The teeth of a tiny mollusk (Patella vulgata), which is a species of sea snails, have been found to be some of the strongest biomaterials in the world. Also known as limpets, these mollusks are a very small crustacean, often around 0.05-2 cm in size with a large cone shell and possess an incredibly complex system of teeth that dazzles the mind.

Research has revealed that the tensile strength of the sea snail’s teeth is higher than that of spider silk and is comparable to only the strongest commercial carbon fibers. It was found that the teeth of sea snails scraping algae off of rocks showed a tensile strength between 3 and 6.5 GPa (gigapascals). Spider silk roughly reaches a tensile strength of about only 1.3 Gpa. Scientists say that the snail’s teeth can even withstand the pressure that turns carbon into diamonds. Studies have determined that, to our current knowledge, there is no other material of this size (roughly 100 μm micrometers) with as much strength and durability.

This exceptional durability has led scientists to do research on the structure and functioning of these teeth, and the studies showed fascinating results.

The role of teeth in nutrition

Sea snails have a special tongue, called a radula, which they use to scrape off food from rocks. The most important feature of the radula is that it contains more than 100 rows of iron-mineral teeth. However, those used for food intake consist of only 10 rows on the outermost part of the teeth. During eating, a tremendous mechanism operates: the teeth are constantly repositioned according to their conditions of maturation and wear. Worn teeth are replaced by newly matured teeth over the course of 12 to 48 hours to ensure that fresh, sharp teeth are used instead of dulled ones.

This wonderful displacement system operates in a similar way to the movement mechanism on a conveyor belt where the teeth begin to grow primarily in the posterior part of the radula. Meanwhile, they are strengthened and matured by iron mineralization. When this mineralization is complete, they are moved towards the front of the radula. In this way, completely matured teeth are permanently retained at the far-front scraping area. During the scraping process, the matured teeth wear out at a rate equal to the growth rate. In the meantime, a new set of teeth begins to grow. By means of this magnificent cycle, new teeth are constantly created and matured so that there are no disruptions in nutrition.

Biomineralization

The structure of the sea snail’s teeth is also a masterpiece of material science. The dazzling durability of its structure provides optimum strength when scraping food off of rock surfaces.

Although the exact process of biomineralization of the teeth is not known, it is believed that it involves reactions of dissolution and re-precipitation. When the non-mineralized matrix is examined, well-arranged and densely packed chitin fibers are observed that are only a few nanometers apart. The matrix is a structure which keeps the reinforcing material together in layers that are composed of different materials. This organic matrix serves as a framework for crystallization in the structure of the teeth. In the mineralization system, the basic macromolecule α-chitin component is created first. The first mineral that then precipitates is the “goethite,” i.e. the aqueous iron-oxide mineral, which crystallizes parallel to the chitin fibers. These crystals are nucleated on the chitin fibers and formed between them by pushing and pulling the fibers. This way, crystals placed in order cause biomineralization of the structure.

It was found that 80% of the overall volume of the structure is composed of these crystals. The gap between the crystals and the chitin matrix is filled with amorphous silica (SiO₂). The iron contained in the aqueous iron-oxide mineral is the metal that constitutes the largest proportion of the composition. Other metals such as sodium, potassium, calcium, and copper are present in different proportions depending on the sea snail’s exact geographic location.

Critical factors in durability

The most important reason that the sea snail’s teeth have such high durability is because the fibers of the aqueous iron-oxide minerals in the teeth are nano-scale. This is due to the fact that materials of this size are not affected by the conditions that reduce strength.

Another critical durability factor is the small length of critical fibers. Critical fiber length is a parameter that defines the length of a material required to transfer strain from the matrix to the fibers at the time of external pressure. To achieve maximum strain, the length must be greater than the critical length. Materials with a large critical fiber length can hardly reinforce the matrix because most of the strain is not transferred to the fibers and remains on the matrix. On the contrary, materials with smaller critical lengths can transfer the strain on the matrix to the fibers. Therefore, they serve as an effective reinforcement for the matrix.

Fibers of aqueous iron-oxide minerals are of a critical length of 420 to 800 nanometers. This is much smaller than the length of the fibers in the teeth of about 3.1 µm (micrometers). This shows that nanofibers are an effective reinforcer for the matrix and contribute greatly to the ability of the teeth to bear loads.

