Now We Can Have Both

  

The Mathematics of Life
By Ian Stewart

   

   Through the early years of my life, I defined biology simply as observation and experimentation. Where teachers would just ask what you had seen and what have you observed. You know, stuffs like going outdoors to explore the beauty of nature or taking up weird dissections to appreciate bloodied bodies? Yeah that sounds gross, but seriously, biology is a way, way farther than mathematics. I can’t imagine myself taking up the Pythagorean Theorem to test if Mt. Mayon really a perfect cone. 

               

     Biology is simply for students who want to escape all the formulas and calculations. So, if you want to break through mathematics then have yourself runaway with biology. I know physics and chemistry are one of math’s lovers, so then biology would be a greater offer (Obviously, it’s the best we can get!). But then as the world evolved and developed through time, descriptive analysis and gathering facts are not enough to make biology work. So then the tables have been turned and today mathematics and biology wound up in pairs.

    Ever since I was born, biology has really been my favorite (No offense, but we do a great team!). That’s why after reading Ian Stewart’s Mathematics of Life; I can’t help thinking both worlds. For a moment both worlds are true, and you cannot quite tell them apart. There is Biology. And there is Mathematics. The two bleed into each other, and I am put into the middle. (Sucks)

   Though there are a lot of relations between biology and mathematics as what other philosophers had said, most of us students or even many biologists and mathematicians are unaware of these relationships. Ian Stewart proved this to be true. In fact he pointed out the premise that mathematics is the sixth revolution to influence biology following the sequence of microscope, classification, evolution, genetics and DNA’s structure. The first part of the book tackled commonly the history of each of these revolutions and its impact towards biology. (Honestly, this is a math book, but as what I can see the book is awkwardly filled to be biology) Anyways, the remainder of the book surpassed your expectation to be an easy-to-read portion, for it stands the vignettes about the interaction between biology and mathematics. Nevertheless, the scope of material exposed made me fascinated to tidbits such as dealing with patterns on fishes, hallucinations, evolutionary niches, and stripes on tigers or even the Fibonacci sequence. After all, nature alike math, followed patterns.  

    Literally, the basic postulate of this book is that there is a lot of mathematics that is applicable in some life sciences such as biology and can be understood by people even with a limited background or no interest towards mathematics, provided it is presented at an appropriate level and connected to biological ideas. Amazing huh? Of course no book on mathematics for the life sciences can be complete. For an author who’ve tried to be a layman and discussed biology using some applications in mathematics, that would be something. However, let us not forget that bringing up this kind of discourse required a deeper explanation and a denser approach.

   Looking forward many years from now, I can say biology will be much, much complicated as what is today yet extremely useful to the world we live in. Biology will remain just a house built with facts as well as mathematics without further assistance from each other. Metaphorically speaking, the muscles of mathematics are connected to the bones of biology by the tendons of mathematical modelling (Ledder, 2013). See? Now, all sciences got teamed up with mathematics. Great.

   Before I end, I just want to clarify that I’m not that mad towards the idea of math-biology-teaming-up-like-lovebirds scenario (uhm, maybe a little… no just a bit). But then, I’m also pleased that this combo made such a huge impact to our technology and for the improvement of many, many things. In general, this book enlightened me for the possibility of appreciating biology more through the help of math. I can simply say that this is a recommendable one especially those who wanted to view biology in a different perspective. Now, mathematics is the backbone for finding biology.

Breaking News! Yearender's Mysterious Couple, Announced!

Ever heard of the saying, “Opposites attract?” Apparently, our little friends, biology and mathematics have a little secret they would like to share. Lo and behold, children of the universe!

Mathematics and biology are now an item! But wait, what’s this? A little bird told me they have actually been together for quite some time now. *Le gasp* And here I thought we could have avoided mathematics by pursuing biology. How could you destroy our little fantasy?

 

Once upon a time, mathematics was only about numbers and calculations of everyday problems in the market, then came the shapes, logic and processes, or anything that shows pattern and has structure. Biology on the other hand was all about the plants, animals and insects, then about cells, and now, it focuses about complex molecules. Do you see any connection between the two? No? Me too. They’re opposites, I tell you! Are you curious about how their love blossomed?

In Ian Stewart’s book entitled, “Mathematics of Life,” he explains about the process about on how mathematics and biology came together which have already existed from the Human Genome Project, the structure and organisation of cells and viruses, and the form and behaviour of organisms and their interplay in the ecosystem, he also explains just how math has done to explain the elements of life.

There are five revolutions which have changed the way scientist think about life. The revolutions were the creation of the microscope which gave us access to see and study the complexity of life, the classification of living creatures which was started by Carl Linnaeus, the theory of evolution which became more popular when “The Origin of Species” by Charles Darwin was published, the discovery of genes by Gregor Mendel, and the structure of DNA which was prompted by the experimental technique, X-ray diffraction. And according to Stewart, his sixth biological revolution, mathematics, unites them all.

Mathematics has already been part of the development and improvement of physical sciences for hundreds of year and in present times, we wouldn’t see physics and even chemistry, astronomy and other related fields without it. In biology, on the other hand, it is mostly about how mathematics helps us to not only understand what life is but also how it works by using mathematical techniques, apparatus, and viewpoints.

Some examples in which mathematics has combined with biology which Stewart has mentioned, are in dealing with the mathematics of optics, which developed after the creation of microscope, but is still useful in inventing better microscope, the mathematical patterns in the number of plants or other living thing that show a specific characteristic, Chargaff’s rule and the numerical relationship with the structure of the DNA, Bragg’s law for X-ray diffraction. He also mentioned about how mathematicians could help biologists with models. He explained about the possibility of other forms of life outside Earth and that part of the art of biomathematics is the selection of useful models. Through this models we could understand life more easily. And if I remember correctly, a month ago, we met a mathematician and she showed us a PowerPoint presentation which had math and biology combines. I now understood how mathematicians could work together with biologist.

