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.

The single biggest problem regarding mathematics and the sciences is motivating younger students to study them.

While the United States excels at welcoming people from all over the world to travel to the U.S. and study science and math, the number of aspiring mathematicians at universities is decreasing. About only 2% of all students in America that pursue a bachelor’s degree are in the fields of mathematics or other physical sciences. On top of that, roughly 48% of students studying a STEM field in a bachelor’s program, and 69% of students pursuing an associate’s degree, changed majors or exited college before earning their degree [1]. One possible explanation for this is the reputation that math has for being boring, uninteresting, and complicated. However, there could hardly be a better time to become a mathematician.

I was watching a documentary about deserts with my 2 year old. At first, she found the documentary to be boring because the desert appeared to be bland and void of life. Then, the screen started showing the lively and colorful aspects of a desert including its oases, various cacti, and small creatures. She was shocked that the arid desert could possess so much color, life, and intrigue. It reminded me of my feelings towards mathematics. For some people, mathematics seems like a dry and dull subject that makes little sense. However, it too becomes full of life and color once one looks in the right places and from the correct perspective.

Ten years ago, the Wall Street Journal ranked jobs based upon a number of parameters such as salary, freedom, the possibility of promotion, and ease of employment. It may surprise you to find out that being a mathematician was ranked as the number one job in the world! [2] Career Cast, a company that started as a spin-off for this kind of ranking in 1988, also ranked mathematician as the number one job in 2014 [3].

In job advertisements, the definition of a mathematician is somebody who applies mathematical theories and formulas to teach or solve problems in a business, educational, or industrial setting. In other words, a mathematician is someone who insists on solving problems, which is what mathematics was invented for. However, a crucial point is missing from this description. There are mathematicians who not only teach or apply mathematics but do math, generate math, and change math.

If a mathematician is one of the best jobs in the world, how many mathematicians are there around the world? Thankfully, it is in the hundreds of thousands: almost 250,000, and it is growing every year, particularly in India and China [4]. These countries encourage their children to participate in STEM fields from a young age and place a very high emphasis upon education that can help foster a love for STEM careers at a young age.

Although mathematics is the science in which theorems last for a long time, it is also a field that is being renewed constantly. There are not many other subjects in which knowledge can last thousands of years and always remain both correct and relevant. For instance, the theorems of Euclid, a Greek mathematician who lived in the third century BC, are still accurate today. If we look at the modern applications of computer science and mathematics we see that people are still applying the contributions of Laplace about the central limit theorem, using the contributions of Shannon in sampling, and applying Fourier’s ideas about signal analysis and signal processing. Paradoxically, mathematics is ancient and contemporary at the same time.

In 2014, Emmanuel Candes of Stanford University gave a short speech about how he had collaborated with medical doctors and mathematicians, and used Fourier’s ideas in analysis and data processing, to drastically reduce the time needed to develop a scan [5]. His machine was a significant evolution for the medical field. In experiments, it was shown that to reconstruct images with the best accuracy, they need to have only 2% of the Fourier transform. Candes managed to reduce this time by a factor of eight by knowing only a very small portion of the Fourier transform. Netflix also uses this technology for reconstructing missing information and predicting the preferences of users for movies.

However, the life of a mathematician is not always full of success. The field is full of uncertainty, intense problem solving that can often take weeks or even months, and waiting. Most of a mathematician’s time as a researcher is spent in failure. That is an objective fact. A common motto is, “Every day is a failure. This is our life.” But when we look back on the amount of time that is spent solving these problems, everything pays off. Every year, the number of new theorems added in mathematics runs into the thousands. Failures are not actually failures, but merely bumps along the path of progress.

Another common problem that befalls mathematicians is that they will be expected to perfectly predict what will happen should their discovery work as intended. This is especially true of work done under the auspices of government agencies, since they will often not grant money without a very clear path towards a desired outcome. Things do not always go as planned, and thus it can be challenging to argue that a desired result will occur 100% of the time.

Despite these drawbacks, one of the most exciting aspects of mathematics is the potential to discover something revolutionary and groundbreaking. History has shown that the ideas and discoveries of one individual can make a tremendous difference in the world. By encouraging and enabling more and more students to study math and science, we thus increase the odds that more discoveries, be they groundbreaking or not, will continue to be made in the future.

Alan Turing was a mathematician who had an outsized impact on human history. He was instrumental in cracking the secret codes that were used by the Nazis during the Second World War. Some have argued that World War II would have lasted at least two more years without Turing’s intervention. In particular, the Normandy operation would have been impossible. What was Turing’s motivation? It was not patriotism, honor, or a strong duty to his country. It was simple: his main motivation was solving riddles and difficult problems. He lived for the thrill of solving his next big challenge.

Paul Erdos, a Hungarian, was the most productive mathematician of the 20th century. Erdos had no home, no car, no bank account, and no salary. He lived with just one suitcase and his ideas. He worked on theorems his entire life. When he got some money from some reward, he would always use part of it to put a reward on another theorem.

Leo Szilard was another revolutionary mathematician. He was the first person to understand the concept of chain reactions between atoms. His inspiration came from a public lecture, in which famed physicist Ernest Rutherford said, “It would be moonshine talking if you are willing to extract energy from the atom.” Rutherford acknowledged that energy existed within atoms but thought it was impossible to do anything with it. Szilard felt that Rutherford was wrong and decided to prove it. He worked and thought for days. And one day, while he was crossing a street in London, he was struck with an idea about the principle of chain reaction and exponential growth of atomic energy. This lead to him eventually meeting with Albert Einstein and the subsequent development of the Manhattan Project.

Steps in developing ideas

But how do scientists find those perfect ideas? What are the steps? Henri Poincare gives us some hints about how the ideas were coming to him. Poincare, who was always considered a genius, experienced many discoveries after working very hard on the problem and he had a lot of failures. He said: “Disgusted from my failure, I went to spend a few days near the sea thinking anything else. And one day, while walking on the cliff, the idea came to me. And as before, it was very brief, sudden, with immediate certainty, that arithmetic transforms of indefinite ternary quadratic forms are identical to those of non-Euclidean geometry.”

So, under which circumstances does a big idea come? In popular culture, we have those myths like Newton saw an apple falling down and changed the world. But in real life, it’s not the way it happens. For Poincare’s example, the cliff has nothing to do with quadratic forms. Poincare was saying that he worked very hard and then he decided to rest a little bit, and finally, he had the enlightening moment. What is important here is if the brain had not been prepared by hard work, the illuminating idea wouldn’t have struck.

So what is the process of discovery?

Of course, a publication will be the last step for the discovery of an idea. Because publication means that the idea is out and going to be seen and read by the world. But before that, we have many steps or ingredients which make our idea stand up on its feet.

1. Fecundation

The first step is fecundation. In other words, conversations and discussions you have with your colleagues. Your interaction has a potential to bring about a new phase, a new idea out of different projects. It may take months or years to decide what you want to prove.

2. Documentation

Documentation is built upon previous research and insights. We may need to document things from several centuries ago or from recent times. Nowadays, all information is stored in computers and the internet, which makes this step easier than before.

3. Motivation

Motivation is the most important ingredient when we pursue a discovery. Psychologists believe that childhood experiences play a big role. For instance, both Szilard and Turing’s lives were strongly influenced by a book they read before they found their ideas. In the case of Turing, the book Natural Wonders Every Child Should Know was his inspiration. When I was a child, I watched “Donald in Mathmagic Land” and thought it was fascinating. It might have played a big role in my choice to become a mathematician.

4. Ecosystem

A discovery or an idea never arrives on its own. A scientist is never alone and there is a whole ecosystem around them. For instance, at one point in history, Persepolis was the most innovative city in the world. Then it was Paris, and then Budapest. Today, we have the well-known Silicon Valley.

If you are working in a lab, you need to have an atmosphere where people can meet, discuss, and be creative. A good idea comes from teamwork.

5. Constraints

The next ingredient that you need for a good idea is constraints. Without constraints, discovering new ideas is not as likely as when there are. Rigorous findings come about mostly with constraints. One of the most famous problems in mathematics is the Riemann hypothesis, which was tested in thousands of experiments. After those experiments, the proof was only a set of logical rules with constraints. Constraints usually help generate authentic results and artistic quality as in rhyming poems.

