We perceive several problems related to the functions in many situations in life and develop solutions accordingly. The function shows the effect of one (or more) variable(s) on another variable. In simple terms, one factor can be called the transformation of another factor. When you send a piece of mail by cargo, you pay according to the weight of your cargo. Or imagine using an hourly Internet service in a library or airplane; the more hours you use the Internet, the more you pay.

A group of people want to rent a bus. The number of people does not affect the cost of rent for a bus. However, the cost per person could change depending on of the number of people. The more passengers, the less fee they pay for each passenger. Conversely, if the number of passengers is less, the cost of the bus fee could be more.

The examples are given above help to understand the mathematical function more easily. We perceive several problems related to the functions in many situations in life and develop solutions accordingly. The function shows the effect of one (or more) variable(s) on another variable. In simple terms, one factor can be called the transformation of another factor.

Consider shipping by mail. There are actually two situations here; the weight of the cargo sent and the amount of money paid based upon the cargo’s weight. This gives us a hint for the payable amount. For example, we may know how many pounds of cargo can be sent for $10. We also may calculate how much money is needed to ship 5 pounds of cargo. We can formulate this shipping problem:  Let x be the weight of the cargo and let y be the amount to be paid. In addition, for each parcel sent, including taxes, let us assume that it costs $3. In this case, we get an equation such as y = 2x + 3. Here, the number 2 given in front of the variable x is the money paid per pound. We calculate how many dollars we will pay for a 4-pound cargo: (2×4) + 3 = $11. If 2 dollars per pound is received, a 4-pound package shipping fee is 11 dollars.

Another example would be the use of the Internet. If 40 cents is requested per hour, $1.2 will be given for 3 hours of internet usage. Thus, the equation can be written as y=40x, where x is internet usage time per hour, y is amount to be paid.

The bus rental example is slightly different from the above two examples. Although this example specifies the function, this time there is a reverse situation. In the first two examples, like (x or) input increases, (y or) output will increase. In the case of bus rental, the bus rental fee is fixed and as the number of passengers increases, the payment per person will decrease. Let’s say $400 is required for the daily rental of a bus. 40 people pay $10 per person while 8 people pay $50 per each person.  This equation would be; y=400/x, where x is the number of people, y is the amount of money paid per person. Functions are important in understanding the relationship between two variables.

Life is a function. In mathematics first, what is the function in its simplest form? Let us give the known definition in schools.

Function: Let A and B be two sets different from the empty set and there is a relation f from set A to set B. If the relation f associates each element of the set A to one and only one element of the set B, this relation is called the function from set A to set B. It is shown as f: A→B or A→B. A is called the definition set of the function and B is called the set of values. A set of elements that match the elements of set A in set B is called the set of images of the function and is denoted by f (A).

In this case, if we clarify the definition a little, a relationship from A to B to be defined in order to function f; the following conditions must be met:

1. There should be no elements in the definition set that do not have an image. However, the element can remain exposed in the value set.
2. Each element in the definition set must not have more than one image.

Let us try to find the reflections of the definition in our lives. We assume that A is the world in which we live. If we say “World” for Set A (Definition Set), we would call Group B “the Afterlife” (Value Set). Because there is a connection from this world to the other world. We will see our values in the afterlife against what we do in this world. As someone who fits the definition of a “good” person will be of high value, the definition of a “bad” person will consequently result in a lower value. So, set A considers the world and its elements as ‘living people’. We can think of all the people in the world and include them in this group since life is finite for all of us. The mathematical meaning of this reality is the following:  all elements will be moved from set A to set B (Let A and B be two sets different from an empty set and a relation f from set A to set B.). There is such a connection (or relation) that one who leaves the world cannot go to two places at the same time. Destinations are clear: abode of reward or abode of punishment. We will all be eventually placed into one of these two groups. In some cases, the last stop of the people will be paradise, even if there are those who go to hell first and purify their sins. Consequently, in the last case, no one will be in two places at the same time (If the relation f associates each element of the set A to one and only one of the set B, this relation is called the function from the set A to the set B).

