet the ball. In this way, the player gains great advantage since, by his or her positioning, the player reduces the area into which the ball can fall to the minimum, and increases his or her own chances of returning the ball (Figure 5). Nevertheless, since the ball reaches the player faster and harder, there is also a raised probability of the player’s failing to return the ball. Therefore, advancing right up to the net may not always be advantageous. Thus, the best position for the player may lie at any point between the net and the baseline when area and speed variables are considered. Similarly, the most advantageous point for the goal keeper lies between the attacking forward and the goal line, at a point which depends upon the variables of the speed of the ball and the area.

Naturally, we do not find tennis and soccer players’ positionings as described above strange since we expect them, as reasonable people, to play in this way. Yet, how would we interpret and explain it if we saw inanimate things acting in the same way? There is a phenomenon that applies this logic consciously but itself does not have consciousness. A phenomenon that astonishes people: light.

Let us think of a rectangular racetrack with points A, B, C, D. While the shortest distance for a horse that will run from one end of this racetrack to the other is the AC diagonal when the ground is homogenous, there will be a reroute if the ground is not homogenous. Assume the length of the racetrack is 80 meters and its width is 60 meters. Half of it is grass and the other half is sand (Figure 6). Also, assume the horse’s speed on the sand is half of its speed on the grass (it runs 10 meters in 1 unit of time on the grass). Under these circumstances, the horse will run the AC diagonal in 15 units of time while it will run AEC route in 14.5 units of time. The ABC route is much longer. Thus, any route which passes between these two routes will be shorter than these two. The point O, which the shortest route (AOC) passes, will be between the points M and E. When we look carefully, we understand that this is the route light follows as it enters environments of different densities; for example, the route it follows when passing from air to water (see a spoon’s broken image in a water-filled glass). As you see, light finds that specific mysterious point and follows that particular path. In other words, while entering different environments of varying densities, it finds the shortest way and follows it in an amazing way.

All these detailed calculations and functioning with great wisdom show that even inanimate beings and atoms are in the hands of a Majestic Will.

Every atom contains two truthful testimonies to the Necessarily Existent Being’s Existence and Unity. Despite being powerless and insentient, it bears decisive witness to the Necessarily Existent Being’s Existence by carrying out important duties and functions as though it were conscious. It also testifies to the Unity of the same Being, Who owns all material and immaterial dominions, by conforming to the universal order in general, and to the rules of each place it enters in particular. It settles in every place as if it were its homeland. All of this shows that the One Who owns the atom owns all the places it enters. By carrying out very heavy duties incompatible with its size and weakness, the atom shows that it acts at the command and in the name of One with absolute power. (The Thirtieth Word, Second Point, Risale-i Nur Collection)

Notes

1. See Al-Anfal 8:17.
2. “… And He knows whatever is on land and in the sea; and not a leaf falls but He knows it” (Al-An’am 6:59).

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.