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.