Just because everyone has one final destination does not mean that that destination can only hold one person. If the levels of Heaven and Hell are considered correctly, it is possible that there is more than one person for each level or that no one has come to that level. It is possible that there are those who have sinners at the same level. We can speculate that there may even be such a level that is inaccessible to all people. The Creator creates such places in order to show His grace, mercy, and power. (In the definition set, there should not be any elements without an image. But in the value set, there may be exposed elements.)

Life itself is a function. God created life according to certain rules. We should do our best to explore, find, and use these rules. Seeing the beauties of life and being amazed by the astonishment and capturing happiness in both worlds is achieved by seeing the manifestations of God everywhere.

Will there be wars over elements like there have been over petroleum and water? What element have we been using in color televisions? What substance is used to make energy saving, environmental light bulbs?

Each of the elements found in the periodic table have their own characteristics. After they have been cooked in the pot of the universe, these substances that are offered to our service can be radioactive (like uranium), metallic (like magnesium) and even gaseous (like helium). Seventeen of the elements not easily found among the layers underground have unique properties. These elements are called rare-earth elements, because it is hard to discover and mine them.

Rare-earth elements are in many of our everyday devices. The data projected on a computer screen is transmitted via optic cables containing erbium. The light of a tablet device is generated by the phosphorescent element europium. We actually touch indium covered surfaces when we scroll our fingers on touch screen monitors. When listening through headphones, we are using neodymium magnets that are ten times stronger than iron magnets.

From space technologies to defense industries, from cell phones to LED lighting, many such rare-earth elements are used in every stage of our lives. These elements – many of which we cannot live without, even though we’ve never heard of them – were recorded into the Critical Materials Strategy Document published by the U.S. Department of Energy in 2010. In a public announcement, the department declared fourteen of the elements as specially significant regarding clean energy, listed six of them as critical, and the other four as near critical. Fifteen elements, beginning with lanthanum and ending with lutetium, numbered between 57 and 71, comprise lanthanides. Combined with scandium and yttrium, these make up the seventeen rare-earth elements.

The elements that we touch on screens

Indium (atomic number 49) gains the properties of electrical conductivity and optic transparency when combined with tin, which, at number 50, is indiums’s neighbor on the periodic table. Optical transparency is a desired property for plasma screen and television technologies. Indium is also an important material for mobile phone touchscreens. Interestingly, when indium combines with cadmium, also as a neighbor at number 48, it loses the optical transparency. Instead, it is able to absorb light. Light harvesting is a very critical feature in the production of solar cells.

The relationship of indium with its two neighbors opens new horizons for scientists. In the near future, it is hoped that many unknown and interesting features will be unearthed by investigating the known elements of the periodic table. It is amazing that these elements have been around for thousands of years in the universe only to be discovered by technological advancements.

The need for rare-elements in the world is around fifty thousand tons. The current recorded reserve for rare-earth elements is 110 Million tons. Currently, 95% of the demand for rare-earth elements is supplied by China, yet the country only has 35% of the world’s reserves. Therefore scientists are constantly searching for rare-earth element mines to eliminate the Chinese monopoly and to boost the production of these rare materials. In recent years, China has gotten into political debates with Japan and the United States by curbing rare-earth element exports. Economic journals covering these debates wondered if “element wars” were near. In 2010, a massive reserve of elements, enough to sustain worldwide demand, was discovered in the Pacific Ocean. Developed countries are now planning to recycle rare-earth elements from used devices due to low reserves.

Yttrium, europium, and terbium (atomic numbers 39, 63 and 65) have been known for a long time. Terbium and yttrium are named after the Swedish town of Ytterby. Yttrium is the first rare-earth element discovered, at the end of 18th century. Plastics containing europium are used to make laser products; it’s also used as an element to provide the red color on television screens. Yttrium has a supplementary role that enhances europium’s red color production. And terbium oxide activates the green phosphorescence of television tubes with its yellow-green phosphorescent property.

Terbium also enables an 80% reduction of energy consumption in light bulbs. This makes it one of the most wanted elements in the $2 billion rare-earth element market. Today, when we purchase class A type light bulbs, we are actually buying rare elements like terbium.

