“Free radicals” are a special type of atom that have been linked to many age-related diseases. They form as a result of a process called Oxidative Stress, which takes place when an oxygen molecule splits into single atoms with unpaired electrons. The nature of electrons is such that they like to be in pairs and as a result will “freely” and “radically” search throughout the body for another electron to pair with. They could almost be considered romantic if they were not so dangerous!

Their main danger comes from the damage that they cause to cells or cell membrane, proteins, and DNA. Cellular damage occurs when free radicals travel through cells and disrupt the structures of other molecules. The gradual accumulation of them, and the increased damage that builds as more and more of them collect, is what helps cause many of the aforementioned aging diseases. Our body is under constant assault from oxidative stress, and cells may function poorly or die if it occurs too frequently and without proper bodily maintenance.

Free radicals are a waste byproduct that form as a result of various chemical reactions that take place during our bodies’ normal metabolic processes. They are then “dumped,” and their eventual buildup will often harm our bodies much like how factory waste harms the environment However, they are not entirely useless; it is impossible for our bodies to turn air and food into chemical energy without a chain reaction of free radicals. Free radicals are also a critical part of the immune system, as they additionally move through our veins and can confront foreign invaders [1].

What are free radicals?

Understanding free radicals necessitates an elementary knowledge of chemistry.

Electrons orbit around atoms in levels called shells. Each shell is filled by a fixed number of electrons, and when the first shell is full then electrons will start to fill the next shell.

If there is an atom whose outer shell is not full then it may bond with another atom by using the electrons to fill its outer shell. These types of atoms are known as free radicals.

Atoms that have a full outer shell become stable, however free radicals are unstable. They are “desperate” to acquire the full number of electrons that are necessary to fill all of their shells and will therefore react quickly with other substances.

Take the example of oxygen molecules. If they split into single atoms that have unpaired electrons then they too will become unstable free radicals that seek other atoms or molecules to bond to. If this procedure continually occurs, then it will begin a process called oxidative stress.

Smoking, UV rays, air pollution, fast food, pesticides, ionizing radiation, drugs, and inflammation have all been linked to the formation of free radicals. We must be diligent when it comes to understanding how these influences can affect our bodily health, and then fight back with natural antioxidants.

Free radicals are heavily linked to aging

One of the effects of oxidative stress is that it can damage our body’s cells and thus promote many of the diseases and symptoms related to aging, such as wrinkles and gray hair. They will take electrons from other atoms in order to become more stable, a process that may cause diseases or signs of aging [2].              

In 1956, the “Free Radical Theory of Aging” was outlined as a way to understand how exactly our bodies age over time. Everybody ages, and as we age our body loses its ability to fight the effects of free radicals. Over time our bodies produce more free radicals and more oxidative stress, which increases the rate at which cells are damaged and thus can bring about degenerative processes.

Many age-related diseases such as muscular degeneration, certain cancers, atherosclerosis, cardiovascular disease, emphysema, Alzheimer’s disease, Parkinson’s disease, ulcers and all inflammatory diseases such as arthritis and lupus, and many others are linked to free radicals. Free radicals can be found in the food we eat such as fried foods, the medicines we take, the air we breathe, and the water we drink. Free radicals are also found in alcohol, tobacco smoke, pesticides, and air pollutants.

Several studies and theories have been linked to oxidative stress and the buildup of free radicals including: [3]

• Genetic degenerative diseases, such as Huntington’s disease or Parkinson’s
• Age-related changes in appearance, such as loss of skin elasticity, wrinkles, graying hair, hair loss, and changes in hair texture
• Cataracts and age-related vision decline
• Diabetes
• Cancer, which is associated with chromosomal effects and oncogene activation due to the reaction of free radicals [2]
• Central nervous system diseases, such as Alzheimer’s and various forms of dementia
• Cardiovascular diseases due to clogged arteries
• Autoimmune and inflammatory disorders, such as rheumatoid arthritis and cancer

The free radical theory of aging is comparatively new; however, several studies boost its credibility. Researchers focused on cell’s mitochondria, the “powerhouse” that process nutrients to power the entire cell. Experiments on rats, for example, showed a noteworthy increase in free radicals as the rats aged. These alterations coincided with age-related declines in their health. These experiments also showed that free radicals produced in the mitochondria harm the substances that the cells need in order to work properly. This damage causes mutations that produce more free radicals, thus accelerating the process of damage to the cell. This helps explain aging since aging quickens over time. The gradual, but increasingly rapid buildup of free radicals, offers one explanation for why even healthy bodies age and depreciate over time [2].