6. Intuition

Intuition usually comes together with hard work, yet it is not easy to understand its process.

In addition to these six ingredients, whether one has good fortune or not also plays an important role. It is human condition that things may not come out as we like although we might have done everything necessary.

Henri Poincare says, “Thought is only a flash between two long nights, but this flash is everything.” Yet, a big idea might take years of work. Still, even after working so hard, our knowledge is like a tiny island in an ocean of unknown. We know almost nothing, but this is such a precious nothing, because that that knowledge came out of the richness of the thought of many people and their efforts. There are still so many ideas just waiting for us to discover them.

Mathematics, like many scientific fields, is an infinite universe with an infinite amount of problems waiting to be discovered and solved. Their applications within our world are endless, and the possibilities to use these results to create real change in our world are also endless. One tends to ask, is math a stand-alone, abstract concept while its vast horizons of knowledge explains the intricacies of our universe, or does it imply an infinitely bigger wisdom from which this abstract knowledge rises from and that relates to our existence? We must continue to motivate students to study math so that they may fall in love with it and continue to develop humanity.

References

1. United States, Congress, Chen, Xianglei, and Matthew Soldner. “STEM Attrition: College Students’ Paths Into and Out of STEM Fields.” STEM Attrition: College Students’ Paths Into and Out of STEM Fields, National Center for Education Statistics, Nov. 2013. nces.ed.gov/pubs2014/2014001rev.pdf.
2. Needleman, Sarah E. “Doing the Math to Find the Good Jobs.” The Wall Street Journal, Dow Jones & Company, 7 Jan. 2009, www.wsj.com/articles/SB123119236117055127.
3. “Jobs Rated 2014: Ranking 200 Jobs from Best To Worst.” CareerCast.com, CareerCast.com, 9 Mar. 2017, www.careercast.com/jobs-rated/jobs-rated-2014-ranking-200-jobs-best-worst.
4. “Mathematics Genealogy Project.” Welcome! – The Mathematics Genealogy Project, genealogy.math.ndsu.nodak.edu/
5. Emmanuel J. Candes. “Mathematics of sparsity (and a few other things), August 14, 2014, Seoul. ICM2014 VideoSeries PL3. https://www.youtube.com/watch?v=W-b4aDGsbJk

It was finally the weekend! After my long mathematics presentation, I came home to watch my favorite tv show, Person of Interest, to de-stress. Surprisingly, the episode was about the most famous mathematical constant, pi (π) which is equal to the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. Mr. Finch (the main character) was acting as a substitute teacher and wrote on the chalkboard 3.1415926535. Then he asked the students, “What does this mean?” I answered the question in my mind, thinking, “If I have a bicycle tire with a diameter of 1, then one full revolution of the bicycle tire would travel the distance pi.” However, in the show, nobody answered. Then Mr. Finch answered the question himself, saying:

Person of Interest, Season 2 Episode 11 “2 Pi R”

“Pi, the ratio of the circumference of a circle to its diameter — 3.1415926535 — is just the beginning. It keeps going forever without ever repeating, which means that contained within this string of decimals is every other number; your birth date, the combination to your locker, your social security number, etc. It’s all in there somewhere. And if you convert these decimals into letters you would have every word that ever existed in every possible combination; the first syllable you spoke as a baby, the name of your latest crush, your entire life story from beginning to end, and everything we ever say or do. All of the world’s infinite possibilities rest within this one simple circle. Now what will you do with that information; what it’s good for? Well, that would be up to you…”

Although that scene was actually inaccurate, I loved it. This scene is beautiful because most teachers in the world struggle to be as good and as interesting of a teacher as Mr. Finch is here. His knowledge about the subject expands the discussion beyond the textbooks and keeps the students focused throughout the lecture.

Wikipedia, gif, “Pi Unrolled”

We have all been taught that pi is the ratio of a circle’s circumference to its diameter.

Unfortunately, this is wrong because mathematicians have not proved that pi has the characteristic of “normality” yet. In other words, mathematicians are not sure if pi contains all the finitely long permutations of digits from 0 to 9. They are not sure if every digit continues to be used after a certain amount of time or an unlimited number of times in pi’s decimal representation. Nobody knows what we will find in the digits of pi if we keep going. For instance, when we check the first billion digits of pi, we see that the digit 7 occurs almost 100 million times. This makes pi a nice random number generator. However, after some points, pi may not contain the digit 7 and might instead have a non-repeating number with just two or three digits such as 010203112233000111222333…

For instance, after the first 761 digits of pi, there is a famous mathematical coincidence where six nines occur in a row which is called the Feynman point.

Twitter, Feynman’s Library, “Feynman Point in Pi”

But we are sure that the digits of pi keep going on forever and in a random order. This makes pi interesting because the value of pi is finite; however, its decimal value is infinitely long. This is not a contradiction. Pi is a constant number because it is the ratio of the circumference of a circle and its diameter, which are finite values. Still, we need an approximate value for pi.

In 1768, Johann Lambert proved that the value of pi is an irrational number and it cannot be written as a rational simple fraction. 22/7 is a commonly used approximation but does not contain all of the digits of pi. This is because irrational numbers cannot be written as a ratio of two numbers, such as , because they continue on to infinity and do not follow a pattern. In 1882, Ferdinand Lindemann proved that pi is a transcendental number because it is not algebraic; it is not a non-constant polynomial equation with rational coefficients (“Transcendental number”, Wikipedia).

We can safely say that pi is transcendental because the mathematician Yasumasa Kanada found that the first trillion digits of pi appear to be statistically random. If you check the table below, you see that the event of each digit occurring is independent, and the probability of it is one-tenth of the time (“Kanada Laboratory,” Super Computing)

After many years, Emma Haruko Iwao found 34.1 trillion digits of pi in 2019. It took 121 days for Haruko and his computer, because calculating pi requires a lot of power, even for a computer. You can picture it in your mind like this; if you were to print a billion decimal values of Pi in normal sized, ordinary font, it would stretch from New York to Kansas.

However, 34.1 trillion digits is still not enough to prove whether pi is normal or not (“Pi in the Sky, Google Cloud Blog). Supercomputers are still crunching the numbers. If you check the graph below, you will see the number of known digits of pi, by year, since 250 B.C.

FiveThirtyEight, Graph, “Even After 31 Trillion Digits, We’re Still No Closer To The End Of Pi”

Going back to Mr. Finch, we see that he is not 100% wrong. We can find our birthdays in pi easily. If you go to mypiday.com and type your birthday, it will give you the decimal place in pi. For example, my birthday occurs at the 675,097th decimal place.

If pi is a normal number, then we can say that our whole destiny is encoded in pi. The pictures we are going to take in the future, will be in pi because there are binary numbers behind images. All digital products are in pi. Even this article has been in pi for thousands of years. Furthermore, the DNA of every creature is in pi. Mr. Finch was actually right.

There is an interesting and artistic way to show the randomness of pi. Some scientists might be happy with their tedious scatter plots, but there are some artists who use colors for data visualization to communicate with the public. Martin Krzywinski is one such artist, who found beauty and artistry in the randomness of Pi. He took the digits of pi and gave each digit a different color. For instance, he gave 3 the color orange, 1 as red, 4 as yellow, and so on. Then he made a beautiful poster. And if you look at it carefully, you do not see any particular pattern to the colors.

Science Art by Martin Krzywinski

Should we stop working on pi? Or should we continue looking for a better approximation? Is assuming pi as equal to 3.14 good enough? Or is it enough to use 40 digits of pi to find the circumference of the Milky Way galaxy to an error less than the size of a proton (JPL NASA)? Are the first 152 digits enough to find the circumference of the observable universe at 93 billion light-years (WIRED)? There are hundreds of mathematicians who have been trying to figure out more digits of pi for years. It is like trying to get to the moon and then to the next planet, and so on…

But why? Why do mathematicians bother calculating any more digits? Why aren’t 34.1 trillion digits of pi enough? Is it because pi lurks in every circle?