Besides the structure and composition of the snail’s teeth, its morphological shape is also important in providing strength. It ensures that the strain is evenly distributed all over the tooth.

Modeling of biomaterials

All these studies indicate the presence of high-strength composites, which is when a material obtained by combining two or more materials with different physical characteristics, in nature.

Sea snail teeth, which have been created as a highly resistant and strong biomaterial, act as an inspiration for engineering and material science. Their characteristics, such as content and design, are expected to be modeled in areas that require durability and rigidity.

These marvelous systems found in the natural world, sometimes in creatures as tiny as a snail or mollusk, serve as a reminder that nature is filled with wonders for us to explore.

References

· Barber, Asa H., Dun Lu ve Nicola M. Pugno, Extreme Strength Observed in Limpet Teeth,  Journal of The Royal Society Interface, April 2015, DOI: 10.1098/rsif.2014.1326, PubMed.

· World’s Strongest Natural Material Discovered, How It Works, Imagine Publishing, No. 71, p. 11.

· en.wikipedia.org/wiki/Limpet
www.iflscience.com/plants-and-animals/worlds-strongest-natural-material-limpet-teeth/

· www.newworldencyclopedia.org/entry/Limpet

· Barber Asa H., Lu Dun and Pugno Nicola M. “Extreme strength observed in limpet teeth.” 12. J.R. Soc. Interface. http://doi.org/10.1098/rsif.2014.1326

Until today, almost all of your organs and systems introduced themselves and explained the great artistry in their creation along with their wisdom and precision. Certainly, these were not just for your information. Of course, it is important for you to know about your organs and their duties, and for you to live accordingly with this knowledge. However, its main purpose has been to introduce you to your Lord, who created you and all living and nonliving things perfectly. Just like seeing a work of art and not appreciating the artist is a twisted view, so is seeing the art exhibited on the body of the world’s most dignified entity, the human being, and not appreciating our Lord. It would just be a worthless and pointless heap of knowledge.

Today, we will look at the human body statistically, have our last lesson, and say goodbye.

Before we talk about the systems and organs that make up your body, you should know that it is a blessing that God didn’t leave you in nonexistence, and put you into existence. Then, you should know that it is also a blessing that He didn’t leave you as inorganic molecules, but created you as a living organism. For you to understand better, I would like you to look carefully at the delicate measures of the numbers I will give you in the tables below and to realize how high your value has been lifted.

The weights and percentages of inorganic elements in a 70 kg human body:

Oxygen…….. 44 kg……. 63%
Carbon……. 14 kg……. 20%
Hydrogen……. 7 kg……. 10%
Nitrogen……. 2.1 kg……. 3%
Calcium……. 1 kg……. 1.5%
Phosphorus……. 700 g……. 1%
Potassium……. 170 g……. 0.25%
Sulfur….. 140 g……. 0,2%
Chlorine……. 70 g……. 0.1%
Sodium….. 70 g……. 0.1%
Magnesium.. 30 g……. 0.04%
Iron…… 3 g……. 0.004%
Copper…… 300 mg……. 0.0005%
Manganese….. 100 mg……. 0.0002%
Iodine……. 30 mg……. 0.00004%

The total percentage of trace elements found in the blood serum and in enzymes, such as zinc, cobalt, cadmium, molybdenum, nickel, lead, fluorine, selenium, mercury, and aluminum, is 0.80526%.

As you can see, 76% of you (53.1 kg of oxygen, hydrogen, and nitrogen) are gases that dissolve into the air. These aren’t worth anything because there are plenty of them in the air. From 14 cents per kilogram, 14 kilograms of carbon (coal) is worth around 2 dollars. One kilogram calcium (lime) is worth around 12 cents. 140 grams of chlorine and sodium together (salt) is worth around 3 cents. All of the other elements (such as iron, copper, and magnesium) are worth a handful of soil, because they are found easily in soil, and there is only very little of them in the human body. So in total, your elements are worth $2.15.

