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Les mathématiques du vivant: ou La clef des mystères de l'existence
La biologie a connu cinq révolutions : le microscope, la classification de Linné, la théorie de l’évolution, les découvertes du gène et de la structure de l’ADN. Une sixième révolution est en marche : on la doit aux mathématiques. Qu’il s’agisse du Projet génome humain, de la biochimie de la cellule ou des processus qui régulent le développement des organismes, la biologie, grâce aux mathématiques, n’a jamais été aussi près d’élucider les mystères du vivant.
Avec un enthousiasme communicatif, Ian Stewart décrit les passerelles qui existent entre la théorie des graphes et la classification des êtres vivants, la géométrie en dimension quatre et la forme des virus, la théorie des noeuds et la structure des brins d’ADN, la théorie des jeux et les stratégies de reproduction, la théorie du chaos et la dynamique des populations, les automates cellulaires… et la définition de la vie. Pour Ian Stewart, la biologie est le grand territoire à conquérir du XXIe siècle, et les mathématiques le moteur de nos avancées les plus spectaculaires.
Couverture : Création Studio Flammarion
Avec un enthousiasme communicatif, Ian Stewart décrit les passerelles qui existent entre la théorie des graphes et la classification des êtres vivants, la géométrie en dimension quatre et la forme des virus, la théorie des noeuds et la structure des brins d’ADN, la théorie des jeux et les stratégies de reproduction, la théorie du chaos et la dynamique des populations, les automates cellulaires… et la définition de la vie. Pour Ian Stewart, la biologie est le grand territoire à conquérir du XXIe siècle, et les mathématiques le moteur de nos avancées les plus spectaculaires.
Couverture : Création Studio Flammarion
475 pages, Paperback
First published January 1, 2011
129 people are currently reading
1595 people want to read
About the author
Ian Stewart
269 books763 followersIan Nicholas Stewart is an Emeritus Professor and Digital Media Fellow in the Mathematics Department at Warwick University, with special responsibility for public awareness of mathematics and science. He is best known for his popular science writing on mathematical themes.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
--from the author's website
Librarian Note: There is more than one author in the GoodReads database with this name. See other authors with similar names.
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Displaying 1 - 30 of 62 reviews
March 9, 2013
My fiance is a mathematician and I am a biologist. One of his professors reviewed this book, and he wound up with a copy. I wanted to like this book, I really did. And there were parts of it that were quite good. The treatment of Darwin was very good -- even though I have read quite a bit about Darwin's life, I still found it enlightening. The there were lively overviews of networked systems and emergent behavior, and the philosophical/logical discussions of what life is and whether it could exist elsewhere were intriguing. However, the book felt hastily written and/or edited. There were numerous factual errors or misstatements. I can't believe that Ian Stewart didn't know that some of the things that he said were wrong (the possible outcomes of some of the Mendelian crosses, for example), but there it is in print, wrongly stated. One or two errors of this type are forgivable, but I spotted quite a few, and it grew very tiresome.
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 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.
September 13, 2011
Having dealt with mathematics as applied to physics all of my professional life, this 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. I had no idea that Alan Turing did work with reaction-diffusion equations, that can be used to model patterns in animal skin stripes versus spots.
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. The penultimate chapter deals with the question of life on other planets. 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.
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. The penultimate chapter deals with the question of life on other planets. 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.
October 16, 2011
Stewart argues that mathematics is becoming increasingly important in biology; an uncontroversial enough point.
In trying to demonstrate this he is alternately very careful (the first few chapters and large swathes of the later ones serve no apparent purpose other than to show that he bothered to open a college-level textbook at some point during his research for this book; presumably he's trying to pre-empt the criticism that usually applies to people who write outside their field, but I like to think he's trying to atone for his part in Science of Discworld III: Darwin's Watch) and his usual sloppy self (the last few chapters, in particular, on the origin of life and its presence on other planets, are likely to anger you even if the general thrust of his arguments is correct), and the whole thing is a bit of a tangled mess rendered more pointless than it has to be because he is, as usual, afraid of discussing interesting mathematics in anything but the shallowest sense, but I can see how it could be interesting to people to whom any of this would be new (that is, people who have never read any popular biology written in the past four decades).