The logical reason seems cryptic: is it because pi is a beautiful source to generate random numbers? Or is it that countries can show off their technology to other countries, because calculating trillions of digits of pi requires a very powerful computer? For instance, in the Star Trek episode “Wolf in the Fold,” Spock foils the evil computer by commanding it to “compute to last digit of the value of pi.” So asking a computer to compute pi is called “a stress test” and may make it crash.

On the other hand, we humans are just weird. Staying at home and drinking tea is a beautiful activity, but when we get bored, we try to climb the highest of mountains, befriend a tiger, or try to memorize the digits of pi, like Chao Lu, who correctly memorized the first 67,890 digits of pi. We will keep doing these things because we like to understand the world around us.

We are inevitably connected to the past, and pi is a thread that’s gone through all of human history. That’s why we can say that as long as there are people, there’s always going to be somebody who wonders what’s next. And I assure you that somewhere in the world there is a mathematician or scientist using pi for something important, because pi is still the mysterious constant of nature.

Finding Pi

The previous statement is utterly true: there has always been someone who works on pi. Math is as old as civilization. Pi has been studied by the human race for almost 4000 years. When the last mammoths were going extinct, people were studying Pi. As far as we know, Archimedes was one of the first humans who calculated pi. He was most likely helping wheel makers. But how did he estimate the value of pi?

Firstly, he saw that all polygons are a circle. According to Archimedes, if you keep increasing the number of the sides of a polygon, you get closer to the perfect circle. In other words, a pentagon is more circle than a square, but a hexagon is more circle than a pentagon, and so on… Thus, more than two thousand years ago, he defined a circle as a regular polygon with an extremely large number of sides.

His definition is useful because measuring a curved surface was hard to do accurately. He found a way to find the circumference of a circle. First, he drew a square with its corners touching the perimeter of a circle and found the perimeter of the inscribed square. Secondly, he drew another square with its sides also touching the perimeter of the circle and found the perimeter of the circumscribed square. He came to the conclusion that the circumference of the circle had to lie somewhere between the value of those two perimeters of squares.

Using this method, however, the difference between those two values was pretty big. So, he drew pentagons to see the upper and lower bounds of the circumference of the circle. This gave him a smaller range of bounds. He kept increasing the number of faces of the polygon that he was drawing inside and outside the circle. Each time he did this, his estimation was getting more accurate. Archimedes got up to a 96 sided regular polygon [called an enneacontahexagon] until he grew exhausted. The lower and upper bound that he found were 3.1408 and 3.1429. Thus, he calculated π to two decimal places.

Archimedes’ method needed improvement because his life span was not going to be long enough to find the other digits of pi by hand. Mathematicians needed to discover more efficient formulas and new techniques.

Before they could do this, they needed to discover algebra. Its discovery by the great mathematicians inspired a whole new way of looking at the world.

The next great jump in calculating pi was the invention of calculus. After that, mathematicians started working on infinite series. An infinite series is an expression with numbers added together until infinity; sometimes these infinite series converge to a particular value.

There are many methods available now to calculate pi. Gottfried Leibniz found pi in infinity. James Gregory was working on one of the astonishing infinite series for the inverse tangent function below. He added infinitely many small numbers together and found pi.

He put x = 1 into the inverse-tangent series. He showed us the further we go, the closer to the estimation of pi we get. However, in order to get 10 digits of pi, we need to write about 5 billion fractions.

After that, another great mathematician, Leonhard Euler – who officially adopted the Greek letter “π” as a symbol to represent the value – found a more efficient equation for pi, when he was only 28. The symbol became iconic. Euler’s Pi equation calculates an infinite sum. The Basel Problem was named after him.

Euler also used pi to write another beautiful equation, Euler’s Identity.

Thanks to the Indian mathematician Ramanujan’s obsession with pi, we have many new formulas to find pi. When he arrived at Cambridge from India, he brought with him a notebook in which there were 400 pages of formulas to find pi.

After the invention of mechanical computers, mathematicians used Leibniz’s, Euler’s, and Ramanujan’s infinite series to calculate a trillion decimal digits of pi (Stanford Cryptography Group). Without a supercomputer, finding this many digits of pi would be difficult. For example, the mathematician William Shanks managed to calculate the first 707 digits of pi by hand but unfortunately, he had made a mistake after the 527th place.

Pi is everywhere

Children start learning about pi when they are in 7th grade and use it until they graduate from college. Even after that, most people use pi again when their children go to school. Pi appears everywhere in the universe. It is literally woven into our universe: the orbits of planets, electromagnetic waves, rivers, the colors of auroras, the structure of DNA, the Great Pyramid of Giza… If a scientist wants to describe the structure of the universe or find the relationship between planets, he/she definitely needs to use pi: anything involving a circle or a sphere is about pi. Circles appear throughout the natural world, whether they’re a soap bubble or the moon in the night sky.

 A Gif showing the clever play on the letters “pi”

Sinuosity of rivers

Pi has a direct relationship with rivers. But how? To figure this out, we need to measure the length of a river in two different ways. Assume that we know the starting and ending point of the river. First, we need the actual length to see how bendy the river is. In other words, the distance that you need to swim from the beginning point to the ending point. This whole length will be “L”. Second, we need to find a straight length. In other words, this time we need to fly from the beginning to the end. And this direct route will be a lowercase “l”. Now we can write the formula for the sinuosity by dividing L by l. The sinuosity is a ratio and measures how bendy the river is.

What is important here is there’s no limit to how high sinuosity can be. Rivers can be really bendy. However, Hans-Henrik Stølum proved that theaverage sinuosity of rivers around the world is pi. If you find the sinuosity of all the rivers and take the average sinuosity of them, you should get pi (Meandering River).

There is another interesting fact about sinuosity. Rivers can be very bendy at some points. But suddenly, those rivers become straight and make the sinuosity around pi. So, it is hard to find the sinuosity of a river equal to 7 because of fluid dynamics. Mathematicians found the highest sinuosity to be around 3.5 and the lowest sinuosity around 2.7.

At the extremely bendy point, rivers cut off after the bend point and make a shortcut to become straight again. This phenomenon is known as an oxbow lake, which controls the sinuosity of rivers. This keeps the sinuosity of a river around Pi.

Pi in Space

There is a mathematical order inherent in our universe. For instance, to understand our solar system, we need pi. We know that our planet moves in front of its host star. And the light comes from host stars. To talk about that light, we need to know how big the host star is. In other words, we need the surface area of the host star. The formula for the surface area of a sphere is 4πr², with r being the star’s radius. The size of a planet also helps scientists to guess whether it is habitable or not.

Another good example to show the relationship between pi and the universe is electrostatic force, which is the force between two electric charges. An electron exerts a force in all directions and forms a sphere field. Electrons also interact with each other on an electric field. To figure out that interaction, we need to find the surface area of spheres, where again pi comes up.

There is also a connection between pi and gravity. If you have had a chance to see Einstein’s field equations, you might notice that pi is there also:

The formula above calculates how objects with a large mass, such as stars and galaxies, can curve space and time with their gravity. Einstein said that, just like a ball sitting on a bedsheet, any form of momentum and energy can also curve space-time around it. In words, the formula is saying:

Gravity = 8 x π x Energy & Momentum

Lastly, if you take the square root of Earth’s gravity, you almost get pi.

Pi Day

After so many years studying pi, people decided to organize an official celebration of pi on March 14th. Since 1988, people have celebrated this magical constant. Coincidentally, Albert Einstein was born on pi day – March 14, 1879. Einstein also published his theory of general relativity on pi day.

The Google logos for Pi Day.

“How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?”
Albert Einstein

I have always been pretty sure that mathematics and science are the best languages to explain the natural phenomena. While for many mathematics is too abstract, for me, it is the beautiful language of the universe.

There is no upper limit to the numerical abilities of humans. First, we discovered fire, to get warm. Then, we needed light, so we invented electricity. When we needed to talk to someone 10,000 miles away, we invented the internet. Behind all these inventions, was mathematics.

Of course, the universe cannot speak or think. However, we, the people, can read the universe. There are many scientifically and mathematically inclined people who can read the universe and find answers and then describe them. We, the normal people, can also use our imagination as an apparatus to read the universe and nature. If we can read, hence, something is written. In order to write, a language is always needed. So, the universe should have a language. The letters are circles, triangles, hexagons, etc.

