More, more, and more

Adams GS et al. People systematically overlook subtractive changes. Nature, April 2021

A recent study showed that human beings are driven by a powerful instinct to add rather than subtract in daily problem solving. Researchers asked 1,585 participants to solve puzzles or problems where they could either add or subtract elements. Strikingly, in every single test the majority of participants chose addition over subtraction even in instances where subtraction made much more sense. For one of the puzzles, participants could either shade in squares or erase them in order to make a symmetrical pattern. Out of 94 participants, 73 added squares, 18 subtracted, and 3 simply moved around the existing squares. In another puzzle, participants were given a Lego structure and told to improve it however they liked. More than 90 percent chose to add blocks rather than remove some of them. This pattern was very consistent over many different problems. When asked to improve an essay most people lengthened it, and when asked to improve a recipe the majority added more ingredients. However, when participants were instructed or incentivized, they finally started to consider the possibility that less is more. For instance, when participants were asked to stabilize a Lego tower, they were told that completion of task will be rewarded with $1 but each new added piece during construction will cost them 10 cents. The participants then seriously considered removing pieces to solve the problem.

There are explanations for why humans might favor addition over subtraction in problem solving. While additive ideas may come to mind more quickly and easily, subtractive ideas require more cognitive effort. Numerical concepts of “more” and “higher” may be associated with the evaluative concepts of “positive” and “better” in our brains. For example, in many areas of life it may be easier to gain recognition for making something than for taking something away. This human behavior has wide-reaching implications in costly modern trends such as overburdened minds and schedules, increasing red tape in institutions, and irresponsible usage of the planet’s resources as a result of greed. Perhaps we should begin asking ourselves what we can take away before looking to see what we can add to solve our problems.

Plastics to be recycled “infinitely”

Vora N et al. Leveling the cost and carbon footprint of circular polymers that are chemically recycled to monomer. Science Advances, April 2021.

Plastics are a part of nearly every product we use. The average person in the U.S. generates about 100 kg of plastic waste per year, most of which goes straight to landfills. The invention of a new plastic called poly (diketoenamine), or PDK, could now potentially solve this global waste and energy crisis. PDK has all the convenient properties of traditional plastics without any environmental pitfalls. Unlike traditional plastics, PDKs can be recycled indefinitely with no loss in quality. The biggest problem in recycling traditional plastics is that chemicals in many plastics that make them useful are tightly bound to the monomers that stay in plastic even after it’s been recycled resulting in a new material with much lower quality. In contrast, PDK plastics solves this problem entirely since they are engineered to easily break down into individual monomers when mixed with an acid. The monomers can then be separated from any additives and the plastics can be reassembled into different shapes, textures, and colors again without any loss of quality. This process is named “chemical recycling” and requires low energy usage and has minimal carbon dioxide emissions and can be repeated indefinitely thus resulting in a completely sustainable material lifecycle.

Initial analysis showed that the best starting application for PDKs are markets in the automobile and consumer electronics industries that can make sustainable branding and savings. The long-term plan is to develop PDK plastics with a wide range of thermal and mechanical properties for applications as diverse as textiles, 3D printing, foams, and other packaging materials. In addition, scientists are looking to expand formulations by incorporating plant-based materials and other sustainable sources.

Genetic consequences of Chernobyl after 35 years

Yeager M. et al. Lack of transgenerational effects of ionizing radiation exposure from the Chernobyl accident. Science, April 2021

Morton LM et al. Radiation-related genomic profile of papillary thyroid cancer after the Chernobyl accident. Science, April 2021

The effects of radiation on human health have been investigated since the atomic bombings of Hiroshima and Nagasaki in World War 2 and the nuclear accidents in Chernobyl, Ukraine and Fukushima, Japan. April 26^th marks 35 years since the world’s worst nuclear power disaster in Chernobyl, where a reactor in a nuclear power plant exploded and released huge amounts of radioactive material into the environment. The Chernobyl accident killed 31 people immediately, and thousands more died over the years from radiation-linked illnesses such as cancer. Millions of acres of farmland in Europe were contaminated. The true toll of Chernobyl’s meltdown remains controversial and simply unknown. Recently, international teams of researchers have looked closely at the genetic damage of the Chernobyl exposures in two separate studies.