Mostly, though, it's a good demonstration of why people shouldn't attempt to write outside of their field without at least a co-author in the field they're trying to write in. As you would expect.
In trying to demonstrate this he is alternately very careful (the first few chapters and large swathes of the later ones serve no apparent purpose other than to show that he bothered to open a college-level textbook at some point during his research for this book; presumably he's trying to pre-empt the criticism that usually applies to people who write outside their field, but I like to think he's trying to atone for his part in Science of Discworld III: Darwin's Watch) and his usual sloppy self (the last few chapters, in particular, on the origin of life and its presence on other planets, are likely to anger you even if the general thrust of his arguments is correct), and the whole thing is a bit of a tangled mess rendered more pointless than it has to be because he is, as usual, afraid of discussing interesting mathematics in anything but the shallowest sense, but I can see how it could be interesting to people to whom any of this would be new (that is, people who have never read any popular biology written in the past four decades).
Mostly, though, it's a good demonstration of why people shouldn't attempt to write outside of their field without at least a co-author in the field they're trying to write in. As you would expect.
October 26, 2022
The other day I found myself in the produce section of my local supermarket staring intently at the pineapple in my hand and seeing its patterns for the first time. Sure enough, as Ian Stewart pointed out, the irregular hexagons fit together into interlocking helical spirals. “One family winds anti-clockwise, viewed from above, and contains 8 spirals; the other winds clockwise, and contains 13. It is also possible to see a third family of 5 spirals, winding clockwise at a shallower angle.” For all the pineapples I have eaten I never noticed what now seem like obvious patterns. It’s funny how we can look and still not see.
Ian Stewart is a prolific popular science writer who generally goes a bit deeper into math and science than the usual “Look, it’s a bird” type of book. Sometimes this approach works very well for explaining complex subjects, but occasionally it wanders too deeply into the technical aspects of things, and the readers can loose the narrative thread.
The book is about the growing field of mathematical biology, which Stewart says will be the new frontier of the twenty-first century. However, he takes awhile to get there. He sees mathematics as the sixth great revolution in biology, the previous five being the invention of the microscope, the Linnean classification system, the theory of evolution, the discovery of the gene, and determining the structure of DNA. Each of these gets a chapter to itself, so if you already have a passing familiarity with Van Leeuwenhoek; Linnaeus; Darwin; Mendel; and Watson and Crick there is not much new here, although to be fair Stewart tells the reader in the preface that the first third of the book is going to be primarily about the history of biology rather than mathematics.
He can do a good job pulling up illuminating statistics that help the reader along, for instance mentioning that human bodies contain more than 200 different types of cells and approximately 75 trillion total cells (though he does not mention that only about half of these are human cells, the rest being bacteria and other fellow travelers, many of which we could not live without).
I also like the way he defined the number of species on Earth, saying “Estimates range from 2 million to 100 million, though a figure of 5 to 10 million is probable,” and then gives an accounting of our part of the animalia branch of the tree of life: “Vertebrates account for a mere 60,000 species: 30,000 fish, 6,000 amphibians, 800 reptiles, 10,000 birds and 5,000-plus mammals. Among the mammals, about 630 species are primates, the order of animals that includes monkeys, lemurs, apes ... and humans.”
There is an interesting discussion of Fermat spirals, such as those seen in sunflowers, which have one spiral of 34 seeds winding clockwise, and another of 21 going counter-clockwise. These are aligned in accord with the Golden Angle, 137.5º, defined in Wikipedia as “the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as the ratio of the length of the larger arc to the full circumference of the circle.” It has some amazing characteristics. “In 1979, Helmut Vogel of the Technical University of Munich considered a simple mathematical representation of the geometry of sunflower seeds, and used it to explain why the golden angle is especially suited to such arrangements. In his model, "the nth primordium is placed at an angle equal to n times 137.5°, and its distance from the centre is proportional to the square root of n.” This book uses that information to present a series of three spirals, one with an angle of 137º, one at 137.5º, and one at 138º. Incrementing or decrementing the Golden Angle by as little as half a degree causes an inefficient arrangement of seeds in sunflowers, resulting in gaps between the arms of the spirals. Only at precisely 137.5º do the seeds completely fill the available space, maximizing their number and thus the likelihood that one or more will germinate and pass on the genetic legacy of the parent plant.