Let’s increase your value a little bit! Our Lord didn’t leave you as elements; He turned you into organic material with very large molecules, such as protein, fat, carbohydrates, and vitamins. That gives us the table below:
Organ…. Water (%) …. Fat (%)…… Protein (%)…. Ash (%)
Skin…… 64.68…… 13.00…… 22.10…… 0.68
Skeleton…… 31.81…… 17.18…… 18.93…… 28.91
Teeth…… 5.00…… 0.00…… 23.00…… 70.90
Skeletal muscle…… 79.52…… 3.35…… 16.50…… 0.93
Brain-Spinal cord…… 73.33…… 12.68…… 12.06…… 1.37
Liver…… 71.46…… 10.35…… 16.19…… 0.88
Heart…… 73.69…… 9.26…… 15.88…… 0.80
Lungs…… 83.74…… 1.54…… 13.38…… 0.95
Spleen…… 78.69…… 1.19…… 17.81…… 1.13
Kidneys…… 79.47…… 4.01…… 14.69…… 0.96
Pancreas…… 73.08…… 13.08…… 12.69…… 0.93
Intestines…… 79.07…… 6.24…… 13.19…… 0.86
Adipose tissue…… 50.09….. 42.44…… 7.06…… 0.51
Other tissues…… 70.40…… 12.39…… 16.06…… 1.01
Blood and lymph…… 93.33…… 0.17…… 5.68…… 0.94
Total…… 67.85…… 12.51…… 14.39…… 4.84

If you wonder about your value as water, protein, fat, and ash, you can calculate it according to a 70 kg person. If you do this, you can see that you are made up of 47.495 kilograms of water, 8.757 kg fat, 10.073 kg protein and 3.388 kg ash (mineral salts). Since the water in you is dirty and not clear, it isn’t worth anything. Your minerals and ash aren’t worth anything because there are plenty of them in soil. For $1.42 per kilogram, your fat is worth around $12.86. Your protein is worth around 16 kilograms of lamb, which costs around $36.57. So when you are elevated from elemental material to organic material, your value rises up to around $50.

Of course, our Lord didn’t leave you like this. He created you in the form of organs and tissues, which carry out miraculous tasks so that you can stay alive. Now, let’s see the groups of trillions of differentiated cells:

Total number of cells in the human body………… around 100 trillion
Number of cells that die in one second…………around 50 million
Number of cells created in one second…………around 50 million
Number of cell types…………more than 200
Number of red blood cells in 5 liters of blood…………25 trillion
Height reached by putting all of our red blood cells on top of each other…………around 60.000 km
Length reached by putting all of our red blood cells side by side…………192.500 km
Red blood cells’ surface area………..more than 1000 m2
Number of white blood cells (leucocytes) in our blood…………40 billion
Number of nerve cells…………30 billion
Length of a sperm…………35 micrometers
Diameter of an egg cell…………100-120 micrometers
Average length of a liver cell…………30-50 micrometers
Lifespan of small intestine mucous cells…………1.4 days
Lifespan of stomach entrance area (cardia) mucous cells…………9.1 days
Lifespan of stomach exit area (pylorus) mucous cells…………1.8 days
Lifespan of epithelial cells in lung alveoli…………8.1 days
Lifespan of large intestine (colon) mucous cells…………10 days
Lifespan of upper skin (epidermis) cells…………19.2 days
Lifespan of covering epithelial cells in the bladder…………66.5 days
Lifespan of neutrophile leucocytes…………45 days
Lifespan of eosinophile leucocytes…………10 days
Lifespan of lymphocytes…………5 days to 1 year
Lifespan of monocytes…………months
Lifespan of red blood cells…………120 days
Number of times a red blood cell travels the body during its life…………300.000
Number of red blood cells generated in a second…………2.4 million
Number of red blood cells generated in a day…………208 billion
Lifespan of a liver cell…………222 days
Lifespan of a kidney cell…………286 days
Number of mitochondria (power plant) in a nerve cell…………up to 10.000
Number of ribosomes created in a liver cell in one second…………180
Total length of the DNA in one cell…………2 m
Number of muscles in the body…………around 600
Number of muscles that work when smiling…………15
Number of muscles that work when frowning…………43
Total amount of work done by our muscles in one day
(Equal to lifting a 6 ton truck 50 meters into the air with a crane)…………around 3.106 Newtons
Total number of capillaries…………30 billion
Number of alveoli in the lungs…………400 million
Total amount of air taken in by the lungs in one day……………around 10.000 liters
Total amount of air we use in 75 years…………around 285 million liters
Total length of the nephrons in the kidney…………around 50 km
Total length of the glomerulus capillaries in the kidney…………around 25 km
Total inner surface area of the kidney channels…………20 m2
Total filtration area of the Bowman capsules in the kidney…………1 m2
Total skin weight…………11.15 kg
Total surface area of the skin…………1.5-1.8 m2
Total length of capillaries in 1 cm2 of skin…………around 1 m
Weight of dead keratin cells that fall off the skin in one day…………10 gr
Length of the nerve fibers in the skin…………80 km
Number of sweat glands…………around 2 million
Number of sebaceous glands in the skin on the head…………around 120.000
Total number of cells in the skin…………around 100 billion
Number of sensory receptors in the skin…………around 60 million
Daily sweat amount…………800 ml
Maximum daily sweat amount…………18 liters
Number of cells in the retina…………127 million
Number of values of the same color our eye can distinguish…………around 200
Number of shades of light that we can perceive…………around 500