The combination of mathematics and biology still seems a bit weird for me, but it also feels right. Mathematics will never dominate biology though unlike chemistry and physics, it will just be a partner or tool in order to unravel the mystery of life.

Biomathematics: Biology Embracing Mathematics

A Book Review to Mathematics of Life by Ian Stewart

Mathematics has long been discovered to be used in one’s life. The application of mathematics to our daily life would be countless in terms of how we include the principles of math to our living. In the early forms of life, mathematics has become a tool to study the science underlying it. No one would ever come to picture in their minds that mathematics and biology could be studied at once. But in this book written by Stewart, he gave substantiation and proofs that biology embraced mathematics long ago before anyone noticed it.

 Biology is the study of life, in all its forms. Life is the condition that distinguishes animals and plants from inorganic matter including the capacity for growth, functional activity and continual change preceding death. That was according to the dictionary. The definition of life according to the biologist: concentrate on what it does rather than what it is.  In which order, growth, reproduction, respond to stimuli, adaptation, regulation and energy process are the features of life. Earthly life is based on carbon, water, organic chemistry, DNA and protein.

Biology was mainly about plants and animals but there were revolutions that changed the way scientist think about life. The first revolution was the microscope. It opened up the complexity of life observation that cannot be seen by the naked eye. It gave way to the discovery of the composition of cells. The second revolution was classification. It brought degree of order to the chaotic world of biology in which the system of nature were put into order and thus were organized. It provided the standard system of naming organisms in terms of species, genus and extensive groupings. The third revolution was evolution. It brought in the mechanism behind the diversity of species. The fourth revolution was genetics. It caused the breakthrough of genes. And the fifth revolution was the structure of DNA. It yield the structure of a complex molecule found in living creatures. The different revolutions indicated that the study of life cannot only be studied through science; it signified that the mathematical ideas should be used for sciences and the demands of biology.

Upon scanning through the contents of the book there were questions that bugged in my mind. Few were: How does mathematics being used to study biology? How did the two complex field of study merge in one? Those questions were filled up and answered. As mentioned by Stewart, there were variety of connections between mathematics and biology. The structure of the viruses, organization of cells, evolution, behavior of organisms and its interaction to the ecosystem were some of those. The mathematics involved were probability, dynamics, chaos theory, symmetry, networks, mechanics, elasticity and knot theory.  The application of mathematical biology concerns with the structure and function of complex molecules, dynamics of ecosystem, work and process of the nervous system and brain, shapes of viruses and the evolutionary ancestry. Moreover, mathematics is being used not just to help manage data or improve instruments but to provide significant insights into the science itself, and to help explain how life works. The application of mathematical insights to biological processes made way to a new branch of learning which is the biomathematics or the mathematical biology that shows how life evolved, how organisms works and relate to its ecosystem and environment. It explains how the techniques and viewpoints of mathematics can help understand not just what life is made from but how it works, on its very smallest molecules to the vast of the entire earth. Mathematical biology shows the interconnections of two different domains can achieve things that are impossible for the individual field.

I come to realize that since mathematics is the science of understanding things, in biology mathematics was just not a way to analyze data about living creatures but a method to understand them. Mathematical discoveries will open up for gigantic realm of revealing simple life processes to do complex things that will bear fruit of more biological inventions.

Solving the Formula of Life

This book is written by Ian Stewart on 2011 and contains 19 chapters. In this book, he discussed about the relationship of Mathematics and Biology. The chapter 8 of this book focuses on the Human Genome Project and the algorithmic challenges of DNA sequencing.

The most direct connection to theoretical computer sciences came in chapter 13 where Stewart considered Alan Turing’s famous paper entitled “The Chemical Basis of Morphogenesis”, and sketched the development of biological thought about animal markings. Stewart said that for half a century, the mathematical biologists have built on Turing’s ideas. Turing’s specific model, and the biological theory of pattern-formation that motivated it, turned out to be too simple to explain many details of animal markings, but it captured many important features in a simple context, and pointed the way to models that are biologically realistic.

Turing proposed the reaction-diffusion equations to model the creation of patterns on animal during embryonic development. Stewart also noted that Hans Meinhardt had shown that the patterns on many seashells match the predictions of variations of Turing’s equations in the book entitled “The Algorithmic Beauty of Seashells”. James Murry, a mathematician, extended Turning’s ideas with wave systems, and proved the theorem: “a spotted animal can have a striped tail, but a striped animal cannot have a spotted tail”. The explanation for this theorem is that the smaller the diameter of the tail leaves less room for stripes to become unstable whereas, this instability as more likely on the larger-diameter body.

In chapter 14, an algorithmic game theory called “Lizard Games” made an appearance. Stewart introduced the readers to Barry Siverno’s studies of side-blotched lizards. These lizards come in three different characteristics which are the orange-throated, the blue-throated, and the yellow-throated. The orange-throated males are the strongest ones while the yellow-throated males are the smallest ones and the most female-colored. The blue-throated males are the best at pair-bonding. So, when the orange-throated males fight with the blue-throated males, the orange-throated wins. The blue-throated are preferable to the yellow-throated, and the yellow-throated males (the kicker) sneak away with the females while the orange-throated fight the blue-throated. This situation suggests an evolutionary game where the orange-throated beats the blue-throated, the blue-throated beats the yellow-throated, and the yellow-throated beats the orange-throated.