Everything in life has mathematical patterns. Think of the wild animals with stripes or patterns for the purposes of camouflage. But why does a leopard or cheetah or tiger have a particular design?

The Enigma codebreaker, Alan Turing, had a mathematical theory about leopard’s spots. Turing suggested in his paper “The Chemical Basis of Morphogenesis” (published in 1952) “a mathematical schema for the formation of the patterns found in animals and plants.” This was 60 years ago [1].

Stars have patterns. Astrologists have been looking at the outer space searching for patterns to better understand life. Whatever it may be that they find, it is always about mathematics.

Seasons have patterns. They come and go. And they influence nature: the climate changes, animals migrate north or south, rain comes, snow melts, the earth changes color, etc.… Of course, seasons cannot make these miracles. They can only have mathematical patterns.

Einstein had pondered for years on how mathematics works so perfectly. He knew that mathematics is the bridge or the language that connects humans with the universe. And being a connection between us and the universe makes mathematics the greatest achievement of mankind.

If you take a closer look at the patterns of our world, you will witness the language of mathematics. Let me give you some specific examples.

Fibonacci, the golden ratio, spiral, cabbage…

Our universe is filled with spiral designs. Spirals can be found in the shapes of the DNA double helix, flowers, elephant tusks, sunflowers, hurricanes, draining water, animal horns, a nautilus shell, a snail shell, a pinecone, a cabbage, a fingerprint, algae, galaxies… the list goes on and on. Tons of lifeless and living things have spiral designs. And they are not random spirals. They have something in common: the golden ratio! And surprisingly, “there is a strong case that this so-called ‘Golden Ratio’ (1.61803…) can be related not only to aspects of mathematics but also to physics, chemistry, biology and the topology of space-time” [2].

All these spirals in nature tell us there are numbers all around us. Let’s observe the numbers of petals on some flowers. When you count the number of petals of the flowers in your garden, you will get the numbers 3, 5, 8, 13, 21, 34, or 55. These numbers are not random numbers. These are very unique numbers; they are part of a sequence developed by Fibonacci, a 13th century mathematician, by adding up the last two numbers starting from 1:

1+1= 2, 1+2= 3, 2+3= 5, 3+5=8 …

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …

F_n= F_n-1+F_n-2, F₁=1, F₂=1

But, why are those Fibonacci numbers so important? The key is, the relationship between the progression of growth and the proportion. There is a harmonic proportion hidden in the Fibonacci sequence.

A fact: If you divide one number in the sequence by the previous number, the answers result in or come closer to phi:

For example: 5/3 = 1.6666;

13/8 = 1.6250; 377/233 = 1.61802575; 317811/196418 = 1.618033399

Definition: In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities [3].

These numbers can be demonstrated with the spiral of the florets in a sunflower. The florets in a sunflower head also form two spirals. If you count the clockwise and counterclockwise spirals that reach the outer edge, you’ll usually find a pair of numbers from the sequence: 34 and 55. If it is a very large sunflower, you will get 89 and 144 [4].

These spirals are not only in sunflowers. You can see them if you look at a pine cone or a daisy. If you mark the spirals and count them, you will always get a number from the Fibonacci sequence. And if you count in the other direction, this time you will find an adjacent Fibonacci number.

The nautilus shell, the golden mean

What makes the nautilus shell so special for mathematicians? Having the Golden Mean. But how do we know that the nautilus shell has the Golden Mean?

First of all, we will start with drawing a small, one unit square. Then we will draw another square which is larger than the previous one. We need to add in a counterclockwise direction. The length of each square has a value from the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … Then we can draw spirals, starting with the smallest one, outward through the largest one. Then the Golden Mean will appear.

Flowers, plants, or objects have no idea about mathematics, yet they manifest the best of mathematical patterns. This marvelous mathematical art has been placed in their nature for us not to be fascinated only but also to explore the mysteries behind it.

Note

1. https://www.bbcearth.com/blog/?article=the-maths-behind-a-leopards-spots
2. https://www.sajs.co.za/article/view/4033
3. http://mathworld.wolfram.com/GoldenRatio.html
4. http://www.sciencemag.org/news/2016/05/sunflowers-show-complex-fibonacci-sequences

The Fountain is a composition, one in which each and every member of the human family can hear his or her conscience’s calling, a reflection of what is not always visible to the eye, or a response to the yearning deep in the heart and mind; a response that sometimes finds its definition best expressed in a poem, and at other times in a journey into outer space or through the veins of the human body. It is reading the universe, the major book of creation, and making sense out of it by way of the manual of Divine guidance.

The Fountain is an effort to try and see the reality through the veils of apparent causes and to obtain our share from each phenomenon, each of which is a letter enclosed with a message addressing us.

The Fountain covers the following themes:

• analytical articles on religious and scientific topics
• reviews for books about new and contemporary issues
• answers for frequently asked questions

The Fountain prefers to publish articles which:

• encourage scientific discovery that is in the service of humanity,
• popularize scientific topics for average readers, rather than addressing to a field-specific audience,
• promote altruism and devotion to positive action,
• adopt a multicultural approach, aiming to find a consensus on universal human values,

• serve to break the stereotyped images in minds about different cultures and faiths, and provide guidance in a world of cultural diversity,
• accept everybody as they are, encouraging dialogue in society and preventing the idea of the other,
• underline that terror has nothing whatsoever to do with religious faith,

• do not deal with temporary agendas, like politics, but promote actuality instead.

Note: The explanations above aim to exemplify the type of topics with which the magazine is concerned in order to help brainstorming. Please do not feel restricted about writing on any other topic that may be suitable for the magazine.

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Proper sources, citations, and endnotes according to the Chicago Manual of Style should be provided. If another style is used, all citations must be consistent. Alphabetize bibliographical references in endnotes. References must contain: Author, (year of publication), title, place of publication, publisher, and page numbers. Citations within the text must be in the Harvard style: Author surname, year, page number(s). Quotations from the Sacred Books must be italicized. Provide the chapter’s name and number, and the number of the verse(s). Send original illustrations or photos in hardcopy, or on disk in Adobe Photoshop or Adobe Illustrator formats.

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In a world of relativities, however, 100 is not immune to varying perceptions. For the young, it is as far as the horizon; for the old, it is as if just around the corner. Maybe it’s not the most pleasing age to aspire to. Some years feel like a century by themselves, especially when so many events are compressed into them. 100, for an institution, is a signpost that proves a level of maturity, establishment, and depth of foundation. But 100 is also a promise for the future.

Here comes the 100th issue of The Fountain (hence you now know why so many words on the number 100!). For a daily newspaper or a weekly magazine, the 100th issue is not the biggest target to strive for. But for a periodical like The Fountain – which publishes serious content on various disciplines while trying to maintain a perspective and level of discourse about issues that pertain to all fellow human citizens, the brothers and sisters of a global home – 100 is not an insignificant number to reach. For over two decades, The Fountain has always chosen to stay above the fray of day-to-day events, temporary politics, or issues that are irrelevant to others. We have been selective in what we publish and tried to ensure content of universal appeal yet with an awareness of differences and respect for local diversities in color, language, culture, and faith.

In this 100th issue, we invite our dedicated readers to write on their takes on The Fountain. Write in 100 words on what The Fountain stands for in your life. What do you understand of its message? How do you think it is different than another publication? Write your life philosophy based on where you stand vis-à-vis The Fountain’s message. Do your best to reach or limit your writing to 100 words, but your reflection does not have to be the exact number. There will be surprise gifts and recognition for participants. Follow our website and social media announcements regarding the deadline and how to submit your work.

In this issue, we continue with Dr. Beecher’s second part on nation and the construction of self identity, the first part of which received positive feedback in the previous issue. His work is complemented by Dr. Kavi’s research on identity and its relationship with religion and culture. Dr. Aydin’s article on memetics is an additional contribution to this issue laying down some perspective on questions such as “How does the mind work? How do humans learn and develop? How does culture form and transfer to future generations?” The lead article sweeps over these issues with a more profoundly human twist on human life, which we are obliged to travel” for the sake of finding ourselves and realizing our true essence. As The Fountain hits 100, it’s a good time to reflect on where we all are in that journey.

Where am I?