The first study investigated whether radiation exposure results in genetic changes that can be passed from parent to offspring. Researchers analyzed the complete genomes of 130 people born between 1987 and 2002 and their 105 parents who had worked in Chernobyl during the accident or lived close to the accident site. Each parent was evaluated for protracted exposure to ionizing radiation. Whole-genome sequencing revealed that there was no evidence of an increase in the number or types of de novo (newly arising) mutations in their children born between 46 weeks and 15 years after the accident. These results suggest that radiation exposure surprisingly does not harm future generations at the genetic level.

The second study aimed to profile the genetic changes in thyroid cancers that developed in 359 people that were exposed as children or in utero to ionizing radiation from radioactive iodine during the accident and in 81 unexposed individuals born more than nine months after the accident. An increased risk of thyroid cancer has been one of the most prominent adverse health effects of radioactive iodine. In high doses, radioactive iodine kills thyroid cells and can actually be used as a treatment for thyroid cancer however the radiation from Chernobyl wasn’t strong enough to kill cells. Instead, the next-generation sequencing data showed that the months-long exposure to lower doses had mutated genes by breaking the double strands of DNA and ultimately resulted in tumors. The association between double strand breaks and radiation exposure was more pronounced for those younger at exposure.

Taken together, these two studies not only give us new insights into the long-term effects of radiation, but they also highlight how important long-term investments in scientific research and proper data collection are. In 1980s, scientists didn’t have the genomics technologies to understand the molecular effects of radiation, but they meticulously collected tissue samples, monitored radiation, and interviewed people over many decades. Investment in long-term scientific research always pays off.

Resurrection plants are desiccation (extreme dryness) tolerant plant species. All are relatively small and mostly found in Southern Africa, North America, Brazil, and Australia. They are able to stay in a dehydrated state under conditions in which other plants would perish. They come back to life and resume their physiological activities when water becomes available again. During the dehydration process, leaves of resurrection plants shrink and curl up due to water loss. Some of them fold up their stems into a tight ball as they desiccate to limit surface area and conserve internal moisture. It is not yet clear how the leaves and stems reduce their size. However, electron microscopy revealed desiccation-induced cell wall folding in the majority of mesophyll and epidermal cells of a resurrection plant. Thick-walled vascular tissue did not fold and supported the surrounding tissue, thereby limiting the extent of leaf shrinkage and allowing leaf morphology to be rapidly regained upon rehydration (Moore et al 2006, 651–62). When the resurrection plant is dehydrated, its stomatal conductance and intercellular CO2 concentration is decreased and hence its photosynthetic rate, but sugar, starch and non-structural carbohydrate reserves increased during this stage. Mature tissues of resurrection plants such as leaves and roots are able to remain in the air-dried state for months by reaching an inactive state, comparable to dormancy in seeds in several aspects. All metabolic functions are reduced to a bare minimum and they appear to be dead. Resurrection plants take immediate advantage of rainfall after dry periods: they absorb water, grow rapidly, and reproduce (Bartels 2005, 696–701; Xu 2010, 183–190).

One of the most common examples of resurrection plants is Myrothamnus flabellifolia, grown in southern Africa, the only known woody resurrection plant. Craterostigma wilmsii and Xerophyta viscosa are other resurrection plants from southern Africa. All these plants are used extensively in African medicine and traditional culture. Ramonda serbica and her sister Haberlea rhodopensis are members of Gesneriaceae family from the Balkan peninsula; they are rare and forbidden for collecting. Anastatica hierochuntica is native to western Asia, while Selaginella lepidophylla is collected from the wilderness of the southwestern United States and Mexico, sold to tourists, and exported worldwide—it can even be bought online, in their dry and lifeless form. After buying this plant, we soak it in water and voila! If one does not have a “green thumb” and still want to have greenery in one’s home, this resurrection plant might work best for you. However, its downside is that sometimes people complain that the gray-brown ball and its branches do not become fully green or open up in water totally, which does not look very attractive. But even though you may not like how it looks, your kids might enjoy it as a science project.

Why is it important to know how these plants survive drought and come back to life?