Stewart introduced von Neumann’s minimax theorem, Smith’s definition of evolutionary stable strategies, and other geometric concepts. Stewart then discussed about the phrase “survival of the fittest”: what it meant in the context where there is no clear winner.

In this the same chapter, Stewart gave many examples of evidence of evolution and the ways in which evolutionary theory has developed since the time of Charles Darwin. An example of this is the conventional biological wisdom in which at one time, sympiatric speciation was impossible. Roughly, the sympiatric speciation occurs when one species develops into two distinct species in a single geographic area. For many years, it was believed that for the speciation to occur, the groups of animals had to be geographically separated. But, this conventional wisdom appeared to be false because of both the empirical evidence and the more sophisticated mathematical models. Stewart said that there are two main forces that act on populations. First is the gene flow from interbreeding tends to keep them together as a single species, and the second is the natural selection that contrasts the gene flow. This natural selection is double edged. Sometimes it keeps the species together because they adapt better to their environment collectively if they all use same strategy. But sometimes also, it levers them apart because several distinct survival strategies can exploit the environment more effectively than one. On the second case, the fate of the organism depends on the force that will win. If the gene flow will win, we will get one species, but if the natural selection will win against a uniform strategy, we will get two species. A changing environment changes the balance of these forces and will have dramatic results.

Other computer-related chapters introduced graph theory, cellular automata and von Neumann’s replicating automaton. In chapter 10, Stewart told us the story of scientists that were identifying viruses with the use of X-ray diffraction and other similar methods. In other chapters, Stewart discussed the importance of symmetry and symmetry-breaking in mathematics with no exception. An example is the herpes simplex virus is mirror-symmetric and has 120 symmetries. Many of the viruses are coated with chemicals with the icosahedron as its shape. These icosahedral coats are made of triangular arrays of capsomers. Capsomers are small self-assembling proteins.

Pure icosahedral mathematics quite did not match on what was empirically observed. In the year 1962, Donald Caspar and Aaron Klug, inspired by the geodesic domes of Buckminster Fuller, proposed a theory that the pseudo-icosahedra will be used to model the virus coats. The Caspar-Klug theory provided an excellent model of many viruses, but over the next forty years, the research teams found structures that could not be explained using this theory. In the start of the year 2000, the mathematician Reidun Twarock and his co-authors finally proposed a unifying framework by using a higher-dimensional geometry.

Reidun Twarock introduced a viral tiling theory that uses the six-dimensional icosahedral symmetry group. He then took a cut from that six-dimensional lattice and projected it into three dimensions. This kind of approach accurately “predicts” both the pseudo-icosahedral virus coats, and the exceptional virus coats that were observed after the year 1962.

Conclusion

I guess this book is a good reference in knowing the relationship between mathematics and biology because of the author’s great “talent” and his knowledge about both fields: the mathematics and the biology.

Reference

Aaron Sterling. Iowa State University. Book Review (3 pages). <http://nanoexplanations.files.wordpress.com/2012/01/mathematicsoflife.pdf>  12/29/2013

Redefining the Norm

   
         Mathematics has been very helpful to humanity for thousands of years. It has been primitively used before to measure a farmer’s land for taxation purposes, calculate distances and angles of elevation. The image of mathematics have been slowly changing. In chemistry, particularly analytical chemistry, mathematics became a useful tool especially in understanding concepts of chemical phenomena. Mathematics is the language of physics, one should learn the different concepts of mathematics in order to gain a clear comprehension to its topics. Now, the book, Mathematics of Life by Ian Stewart has shown how mathematics has proven its worth not just by analysing data but became a way in understanding them.

        The book mainly discusses on how mathematics became the partner of the fastest growing branch of modern science, biology. While reading the book, every page excites me, they might say that it is odd when mathematics is applied to biology but I deem that the world really needs maths especially when things become complex in order to increase our understanding to the different topics concerned.

        The author, Ian Stewart stated in his book the concepts about Fibonacci and Lucas sequences and its relationship to nature. Plants, particularly shows a repeated specific particularly in plants for example, the number of petals in a flower, the way leaves are arranged in a stem and the geometry in seed heads. Stewart also shared his insights about taxonomy and talked about Charles Darwin’s ‘The Origin of Species’.

       Stewart also explained in his book about genetics, he discussed about Gregor Mendel and clearly expounded the idea about the probabilities in breeding plants. It only shows that Mendel’s experiments involves numerical relationship, for example, calculating the probability of the characteristics of the offspring of two cross-fertilised plants. He also discussed about the reproduction of cells of eukaryotes and prokaryotes. Eukaryotes reproduce through mitosis and meiosis while prokaryotes reproduce through binary fission.

        The book also tackled about Alan Turing’s work, he used reaction and diffusion as his two main ingredients in modelling the creation of patterns (spots, stripes and etc.) in animals during embryonic development. He visualized a system of chemicals which acts as a form-generators called morphogens. These morphogens react together and form other molecules. The molecules and its reaction products will disperse and travels across the skin at any direction.

        Aside from being easy to comprehend, the topics inside the book are very interesting. This reading material really have aided me to understand more about the biology. I would like to recommend this book especially to students who have a great interest in biology or in mathematics and to greatly appreciate the team-up of the two different fields. This book explains how mathematicians and biologists have come hand in hand to be able to answer the different dilemmas that the humanity have been facing today and to gain more knowledge to the nature of life.

