I'm reading this really good book called The Mathematics of Life, by mathematician Ian Stewart; I'm enjoying it so much that I decided to post a discussion on it even though I'm only 1/2 way through the book, to recommend it to you guys. The book basically explores the mathematical aspects of nature, and speculates that the use of mathematics in biology will be the 6th revolution in biology [according to Stewart, there were 5 revolutions in biology: discovery of the microscope, the classification of organism (Linnaeus' idea), evolution, genetics and the structure if DNA]. I find Stewart a very clear writer; I like how he blends mathematics and biology in every chapter, yet I think it is accessible for lay people that are science aficionados. He looks at the patterns in organisms, from viruses to plants to the stripes in a zebra, and explains how mathematical models can tell us a lot about how and why the patterns arise. For example, he begins his collection of examples by examining the Fibonacci sequence in botany. I had never heard of this, and it is fascinating: it is the growth at the tip of a plant that determines that petals, the seeds in sunflowers, or leaves, follow a Fibonacci series that reflect an angular version of phi, the Golden Ratio, a ratio reflected in successive numbers of the Fibonacci sequence. By following the golden angle (137.5 degrees), and not 1/3 degree more or less, plants achieve the perfect packing of seeds or leaves. Mind boggling.
Here is a succinct review from The Guardian that you guys may find useful:
Mathematics of Life by Ian Stewart - review
A timely account of why biologists and mathematicians are hooking up at last
Dairy cows are not, on the whole, spherical. Photograph: John Mason/SWNS.COM
Did you hear about the farmer who hired some mathematicians to help him increase his milk yield? Their report began: "Consider a spherical cow . . . "
This is a famous old joke about the disconnect between mathematics, the language of clear abstractions, and the life sciences, the domain of messy organic forms. For much of the history of science, biology and maths have barely been on speaking terms. When I was at school, biology was the science you took precisely to avoid calculations and formulae. Maths was firmly in bed with physics, its muse.
Ian Stewart says this is changing. He claims that for the next century the driving force behind mathematics will be biology, and that this marks a fundamental, and exciting, shift in how the sciences inter-relate. "Mathematicians like nothing better than a rich source of new questions," he writes. "Biologists, rightly, will be impressed only by the answers."
Stewart is Britain's most brilliant and prolific populariser of mathematics, the author of at least 30 books, as well as academic texts and influential research papers. His recent collections of playful miscellany, Professor Stewart's Cabinet of Mathematical Curiosities and Hoard of Mathematical Treasures, have been bestsellers. Mathematics of Life is a much more serious book. Through mathematical eyes, Stewart chronicles the major advances of biology, from the invention of the microscope three centuries ago to the discovery in 1953 by Crick and Watson of the structure of DNA. He shows just what maths has done to explain elements of life, and where research is taking us next.
Read the rest here.
Also, another very good review, more extensive, from the WSJ:
New Angles on Biology
Life sciences, meet mathematics: How viruses resemble Buckminster Fuller's geodesic dome, and other discoveries.
According to Ian Stewart, biology is in the early stages of a sixth revolution, by which he means a sixth major transformation where scientists change the way they think about life. The first five were: inventing the microscope; systematically classifying the planet's living creatures; recognizing evolution by natural selection; discovering the gene; and determining the structure of DNA. The nascent sixth, Mr. Stewart says, is mathematics.
His point in the patchily interesting "The Mathematics of Life" is not that biologists have suddenly noted that mathematics is pretty useful in doing science. Mathematics has played a leading role for centuries in the physical sciences, most spectacularly in physics. But as Mr. Stewart notes, the life sciences have traditionally regarded mathematics as little more than a tool for analyzing data. Now the life sciences' relative indifference is changing, Mr. Stewart says, as biologists are using mathematics and mathematical ideas in central ways to make new discoveries and achieve new understandings.
An early stirring of the alliance between biology and mathematics came in the 1950s, when Alan Turing—the British mathematician famous for helping to crack Germany's Enigma code during World War II—suggested a plausible mechanism for creating animal markings like leopard spots and tiger stripes. In 1952, Turing proposed that a biochemical process called reaction-diffusion could give rise to the coat patterns we observe. The key aspect of Turing's proposal, as far as Mr. Stewart's account is concerned, is that the coat patterns resulted from mathematical rules. Turing's specific model turned out to be too simple, but his general approach was correct and set the stage for more accurate theories that came later.
"The Mathematics of Life" is at its best in discussing the role that the discipline has played in our understanding of viruses. Mr. Stewart observes that viruses consist of genetic material wrapped in a protein coat, with each virus having a definite structure. Most are either icosahedral or helical, which means (as the author helpfully notes) that they are shaped like a football or a spiral staircase. These shapes open the door for the application of geometry, but there is an unexpected twist: It is geometry in six dimensions.
The complicated three-dimensional shapes we see in viruses turn out to be best thought of as "shadows" or slices of shapes that, though six-dimensional, are simpler. This surprising observation is a result of nature's familiar tendency to seek solutions that minimize energy consumption.
Read the rest here.