There are 46 chromosomes in your body, carrying 20-25 thousand genes. Chromosomes and the genes they contain shape the genetic memory of a human being. Genes can contain hundreds of features, and these are revealed over time. For instance, you do not have any teeth when you are a newborn, but the time when you will get your teeth is encoded into your genetic memory. Once genes receive the action command, teeth start to emerge.

There are hundreds of genes located on chromosomes, all the way from the chromosome number 1 and 2, to chromosome number 46. For example, there are around three thousand genes found on chromosome number 1. The Y chromosome, in charge of male development, only contains 125 genes. A distinct address (locus) for each gene on the chromosomes is recorded. If you ask about the address of the fibrillin gene that synthesizes me, it is 15q 21.1, i.e., 15th Avenue, Long arm street, 21st pl, Number 1.

In other words my residing address is the 1st subband of the 1st band of the 2nd region located at the long arm of chromosome number 15. We are three siblings, known as fibrillin1, fibrillin2 and fibrillin3.

We stretch and relax like an arch. We can expand and tighten like an inflated balloon and then return to our previous state. If by an error, we happen to fail to restore ourselves after inflation, the tissue’s architecture gets deformed and expanded fibers cannot regain their original shape anymore. When observed in veins, this situation is called an aneurysm. The frequency of this disease is approximately one in ten thousand, which is also called ballooning. That said, my flexing is necessary. Veins flex so that the blood pumping through them doesn’t cause any turbulence, as it would otherwise be during a vacuum occurring inside metal water pipes. Flexible sportsmen who do acrobatic moves do not compare with me. I can bend, curve, flex, relax and constrict, inflate, deflate and transform like elastic, from one shape to another, for your health and overall convenience – all because of the wondrous features granted to my nature.

What kind of a fiber am I?

I provide structural support for the fabrication of elastic fibers in the connective tissue as a protein synthesized according to the code of the fibrillin gene. In case of my failure or absence, weaknesses occur, especially in the connective tissues of organs that are rich in elastic fibers, such as the aorta, lungs, and eye balls. The iris (the colored part of the eye), pupil, and eye lens display changes in accordance with levels of light or distance of objects observed. These changes are controlled perfectly according to my work, and humans often don’t even notice this. We also help the eye lens constrict and relax. It can be understood that we are such a great blessing granted for your service. Of course, if we tried to count all the blessings we’ve been given, and never even consider, it would be impossible!

My weight is 350 kilo daltons. A Dalton is an atomic mass unit approximately equal to one hydrogen atoms’ mass, which is 1.66×10-24. I consist of 2.871 amino acids. I am formed by the sequential arrangement of 20 amino acids that exist in your body as the smallest unit of proteins. We bind each other to become 10-12 nanometers wide microfibers as the result of a process called polymerization that brings loops of a protein chain together. These microfibers are brought together with the elastin protein that provides elasticity in our body. The system that we form with elastic fibrils constantly serves the body’s blood vessels, primarily the vessels located in your eyes, heart, and many of your tissues, such as your skin and nerves.

What do I do? We fulfill commands that are requested from us in many tissues and organs, without any flaws. Scientists call us the wonderful building blocks of the body’s architecture. We can extend twice as much of our length. We are always on task: while you are breathing, when your heart is pumping blood and your stomach is digesting food, or the moment you are gazing at nature with your eyes. We are given the duty to prevent many organs from tearing, including the heart, lungs, stomach, and blood vessels. One of the places I work most frequently is the aorta, the body’s major artery. Your heart beats approximately a hundred thousand times a day. A high level of pressure develops in the arteries during the pumping process. You would suffer greatly without the help of our elastic fibers. Blood vessels would rupture, ending your life. This high pressure is tolerated only through the expansion of the vessel’s diameter without any decrease in length of the artery. This diameter regulation is designed so wondrously that blood flow remains the same; no shaking or waves are observed. This diameter control happens via the fibrillin protein located inside the vessel.

I also play a role in the vitality and tension of your skin. Skin is essentially a dense fibrous connective tissue composed of a protein called collagen. I am also one of the main elements of this connective tissue. As you age, this layer starts to dry and has lesser fibrous proteins; therefore, as fibers decrease, so does my tension, and I start to wrinkle. Elderly people do not like getting wrinkly, but this is your fate. Whatever you do, I will also age and die.

I cannot go without pressing this important issue: Staying under the sun for a long time degrades me. If done properly, sun light is useful for skin. But solar radiation damages the live tissues and organs. This radiation is an effective factor both in degradation of protein structures, and the formation of varicose veins and skin damage. It is reported in various sources that exposure to sun rays leads to alterations in the genetic material of skin. Ultraviolet rays speed up the degradation of skin. In medical language, this is called oxidation via free radicals. Please do not burn us and yourself while sunbathing. Even if you do not care for yourselves, you should still be considerate of us. If you say that sunbathing both helps, with vitamin D synthesis and reducing the risk of osteoporosis, I would like to remind you that for the vitamin D synthesis of skin, it is sufficient to expose your hands, feet and face to the sun.

How is life without me?

Though we were wisely designed, sometimes, you are tested by certain diseases in which we are not present. Absence, as they say, makes the heart grow fonder!

Life without me is unbearable. I could give a couple of examples, should you like. If I was not created, your skin would not be flexible. You wouldn’t be able to control your eye lenses. Your aorta would not be flexible and your heart, which beats thousands of times a day, would be torn under the high pressure in a short amount of time. Major problems would occur with the development of your stomach, lungs, and other organs.

I also have a significant job keeping TGF-Beta (which helps cells grow) function under control. To give you an idea of how important this is, imagine your communication system turned upside down. Now imagine how complicated are the communication systems connecting billions of people around the world, how a mess it would be when they are out of service. These are nothing when compared to the human body. There are 100 trillion cells in the human body, communicating with each other instantaneously. A cellular community that is fifteen thousand times more crowded than the earth’s population communicates via small molecules, like us. Cellular proliferation and tissue differentiation would fail if cells failed to communicate. The full spoon of food in your hand would not end in your mouth but maybe in your ear or your eyes.

If a mutation happens with the Fibrillin-1 gene, Marfan syndrome can occur. This disease, which was defined in the 1800s, is named after its discoverer. The frequency of this disease is one in five thousand. One of the major lethal consequences of Marfan syndrome is an aorta tear. This is in addition to many problems with the eyes, skeleton, and cardio-vascular systems. Many of the patients die in their 30s or 40s because of the flaws in the cardio-vascular system. Of course, death may occur at any age because of an aorta rupture. 14% of the patients with Marfan syndrome display chronic obstructive pulmonary disease (COPD), which is associated with breathing problems, because the integrity of lung tissue is compromised. Another disease I help prevent is called Ektopia lentis, in which the eye lens is displaced from its original position. Normally, I help eye functioning. When my fibers relax or constrict, depending on light, I help the eye to relax, enabling both near and far sightedness. With Ektopia lentis, anomalies on the front vestibule of the eye, a high degree of myopia, and retina damage occur.

If overproduced, I can cause another problem with the eye, called exfoliation syndrome. This is when fibrous connective tissue, like me, accumulates in the eye – it’s commonly called glaucoma, or ocular hypertension. In some people, as they age, a fibrous material like hair dandruff collects on the eye lens. This material, dislocated by movements of the iris, blocks the drainage channels that discharge the intraocular fluid. Eye pressure increases as the result of failed drainage. As you see, I am not a problem when I am synthesized normally, but can be trouble if over produced! My final request from you!

You have seen our amazing works and complicated functions. Therefore, please remember me and my friends. Please do not ignore our efforts and activities. Be grateful for the blessings provided through us, even if you can’t see them. And take care of us, please – don’t get carried away with too much tanning!

Loneliness is a serious public health concern, akin to both obesity and smoking. Why is it not treated as such? Through faith, we can combat this growing crisis.

Loneliness is a state when people are unable to share their inner world with anyone around them. It is very natural that a person desires to be alone from time to time. When this is a short term desire, it can be a means of acquiring harmony with life; however when it becomes chronic, it is harmful for human health. Therefore, solitude is like a sword which has two sharp sides. Solitude in itself is not good or bad; rather the period and severity of it defines if it is good or bad. The severity of loneliness is not measured by how many people that individual has in their social environment; it is measured by how the individual feels in his inner world. In modern societies, loneliness is an important topic of multidisciplinary research, especially in our times due to overuse of social media, as “loneliness” is quickly becoming endemic, threatening our public and individual health.