The world’s need for water is likely to become one of the most critical resource issues of this century. The International Water Management Institute predicts that by the year 2025, one-third of the world’s population will reside in regions that experience severe water scarcity (www.iwmi.org) (Bartels and Salamini 2001, 1346–1353). Drought is a factor that dramatically threatens the world’s food supply. Therefore, plant scientists have been interested in using resurrection plants as model organisms to find out noble cellular mechanisms for improving the drought tolerance of important crop plants. Research on the molecular genetic mechanisms, metabolic and antioxidant systems as well as macromolecular and structural stabilizing processes in resurrection plants have been carried out (Moore et al 2009, 110–7). One study of Craterostigma wilmsii demonstrates that it relies almost entirely on protection during natural drying; however, it also induces a repair mechanism during rehydration that enables recovery from rapid drying. Thus, it apparently has the ability to repair if protection is inadequate and damage is incurred (Cooper 2002, 1805–13). In addition to repair mechanisms of resurrection plants, the processes that involve regulation of gene and protein activity that allow these plants to use energy storage efficiently have been investigated. The resurrection capability appears to be associated with the accumulation of a carbohydrate in the tissues as they dry. In a majority of cases, sucrose is the major carbohydrate that accumulates (Norwood et al. 2000, 159–65). In addition, an unusual disaccharide named trehalose, which is the main blood sugar in insects and serves as a major energy storage molecule enabling flight, is found in high levels in resurrection plants. This is unusual, because normally there is not much trehalose in plants. It has been proposed that trehalose serves as an osmoprotectant (Avonce et al 2005, 276–279). Osmoprotectants are small molecules that help organisms to survive when a rapid change in the movement of water across their cell membrane occurs. Peter Scott of the Annuals of Botany wrote a summary of the ability of resurrection plant Craterostigma plantagineum to survive dehydration and revive (Scott 2000, 159–166). According to his botanical briefing the roots, being in the soil, are most likely to sense the decrease in water availability first. Abscisic Acid (ABA), a plant hormone, is synthesized and released by roots as a response to drought stress. Once released, ABA could activate batteries of genes required for metabolic processes such as the accumulation of sucrose from either stored carbohydrates or through an alteration in photosynthetic carbon partitioning. In addition, the synthesis of other proteins such as dehydrins and Late Embryogenesis Abundant proteins (LEAs) could help to stabilize the plant cells as they lose water. Thus as the tissues dehydrate, leaves shrink, chlorophyll is degraded, sucrose accumulates and ultimately the xylem, which is one of the transport tissues in plants, fills with air and the plants become desiccated. On addition of water, the xylem refills with water and cells begin to take up water and expand, enzymes present in the tissues are activated, sucrose is metabolized, and chlorophyll is resynthesized. Within 24 hours the plant is restored, and is reproductively active within two weeks.

Based on these findings, it is of particular significance to understand the cellular and molecular mechanisms of resurrection plants and focus on biological engineering strategies for improving plant drought tolerance in important crop species such as cotton, soybeans, peanuts, corn, and potatoes. But these plants do not merely represent a unique model for scientists to understand a plant’s ability to cope with drought; they also serve us to deepen our faith for the Day of Judgment and rationalize it in our minds. The astonishing changes in the tissue of resurrection plants, and how they are brought back to life when they appear to be completely dead, remind us of Qur’anic verses such as the one below regarding the resurrection of decayed flesh and bones (36:78–79).

“And he puts forth for Us a parable, and forgets his own creation. He says: ‘Who will give life to these bones when they have rotted away and became dust?’ Say: ‘He will give life to them Who created them for the first time! And He is the All-Knower of every creation!’”

Time-lapse videos of resurrection plants in action, like Xerophyta and Jericho rose, are available on the web. Enjoy!