Two Is Better Than One

Man have innovated mathematics to know the secrets of the world. In physical science, it became the main exemplar in studying for heat, light, sound, fluid mechanics, relativity and quantum theory. Unfortunately, mathematics in this field was just a mere thought. This perception was then changed in the field of life science where mathematics finally became motile. In life science, mathematics has become a new thing, focusing on the demands of the living processes. It is in biology where mathematics became a tool in solving the most difficult scientific problems that man had ever attempted. Mathematics has evolved as man’s questions about the living world arise. Man’s hard work in figuring out the intricacies in his surroundings led him to a new knowledge that mathematics can be possibly associated with life. And this interaction between mathematics and biology was portrayed in Ian Stewart’s book entitled The Mathematics of Life.

Biology is the study of life. According to Stewart there were five great revolutions which altered the scientists’ view about life. First is the invention of the microscope. This revolution led to the discovery that living creatures are made up of cells. Next to this is the revolution which he called the systematic classification of the planet’s living creatures. Carl Linnaeus’ system classified natural objects into kingdom (animals, plants and minerals), class, order, genus and species. He was the founder of the science of taxonomy which classifies the living creatures into related groups. Thirdly, the theory of evolution by Charles Darwin crushed all biologists by the evidence that evolution has been the dominant mechanism behind the diversity of today’s species. He revealed the fourth one to be the discovery of gene. After seven years of breeding pea plants, Gregor Mendel was persuaded by his observation that inside every living organism there are ‘factors’ or ‘genes’ that somehow define many features of the organism itself. Fifth is the discovery of the structure of DNA. Francis Crick and James Watson conducted X-ray diffraction experiments which led them to propose the double helix structure of DNA: two-stranded, like two intertwined spiral staircases.

Mathematics really succeeded in penetrating into a few areas of biology. In his book, Stewart talked about the strange numerology of the plant kingdom. Plants do have a very specific sequence of numbers which shows up repeatedly like in the number of petals in a flower, the geometry of seed heads, the arrangement of leaves along a stem, the lumps on a cauliflower, and the way pineapples and pine cones fit together. The members of this sequence were later called the Fibonacci numbers from the nickname of Leonardo of Pisa, ‘Fibonacci’. Stewart was able to discuss these patterns in his book by using modern mathematics combined with a little chemistry.

Geometry which is the branch of mathematics concerned with the properties and relationships of lines, angles, curves, and shapes has something to do with biology too. Viruses which are a major cause of diseases in humans, animals and plants were noticed to be either icosahedral (shape of a football) or helical (shape of a spiral staircase). Not all viruses have these shapes. Some have a more complex structure. But the most common is Euclid’s elegant icosahedron which he claimed to be perfect for creating a virus. This structure is essential in the arrangement of protein units. American and British biophysicists Donald Caspar and Aaron Klug discovered that most viruses have an analogous geometry to architect Buckminster Fuller’s geodesic dome. From that, they have created a theory regarding the specific numbers of protein units that would form corners on the surface. This theory was tested and was later discovered to be successful. Nevertheless, Stewart stated that the Caspar-Klug theory has still exceptions.

Another field of biology which was associated with mathematics is Neuroscience. It is one of the fields where mathematics was first applied. It started with the problem pertaining to the transmission of individual pulses of electricity along a nerve axon. A mathematical model was developed for this process and was called the Hodgkin-Huxley equations, developed by Cambridge biophysicists Alan Hodgkin and Andrew Huxley. This mathematical model defines the way axon responds to incoming signal received by the nerve cell. Hodgkin and Huxley both became Nobel Prize awardees for this work.

The noticeable markings of many animals can be added to the list of various applications of mathematics to biological development. Stewart meant the stripes of the tigers and zebras, the spots of the leopards and the dappled patches of Friesian cows. An English mathematician, Alan Turing, became interested with this area and became known with his biological theory of pattern-formation. He modelled the formation of animal markings as a process that laid down a ‘pre-pattern’ in the developing embryo. His model involved two main components: reaction and diffusion. According to him, some systems of chemicals called morphogens react together on the embryo’s surface to create other chemical molecules. These chemicals and their reaction products can diffuse and then move across the skin in any direction. Chemical reactions involve nonlinear equations while diffusion can be shown by simpler linear equations. In Turing’s reaction-diffusion equations, local nonlinearity when added with global diffusion makes striking and often complex patterns.

Those applications mentioned above were just some of Stewart’s insights in his book ‘The Mathematics of Life’. Here, he tried to capture his readers by putting lots of examples to explain his points. Frankly, some of his points were not that clear to me but through his examples, somehow I managed to understand it a bit. In the last chapter, he slowly revealed the sixth great revolution to be mathematics. I agree with his statement that it was doing so long before anyone noticed that mathematics is starting to embrace biology. Mathematics was undeniably enclosed in its own shell for a long time until man recognized its use to other fields and made it free. “Two is better than one”, simply describes mathematics and biology. With the two fields helping each other, man will be able to find answers to questions with relevance to life. As what Stewart stated, it is that interconnected communities can achieve things that are impossible for their individual members. Instead of keeping the problem and just figuring things out alone, share it to others or make a team so that a lot of brains can contribute and the knowledge will be spread. In this way, all of us can be the possible contributors of what Stewart calls the global ecosystem of tomorrow’s science.

Collaboration of Mathematics and Biology

                We all know that biology is the study of planet Earth’s living matter. First, biology was just about the plants and animals but later on, cells were being studied by the scientists. In the present time, there’s a great aid for studying the life science— mathematics. The relationships of these fields are tackled in the book: Mathematics of Life by Ian Stewart.