Antioxidants can stave off free radicals

Antioxidants, molecules that prevent other molecules from oxidizing and thus undergoing oxidative stress, can help to avert the harmful effects of free radicals. They can also decrease or even nullify the effects of free radicals, as they can provide an electron to free radicals and thereby reduce their reactivity. The uniqueness of antioxidants is that they can donate an electron without becoming reactive free radicals themselves.

There is no single antioxidant that can combat the effects of every free radical. Free radicals have different effects in different areas of the body, and every antioxidant performs differently due to its chemical properties. Antioxidants such as vitamins C and E, beta-carotene, glutathione, and plant estrogens called phytoestrogens all scavenge the body and help remove free radicals. Honey can also function similar to antioxidants by removing free radicals. Additionally, selenium, a trace metal that is required for proper function of one of the body’s antioxidant enzyme systems, is sometimes included in this category. The body cannot manufacture these micronutrients so they must be supplied in the diet.

Foods that are rich in antioxidants include citrus fruits such as oranges and limes, berries, and many other fruits that are rich in vitamin C. Carrots are known for their high beta-carotene content, while the soy in soybeans, and some meat substitutes, are high in phytoestrogens. Apricots, spinach, mangoes, pumpkins, broccoli, and eggplants are all also helpful, along with a plethora of other fruits and vegetables [4].

More research needed

A 2010 study on antioxidant supplementation for the prevention of prostate cancer found no benefits. Furthermore, a 2012 study found that antioxidants did not lower the risk of lung cancer. On the other hand, the study found that people who were already at a heightened risk of cancer, such as smokers, actually had a slightly elevated risk of cancer due to antioxidants.

Some investigators have found that supplementation with antioxidants is injurious when people take more than the recommended daily allowance (RDA). A recent analysis found that high doses of beta-carotene, or vitamin E, appreciably increased the risk of dying. One study found that long-term use of beta-carotene could reasonably reduce the risk of age-related mental problems [4]. But perhaps one of the most important discoveries is that antioxidants are unable to “cure” the effects of free radicals completely [5].  

Additionally, we do not yet fully understand why free radicals form in the first place. They may result as an early sign of cells fighting diseases, or that free radical formation is simply a natural expectation that comes with aging. It is not possible to understand them completely without more conclusive research, which should be encouraged considering the significant impacts that free radicals can have upon our bodies.

References

1. https://www.rice.edu/~jenky/sports/antiox.html
2. https://www.medicalnewstoday.com/articles/318652#How-do-free-radicals-damage-the-body
3. http://www.mytruehealth.info/mytruehealth_antioxidants_freeradicals.html
4. https://www.medicalnewstoday.com/articles/318652#Antioxidants-and-free-radicals
5. https://www.medicalnewstoday.com/articles/318652#What-we-do-not-know

“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

One category of galaxies is the spiral; this is dependent on the galaxies’ appearance. The magnetic field of the Sun is also a spiral. Among many things that have a spiral form are the cochlea inside our ears, our navel cord, our fingerprints, the teeth of mammoths, elephant trunks, some spider webs, the horns of some goats, cluster of sunflowers, thousands of types of mollusks, the pattern in which subatomic particles move, plus many more examples. Grapevine shoots, ivy, some microorganisms, and the positioning of some leaves around their branches are in the form of a helix. Nature displays brilliant examples of spiral and helix forms over a wide spectrum, ranging from fossils to galaxies. Below we will discuss some of them:

The Archimedean spiral

Named after its discoverer, this spiral is the geometrical location of a point which moves across a line turning around a fixed point at the speed of q and with a straight angle (Figure 1). The equation for the polar coordinates is p=aq. The distances between the curves are equal. A good example of this type of spiral is the spider web constructed with equal distances from the center.