References

• Moore JP, Nguema-Ona E, Chevalier L, Lindsey GG, Brandt WF, Lerouge P, Farrant JM, Driouich A. 2006. Response of the leaf cell wall to desiccation in the resurrection plant Myrothamnus flabellifolius. Plant Physiol. 141:651–62.
• Bartels D. 2005. Desiccation Tolerance Studied in the Resurrection Plant Craterostigma plantagineum. Integr. Comp. Biol. 45: 696–701
• Xu D, Su P, Zhang R, Li H, Zhao L, Wang G. 2010. Photosynthetic parameters and carbon reserves of a resurrection plant Reaumuria soongorica during dehydration and rehydration. Plant Growth Reg. 60: 183–190.
• http://faculty.ucc.edu/biology-ombrello/pow/resurrection_plant.htm
• Bartels D, Salamini F. 2001. Desiccation tolerance in the resurrection plant Craterostigma plantagineum. A contribution to the study of drought tolerance at the molecular level. Plant Physiol. 127:1346–1353.
• Moore JP, Le NT, Brandt WF, Driouich A, Farrant JM. 2009 Towards a systems-based understanding of plant desiccation tolerance. Trends Plant Sci. 14:110–7.
• Cooper K, Farrant JM. 2002. Recovery of the resurrection plant Craterostigma wilmsii from desiccation: protection versus repair. J Exp Bot. 53:1805–13.
• Norwood M, Truesdale MR, Richter A, Scott P. 2000. Photosynthetic carbohydrate metabolism in the resurrection plant Craterostigma plantagineum. J Exp Bot. 51:159–65.
• Avonce N, Leyman B, Thevelein J, Iturriaga G. 2005. Trehalose metabolism and glucose sensing in plants. Biochem Soc Trans. 33:276–279.
• Scott P. 2000. Resurrection Plants and the Secrets of Eternal Leaf Annals of Botany. 85: 159–166.

I am placed inside your chest cavity as two air sacks-or bellows-surrounded by your muscles. I took my first breath right after birth and I still keep working non-stop. Even while you are sleeping, I fulfill my function with the automatic command I receive from the respiratory center at the back of your brain. My close friend Heart started working even before me while you were in the womb. I was resting then; actually I hadn’t even formed fully. As all your needs like food and oxygen were met in the body of your mother-whose heart you occasionally break-I didn’t have to make extra effort to get air, being filled and emptied. Even if I had attempted to do so, I would have had no chance of succeeding; since you were contained in the amniotic fluid, an attempt to breathe could have caused you to drown.

The first breath I take after birth is critical and rather difficult, since the windpipe is still much narrower than normal. On the other hand, the number of my alveoli where oxygen exchange with the capillaries is realized is so high in relation to body size that it balances the situation. When I make my first move and fill with air, I put pressure on the arteries and veins. Then the vessel directly connecting my artery to my mother’s aorta is dismissed, the curtain between the valves is closed and the blood circulations are separated. If this curtain is not properly closed and a gap remains in between, the oxygen-rich blood and the used-up blood mix and result in the disease known as cyanosis-or “blue baby” syndrome. As these two kinds of blood mix, the tissues are not supplied with sufficient oxygen and the white parts of the skin and eyes assume a bluish appearance.

Turning blue-purple due to lack of oxygen in the tissues is the same for smokers. Cigarettes-my archenemy-contain hundreds of toxic substances, such as carbon monoxide, which combine with the hemoglobin in blood and prevent oxygen transfer. Therefore, the lips of smokers turn slightly purple. You need to be careful with the air you inhale. The windpipe which brings air into me is covered with a ciliated epithelial tissue which catches the dust brought along and sweeps it outside. While you are asleep, the vibrating cilia of this sweeper work throughout the night and in the morning you get rid of the outcome of their propulsion by clearing your throat. However, every draw of a smoker kills 800–1,000 of our ciliated epithelial cells. After some time, they become unable to sweep the toxins (carbon, sulfur, lead, etc) inhaled with the air. I can’t stand it anymore! The increased air pollution is already putting enough strain on us… this habit is just too much for a lung to handle! It is just… an open invitation for cancer! Sorry, Peter, I didn’t mean to be rude. I appreciate that you don’t smoke, but I wish those who do would realize how splendid a mechanism they are destroying.

Now let me tell you about what a work of art I am. As you also know, art in a structure becomes more meaningful with functionality. As is the case with my other friends with which I work in your body, I am perfectly made to fulfill my duty. In other words, never mind forming an organ like me as a consequence of molecules and cells accidentally coming together, even a single protein molecule in my structure does not come to existence through unconscious causes.

