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The Invisible Script on the Visible : Mathematics
Oct 1, 2003

Af you follow scientific magazines, you may have realized one thing: articles on mathematics are seldom published in such magazines. The major reason is that, in a way, mathematics is a world which is difficult to comprehend, a world where abstract logic is embodied in concrete statements. It cannot be said to be popular among people except for mathematicians, for it is thought to lack a literary side and emotional appeal, and to be rather uninteresting. Mathematics draws the attention of those who try to understand the universe and the reason of creation; it fulfils this duty by unveiling the secrets of creation.

In a book that deals with questions of logic, when we see numbers written in succession, such as 5, 15, 25; then we are able to discover the relation between these numbers, to predict the next number and to realize that this pattern was made by somebody. However, if we were to be told that these figures indicate the distance covered in equal segments of time by a pebble that has been dropped from a certain height, most of us would not think about the One Who made this general rule.

Or for example, the equation 11.111.111 x 111.111.111 = 12.345.678.987.654.321 may be as amazing to some people as the verses of a beautiful poem, whereas it will leave others cold.

Likewise, the famous mysterious symbols of mathematics, e, i, , are nothing more than some alphabetical signs for most of us, nevertheless they must have meant a lot to the famous physicist, Richard Feyman, since he wrote the following equation in his diary, noting that he admired it: ei+1=0

If we write f (z) = Z2 + c;, this will not be a meaningful sentence for most people. But that will not change the fact that it is an incredibly simple expression of biological and physical reality in an expression which concerns our lives (as in fractal logic). And the picture you see here (Figure 1) is nothing but the analytical projection of this equation on a computer screen.

The spiral form (Figure 2) which can be seen in various things from cone shells to nebulas, has a very simple formula, r2=a2/A which is fascinating for those who spend some time to think about it. All these examples have a point in common. These numbers, which are abstract concepts, are as real as the concrete objects of the physical world. While other sciences make sense, more or less, for a layperson, mathematics can only be appreciated by people who know it well.

The mythological Princess Dido of Phoen-icia fled from the city where her husband (the King;s brother) had been slain by the King. She wanted to settle in Carthage, in North Africa. There the King only allowed her to buy as much land as could be covered by the skin of a cow. Dido decided to interpret the word ;cover; in a wider sense. She had her servants cut the skin in thin strips, connecting them to each other. In the end, she obtained a long cord, estimated to be somewhere from between 1,000 to 2,000 m. long. When it came to placing it on the ground, Dido wanted to find the shape that would cover the largest area. She found the right shape. She made a circle on the ground and she was able to encompass quite a large area of land. As a matter of fact, looking at some ancient castles, we can understand that they were built in this way in order to create the largest structure over the smallest possible area. This explains why the cross-section of a vessel tissue is circular, because it occupies minimal space in the body (Figure 9).

Did you know that mathematical reality applies in our body and in the universe? This fact was realized when scientists developed fractal geometry. The fractal structure we see in the roots and leaves of plants and in the human respiratory and vascular systems are very good examples of this fact. Such excellence indicates the All-Knowing Omnipotent One Who is behind these geometrical designs (Figures 4, 5, 6).

What is the invisible secret of this visible structure? Dido had to enclose the maximum area by using limited material, which she accomplished. Such optimization also exists in the human body and in other living things. The biological systems we have mentioned above have vessel systems designed as fractal networks, delivering the necessary substances to cells. Essentially, these systems are designed in such a way that the vessels occupy minimal space while serving all the cells within the system; this can only be realized through such a fractal structure.

The most striking proof supporting this idea is that if the human veins, which do not take up a great deal of space in the body, were all added together, they would reach a length that is three times the circumference of the world.

How can this be possible? This can be explained quite simply: find an equilateral triangle and carry out the following instructions. First, divide each side of the triangle into three equal sections and place another (smaller) equilateral triangle on the middle section of each side you have divided, facing outwards. If you repeat the same thing for each of these small triangles, you will create the pattern below (Figure 8).

In a fractal structure, as the number of branches near infinity, the shape of the structure resembles a circle more and more. The new area we will find cannot be bigger than the area of the circle, and the points of contact with the circle will approach the maximum value (Figure 9).

We can also explain this fact in the following way: take a circle with a radius of 3 cm. This will serve as the cross-section of a cylindrical object. Then draw seven smaller identical circles inside the first circle. You will see that the proportion between the sum of circumferences and the sum of areas is 5/7. Those who are interested in mathematics will see that as the value of the r (radius) decreases, the difference increases. This clearly indicates that fractal structures are always advantageous. So, what about organs like the brain or the lungs? They do not have a completely fractal structure, yet they really need to have a larger surface area than other objects of equal size. These organs have been enabled to have the largest possible surface area by being convoluted. Otherwise, man would be a strange creature, burdened with a huge mass on his back. Similarly, when we look at a map that shows the coastlines, we see that a coastline that has many capes and bays has a longer coast line than its counterparts, which run straight along the land. All these living things or organs (man, trees, brain etc) have such structures from the very moment they are created. This system or project (Figure 10) cannot have developed on its own, by chance, without there having been a Creator.

Sir James Jean says, ;The Creator must be a perfect Mathematician; in his book The Mysterious Universe. In so saying, he draws attention to mathematics, the mysterious pattern in the universe, and points to the Artist behind the ornamented beauty seen in Creation. The magical science of mathematics whispers its secrets to those who try to perceive it through the eyes of wisdom.