He also has an excellent discussion of genetically modified plants. I had never given the issue much thought, assuming it was just a modern version of the kind of selective breeding that farmers have been doing for thousands of years, but it is more problematic than that. The procedure involved is essentially a shotgun blast of new genes into the plant’s existing DNA. The problem with this is that gene interaction is complex; pieces of individual genes are located in various sections of the chromosome, and some of them are required to be close to one another to function correctly. Adding new genetic information without controlling where in the plant DNA it lands could cause trouble, which might not be immediately apparent. It sounds to me like something too important to have decisions left solely to companies focused on making a profit off patenting their work.
There is a good section on cladistics, and once again Stewart showed me that it is more complicated than I had previously thought. Cladistics is a method of graphically depicting the relationship between any two organisms by tracing their paths independently back to their last common ancestor. It sounds straightforward, and in many books on evolution it is presented as a clear and accepted procedure. As in so many things, however, the devil is in the details. Stewart uses an example showing the evolutionary relationship between a leopard, a cheetah, and a house cat. One possible representation is to show that the cat branched off from the leopard after the cat/leopard branch had split from that of the cheetah. Another way to look at the data is to say that the leopard first branched off from the line leading to the cheetah, and then the cat, separately, before the cheetah evolved. It is possible to further refine the model (and in fact, the second of the above scenarios is correct), but it involves sorting through vast numbers of pair-wise comparisons requiring considerable computing power. The further back in time you go the more problematic the cladistic diagrams become, and finding the relationship between a human and, say, an iguana, would involve so many steps and so much inferential analysis that any purported clade should be seen as notional at best.
And finally, the book has a good discussion of the relationships between DNA, amino acids, proteins, and genes.
Proteins are long chains of amino acids, which “fold up in a complex way under the influence of molecular forces. The basic point here is that the DNA, interpreted as amino acids, does not ‘contain the information’ that tells the protein how it should fold. Instead, the protein folds automatically, in response to the chemicals in the surrounding medium.”
Advanced mathematics are providing new insights into the biological processes which shape life, but Stewart is careful to set the boundaries of what is possible today. There is still much to learn and there will be many dead-ends ahead. After all, “Neither relativity nor quantum mechanics captures the universe precisely, even though these are the two most successful physical theories ever. It is pointless to expect a model of a biological system to do better.”
I enjoyed the book, although I have to admit that the chapter on Spots and Stripes required me to focus closely on the arguments and re-read some sections. And I was surprised to learn that Alan Turing, the genius who helped break the German Enigma encryption system during the Second World War, also created mathematical models to try to explain the spots, stripes, and dappled patterns exhibited by animals.
If your interest in life sciences skews toward math and physics, but you don’t want to wrestle with integrals and differential equations, Ian Stewart’s books offer good introductions, and he is adept at picking the examples he uses to make his points. I enjoyed this book and am going to put several others by him on my reading list.
Ian Stewart is a prolific popular science writer who generally goes a bit deeper into math and science than the usual “Look, it’s a bird” type of book. Sometimes this approach works very well for explaining complex subjects, but occasionally it wanders too deeply into the technical aspects of things, and the readers can loose the narrative thread.
The book is about the growing field of mathematical biology, which Stewart says will be the new frontier of the twenty-first century. However, he takes awhile to get there. He sees mathematics as the sixth great revolution in biology, the previous five being the invention of the microscope, the Linnean classification system, the theory of evolution, the discovery of the gene, and determining the structure of DNA. Each of these gets a chapter to itself, so if you already have a passing familiarity with Van Leeuwenhoek; Linnaeus; Darwin; Mendel; and Watson and Crick there is not much new here, although to be fair Stewart tells the reader in the preface that the first third of the book is going to be primarily about the history of biology rather than mathematics.