                The first chapter of the book was all about the five revolutions of biology namely the microscope, the classification of different species, the theory of evolution, the discovery of genes and DNA structure. These discoveries were great eye opener to the world of biology.

                I must say that human eye is not enough to discover the realms of life matter. There are things that are too small and too far that it becomes invisible using only the naked eye, we must need apparatus that will aid us to see these things. These are the microscope and the telescope invented by Zacharias Janssen and his son Hans. Small organisms were now seen because of these inventions.

                There are many different organisms in this planet, this must seem impossible to know but Carl Linnaeus did a systematical way of classifying living organisms. He classified the organisms according to its domain, kingdom, phylum, class, order, family, genus and species.

                The fourth chapter of the book discussed about the geometry of the plants, the flower’s petals. It is said that the arrangement of the petals are close to the golden angle which is 137.5° and there numbers are following the Fibonacci numerology.

                Chapter five discussed about the natural selection that is imposed by Charles Darwin. He wrote the book On the Origin of Species by Means of Natural Selection. This book states that an organism can change its certain characteristics depending on its environment. He voyaged at the Galapagos Island and there he collected samples of finches with different size and shape of beak.

                Chapter six to eight discussed about genetics. Characteristics and traits of an organism can be predicted using the Punett square, where there is a dominant and recessive allele. One of the chapters also stated that the DNA is the molecule of life which is true. The DNA is the mastermind of all the things that we can observe in a certain organism, especially its morphological characteristics. In chapter 8, it is stated there that, “Genes make you fat, they make you homosexual, they cause diseases, they control your destiny.”

                The ninth chapter is more on the classification and the relationships of different species. Their relationships are shown as a tree diagram, it looks like a root but a tree won’t be a tree if there’s no root so it is considered to be a tree diagram. This tree diagram also shows how genes are passed from ancestral to descendant species.

                Euclid classified the five regular solids namely the tetrahedron, cube, octahedron, dodecahedron and icosahedron. These solids acquired their names according to the number of faces that it have. In chapter 10, the geometry of the virus was discussed.

                The brain is the controller of the body, and this organ consists of nerve cells. These nerve cells serve as hidden wiring to make the body of the organism work. This cell is so complex but it has the ability in networking, that’s why an organism can react to its stimuli because of these nerve cells that are signaling the organism on what to do.

                The preceding chapters talked about life, population and some more about the DNA. In the second to the last chapter, aliens were discussed. The book also shown a picture of an allegedly alien that was named Grey, it has big dark eyes and it is grey in color. The existence of alien is still questionable until today, there were rumors that aliens visit the planet and the US government is just covering them up. The last chapter of the book stated Stewart’s sixth revolution but I didn't quite understood what was his revolution.

                Though I have a small knowledge in the topics discussed in the first nine chapters because it was taught in our Biology 10 class last semester, I still got some new information about how mathematics collaborate with biology. It is a very interesting book especially when you are fond of exploring new things about how math explained the science of life.

References:

Stewart, I. 2011. The Mathematics of Life. The Book of Life. pp. 117

And there it goes again..

As we know mathematics is the comprehensive study of numbers, shapes, symbols and data’s that come together as important quantitative or qualitative information. None the less, when we talk about mathematics our common knowledge are just numbers in algebra forms, but we do not realize that mathematics scopes in different fields that help towards understand the complexity of it.

As we are given the second book review I was enthralled with the tittle of the book Ian Stewart wrote, it was “The Mathematics of Life” I can barely decipher the meaning of the title, but if we divide it, we say mathematics is subjected to numbers and life is subjected to existence so before I read the book I predicted it as a book about the involvement of mathematics and biology that co-exist to build a better understanding of each other.

The Mathematics of Life is a book that talks about the 5 great revolutions in which scientists' life revolved. These were (1) the microscope; (2) classification; (3) evolution; (4) Genetics; and (5) the structure of DNA. However, Stewart discussed that biology is in the early stage of a sixth revolution, no other than mathematics.

Basically mathematics along with biology did a big evolutionary advancement. None the less with each other handling each other’s back they propel into a high advance technology.

Mathematics and Biology

I got so many plans for Christmas break-sleep, wake-up and eat. I never thought that I would find myself reading a 319-page book, counting only the content, considering that I do not actually read a book normally. Honestly, it bores me reading a book, but I got no choice since I have to be responsible and do enthusiastically my part as a student. Looking on the bright side, at least I got something to be busy about since I got myself a "fun and exciting" Christmas break. I am not quite sure if I have absorbed everything I have read, but I’ll be doing my best to say something knowledgeable about it.

Since I have been in this class I have manage to learn and appreciate more about mathematics. Mathematics is said to be a universal language, and I actually don't have any objections with regards to it. Mathematics has been the spearhead to almost anything or everything in this world. Mathematics has become the reason for our world's progress or development. Before, biologists don’t seem to think that mathematics can help meaningfully in understanding the complexity of life. In this book, the author explained how mathematics and biology was joined or collaborated to solve or attempted to solve various difficult scientific problems regarding life and even its origin. In order to appreciate the book, you really have to concentrate on comprehending it, because somehow I find it difficult to follow. I was deeply fascinated on how mathematics and biology intersects. Because of mathematics, the study of life was even pushed further to its limit. It really is amazing how various mathematical approaches such as, Fibonacci sequence, cellular automata, game theory, topology, networks, multi-dimensional geometry and whatsoever is being related to biology, even if I am not very much acquainted with most of the mathematical approaches that I stated still I am certainly amazed how these mathematical approaches functioned to the world of biology. We all know that biology is such a difficult matter or subject to study however mathematics have helped us to understand biology even more since mathematics has provided us explanation in a much less complicated and a more reliable way of expressing the given matter or topic that is being discussed.