One of the leading factors behind the increase of loneliness is the spread of immigration, which suddenly tears people from their original cultures and from their families. With the social bonds weakened or broken, loneliness is more severely and increasingly felt. For example according to the 2006 records, 29 million people in the US, a predominantly immigrant nation, were living alone. When compared to the records from 1980, this means a 30% increase in the number of people living alone. Another shocking number is that while 10% of people said they wouldn’t share their personal matters or trust with another person in 1985, this number increased to 25% in 2004.

In our times, loneliness and isolation have become as risky as smoking and obesity. The latest research in neurobiology and clinical research has shown that chronic loneliness has negative effects on the heart, and the immune and nervous systems. Contraction and resistance are much higher in the veins of people experiencing chronic loneliness. Blood pressure rises with the arteries narrowed and shrunk. This makes the heart beat abnormally faster, and this results in the corrosion and laceration of the capillaries. According to epidemiological studies, people who feel alone tend to have shorter life spans and illnesses such as heart disease and depression are at higher risk. They’ve also proven that people socially isolated or feeling lonely are more likely to catch a viral infection.

Studies have shown that, an individual can still feel lonely even though the number of people around them is high. Their social environment, statue, reputation, and property are only of formal assistance and they do not directly prevent an individual from feeling alone. Spiritual loneliness can exacerbate this feeling. Without a deep spiritual life to seek comfort in, they can fall further into depression when faced with problems.

Genetic thermostat and activation of loneliness

There are parts of the human brain which almost work as a thermostat and activate loneliness. Since the information for these parts of the brain are encoded in our genes they are called the genetic thermostat. This genetic thermostat, which we have inherited from our parents, has the duty to adjust the time of response we give to a trigger. Socio-cultural factors and genetic inheritance are assigned to determine the thermostat’s intensity and period of operation. These principles are mostly shaped in childhood and determine the threshold and intensity of the loneliness that is felt later on. In other words, the pain and suffering caused by loneliness depends on the genetic thermostat of the individual. In some genetic structures, the activation settings of the thermostat are low; and in some they are high. Therefore, the feeling of loneliness resulting from social isolation triggers a different response in every person. Even though clinical loneliness does depend on genetics to some extent, it is a curable. Around half of the factors that are behind feeling lonely depend on genes. A study about loneliness conducted on 8,683 twins showed that genetic treatments are 37% effective in treating this feeling. In summary, a departure from our social environment makes us go through different levels of pain depending on our genetic thermostat. Therefore, loneliness is felt in different forms in different natures.

The biological consequences of loneliness

Our body gives out different messages through pain and suffering. In the same way pain and suffering gives us messages of something going wrong in our body, extreme loneliness also has effects on the body, alerting us of something going wrong. Anxiety and physiological changes in our body give out alarming signals when our relationships weaken. These signals warn us that we have to change our attitude and actions in a way that will strengthen our relationships.

It has been observed that stress molecules (cortisol in saliva, adrenalin in urine) increase significantly in people who go through deep phases of loneliness. It was also observed that the body’s sympathetic nervous system, which is responsible for a “fight and escape” response, increased these activities, too. In people who are lonelier, the amygdala is triggered; this further heightens a person feeling of risk. These people are constantly on edge, their “flight” response activated. Therefore, people going through chronic loneliness have very low sleep quality. They wake up tired or even exhausted. They take less pleasure from activities that give rest and bring joy to other people. The degree of their satisfaction and happiness is low. They start losing the joy of living.

Another area of the body affected is the ventral striatum area, which is the award mechanism activated by factors such as food or money, as well as social feelings like sympathy. In a study conducted at the University of Chicago, the activity of the ventral striatum in 23 female university students feeling deep loneliness was measured with magnetic resonance scanning. The study showed that when these females were shown pictures of laughing and happy people, there was a significant decrease in their award mechanism compared to a normal person. So the deep feeling of loneliness locks the award mechanism of the brain, preventing the person from taking pleasure from life, thus leading the person to anxiety and sorrow.

Deep loneliness also affects the activity of the prefrontal cortex of the brain. This is the area of willpower; it brings a limit to activities triggered by instincts, such as eating or drinking. Field studies and surveys have shown that people feeling deep loneliness are more likely to have an unhealthy diet, increase their consumption of alcohol, and live a passive life style without exercising. Moreover, in the management control conducted in labs and that require prefrontal cortex activation, lonely people show little success. The prefrontal areas of these people do not respond fast enough, leading them to little success in these experiments.

Lonely people are more emotionally unbalanced when faced with stress. They find it very hard to control their emotions. They are more sensitive to negative hints when they are among people. They tend to interpret social interactions negatively rather than positively. In one study, the words that address the emotional state of a person were flashed on a computer screen with different colors. Later on, the colors of these words were asked to people feeling deep loneliness and to people who did not feel lonely. People feeling deep loneliness gave delayed answers about the colors of words such as “isolation, rejection, exclusion.” The people who did not feel lonely showed no such delay. This experiment shows that the human brain was created to give alarm signals in case of deep loneliness.

Social bonds and interactions enable a person to be open and accessible to other people. To make this openness and accessibility beneficial is both easy and difficult, simple and complex. People go through periods of wanting to be alone – with themselves or with God – just as they go through periods of desiring more social contact. A healthy person moves freely from state to state. To discover and control this oscillation between the two needs is to learn the best way to manage our lives.

How can deep loneliness be cured?

Since social isolation and loneliness affect people differently, a person should know the nature of his genetic thermostat and should make an effort to stay at his individual comfort zone. Every person has zones or intervals where they feel comfortable expressing their emotions, ideas and attitudes. Similarly, every person has different zones and thresholds for loneliness. Every person needs to understand their limits. Just as our fingerprints are unique, so, too, is the amount of solitude we need.

For those already suffering from loneliness, one of the best cures is a change in point of view. In other words, loneliness is cured by changing the person’s focus from the negative to the positive. People lead better lives when they adhere to the maxim, “Those who attend to the good side of everything contemplate the good. Those who contemplate the good enjoy life” (Nursi, The Letters, Epigrams – Seeds of Truth). People who understand and practice this in their lives have obtained the key to happiness.

A deep, personal relationship with faith is also a major cure for loneliness. Friends and earthly occupations only give comfort to a person until the grave. If the person who is isolated has very solid spirituality, and has acknowledged God as his real friend, he never undergoes a feeling of loneliness that would otherwise destroy his health. With faith and hope, the dungeon of loneliness becomes a school of imprisoned Prophet Joseph. Faith reminds him: “If you want a friend, God is sufficient. Indeed, if He is a friend to you, so is everything. If He is pleased with you, even if the whole world is displeased, it is of no consequence” (Nursi 23rd Letter, 21st Gleam). Sorrow, grief, sadness will not stop by you. Even if they do stop by you, they are bearable since they come from Him. They turn into worship by activated patience. Through faith, a person can achieve fulfillment in both this world and the next.

References

• Miller, G. 2011. “Why Loneliness Is Hazardous to Your Health.” Science. Vol. 331. 14 January, pp. 18-140. www.sciencemag.org
• Cacioppo, J. T. and Patrick W. 2008. Loneliness: Human Nature and the Need for Social Connection. W.W Norton Company. New York.

Concepts like the number zero, negative numbers, complex numbers, matrices, and spatial geometry are inventions of mathematicians which were studied earlier and presented especially for the use of physicists. When mathematicians theorized the “Group Theory,” they were reported to have said, “Finally we have developed something that physicists cannot use.” However, this theory, which stemmed from intangible algebra, was found to be useful in investigating the symmetry of physical systems and had serious applications in particle physics.

If there were no mathematical advances, would physics and other sciences have developed as far as they have? What does it mean that sciences are found in such an interrelated state, and thus support each other?