The reason I gave all these numbers was not just to show the multitude of cells, organs, and tissues, but to emphasize that our Lord can create these with the precision that He creates a single cell. Mammals also have the organs and tissues that I have mentioned. Besides, some mammals have different organs with superior aspects. From this point of view, we are not much different from a cow or a horse. However, our Lord says that He created us in the best form possible, equipped us with superior qualities, and granted us the authority over all creation. Dear Peter! It’s time that you shed out of being an animal and rise to the degree of humanity. You cannot do this with your cells, organs, or tissues, but by gaining knowledge of divinity via spiritual virtues (such as the mind, conscience, and free will) that our Lord gave you.

If we see our body as a palace, could the stones, glass, porcelain, and wood come together and say, “Come on let’s make a palace, which will be the greatest palace in the world.” Could elements first turn into organic matter with macromolecules, then into cell organelles, then into cells, and finally into cells with different special duties, all on their own?

Finally, I believe it will be useful to give a table that shows every organ’s share in your body. My advice is not to evaluate anything materially. You cannot live without your pancreas, which only takes up a very small part of your body. Your heart, which is only 0.7% of your body, pumps the water of life (blood) to all of your organs; and your brain, which is 3.5%, manages your whole body. You can never give up on your kidneys, which take up only 0.5%.

Percentages of organ weights to the total body weight
Skeletal muscle (red meat)…………31.56 %
Skeleton and teeth…………14.90 %
Adipose tissue…………13.63 %
Skin…………7.81 %
Blood and lymph…………3.77 %
Lungs…………4.15 %
Brain and spinal cord…………3.52 %
Liver…………3.41 %
Intestines and stomach…………2.07 %
Kidneys…………0.51 %
Heart…………0.69 %
Spleen…………0.19 %
Pancreas…………0.16 %
Cartilage, ligaments, blood vessels and peripheral nerves…………13.63 %

All in all, we can say that the human body has holistic perfection with its functional parts, from hair to nail, to intestines and kidneys, as well as its aesthetic beauty.

Dear Peter! We have talked with you for a long time. I hope it was useful. I did everything I could. I am sorry that I couldn’t portray your true value!

It wasn’t…

Worse than that, in the third grade we had to learn about “conversion of units.” I figured it was good source of test problems. So I couldn’t escape from learning it. I admit it was difficult in the beginning. “The strange rule” said if we are to measure with a bigger scale, then we had to divide the number by ten and vice versa. Why was 120 cm equal to 1.2 m? If we knew that it was 120 already why did we bother to say it was also 1.2 in another unit? I got confused whether I should multiply the number by ten or divide by ten? (At least it was easy to multiply or divide by ten instead of another number, so I kept silent.)

In time, I realized that people used the unit to measure almost anything. Length is measured in meters, mass is in kilograms, time is in seconds. Wherever there was quantity, there was also a base-unit associated with it. Of course I never asked what a “second” was, because our teacher said everyone accepted this unit of time. Since it was a world-accepted “standard measure,” I subconsciously got the impression that the universe had a clock* and that people calibrated their time accordingly. In the same way, one kilogram was an absolute quantity in my mind by which every other mass can be measured.