In the modern world that we live in today, since then mathematics is continuously evolving and increasingly developing, we are the living witnesses on how mathematics has been a great help in almost all aspects of life. A long time before, mathematics was limited to solving only our simple daily problems, but now, mathematics has drastically affected almost everything not only in the world that we live in. Carelessly speaking, everything is in need of mathematics. Now, it really makes me wonder what mathematics will be in the future, what mathematics will be introduced to my great grand grand grand children, what more discoveries mathematics will unveil and other curiosities I have in mind that is just too many to be stated. If mathematics is already this evolved, diverse, developed and so many synonymous and connecting words that I can think of, what more in the next few years to come?

Systematic Codes about Life

Life is not simple and studying life is more complex than we thought. The invention of the microscope, systematic classification of living organism, theory of evolution, the gene and DNA structure; these are the 5 revolution that changed the perceptions of the scientist about life and here it comes Biology became advanced.

Mathematics has been with us for thousands of years since ancient time. Numbers are just basic in mathematics yet it is much broader- anything about shapes, logic, processes, structure or pattern and even abstract. What we’d learn at school is just arithmetic a tiny and limited knowledge about mathematics. Then there is the mathematics- especially statistics- as biological toolbox not just to analyse data but a method to understand living creatures and this makes as the 6^th revolution that provides a broader, more advance, furious biology, and the best tool to address not just the components of life but the processes used of those components.

The invention of Microscope and Telescope is the first revolution that took place. Due to our limited human scale microscope was created and manufactured opening the door of other world to be entered and studied due to curiosity; these revealed that the world is taken for granted by humans. In human level, milk and grasses are simple but seen through a microscope these substances are complex. It can deduced that the closer we look it became more complex. In 1590, Zaccharias Janseen discovered the first microscope by putting several lenses inside a tube. This discovery is followed by a tradesman and a scientist Anton Van Leeuwenhoek who developed the microscope by using Geometry that lead him to discover that blood is a tiny disc shaped object, and protists like amoeba; the slipper shape organism with wave-like motion- Paramecium and a colony of single celled algae- Volvox.

Opposite function of the microscope is the telescope, which makes possible for us to observe distant and enormously large celestial objects like planets. The lens technology really brought up our knowledge in Biology especially the organs at the molecular level. Furthermore, the shape which the function of an organ depends (i.e, limbs cannot function as limbs if it is on a wrong shape).

The second revolution took place by making a list and then organizing the diversity of life on earth. We know that earth is lived by millions of species where each of them needs its own habitat and food. The enormous diversity of life on earth led Carl Linnaeus to a systematic approach to the classification of living organism. Through him, taxonomists nowadays organized the living kingdom into 8 major hierarchies- Domain, kingdom, phylum, class, order, family, genus, and species. From an enormous organism to the simplest, one has internal complexity that provides a deeper comparison to every organism and there is a search for general pattern. Due to these general patterns, taxonomists can now identify 300,000 species of plants, 30,000 fungi and other non-animals, and 1.25 million animals.

Nature follows a pattern. Plants’ flowers and leaves have a striking pattern of shape and numbers and by counting plant’s organ, a mathematical application is created and became an answer to Biology.  The first two revolutions were to record life diversity and celebrate its richness. So, mathematics gives the strange numerology of the plant kingdom. Plants exhibits a numerical pattern such as the number of petals, arrangement of leaves along a stem (phylotaxy), geometry of seed heads, lumps on a cauliflower, and the way pineapples and pine cones fit. This pattern is called Fibonacci numbers (1, 2, 3, 5, 8, 13...). Fibonacci numbers are nature’s favourite because most of the arrangement of the leaves, petals, branches, bracts, florets and scales or collectively known primordia which formed near the plant’s apex plant kingdom follows this pattern. For example, the Genetic spiral- “The spiral resulting from connecting chronologically successive primordial” (Adam 2011) - that appears as intersecting sets. One set is at clockwise direction and the other is counter-clockwise (i.e. sunflower 55 clockwise spiral and 34 counter-clockwise).

Before, Biologists believed that inheritance is passed through blood by blending. Gregor Mendel’s idea about inheritance was first rejected by Biologists due to their belief in Blending Hypothesis. It was a widespread belief until it was diminished when Gregor Mendel’s Cousin Francis Galton did a long series of experiment of paragenesis (inheritance is passed through blood by blending) by transfusing rabbit’s blood to other organism but didn’t found any trait of a rabbit.

Gregor Mendel’s qualitative experiment about pea plants led to the discovery of the “heritable factor” (the 4^th revolution) or the gene. This qualitative observation of Mendel was rejected. One of the first characters that Gregor Mendel studied was the colour of the flower of the pea plant (white and purple). He observed that when he crossed breed purple + purple, all offspring are purple (1^st generation), 1/3 are purple and other quarter are white (2^nd generation; 1^st generation was cross pollinated), then (3^rd generation) half of the offspring of the quarters are purple and white. And when white is cross pollinated with white the 2 observation can be observed except the last one. And when white + purple the offspring is always purple, he observed that there was no blending hypothesis occurred.

                                                          Figure 1: Punnett Square

Mendel did this experiment and found a pattern of 3:1 of purple is to white. The law of probability govern the Mendelian inheritance. In each combination of traits in the punnet square is ¼. Since there was only white region, that region is ¼ and the other dark region is ¾. It can be deduced that between 2 traits, we choose one factor from each parent at random with equal probability. Furthermore, Meldel also did an experiment for dihybrid combination and found a 9:3:3:1 pattern and abiding the law of probability. Gregor Mendel died and few generations had passed, and his theory was supported by biologist.