The perfect relationship between physics and mathematics, as in the expression of many physical laws via simple mathematical equations, is truly amazing. The laws that describe the physical world – from equations expressing the laws of motion (like X=V.t, V=a.t, F=m.a h= (gt2)/2), to basic electrical equations (like V=I.R, P=I.V, E=V/d), going all the way to the equations that define gravitational forces and the expansion of the universe (like F=G.m1.m2/d2, V=H.d) – can easily be expressed through mathematics. Furthermore, this simplicity and plainness in creation of the universe fascinates many scientists. Einstein expressed this fascination when he said, “The most incomprehensible thing about the universe is that it is comprehensible.”

One of the most important relations between mathematics and physics is that the independent study of intangible works of mathematics unexpectedly became one of the best tools to describe the physical world. Numbers, for example, are one of the greatest inventions of humanity. Humans have used them to quantify their properties. For thousands of years, people used numbers, but then the concept of negative numbers developed for seemingly no reason. For centuries, negative numbers were seen as nonsense. Of course there is not a square with a negative side length, a circle with a negative value area, or a classroom with negative number of students. However, negative numbers were found to be applicable in many areas of physics; they are now accepted as being as real as positive numbers. For instance, it is almost impossible to graph position-time, speed-time, acceleration-time, and the momentum-speed relation of objects without negative numbers.

Ellipses, parabolas, and hyperbolas (plane sections of cones cut in different shapes) were studied by Apollonius (BC 262-200), who was a contemporary of Archimedes. Interestingly these shapes were one day used by Kepler and Newton to describe the orbits of heavenly bodies like planets. Three dimensional pentagonal and hexagonal patterns, like those on the surface of a soccer ball, were also investigated by Archimedes. This shape has been found to be in exact configuration of a special carbon molecule composed of 60 atoms.

Likewise, the number zero, which was introduced by Muhammad bin Ahmad, in 967, led to many innovations in mathematics, as well as physics. Did al-Khwarizmi (780-850) know, when he found and utilized 1st and 2nd degree equations, that he was working on something mathematicians and physicists could one day never do without?

Imaginary numbers, as proposed against the main principles of arithmetic, also provides a very good example for this topic. We cannot think of a number whose square is negative in normal conditions. In other words, when a number is multiplied with itself, the resulting number is always a positive number. But mathematicians thought of a number that is negative when squared and continued various studies accordingly. Again, these studies have proven to be an important tool, especially in understanding electrical circuits by physicists.

Let’s finish our examples with ones from modern physics. Riemann (1826) was a mathematician who studied spatial geometry and proposed the concept of space curves. Mathematical equations designed by Riemann, pertaining to spatial geometry, were used by Einstein in 1908 to describe and formulate the concept of general relativity. Einstein also used Minkowski’s four dimensional geo-spatial continuum when developing his theory of general relativity.

There are many more examples. The famous Russian mathematician Friedman established a mathematical model that allows the expansion of the universe by improving Einstein’s model of universal geometry. This model was also later confirmed by the physicist De Sitter in discovering universal expansion and by Hubble in formulating the expansion. In addition, well before the discovery of quantum mechanics, Davit Hilbert proposed the complex vector space with a very different mathematical purpose known as “Hilbert Space.” This concept of space with an infinite number of dimensions is today used by quantum mechanics.

Sometimes physical realities can be foreseen via these invented equations. For example, Dirac proposed the existence of a particle known as the positron (or as we call it, the twin of the electron; it just differs by the charge) through his mathematical equation that he wrote in 1928. Four years later this particle was discovered by Carl D. Anderson, as predicted. To name, James Clerk Maxwell (1831-1879), a famous physicist and mathematician, predicted the presence and speed of electromagnetic waves mathematically via his own equations. Later, these waves were detected by Hertz (1886) through experiments. Again, Maxwell calculated the speed of electromagnetic waves via his equations, and by revealing that it was equal to the speed of light, it was understood that light was also a type of electromagnetic wave. Nowadays, the particle called the “graviton,” which is supposed to be in charge of gravitational forces, and the “Higgs” particle, that theoretically fills space according to quantum theory, are waiting to be discovered.

The book of nature is written in such a way that it is expressible by mathematical language. Famous physicist Sir James Jeans (d. 1946) expressed this situation as follows: “From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician.” Yes, the level of knowledge that is at play in the universe encompasses both physics and mathematics. The overall interconnectedness of sciences and the interdisciplinary character physics and mathematics point to an owner of this knowledge.

As a conclusion we can deduce that physics and mathematics, just like material and non-material worlds, are in fact intertwined with each other’s various dimensions. The physical face of the universe is the place where records are kept and concepts of matter like heavy or light, big or small, and soft or hard, exist. The mathematical face of the universe (as if spiritual) is the unseen side of events or materials that are hidden and intangible. In a way, this relation between physics and mathematics is a display of the material and spiritual sides of universe.

Nuri Balta is the Head of Physics department at Samanyolu Schools in Turkey. He is also pursuing a PhD degree in Physics at Middle Eastern Technical University, Ankara, Turkey.

If you are involved in an educational system either as an educator or the parent of a high school student, then you might be familiar with the important role of AP courses in the life of high school students across the United States. AP courses also play important roles for high school students in other countries because AP courses are offered at all International schools opened by the United States. For instance, according to the 7th AP Report to the Nation, “universities in more than 60 countries recognize AP Exam scores in the admission process and/or award credit and placement for qualifying scores” (College Board, 2011, p. b). In other words, students enrolled in AP courses in any of those countries can earn college credit the same way they would do in the United States. So this is not a local phenomenon at all. Naturally, any parent or educator might wonder what the history of AP courses is, and what their benefits and roles are for high school students.

I have worked as an AP Coordinator and Guidance Counselor for a public school for more than three years. Unsurprisingly, many middle and high school parents have asked me numerous questions regarding the AP program. The following interview, which took place between one of the parents who had a daughter at the school and myself, should help the reader develop a good understanding of AP programs and their benefits for both parents and students.

Q: What is the Advanced Placement program?

A: The AP Program was created by the US College Board in 1955 with the motto “Connecting Students to College Success.” The AP program aims to prepare students for an academically demanding college experience. “Advanced Placement is a curricular option for academically superior tenth, eleventh, and twelfth-grade students. Naturally, courses offered in the program are more demanding in terms of time and intellectual skills than corresponding courses in the regular high school curriculum” (Postsecondary Educational Planning Commission, 1988, p. 4). Initially, AP courses began as a program for elite private school students to take college-level course while still in high school. This way, outstanding students could begin college with already earned credits needed for freshman year, which potentially would help them graduate college earlier.

Q: What is the role of the College Board regarding AP courses?

A: AP courses are developed and maintained by a non-profit organization, the US College Board, founded in 1900. This organization provides training for AP teachers, provides curriculum resources for both teachers and students of AP courses, and supports universities as they define their policies regarding AP grades, and develops and coordinates the administration of annual AP examinations. According to the US College Board, the AP program offers more than 30 different courses as of 2010. In 2009, nearly 1.7 million students worldwide took 2.9 million AP exams.

Q: Are AP takers increasing or decreasing?

A: According to the recent data released in the 7th AP Report to the Nation, the number of seniors taking at least one AP course and scoring 3 or more on AP exams has increased significantly (College Board, 2011, see Table I). The increases are due to growing awareness of the program, obvious benefits of taking AP courses, and the significant role of AP courses in the college admission process (Reichard & Keirn, 1999). Moreover, the No Child Left Behind Act (2001) offers states substantial federal funding, $24 million annually, to expand AP programs in underserved populations (Manzo, 2005).

Q: Are AP classes smaller than regular classes?

A: Since only academically outstanding students are accepted into AP classes, they are to be smaller, usually less than 15, as opposed to regular classrooms with 25 to 35 students. For instance, smaller schools like charter schools, might provide better opportunities for AP students in terms of class size because their student population is usually smaller than local public schools. Therefore, as is the case in my school, it is not a surprise to see AP classes with as low as 2 or 3 students per course. On the other hand, smaller schools may not offer as many AP courses as other public schools due to its student size.

Q: What about teacher quality? Do better teachers teach AP classes?