As we grew up, more and more types of measures and units entered our lives: Volt, Joule, Ampere, Newton, and many others. Dealing with the “old” units of length and time was a piece of cake then. However, my faith in “standard measures” as universal remained unchanged until high school.

I was quite surprised in high school when our chemistry teacher told us that our very fundamental units of measures were actually not absolute. They were not fundamental in the sense that they, too, were defined in terms of other quantities. In fact, there is a history of “what to define as a unit” and “how to measure it.”

Let’s take time, for instance. We measure years by days and days by hours. Have we ever thought about why a year is 365 days and one day is 24 hours? Can’t we divide a year into 400 days or a day into 25 hours? Is this an artificial choice or a natural timing? It all depends on how we define a year and a day. We can identify a year by a full rotation of the earth around the sun. Also we can distinguish the beginning of day and night clearly. These are definite intervals of time dictated through our observations, and so there is not much choice other than setting one year at 365 days. Is there a similar fact behind the relation of day to hours? Not at all! It was in ancient Egypt, around 2000 BC, that days for the first time were sliced into 24 pieces of time. In the age of Babylonians, however, a day was designed to be 60 hours. Perhaps the reason for such division of the day (into 24 or 60) hours was that 24 or 60 are nice numbers which are divisible by many integers; the same reason why a full-angle is 360 degrees instead of 2π.

In the Middle Ages, for Muslims, measurement of astronomical phenomena was a very serious affair. They were very concerned about accurate timing. Determining the changing time of the five daily prayers and the beginning and ending of the month of Ramadan was more than a custom, it was a religious duty. And such calculations required high precision. This precision was exemplified in year 1000 AD by the Muslim scholar al-Biruni who gave the times of the new moons in terms of days, hours, minutes, seconds, thirds, and fourths after noon Sunday.

In the West, the first accurate time measurements were made by Roger Bacon in thirteenth century. In 1657, Christian Huygens invented the pendulum clock, which uses swinging weights to keep time. Later, Hyugens and William Clement refined the design so that clocks were accurate up to seconds. Another problem with older clocks was that although they worked fine in the local region, they lost accuracy at different parts of the globe and were thus unsuitable for navigation. The reason for the lack of accuracy was that earth’s rotation around the sun on its axis (which definitely affects the period of the pendulums) was not uniform. Several adjustments were made in the nineteenth century for better accuracy by improving the design to compensate for thermal expansion of the metal rods and air drag, which globalized the measurement of time. In 1956, the “second” was redefined in terms of the earth’s revolution around the sun, according to data gathered in year 1900. As the scientists were not completely satisfied, they re-defined the second (as the atomic second) a decade later. In 1967, the Thirteenth General Conference on Weights and Measures defined a second of atomic time in the International System of Units as:

The duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.

Measuring the length was another important task for ancient peoples. Among the earlier civilizations, the most accurate system was developed by Indus Valley Civilization. While their contemporaries were using parts of the body for measurement, as early as 2600 BC, the Indus civilization had a much finer unit system that accounted even for millimeters. Most societies continued to use their own length scale until eighteenth century.

As early as seventeenth century, with the advances in the accurate measurement of time, pendulum motion was suggested to measure standard length. In the eighteenth century, there were two main approaches for measuring the standard unit of length. One suggested defining the meter as the length of a pendulum with a half-period of one second. The other suggested defining the meter as one ten-millionth of the length of the Earth’s meridian along a quadrant, which is the distance from the equator to the North Pole. In 1791, the French Academy of Sciences selected the choice based on the meridian. After several changes in the definition in 1960, the International Bureau of Weight and Measure organized the 11th CGPM (General Conference on Weights and Measure), during which the meter was redefined as 1,650,763.73 wavelengths of the orange-red emission line in the electromagnetic spectrum of the krypton-86 atom in a vacuum. The final decision came from the 17th CGPM as: “a meter is defined as 1/299,792,458 of a light-second.”

Figure 1. Historical International Prototype Meter bar, made of an alloy of platinum and iridium, was the standard from 1889 to 1960.