With every breath you take, the pressure of the oxygen within the air inhaled rises, so it passes through my membranes by diffusion and into the adjacent capillaries; there it combines with hemoglobin molecules. At the same time, the carbon dioxide passes through the same membranes into me, and I dispose of it. Both of these are easier said than done! You breathe 13–14 times a minute and the whole thing is repeated over and over. As I keep expanding and contracting during breathing, which you are unaware of most of the time, first of all I need to be very flexible. Together with this flexibility, my most important quality is having the largest possible surface area within the smallest volume. My surface area of around 100m2 (as large as a tennis court) is made to fit into your chest cavity in the form of thin membranes so that my large surface allows gas diffusion. These membranes need to be kept wet; a special fluid is secreted as a precaution and respiration is realized smoothly. Without this fluid, my membranes would just stick together, unable to carry out their duty.

You can compare the course of the air inhaled to that of a car passing from a highway onto increasingly smaller roads and in the end reaching a dead end in the small sacks named alveoli. The air coming in through the mouth and nose unites at the expressway named the trachea, or the windpipe, which is 15cm long and 2–3cm in diameter. Incidentally, I have a couple of things to tell you about the way you breathe. As a matter of fact, inhaling is the duty of the nose. I’m sure it also has a lot to say as well, but let me just mention a simple fact about it. Now, you should inhale through your nose, so that the air you take in gets warm, wet, and is cleaned from dust. If you try to breathe this way, you do not trouble me much, and reduce the risk of catching a cold or an infection of upper respiratory system. Inhaling through the mouth helps dust and germs get into me and you might contract various illnesses from bronchitis to pneumonia. Now you know why kids who have adenoids who sleep with their mouth open get ill so easily. Sorry, I couldn’t help speaking on behalf on the nose.

Well, what were we talking about before that? Oh yes! The ways through which the inhaled air passes. As the name suggests, the windpipe which makes the air reach me is a cylindrical tube surrounded by 16–20 cartilaginous rings. As it is placed beside the esophagus, one side of the rings is made of soft cartilaginous tissue instead of hard, so that they don’t hinder swallowing. The muscular tissue near these rings helps them widen and narrow during respiration or coughing. I sometimes warn you by making you cough. Maybe it seems to be a disturbance, but if I don’t push out air by coughing through the contracted windpipe, contaminants can clog me up and cause you to suffocate. Therefore, the burst of air-what you call a cough-is a great blessing to you.

The sound system at the tip of the windpipe is another wonder. The used air I send out vibrates the cords in that voice-box and produces such melodies, gives voice to such speech! The air divides into the two lungs. My two sides are not symmetrical; the one on the right is divided into three, and the one on the left into two. I think this was meant to make room for the neighbor on the left, the heart. In addition, if there’s any cancer growth in me, the diseased part can be taken out by an operation and I can keep on functioning. God knows the wisdom behind this form. After that, these main bronchi separate into 8–10 thinner branches, like highways connecting to narrower roads. This branching resembles a tree turned upside down. At the tips of these thin branches are the respiratory bronchioles resembling clusters of grapes. The small spheres which make up the cluster are the end of the road and are the most vital parts. These spheres named alveoli are made of very thin membrane and they are surrounded by a net of capillaries (picture 5). These are the functional spots where gas exchange is realized.

I hang in the thorax with veins and arteries all around. There are two layers of protective membrane over me. One of them is stuck on me, whereas the other is stuck on the ribs which form the chest cavity. There is a fine and slippery fluid in between these two layers and it neutralizes the friction every time I inflate and deflate. If it hadn’t been placed there, I would wear out and be damaged. As I inflate during inhalation, the chest cavity should expand simultaneously to make space for me. If it weren’t given a flexible form, I would fail to breathe and you would eventually die. Fortunately, the protective set of ribs and their connection with the spine are flexible enough to make me work comfortably. In addition, the dome-shaped muscular partition (diaphragm) separating the thorax from the abdomen contracts and pushes down the organs in the abdomen. Thanks to the simultaneously programmed movement of both the ribs and the diaphragm I inflate with air and expand.

Being in constant contact with the outer environment makes me susceptible to various diseases. Coughing is among the foremost signals I give in the case of disease, and sometimes-excuse me-I produce a mixture of blood and phlegm. Also, I may have difficulty in breathing and warn you with chest pain. You should be alert to my signals. If bacteria and viruses infect me, they might reproduce inside my air sacs, and cause stiffening and suppuration.