Greeks are known as geometers and the famous of all the ancient geometers is Euclid of Alexandria. In his book “The Elements”, he featured the classification and construction of the 5 regular solids.

        Figure 2: The regular solids.  Left to right: Tetrahedron, cube, octahedron, dodecahedron, icosahedron.

                                                 Figure 3: Enterobacteriophage T4

The icosahedron though it does not appear naturally in nature yet it plays an important role in pure mathematics, engineering, chemistry and biology- especially the shape of viruses. In 1956, it was noticed that most of the viruses have icosahedral shape.

Mathematics became a force in the advancement of physical sciences. Until, it played a role in biology by using mathematical models. It reminds me about our symposium with a mathematician named May Anne Mata. She told us that today’s “in” in discovering/studying new things is not through an independent research instead using another field to study other field, such as applying mathematics in biology. The discovery of marks on the animal body, networking at the molecular level, lens development, shapes and patterns on DNA is what Mathematics did in the development in studying life and it was like “hidden” before but now it changed, mathematics became a tool in science and medicine. And according to Stewart, by the time we get, biology will have changed just as mathematics and physics. That can’t be! Because I believe that, biology is a way to get rid of Mathematics among other science field but I am totally wrong. Instead the achievements of Physical Sciences and Biology were dependent on Mathematics and it will depend to Mathematics.

References:

Stewart I., (2011). Mathematics of Life. 1st ed. United States: Basic Books.

Stewart I., (2011). 'In a Monastery Garden'. In: (ed), Mathematics of Life. 1st ed. United States: Basic Books. pp. 77-90

Stewart I., (2011). 'Virus From the Fourth Dimension'. In: (ed), Mathematics of Life. 1st ed. United States: Basic Books. pp.138-157.

The Harmony of Biology and Mathematics

            As we all remember in our high school or even in our college days there weren’t any equations or any formulae that arose in any biology subject. The book of Ian Stewart titled “The Mathematics of Life” puts the notion of a “math-less” life science to rest. He starts his fight with five biology-related topics: (i) the microscope; (ii) classification; (iii) evolution; (iv) Genetics; (v) The Structure of DNA.

            The microscope has math in it through its magnification and even in the lenses. Classification in idea can be broken down into basic binary. For example, you need to find the differences between two animals so if this animal has the trait that was being searched for then give that trait a one and if it doesn’t give that trait a zero. Evolution, Genetics can also be made into a binary sequence wherein these specific sequences can determine how animals would behave or look and even the lineage of such animals. Math basically is about patterns and also that is what the structure of DNA is. It’s a pattern of Adenine, Cytosine, Guanine and Thymine in a long double-helix strand that determines heredity and paternity. Math can find these patterns and help determine how a future infant can look like by using determined patterns in the DNA or the DNA can be used to determine what are the possible ailments that the individual can get may it be curable or incurable.

            For what medical research may had been, it is taking a bigger and faster leap for what can biology and mathematics can do together rather than individually.  

Mathematics as a Way of Life

          Throughout the history of science, biology and mathematics have barely been on speaking terms. (Bellos, A., 2011) Biologist have long dismissed mathematics as a separate discipline which is unable to meaningfully contribute to the understanding of living beings. (goodreads.com, 2013) To us, mathematics is a mere scientific discipline that can never go hand in hand with other branches of science. And through time, it was not only us who were lead to believe this, but specialist and scientist were also lead to believe this. We were accustomed to seeing these two disciplines as separate, different and distinct from each other thus can never fuse with each other. And to specialist, especially those who are biologist, views mathematics as a baggage that will only burden and might even hinder their discoveries that will help them understand living things.

          However Ian Nicholas Stewart, a mathematics professor and famous popular-science writer, says this belief or trend is now shifting anew. (Wikipedia, 2013) In his book, The Mathematics of Life, he tells us that it evident, in the past ten years, that mathematicians has proven to hold the key to unlock some of the mysteries of our world – and even ourselves. (goodreads.com, 2013)

         Stewart also provides an enthralling overview of the vital but little-recognized role mathematics has played in the unraveling of the hidden complexities of the natural world. Aside from this, he explains how mathematical contributions will be even more vital in the years to come. Also in this book, Stuart records how mathematicians and biologist have already come to work together, hand in hand, on some of the most difficult scientific problems that the human race ever embarked on – one of which deals with the nature and origin of life itself. (goodreads.com, 2013)

          The 19 chapters of this book is divided into three parts. The first third of the book provides a well done capsule on the history of biology. (James, 2011) Here, he introduces to us the five scientific revolutions that have brought biology into the modern age biology we have today: 1.) invention of the microscope, 2.) A systematic means of classifying species, 3.) evidence of evolution, 4.) Expansion of the field of genetics and 5.) Discovery of the structure of the DNA. (Parker, N., n.d.)