As for the measurement of mass, the situation is even more complicated since scientists cannot even agree on what mass is. There are mainly two different understandings of mass based on its features. One is called inertial mass (related to the quantity of a material); the other is gravitational mass (related to gravitational pull and acceleration). Whether these two concepts are equivalent or not is still in debate though in modern theories like Einstein’s general relativity, these two definitions are equivalent. We can, therefore, leave these philosophical discussions about the concept of mass to the scientists and go back to its measurement.

Just like the measurement of time and length, scientific mass measurement gained a boost after the French Revolution. At first, a gram, defined as the absolute mass of 1 cm3 of water at 0o C, was chosen as the standard. In 1799, scientists made a slight modification to the unit of mass by re-setting the definition at 4oC since it is the temperature at which water is most stable. Later, officials noticed that this unit was too small to be a standard of everyday commercial materials, which usually appear in large amounts. In 1889, the International Prototype Kilogram (IPK), made of an alloy of 90% platinum and 10% iridium (by weight), was designed to define the standard mass (Figure 2). After the first production, several more stable replicas of IPK have been produced to replace the older ones. Today every government who subscribes to this standard must have an exact copy of IPK, and these replicas must be returned to Paris periodically as they may get rusted or dirty with time.

Figure 2. Shown above is a computer-generated image of the International Prototype Kilogram (IPK). The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France.

These facts may sound very odd to some, as it did to me when I first heard of them. I asked myself: If all these measures are defined in terms of something else, what is the point of defining them in the first place? For example, if we can agree to use the second as some interval of time, why do we bother to count the number of oscillations of Cesium. The answer is: We cannot agree unless we use a reference time which is geography-free, climate-free, and politics-free. Only then we will be sure that I, here in Western Pennsylvania, a person on the top of Everest, or a person in a submarine under the Pacific Ocean will call the same interval of time a “second.” In other words, the oscillation of the cesium isotope was believed to be free from all possible deficiencies that are results of physical location (Australia or America), environmental change (the Amazon Forests or the Sahara Desert), and politics.

In short, sand-clocks for measuring time (think of what kind of sand in what shape of glass tube) or the arm of a king as a length unit (imagine a king who seized the throne at 13 and died at 60), or weighing with iron cylinders (common in small grocery stores in some countries) is too unreliable, too unstable, too local, and of course, inaccurate to create a standard. Especially in this age of globalization, a consensus on measurement is absolutely necessary.

It seems a bit ironic that a simple-looking concept of science, measurement, could cause such controversy. A simple way to keep track of numbers that belong to different kind of quantities evolved into an area of serious research through time. Perhaps then, I should have not worried that much about my bad math grades on a subject which troubled the scientist themselves. After all, my grades were just my teacher’s own measurement.**

O. S. Caglayan has a PhD in mathematics. He is a freelance writer. He lives in Pittsburgh, Pennsylvania.

* This famous quotation attributed to Newton was opposed by Leibnizian view of time: “The universe is the clock.” The scientist as philosopher, Friedel Weinert, Springer; 1 edition (May 27, 2004)

** The author is indebted to his dear elementary school teacher Muazzez Ozalp for instilling in him the love of science.

References

1. G. J. Toomer. Ptolemey’s Almagest (Princeton, New Jersey: Princeton University Press, 1998)
2. The History of Time (Leofranc Holfrod-Strevens).
3. al-Biruni (1879). The chronology of ancient nations: an English version of the Arabic text “Vestiges of the Past”. London: W.H. Allen, 147-149. OCLC 9986841.
4. Matthew Bennett, Michael F. Schatz, Heidi Rockwood and Kurt Wiesenfeld, Proc. R. Soc. Lond. A 2002 458, 563-579.
5. Ian Whitelaw. A Measure of All Things: The Story of Man and Measurement, St. Martin’s Press, 2007.
6. http://physics.nist.gov/cuu/Units/meter.html
7. www.bipm.org/eng/home

We certainly fail if we try to consider time as only a matter of determining the hour. It is, in fact, a dimension like depth, height and length. One reason of our difficulty in perceiving time may be caused by the fact that our optical perception is sensitive only to three dimensions, but no others. Many animals cannot comprehend the dimension of depth. Some animals see their environs in two dimensions as in pictures. We have difficulty perceiving other dimensions just as animals which see the world in two colors live without any awareness of other colors.