He can do a good job pulling up illuminating statistics that help the reader along, for instance mentioning that human bodies contain more than 200 different types of cells and approximately 75 trillion total cells (though he does not mention that only about half of these are human cells, the rest being bacteria and other fellow travelers, many of which we could not live without).
I also like the way he defined the number of species on Earth, saying “Estimates range from 2 million to 100 million, though a figure of 5 to 10 million is probable,” and then gives an accounting of our part of the animalia branch of the tree of life: “Vertebrates account for a mere 60,000 species: 30,000 fish, 6,000 amphibians, 800 reptiles, 10,000 birds and 5,000-plus mammals. Among the mammals, about 630 species are primates, the order of animals that includes monkeys, lemurs, apes ... and humans.”
There is an interesting discussion of Fermat spirals, such as those seen in sunflowers, which have one spiral of 34 seeds winding clockwise, and another of 21 going counter-clockwise. These are aligned in accord with the Golden Angle, 137.5º, defined in Wikipedia as “the smaller of the two angles created by sectioning the circumference of a circle according to the golden ratio; that is, into two arcs such that the ratio of the length of the smaller arc to the length of the larger arc is the same as the ratio of the length of the larger arc to the full circumference of the circle.” It has some amazing characteristics. “In 1979, Helmut Vogel of the Technical University of Munich considered a simple mathematical representation of the geometry of sunflower seeds, and used it to explain why the golden angle is especially suited to such arrangements. In his model, "the nth primordium is placed at an angle equal to n times 137.5°, and its distance from the centre is proportional to the square root of n.” This book uses that information to present a series of three spirals, one with an angle of 137º, one at 137.5º, and one at 138º. Incrementing or decrementing the Golden Angle by as little as half a degree causes an inefficient arrangement of seeds in sunflowers, resulting in gaps between the arms of the spirals. Only at precisely 137.5º do the seeds completely fill the available space, maximizing their number and thus the likelihood that one or more will germinate and pass on the genetic legacy of the parent plant.
He also has an excellent discussion of genetically modified plants. I had never given the issue much thought, assuming it was just a modern version of the kind of selective breeding that farmers have been doing for thousands of years, but it is more problematic than that. The procedure involved is essentially a shotgun blast of new genes into the plant’s existing DNA. The problem with this is that gene interaction is complex; pieces of individual genes are located in various sections of the chromosome, and some of them are required to be close to one another to function correctly. Adding new genetic information without controlling where in the plant DNA it lands could cause trouble, which might not be immediately apparent. It sounds to me like something too important to have decisions left solely to companies focused on making a profit off patenting their work.
There is a good section on cladistics, and once again Stewart showed me that it is more complicated than I had previously thought. Cladistics is a method of graphically depicting the relationship between any two organisms by tracing their paths independently back to their last common ancestor. It sounds straightforward, and in many books on evolution it is presented as a clear and accepted procedure. As in so many things, however, the devil is in the details. Stewart uses an example showing the evolutionary relationship between a leopard, a cheetah, and a house cat. One possible representation is to show that the cat branched off from the leopard after the cat/leopard branch had split from that of the cheetah. Another way to look at the data is to say that the leopard first branched off from the line leading to the cheetah, and then the cat, separately, before the cheetah evolved. It is possible to further refine the model (and in fact, the second of the above scenarios is correct), but it involves sorting through vast numbers of pair-wise comparisons requiring considerable computing power. The further back in time you go the more problematic the cladistic diagrams become, and finding the relationship between a human and, say, an iguana, would involve so many steps and so much inferential analysis that any purported clade should be seen as notional at best.
And finally, the book has a good discussion of the relationships between DNA, amino acids, proteins, and genes.
Before the human genome was sequenced...the conventional wisdom was that one gene makes one protein, and since humans have 100,000 proteins, they must have 100,000 genes. This was pretty much considered to be a fact. But when the sequence was obtained, the number of genes was only a quarter of that. This unexpected discovery drove home a message that biologists already knew, but had not fully taken on board: genes can be chopped up and reassembled when proteins are being made. On average, each human gene makes four proteins, not one, by exploiting this process.