I am particularly sensitive to allergic disorders. When the straight muscles on the walls of my bronchi contact an alien substance, pollens for instance, the consequent histamine secretion makes my muscles contract. In addition, allergic diseases, which can affect blood vessels, affect me a lot since I happen to be one of the major organs contributing to blood circulation. As a result of the contraction of my bronchial muscles and difficulty in disposing of the mucus I secrete to defend myself, I have trouble with breathing-you call it asthma.

In addition to this, we can mention diseases like emphysema, acute or chronic bronchitis as problems I frequently face. Even your anger has a great impact on me. Breathing becomes more difficult immediately.

Peter, I’m sorry, it is not possible to summarize a work of art like me within a few pages, but I need to stop now… but please, keep away from polluted areas and cigarette smoke! Send me as much fresh air as you can. And even though you mostly take me for granted, like my other teammates, please reflect upon what a blessing I am.

Irfan Yilmaz is a professor of biology at Dokuz Eylül University, Izmir, Turkey.

There are two major theories about the origin or essence of mathematics. One of these theories is attributed to Plato, and the other to the so-called Formalist school. According to Plato, mathematics exists independently of man. What man does is to discover its objective reality, just as other ‘laws of nature’, which we tend to call ‘Divine laws of nature’, are discovered. The Formalist school by contrast asserts that mathematics is a product of human thinking. In order to understand the difference between these two schools, we may cite as an example their view of prime numbers (that is, numbers like 7, 17, 41 which can only be divided exactly by themselves and the number 1). Platonists argue that the prime numbers exist independently of us: before we discovered their existence, they existed in infinite number. Whereas, Formalists are of the opinion that the prime numbers exist because we have defined them as such, and it is meaningless to think about whether they are of infinite number or not.

The language of numbers

Formalists assert that numbers came into existence when human beings began to count. A well-known account of how this happened is that of a shepherd who used to put a stone in his bag for each of his sheep and by matching a stone with a sheep could find out whether any of his sheep had been lost or not. Later on, people began to call numbers each by a different name and since there were two fingers in the two hands, they found it easier to make calculations by the decimal system. This was followed by the operations of addition and subtraction.

According to the Formalists, even the simplest mathematical operations like the four basic ones consist in some logical rules based on certain axioms. They say that we do mathematics by expressing certain rules with certain symbols. That is, we take, say, 5 and 7, a couple of signs whose meaning in the physical world we do not know, and put between them the plus sign, a third sign whose meaning in the physical world we do not know, followed by an equals sign. And we know we must write 12 after the equals sign because that is a requirement of the axioms and rules of logic we are using. This is just what a calculating machine does, that is, it goes through the operation required of it without knowing what it is doing.

Let us suppose that an adding operation consists only in applying axioms or certain logical rules, and has nothing essential to do with the physical world. If we were to take our number signs and apply them to physical objects like stones and sheep, we should be surprised, amazed even, as if by a miracle, that 5 and 7 stones or sheep added together (according to the same rules as 5+7) make 12 stones or 12 sheep. We would come to know that the abstract, conceptual realities in our mind correspond to physical realities in the outer world. According to Paul Davies, the renowned physicist, if we lived in a universe where different physical realities prevailed, in a space where, for example, there were not any countable things, we would not be able to make most of the calculations we make today. David Deutsch claims that counting emerged as the result of experiences. According to him, we can do arithmetic because physical laws allow the existence of physical models convenient for arithmetics.

Richard Feynman, regarded as the greatest physicist after Einstein, says about mathematics that the problem of existence is a very interesting and difficult problem. When you take the third power of certain numbers and then add them with each other, you obtain interesting results. For example, the third power of I is 1, of 2 is 8, and of 3 is 27. The addition of these numbers gives the result of 36. The addition of 1, 2 and 3 is 6 and the second power of 6 is also 36. When you add to this the third power of 4, which is 64, the result is 100. The addition of 6 and 4 is 10 and the second power of 10 is also 100. Added to this the third number of 5, which is 125, the result is 225. 225 is the second number of 10 plus 5, i.e. 15. And so on. According to Feynman, we may not have known this typical characteristic of numbers before but when we do come to know such characteristics of numbers, we feel that they exist independently of us, and that they existed before we discovered them. However, we cannot determine a certain space for their existence. We feel their existence as conceptions only.

