Having dealt with mathematics
as a medium of everyday life, the book provides a welcome change. What amazed
me is the sheer variety of mathematical approaches that are being applied to
biology, including Fibonacci sequences, networks, cellular automata, topology,
game theory, multi-dimensional geometries.
The book is written very
clearly, well organized, and is completely understandable to the layman.
Stewart explains that while mathematical models are not completely realistic,
simplifying approximations help to generate insights into the underlying
biological mechanisms. And, this book is jam-packed with wonderful insights
into an array of biology issues.
While not dealing directly
with mathematics, Stewart explains that the possibility of alien life does not
necessarily require a planetary system "just like the Earth". A wide
range of planetary conditions may be able to foster life, and we should not
jump to hasty conclusions based on the conditions that seem "normal"
to us on Earth.
This book was tricky after
all . If you read the first few chapters, you’ll start to wonder that you’ve
made a mistake and picked up a book that’s going to be TOO easy to read. You’ll
start with the history of the microscope and the “structure of DNA,” and
re-read things you learned in high-school biology like the structure of a cell
or how plants and animals are classified into various orders or kingdoms.
After being lulled into a false-sense of security, you’ll learn about how the spirals in the head of a sunflower grow at an exact rotation of a specific degree of angle, or how leaves on plants bud at common and predictable angles, or why 137.5 degrees is the golden angle and how nature uses it to produce beautiful displays of art.
At this point, you might think, hope even, that the book will tell you all of nature’s mathematical secrets—and in a way, Ian Stewart does. But with each successive page, the depth of his examples made me feel less and less adequate to take on such a book. By the end, I was hopelessly clamoring to understand everything he was telling me, but finding myself unable to do so.
Even worse than the occasional factual misstatement, there were a few places where the logical underpinnings of some ideas were not fully explained or explored in a way that made them misleading. For example, in the "Lizard Games" chapter, he talks in depth about the mating strategies of the side-blotched lizard. There are three different types of male lizard: fighters can defeat pair-bonders, pair-bonders can defeat sneakers, and sneakers can slip past fighters. This is sort of an oversimplification of the system, but you can see how it is analogous to the game rock-paper-scissors. Stewart explains that if Alice and Bob play rock-paper-scissors over and over, if Bob always plays rock, Alice can figure out how to beat him. Therefore, both players should play all three strategies in roughly equal frequency. But wait! Each individual lizard does only play one strategy! How does that work? Who are the "players" in this game? Stewart just leaves the argument there and doesn't close the loop. The "players" aren't necessarily the male lizards themselves, but their mothers. A mother will be most fit if her sons successfully father offspring. She will do the best if she always "plays" the best strategy by having the type of sons that defeat the most common type of male in the population -- she doesn't have to do this consciously. Therefore the system as a whole will tend to have equal numbers of all three types of males; whenever fighters are most common, sneakers will be selected for until they are most common, in which case pair-bonders will be selected for, and on and on. By failing to finish the logical progression in his argument, Stewart left the reader with an incomplete perception of how this type of system becomes stable, and how evolution in general works. The rest of that chapter has nothing to do with game theory, and in fact, ends with a very misleading hint that the lizards might be in the process of becoming separate species (which they aren't, because their genes are always mixed in the same pool of females -- unless females strongly prefer to mate with males of their father's type).
After being lulled into a false-sense of security, you’ll learn about how the spirals in the head of a sunflower grow at an exact rotation of a specific degree of angle, or how leaves on plants bud at common and predictable angles, or why 137.5 degrees is the golden angle and how nature uses it to produce beautiful displays of art.
At this point, you might think, hope even, that the book will tell you all of nature’s mathematical secrets—and in a way, Ian Stewart does. But with each successive page, the depth of his examples made me feel less and less adequate to take on such a book. By the end, I was hopelessly clamoring to understand everything he was telling me, but finding myself unable to do so.
Even worse than the occasional factual misstatement, there were a few places where the logical underpinnings of some ideas were not fully explained or explored in a way that made them misleading. For example, in the "Lizard Games" chapter, he talks in depth about the mating strategies of the side-blotched lizard. There are three different types of male lizard: fighters can defeat pair-bonders, pair-bonders can defeat sneakers, and sneakers can slip past fighters. This is sort of an oversimplification of the system, but you can see how it is analogous to the game rock-paper-scissors. Stewart explains that if Alice and Bob play rock-paper-scissors over and over, if Bob always plays rock, Alice can figure out how to beat him. Therefore, both players should play all three strategies in roughly equal frequency. But wait! Each individual lizard does only play one strategy! How does that work? Who are the "players" in this game? Stewart just leaves the argument there and doesn't close the loop. The "players" aren't necessarily the male lizards themselves, but their mothers. A mother will be most fit if her sons successfully father offspring. She will do the best if she always "plays" the best strategy by having the type of sons that defeat the most common type of male in the population -- she doesn't have to do this consciously. Therefore the system as a whole will tend to have equal numbers of all three types of males; whenever fighters are most common, sneakers will be selected for until they are most common, in which case pair-bonders will be selected for, and on and on. By failing to finish the logical progression in his argument, Stewart left the reader with an incomplete perception of how this type of system becomes stable, and how evolution in general works. The rest of that chapter has nothing to do with game theory, and in fact, ends with a very misleading hint that the lizards might be in the process of becoming separate species (which they aren't, because their genes are always mixed in the same pool of females -- unless females strongly prefer to mate with males of their father's type).
That chapter was the worst
offender for incomplete and therefore incorrect logic, but it wasn't the only
case in which his analogies were bad or his arguments left puzzlingly open.
Which is too bad, because when I wasn't annoyed at the errors and
inconsistencies, I liked the book. It just felt like it was maybe pushing up
against a deadline, and Stewart or his editor didn't do the final careful read
through that it really needed.
“Even in the physical
sciences, models mimic reality, they never represent it exactly…. It is
pointless to expect a model of a biological system to do better . In essence he
is saying that different models of a phenomenon, each focusing on a different
aspect of the problem, when combined, can provide complementary levels of both description
and explanation.”
“The complexity of biological
systems, often presented as an insuperable obstacle to any mathematical analysis,
actually represents a major opportunity. For whom? For biology, mathematics, biologists,
and mathematicians. This is Stewart’s sixth revolution.”
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