Proteins are long chains of amino acids, which “fold up in a complex way under the influence of molecular forces. The basic point here is that the DNA, interpreted as amino acids, does not ‘contain the information’ that tells the protein how it should fold. Instead, the protein folds automatically, in response to the chemicals in the surrounding medium.”
Advanced mathematics are providing new insights into the biological processes which shape life, but Stewart is careful to set the boundaries of what is possible today. There is still much to learn and there will be many dead-ends ahead. After all, “Neither relativity nor quantum mechanics captures the universe precisely, even though these are the two most successful physical theories ever. It is pointless to expect a model of a biological system to do better.”
I enjoyed the book, although I have to admit that the chapter on Spots and Stripes required me to focus closely on the arguments and re-read some sections. And I was surprised to learn that Alan Turing, the genius who helped break the German Enigma encryption system during the Second World War, also created mathematical models to try to explain the spots, stripes, and dappled patterns exhibited by animals.
If your interest in life sciences skews toward math and physics, but you don’t want to wrestle with integrals and differential equations, Ian Stewart’s books offer good introductions, and he is adept at picking the examples he uses to make his points. I enjoyed this book and am going to put several others by him on my reading list.
March 10, 2024
Very interesting to read the connections between mathematics and the life sciences. I actually enjoyed the deep dives into biological concepts like cell division or evolution. It was especially cool to learn about mathematical applications to these areas.
The ending of the book was disappointingly not as mathematical and it really felt like the author was like “…and now we’re going to talk about my favorite subject…aliens” for way too long. I didn’t care for that chapter.
I read most of this last summer, but finally came back to it and read the last third.
The ending of the book was disappointingly not as mathematical and it really felt like the author was like “…and now we’re going to talk about my favorite subject…aliens” for way too long. I didn’t care for that chapter.
I read most of this last summer, but finally came back to it and read the last third.
March 4, 2016
I had a notion of Biology as a safe-haven for students challenged by Mathematics. Author Ian Stewart deals a permanent blow to this notion in this book . He says that Biology is at the cusp of what he calls a sixth revolution. According to him, the Life Sciences have gone through five revolutions in the past. They are as follows:
(i) the invention of the Microscope,
(ii) the systematic Classification of Earth's living creatures,
(iii) the theory of Evolution,
(iv) the discovery of the Gene and
(v) the discovery of the structure of the DNA.
The embrace of Mathematics by the Life Sciences now would be the sixth revolution.
In some ways, this foray of Maths into the Life Sciences should not come as a surprise. Over the years, we already have an image of the Life Sciences as consisting of a lot of Physics and Chemistry. For example, the study of the Brain morphs at times into a study of networks of Neurons. The study of the DNA is often about various chemicals and helix-like structures. Where there is Physical Science, there is Mathematics.
This book contains nineteen chapters. It provides an overview of the role Mathematics has played in unlocking the secrets of the Natural world. It also shows what prospects lie in store for us in the future. I will touch upon a couple of examples from the book as a sample. The chapter 'Florally finding Fibonacci' elaborates on the Fibonacci series and the Golden Ratio. The Golden Ratio of 'phi' (phi = 1.61803....) is a major player in many patterns which occur in the universe. The number of petals in a flower follows the Fibonacci sequence. Each petal is placed at 0.618034 per turn (out of a 360° circle). This allows for the best possible exposure to sunlight. Snail shells follow the logarithmic spiral. Spiral galaxies in our Universe follow the familiar Fibonacci sequence.
The chapter 'Lizard Games' touches on the mathematician Alan Turing's work. Turing gave a mathematical explanation for the patterns in the spots on a leopard and the stripes of a tiger. The chapter 'Virus from the Fourth Dimension' discusses the structure of Viruses. It deals with the application of multi-dimensional Geometry in their understanding. As early as 1956, scientists observed that a majority of Viruses are either like a football or a spiral staircase in shape. In other words, they have a shape as an icosahedron or a helix. Abstract Geometry in higher dimensions is used in the study of Icosahedrons. An Icosahedron is a solid figure with twenty plane faces, especially equilateral triangular ones. At the heart of the Icosahedron is the concept of symmetry. Mathematicians have developed a profound theory of symmetry called group theory. It has applications throughout the sciences. All this is applicable to real viruses, which we observe in three dimensions. The one catch is that we need to apply a geometry in six dimensions!