Let us take another example. Ibrahim Haqqi of Erzurum, a Turkish Sufi, religious scholar and scientist of the 18th century, discovered a way of checking the correctness of an operation of addition which may still be unknown to modern mathematicians. In order to check or prove the addition, we first add up the digits of each of the two numbers we are going to add up. Let us say, we are going to add 154 to 275, for which we get the answer 429. Adding the digits of each of the first two numbers, we get 1+5+4 = 10 and 2+7+5 = 14. The next step is to subtract 9 from each of these two sums, giving us 1 and 5 respectively. The third step is to add these two results together, 1+5 = 6. Now we do the same thing with the digits of the answer we are wanting to check, namely 429, and again subtract 9: 4+2+9 = 15, 15-9 = 6. The fact that we end up with the same number (i.e.6) means that our addition was correct. This way of checking an addition exists independently of us. We did not create it, we discovered it.

As water had the force of lifting objects of certain weight before Archimedes discovered it and, again, objects thrown into air or a fruit disconnected from its branch fell before Newton discovered the law of gravity so also numbers have many characteristics only some of which have been discovered.

Heinrich Herzt, a physicist, says that we cannot help but feel that the mathematical formulas discovered so far exist out there independently of us. We know that these formulas existed before we discovered them but we cannot determine a space for them. Rudy Rucker, a mathematician, is of the opinion that there is, besides the physical space, a space of mind, which he calls ‘mindspace’ and it is that that mathematician study.

Most of the distinguished mathematicians follow the view of Plato. Kurt Godel is one of them. Before Godel, it was almost a generally accepted view that mathematics is a function of the working of mans brain consisting in the collection of the logical rules which we establish between the symbols of two sets. Godel persuasively argued that there have always been correct mathematical expressions even though their correctness cannot always been proved. Another Platonist mathematician, Roger Penrose, believes that beyond the thoughts of mathematicians there are profound truths or realities in mathematical conceptions. Human thought is directed to extend into these eternal realities and they are there to be discovered as mathematical facts by any one of us. Penrose mentions complex numbers as an example for his argument. According to him, there is a profound, timeless truth in complex numbers. Penrose cites the set of Mandelbrot as another example to prove his argument. The reality this set reveals is the fact that even the lines, twists and shapes of mountains and clouds were or are formed according to certain mathematical formulas. 

What flowers reveal

Almost everyone has heard of the series of Fibonacci. This series, named after the famous mathematician, Leonardo Fibonacci, progresses as 1,1, 2,3,5,8,13,21,34,55,89,144, and so on, each term being equal to the addition of the previous two. That is, I and I make 2, and I and 2 make 3, and 2 and 3 make 5, and 3 and 5 make 8, and so on. This is the series found in nature. For example, when we count the spirals formed of the seeds in a sunflower, we find that those arranged clockwise are 55 and the others arranged anti-clockwise are 89. Both of these figures are among the consecutive terms in the Fibonacci series. These figures may vary according to the size of the sunflower: we may find the figures of 34 and 55 in a relatively small flower, and 55 and 89 in a normal sized one, but the arrangement is always as consecutive numbers in the Fibonacci series. The spirals are arranged in pine cones in 5 to 8. We may encounter the same figures in the arrangement of tobacco leaves. Another extremely interesting characteristic is found in the numbers of petals of flowers. A lily has 3 petals, while a buttercup has 5, a velvet 13, a dahlia 21, and a daisy 34 or 55 or 89, varying according to its family. It is impossible to attribute this miraculous arrangement to chance or ignorant nature. If the DNA of a sunflower or a pine cone determines random numbers for its petals or spirals, how can you explain their correspondence with the terms of the series of Fibonacci? The ratio between the consecutive terms in the series of Fibonacci is quite near what is called the golden ratio’ and known in classical art as the ratio most pleasing to human eye. In order to explain the origin of this miraculous reality, you have to either accept that flowers know what is most pleasing to human eye or that the ‘Hand’ of One, the All- Knowing, the All-Wise and the All-Beautiful, is working in nature.

In short, what Fibonacci did is to discover this characteristic in nature. This means that the universe has a mathematical order or mathematics is the branch of science studying the miraculous order of the universe, the order which the Absolute Orderer and Determiner, One Who determines a certain measure for everything, has established.