Humankind, with the most sophisticated aspects, has a very different and privileged position above all creation. In spite of this, we have limited sight, hearing, and other senses. Many a world that is beyond our senses remains imperceptible to us.

Another aspect of time that supports its dimensional feature is that it is in full conformity with and proportional to other dimensions. In terms of its extent, duration of events increases or decreases in parallel with spatial dimensions. Man lives for around sixty to seventy years, while microscopic animals live around one or two days. The life of the sun and the universe which constitute the macrocosmos is expressed in billions of years. On the other hand, the life of subatomic particles is expressed in billionths of a second. Thus, we assume them as being resonances. There is time reduction together with and compatible with space constriction on the sub-atomic scale, and this fact is yet another proof that time is also a dimension.

How shall we understand the other dimensions of space? What does the fourth dimension of space mean? Let alone describing, it is not easy to even imagine this.

If a is the length, a2 is the area and a3 is the volume of a thing, then what is a4? If we see space as a giant plain sheet of paper, that sheet of paper has no depth but only a surface. If we fold crumple it into the shape of a sphere, we obtain “Riemann space.” Just like we perceive the three-dimensional earth as a two-dimensional surface while we are on it, this 3-dimensional sphere made of 2-dimensional paper will be perceived as 2 dimensional by us. We can only talk about the third dimension after we generate a depth, that is, after we step outside the paper and move above and below it.

The fourth co-ordinate of space is a tunnel. Let us suppose that the universe is two-dimensional, that is, it is like a thin sheet of paper, and let us human beings be like pictures with no thickness over its surface just like the pictures on a newspaper. We are free to move in all directions on this sheet of paper. We can sense four directions. But we will never perceive the terms “up” and “down” (or “upper” and “lower”) since we will never leave the surface of this sheet of paper. Such terms will seem unacceptable to us even we are told of them. Accordingly, we will never hear of a third dimension and our vocabularies will never contain such terms as “up” and “down.”

If a three-dimensional object existed above our fictional paper realm and if this object even slit our paper realm and went away, we still would not see it in three dimensions but only the part of it intersecting our paper realm. If such a thing were a sphere, for instance, we would see its projection in a circular form. Its latitudinal sections would gradually expand starting from the poles, reach their largest on the equator line and its ring-like (circular) shape would gradually decrease and finally disappear at the other pole. That is, we would see it only as its cross section or shade. Such a three-dimensional object would seem two-dimensional to us since we would suddenly see its cross section. The sudden appearance, expansion, decrease and final vanishing of that spherical object in our two-dimensional realm would seem quite amazing to us since our shapes are fixed and immovable.

The three-dimensional shade of an extraterrestrial four-dimensional object overshadows our three-dimensional space. We see the linear tunnels in cross-section, not longitudinally, just as we see the sphere as circular. Though the sphere is a simple object, it amazes us.

Let us now imagine a more complex form. Let us, for instance, reflect the shadow of a vase onto a wall and obtain various shades by turning it repeatedly. A fixed and immovable portrait on the wall would regard the shadow and its variations reflected over the same plane with surprise and fear, since that portrait, or that person without depth, sees only what is reflected on the wall, but not us and the vase. The wall is the only realm for him and there is nothing for him beyond and behind the wall even if we say so.

We humans tend to assess events within the narrow limits of space and within certain dimensions, since we are bound within a single space–time cone. The conceptualization of space with its dimensions of height, length and depth is possible for us. However, the fourth dimension, time, is an abstract and metaphysical measure even though it is studied within physics. The tunnel thus seems to us like an incredible dimension.

Our perceptions with the five senses in the visible universe can be considered as the projections of non-physical and multi-dimensional realities (the eighteen thousand realms) to our domain. Clearly, in order to gain a better understanding of those realms, which we do not see but which we feel exist, with the help of the physics, we need to emancipate ourselves from the narrow patterns of time and space in this world of trial. We need to travel toward the horizon of spirit and develop an all-new scientific language which approaches physics and metaphysics together. Finally, we can say, in Bediüzzaman’s words, that the physical and observable universe which is the domain of research for modern physics is an ornamented curtain veiling the world of the unseen.

Osman Cakmak is a professor of chemistry at Gaziosmanpasa University, Tokat, Turkey.