The author makes some philosophical observations on Science and Mathematical models. He says that Science is rarely about direct observation but mostly about indirect inference. For example, no one observed the evolutionary divergence of humans from chimpanzees. Still, we know for sure through indirect evidence that it did happen. On models, he says "What counts is what the model predicts, not what it leaves out”. In other words, it is important that a model must be consistent with existing data. But its real value comes from its predictive capabilities.
I must say that I found the book a tough read, because of my lack of grounding in the Life Sciences. I had started reading the book with certain assumptions. I thought that it would be about the application of Mathematical concepts in Biology as of today. But the so-called sixth revolution is just beginning, according to the author. So, there is a lot less Maths and a lot more of Biology in the book. This makes it difficult for readers who do not have a good grounding in Biology. I would say that this is a serious book on Biology rather than a popular one on Mathematics. Still, I could get a broad idea of the fundamentals of the elements of Life and how Mathematics interacts with it. The author himself sums it all up quite well in the end as follows:
" In Darwin's day, geology, not mathematics, was vital to the nascent theory of evolution. In the 1960s, Chemistry became an essential foundation for cell biology. Then, computer science joined in, with the advent of bio-informatics. Now, physics and mathematics are entering the fray. ....you can no longer study biology as if the rest of science didn't exist"
(i) the invention of the Microscope,
(ii) the systematic Classification of Earth's living creatures,
(iii) the theory of Evolution,
(iv) the discovery of the Gene and
(v) the discovery of the structure of the DNA.
The embrace of Mathematics by the Life Sciences now would be the sixth revolution.
In some ways, this foray of Maths into the Life Sciences should not come as a surprise. Over the years, we already have an image of the Life Sciences as consisting of a lot of Physics and Chemistry. For example, the study of the Brain morphs at times into a study of networks of Neurons. The study of the DNA is often about various chemicals and helix-like structures. Where there is Physical Science, there is Mathematics.
This book contains nineteen chapters. It provides an overview of the role Mathematics has played in unlocking the secrets of the Natural world. It also shows what prospects lie in store for us in the future. I will touch upon a couple of examples from the book as a sample. The chapter 'Florally finding Fibonacci' elaborates on the Fibonacci series and the Golden Ratio. The Golden Ratio of 'phi' (phi = 1.61803....) is a major player in many patterns which occur in the universe. The number of petals in a flower follows the Fibonacci sequence. Each petal is placed at 0.618034 per turn (out of a 360° circle). This allows for the best possible exposure to sunlight. Snail shells follow the logarithmic spiral. Spiral galaxies in our Universe follow the familiar Fibonacci sequence.
The chapter 'Lizard Games' touches on the mathematician Alan Turing's work. Turing gave a mathematical explanation for the patterns in the spots on a leopard and the stripes of a tiger. The chapter 'Virus from the Fourth Dimension' discusses the structure of Viruses. It deals with the application of multi-dimensional Geometry in their understanding. As early as 1956, scientists observed that a majority of Viruses are either like a football or a spiral staircase in shape. In other words, they have a shape as an icosahedron or a helix. Abstract Geometry in higher dimensions is used in the study of Icosahedrons. An Icosahedron is a solid figure with twenty plane faces, especially equilateral triangular ones. At the heart of the Icosahedron is the concept of symmetry. Mathematicians have developed a profound theory of symmetry called group theory. It has applications throughout the sciences. All this is applicable to real viruses, which we observe in three dimensions. The one catch is that we need to apply a geometry in six dimensions!
The author makes some philosophical observations on Science and Mathematical models. He says that Science is rarely about direct observation but mostly about indirect inference. For example, no one observed the evolutionary divergence of humans from chimpanzees. Still, we know for sure through indirect evidence that it did happen. On models, he says "What counts is what the model predicts, not what it leaves out”. In other words, it is important that a model must be consistent with existing data. But its real value comes from its predictive capabilities.