Neodymium (number 60), which emits a green light via laser pointers, is also used in the magnets of electric motors. When neodymium combines with boron and iron, it makes a magnet twelve times stronger than simple iron magnets. Because it is significantly less dense than iron, it makes electric motors and laptop computers much lighter. Another interesting feature of neodymium is that it enhances the data storage capacity of hard drives. Furthermore, neodymium is wanted for electrical devices and wind turbines.

The union of elements

Dysprosium was discovered in 1886 and can never be found in a free form in nature. This is because it exists in a compound form with other minerals, like gadolinite. Dysprosium is also known for its magnetic property, and when mixed with terbium and iron, it forms a substance called Terfenol-D. In a magnetic field, Terfenol-D has unique transformational abilities. Dysprosium is utilized in laser production together with vanadium, and it emits infrared radiation when used with cadmium.

The magnetic alloys of iron, boron, and neodymium lose their magnetic features beyond 300 degrees Celsius. However when this alloy is combined with dysprosium at a 5% ratio, that problem disappears. Therefore, these magnets are used for electric turbines and hard disc motors. Dysprosium also makes magnets in electric motors 95% lighter. And dysprosium and nickel mixed fillings are used as cooling rods in nuclear reactors.

The human mind becomes fascinated after seeing all the wisdom and properties involved in these lifeless elements. Either we conclude that these elements have doctorate degrees in physics and chemistry from Harvard University, or we may express our weakness and fascination in front of The Grand Creator who created and presented these elements for our benefit.

Is the yellow color in glasses from the planet Ceres?

Since Dell recalled four million laptop computers in 2006, because of a possible explosion caused by overheating battery, scientists’ eyes have been focused on lanthanum and cerium. These two elements are considered to be safer than other alternatives. Lanthanum and cerium are used in electrical equipment and energy saving light bulbs, and are classified as critical elements in these processes, along with tellurium. Cerium, named after the planet Ceres, is responsible for the yellow coloration in glasses. Cerium is also used in polishes, ceramics, and petrol refineries. Tellurium is produced indirectly, unlike most other elements. The production of cadmium takes place during zinc production, and tellurium during copper refining. Tellurium is a cheaper element that has been used in combination with cadmium on solar cells since 2009; before then, most solar cells used expensive silicon panels.

Elements in our lives, from space rockets to ultrasound imaging

Hafnium, tantalum, erbium, and technetium are important elements, even though they are not listed critical. Even though hafnium and technetium are not rare-earth elements, they were still added to the critical material strategy document produced by the US Department of Energy. Hafnium is employed in space rockets for its resistance against extreme temperatures and wearing. Hafnium oxide is a valuable material for electronic transistors since it is a very effective electric insulator. It is 20% faster than the silicon oxide that is commonly used in transistors. A transistors length is around 65 nanometers when silicon oxide is used, but it is only 32 nanometers with transistors made of hafnium oxide. This 50% decrease enables smaller devices.

Touchscreens containing indium, laptop computers powered by lithium ion batteries, and cell phones with hafnium transistors are some of today’s technological wonders. Would these inventions still be possible without these elements? Could we reach the high capacities in hard discs without the tantalum? Would we be able to protect ourselves from electric leakage in computers without high quality electric insulators such as tantalum oxide?

Radioactive technetium, which was discovered in 1937, is the first artificially produced element. The technetium 99 isotope is used in nuclear medicine. Technetium produced from uranium has a half life of 211,000 years, as opposed to the 6 hour half life of the technetium 99 isotope. The number of technetium based nuclear medicinal tests, like ultrasounds and x-ray imaging, is estimated to be above thirty million annually.

We take advantage of these elements in every stage of our lives, from medicine to technology. Could we become dependent upon elements the way we are upon petroleum? Only time will tell. Either these elements will be replaced by other materials, or other technologies will outdate the current technologies. It is also possible new elements will be discovered.

A majority of our modern technologies would not exist without these elements that were dispersed among the earth billions of years ago. These elements were placed here for our benefit, and so we could utilize them, and produce institutes of scientific research and education to study them.

Kadir Can and Mehmet Ramazanoglu are science teachers in Ankara, Turkey.