The Equiangular (Logarithmic) spiral

This spiral type was defined by Descartes in 1638. In an equiangular spiral, any line that crosses the center cuts through all coils of the curve (Figure 2). The equation for polar coordinates is Inr=a.q or r=ea.q. Sea shells and the shells of snails are formed with this spiral.

Fibonacci Numbers and the Golden Ratio

The following numbers, the sequence of which is made by adding the last two numbers together, are known as Fibonacci numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … In other words, each number is the sum of the preceding two numbers. Let us divide each number with the preceding one and write down the quotients:

1/1=1; 2/1=2; 3/2=1.5; 5/3=1.666…; 8/5=1.6; 13/8=1.625; 21/13=1.615…; 34/21=1.619…; 55/34=1.6176…; 89/55=1.618…

If we continue to divide in this way, we will reach a mathematical constant, i.e., 1,618034, which is known as the golden ratio (φ).

Let us now draw a new geometrical shape with the Fibonacci numbers. Next to a 1-unit side square put another square that has equal dimensions. Then add another square, this time equaling the sum of the sides of the previous two (2 units). As we continue to add new squares with double the units of the previous two we get what is called the Fibonacci or golden rectangle. When we draw an arc from one corner of this rectangle to an opposite corner and continue drawing through neighboring squares, as in Figure 3, we will get a spiral. A good example of this is the nautilus shell. The golden rectangle and the spiral is frequently used in fine arts, architecture, and technology.

The Helix

The space curves that coil around a cylinder and cut through its main axis at a right angle is called a cylindrical helix (Figure 4). An ivy plant climbs a tree in a helix, and a helix is the shortest distance to a certain height. The Selimiye Mosque, Edirne, Turkey, features one of the best examples of helices in architecture. The architect Sinan designed the minarets of this mosque with three balconies, which are reached via different stairs that have no connections between them.

The 3D Archimedean spiral and the Logarithmic spiral (Helico spirals)

Conical helices are the space curves that coil around a right cone and cut through its main axis at a right angle. Sea snails, or limpets, have this spiral shape (Figure 5).

Galaxies and hurricanes

Galaxies and hurricanes are also spiral in shape and they have some similar features. Sharing the Stamp of Unity, the law of which governs the entire universe, both galaxies and hurricanes are affected by major forces, like the force of gravity, angular momentum or rotation.

Spiral galaxies are divided into two categories: elliptical and barred spiral galaxies. Barred spiral galaxies have arms that extend away from the main core (Figure 6).

(As evidence for a people open to belief) We have assuredly set in the heaven great constellations, and We have made it (the heaven) beautiful for those beholding. (Hijr 15:16)

The Nautilus: A wonder of creation

The hard shell of the nautilus has a beautiful logarithmic spiral shape. Each coil is at a distance from the next at an increasing proportional distance, each coil is multiplied by a constant. The chambers in the shell are similar, but they widen in a geometric sequence. It is amazing that calcium carbonate, the material that makes up the shell, can accumulate in such a way so as to comply with this geometrical pattern. In this pattern, the nautilus occupies the least space that is possible, thus losing as little heat as possible. Architects have been inspired by the nautilus to produce designs to use the smallest possible space to contain the most possible room.

The Cochlea

The cochlea in our ears is like a double-ramp tunnel coiled upon itself. Etymologically, the word cochlea comes from a Greek word that means snail. The spiral shape of the cochlea reminds one of sea shells.

Horns

Horns of the sheep and goats have the shape logarithmic spiral; they grow in the form of helicoids, as if coiling around a cone.

The Rose

The leaves of a rose are lined up and shoot out in a spiral shape.

Spirals open for us gateways to thought in our efforts to explore the wisdom and beauty that have been set in motion in the universe and are constantly maintained. Spirals, like other living or non-living objects or beings around us, are exquisite works of art that point to the fact that nothing exists from coincidence. Looking through a telescope to a marvelous galaxy in outer space or examining a sea shell on the beach or holding a rose in the spring may become a rewarding act if we contemplate on their Fashioner, for such “contemplation for an hour is worth voluntary prayer for a year.”