A: Yes, it is likely that AP teachers have either better training than other regular course teachers or more years of teaching experience, with higher degrees in subject areas. Moreover, AP teachers receive annual trainings in the subject they teach which is organized by the College Board. For example, I attended one of those trainings when I was assigned to teach AP Calculus in 2009. In trainings, you learn how to teach the course and they provide you with lots of resources to teach your course in depth. Conclusively, I believe that AP teachers may be better prepared in their content area as opposed to non-AP teachers.

Q: Can my daughter graduate early from college if she takes AP courses?

A: Yes, taking AP courses in high school will enable your daughter to realize her goal of graduating early from college because students can pursue college level studies while still in high school. That means AP students can transfer their high school credits to college and can replace them with their required college classes thus eliminating some freshman courses and graduating early. As a result, AP courses have become very popular among parents. They want their children to take as many AP courses as they can take. But taking an AP course is not enough to earn a corresponding college credit.

Q: What else should my daughter do in order for her to earn college credit?

A: For that purpose, students are required to take the AP exams administered annually in May prepared by the Educational Testing Service located in Princeton, New Jersey. This is where AP teachers, parents, and students’ decide if students should take the AP exams of the courses they are taking. They usually look at students first semester performances in those classes. If students do not perform well in those classes, they are either recommended to continue taking the AP courses but not to take the exams or drop the course before first semester ends and start taking regular classes of the same course. AP exams consist of a multiple-choice section and a free response section. College professors and AP teachers score the open-ended questions once a year in June. The results of the multiple-choice and free response sections are combined to determine a composite score and then converted to a 5-point scale: 5 being extremely well qualified; 4, well qualified; 3, qualified; 2, possibly qualified; and 1, no recommendation.

Q: Do all colleges give credits for AP courses?

A: As common practice, more than thirty five hundred colleges give college credit to test scores 3 and above. Although this is still a common practice in almost all colleges, some universities and colleges have recently started to limit credits by requiring either a 4 or 5 exam score. For example, the University of Pennsylvania is very strict in awarding the AP Calculus credit and MIT is requiring its students to re-take a college introductory chemistry course at their institution regardless of their AP Chemistry scores while they are all still accepting other AP courses (Manzo, 2005).

Q: Do having AP courses on my daughter’s transcript increase her chance in college admission?

A: The use of AP courses in the admission process began after the 1980s. At first, only highly selective colleges and universities considered AP courses to make fine distinctions among the increasing number of applicants (Reichard & Keirn, 1999). Today, AP and honors courses receive special consideration by almost all selective colleges and universities in the admissions decision. The way AP scores are used may vary from one institution to another. For example, the University of California recalculates an applicant’s high-school grade-point average (HSGPA) by giving additional “bonus points” for approved AP courses while others do not recalculate but accept the school’s weighted HSGPA. Regardless of how colleges evaluate students’ AP courses, yes, having AP courses on a transcript puts a student in a more advantageous position as compared to non-AP students in admission decisions. Once, I remember a parent who was evaluating all the high schools in her district in terms of their AP offerings to enroll her son. When she was asked why she was doing so, she said it was because colleges look at the number of APs on an applicant’s transcript to make an admission decision. As a high school counselor, I know that this is a common practice among upper middle-class parents to ensure their children get a college admission. Thus, this puts great pressure on schools to expand their AP offerings.

Q: Then, can I say that I will pay less tuition and save time?

A: Yes, indeed, taking AP courses in high school will save the student and parent, both time and money. As of today, skipping an introductory course in college could translate to an average of $3,000 per course. For example, one of my students took 9 AP courses while she was in high school. It is equivalent to almost a year of time and $27,000 money. Why would a reasonable parent and/or student miss this great opportunity?

Q: But I am afraid that my daughter may not graduate from a college because many high school students are not ready for college challenges both in terms of academics and in life?

A: Yes, you are right to have such concerns because Lewis (2010) reports that just 56 percent of those who enroll in a four-year college earn a bachelor’s degree. The number one reason why the rate is low is because students are mostly unprepared for the college experience. On the other hand, research has revealed that students who pass AP exams are more likely to graduate college on time (College Board, 2011). For example, in a study sponsored by the College Board, it was found that taking AP courses in high school and passing the exams appear to help students perform better in college classes and graduate on time. They analyzed four incoming classes at the University of Texas from 1998 to 2001 by looking at their ten individual AP subjects. These researchers reported that, “AP Credit students consistently outperformed non-AP students of similar academic ability in all college outcome measures” (Keng & Dodd, 2008, p. 1). Thus, taking AP courses and passing its exams usually put students one step ahead of their non-AP counterparts.

Moreover, according to Dillon’s (1986) study, completion of AP courses convey to colleges that students who have taken AP classes have developed scientific inquiry, reasoning, problem solving, and analysis methods. In other words, they are more ready for college challenges. As a result, it is not surprising to see that academically prepared high school students are not only more successful in academic work in college, but they are often more self-confident, have increased aspirations and “fit-in” more easily into college. This is true because AP students are exposed to the academic rigor, expectations, and autonomy, which are usually linked with the content and rationale of college curriculum. For instance, Syracuse University found that students with AP credits showed as high as a 96% first-year retention rate while the national average was 79% (Miller, 1994). Therefore, taking and completing AP courses help students have a smoother transition from high school to college in terms of both curriculum and lifestyle.

Q: My last concern is about my daughter’s senior year. I know from my oldest son who didn’t study much and skipped his classes a lot. Therefore, he barely passed his classes and graduated. Thus, he did not get an admission to a 4-year college. Can my daughter really take AP exams during her senior year?

A: All high school counselors know that “senioritis” is a disease and that it is contagious and there’s no vaccination or cure for it. Delicath (1998) found trends in AP courses as they deal with high school seniors. Delicath stated that AP classes help solve the problem of “senioritis,” defined as senior-year boredom among capable high school students who complete most of their graduation requirements by the end of their junior year. The good news is that the seniors who enroll in AP courses often remain more focused and attached to learning than their non-AP counterparts. Thus, seniors overcome their stresses and last year boredom.

In conclusion, in light of all its benefits, I would strongly suggest all high school administrators and counselors to be more knowledgeable about AP and try to create a very strong AP program at their schools so they can send more students to four-year colleges. Also, having a strong AP program at schools prevents students from dropping out due to financial reasons, first generation fear, and so on. Therefore, it should be the goal and duty of all high school teachers and counselors to inform and prepare their capable students to benefits from this great opportunity.

Alpaslan Sahin, PhD from Texas A&M University, College Station TX, is a school administrator. His research area is Mathematics Education.

References

• College Board. (2011). The 7th annual AP report to the nation (100084202 10b-2333).
• Delicath, T. A. (1998). The influence of advanced college credit on college students’ integration and goal attainment: A longitudinal study. Dissertation. (UMI No. 9911930).
• Dillon, D. H. (1986). The advanced placement factor. Journal of College Admissions, 113, 14-17.
• Keng, L., & Dodd, B. (2009). A comparison of college performances of AP and non-AP student groups in 10 subject areas (College Board Research Report No. 2008-7). New York: The College Board.
• Lewis, K. R. (2010). High college dropout rate threatens U.S. growth. The Fiscal Times. Retrieved March 19, 2011, from
• http://www.thefiscaltimes.com/Articles/2010/10/28/High-College-Dropout-Rate-Threatens-US-Growth.aspx
• Manzo, K. K. (2005). Mass appeal. Teacher Magazine, 16(5), 11-12.
• Miller, L. (1994). Effects of racial and socioeconomic factors on advanced placement programs. Dissertation. (UMI No. 9606827)
• Mores, R (2009). Methodology: America’s best high schools. Retrieved February 27, 2011, from http://education.usnews.rankingsandreviews.com/education/high-schools/articles/2009/12/09/methodology-americas-best-high-schools
• Newsweek (2008). FAQ: best high schools. Retrieved February 8, 2011, from
• http://www.newsweek.com/2008/05/17/faq-best-high-schools.html
• Postsecondary Education Planning Commission (1988). Funding of acceleration mechanisms. Report 1. Tallahassee, FL: Author. (ERIC Document Reproduction Service No. ED 293 452).
• Reichard, G. W., & Keirn, T. (1999). The advanced placement exam in history: Growth, controversies, and new perspectives. The History Teacher (Long Beach, Calif.),
• 32(2), 169-73.