          However, Stewart argues that biology is currently in the early stage of a sixth revolution. This sixth major transformation is where scientists change the way they view and think about life. This sixth revolution is no other than mathematics. (Devlin, K., 2011)

          Stewart notes that the life sciences have traditionally regarded mathematics as a mere tool to analyze data, now, these life sciences’ relative indifference is changing. According to Stewart, biologist are now understanding the importance of mathematics through their use of “mathematics and mathematical ideas in central ways to make new and achieve new understandings.” (Devlin, K., 2011) This is why the remainder of the book discusses the different areas of mathematics and their application to the numerous topics in biology. Some of which are Fibonacci sequence, Lucas sequence, geometry, topology, probability theory, group theory, network theory, and mathematical modelling. (James, 2011)

          Stewart argues this thesis through deeper explanations on how mathematical ideas can be applied to the numerous topics in biology. One great example of how he argues his proposition is seen on how he explains by going beyond the Fibonacci explanation of petal patterns to discuss why the associated mechanics and biochemistry generate these patterns. Aside from this, crucial to his argument to prove that mathematics plays a major role in biological discoveries and advancement is through the use of breadth of examples - making use of other branches of mathematics to explain even deeper the relationship between how mathematical ideas can be applied to biological topics.  (timeshighereducation.co.uk, 2013)

         Aside from Stewart’s argument that mathematics plays a crucial role in the study of biology, he also acknowledges the importance of many disciplines, some of these topics that were covered in the book includes the basics of genetics, DNA structure and replication, molecular biology, taxonomy, game theory, evolution, neurobiology, virology, population dynamics, knot theory and many more. (Parker, N., n.d.)

          Growing up, we have been accustomed to seeing mathematics and biology as completely different disciplines that can never go side by side with each other. However, through this book, we come into realization that mathematics can revolutionize biology. Here we see the evident fusion that can happen between these two completely different disciplines, that they do not exist in opposing end of the pole, rather can accompany each other. We also see evidences that mathematics can lend itself to other discipline. And this in turn will caused a series of events that will lead not only to mathematics lending itself to other disciplines but also mathematics that lends itself to discoveries and advancement that are outside the field of just plain mathematics.

          Mathematics lends itself to other disciplines. In this book, we can see that though mathematics and biology exists in the opposing ends of the pole, yet we can also see that mathematics can actually lend itself to biology and help make sense of biological patterns in that discipline. And conclusions from those patterns can be made and this in turn will help biologist understand the living beings that it studies. Here we can denote that mathematical principles can be used to understand not only patterns in numbers and formulas in mathematics but also the patterns in other fields of discipline. Mathematics to some biologist may seem unable to meaningfully contribute to their understanding of living beings, but it does not mean that mathematics is completely unable to contribute, it only means that mathematics contributes in a different way – by making sense of patterns through its mathematical ideas and principles. And once we make sense of patterns, only then will we be able to understand how things really work. And this is not limited to biology but the mathematical ideas and principles can be used to other fields of discipline.

          Mathematics lends itself to discoveries. When mathematics lends itself to other disciplines, it already is lending itself to meaningfully contribute to the discoveries of those disciplines. It is through the mathematical ideas principles, and making sense of patterns where we can see that math is already lending a hand to help solve problems, unravel mysteries and help discover what is concealed from our knowledge. This basically means that mathematical principles and ideas can be used by other fields in solving complex solutions and problems to help them understand and find the answer to the questions bothering them in their own specific fields. Thus, mathematical ideas and principles helps generate solutions and answers to the complex formulas, patterns, and question that is delved by other disciplines.  

          Mathematics lends itself to advancement. Once discoveries are made, only then can advancement can be pursued. The mathematical equations that helps solve complex problems of different fields will be a springboard for development and advancement. Through those discoveries, new ideas can be suggested to further improve the way things are or to give clarity to what is unknown or blurry from our minds. This then would lead to the implementation of the ideas to pursue advancement. We have to remember that suggestions and implementations made should aim for the wellness of not only mankind but of all the components in this world. Only then would it be possible to create a better world through mathematics.

          Growing up, mathematics is seen as a distinct discipline, one that is different from other discipline. We were accustomed to believe that mathematics exists only by itself, which it will be unable to meaningfully contribute once paired up with another. However, this is changing.  Mathematics being a single discipline that only consist of mathematical ideas, principles and theorems does not really define the life of mathematics and what it is all about. For mathematics is much more than that. Mathematics is a way of life. Mathematics is a way of life for it lends itself to other disciplines to create understanding of the world and of us. Mathematics is a way of life for it lends itself to discover the things that are concealed from our knowledge. Mathematics is a way of life for it pursues advancement in everything it does. And most of all, mathematics is a way of life for it was, is and will always be part of us and who we are.


References:

Bellos, A. (2011, April 16) Mathematics of Life by Ian Stewart – review [Review of the book The Mathematics of Life].  Theguardian. Retrieved December 21, 2013 from http://www.theguardian.com/books/2011/apr/16/mathematics-of-life-ian-stewart-review

The Mathematics of Life. (2013). In Goodreads. Retrieved December 21, 2013 from http://www.goodreads.com/book/show/11298890-the-mathematics-of-life

Mathematics of Life: Unlocking the Secrets of Existence. (2011, August 11). In At the Heart of Higher Education Debate. Retrieved December 21, 2013 from http://www.timeshighereducation.co.uk/417070.article

Ian Stewart (mathematician). (2013, December 16). In Wikipedia. Retrieved December 21, 2013 from http://en.wikipedia.org/wiki/Ian_Stewart_(mathematician)

James. (2011, July). The Mathematics of Life by Ian Stewart [Review of the book  The Mathematics of Life].  goodreads. Retrieved December 21, 2013 from http://www.goodreads.com/review/show/176745546

Parker, N. (n.d.). The Mathematics of Life [Review of the book The Mathematics of Life].  New York Journal of Books. Retrieved December 21, 2013 from http://www.nyjournalofbooks.com/book-review/mathematics-life

Devlin, K. (2011, June 9). New Angles on Biology. The Wall Street Journal. Retrieved December 21, 2013 from http://online.wsj.com/news/articles/SB10001424052702304066504576345382084988252