I must say that I found the book a tough read, because of my lack of grounding in the Life Sciences. I had started reading the book with certain assumptions. I thought that it would be about the application of Mathematical concepts in Biology as of today. But the so-called sixth revolution is just beginning, according to the author. So, there is a lot less Maths and a lot more of Biology in the book. This makes it difficult for readers who do not have a good grounding in Biology. I would say that this is a serious book on Biology rather than a popular one on Mathematics. Still, I could get a broad idea of the fundamentals of the elements of Life and how Mathematics interacts with it. The author himself sums it all up quite well in the end as follows:
" In Darwin's day, geology, not mathematics, was vital to the nascent theory of evolution. In the 1960s, Chemistry became an essential foundation for cell biology. Then, computer science joined in, with the advent of bio-informatics. Now, physics and mathematics are entering the fray. ....you can no longer study biology as if the rest of science didn't exist"
May 15, 2013
A better book than I originally gave it credit for, and an amazingly educational book for me. The writing was good and clear, and there was surprisingly little mathematics in a book that is titled The Mathematics of Life. What Stewart did was deal in concepts, which you can actually more readily do in higher mathematics. He was so good at it at one point that the chapter "Viruses from the Fourth Dimension" finally had me understanding n-dimensional mathematics. You would think that I would have understood that in graduate school when I was doing tensor mathematics, but, not so much.
Two things that need to be communicating clearly to the general public were brought out clearly by this book. First, science is usually far more complex than is communicated to us, but that complexity - and what we don't know - does not necessarily lead to invalidating the basic concepts. Stewart, for example, thinks its crazy that we are genetically modifying foods and giving them to consumers as we are. Worse, he thinks that the companies involved know this or else they wouldn't be reacting as they are by wanting to hide what they're doing. However genetic modification, per se, is NOT bad, just how we're going about it by thinking that we can write Shakespeare when, right now, we just learned the letters to the alphabet.
The second thing is best characterized by the following excerpt from the chapter, "Lizard Games:"
You may wonder how scientists can be sure that evolution happened when they don't understand many of the details. However, we are faced with exactly this situation on a regular basis. [...] We know that the cat brought a mouse in last night, because the gruesome evidence is on the kitchen floor, but we never saw the cat do it. Science is seldom about direct observation: it is nearly always about indirect inference.
(Emphasis mine)
If you're interested in the titled subject matter - but more, if you're interested in how science can work in the face of piecing things together across multiple areas and disciplines - The Mathematics of Life is worth it.
Two things that need to be communicating clearly to the general public were brought out clearly by this book. First, science is usually far more complex than is communicated to us, but that complexity - and what we don't know - does not necessarily lead to invalidating the basic concepts. Stewart, for example, thinks its crazy that we are genetically modifying foods and giving them to consumers as we are. Worse, he thinks that the companies involved know this or else they wouldn't be reacting as they are by wanting to hide what they're doing. However genetic modification, per se, is NOT bad, just how we're going about it by thinking that we can write Shakespeare when, right now, we just learned the letters to the alphabet.
The second thing is best characterized by the following excerpt from the chapter, "Lizard Games:"
You may wonder how scientists can be sure that evolution happened when they don't understand many of the details. However, we are faced with exactly this situation on a regular basis. [...] We know that the cat brought a mouse in last night, because the gruesome evidence is on the kitchen floor, but we never saw the cat do it. Science is seldom about direct observation: it is nearly always about indirect inference.
(Emphasis mine)
If you're interested in the titled subject matter - but more, if you're interested in how science can work in the face of piecing things together across multiple areas and disciplines - The Mathematics of Life is worth it.
February 10, 2019
Wow! Quite a dense book. When you first start this book, it almost seems like it's going to be an easy read. If you have a background in the sciences or biology, you'll notice even more how easy of a read it is. Boy does it turn out to be otherwise. I kept reading through this book for months. I have finally finished it, truthfully by skimming the last twenty pages or so. I'm entering a quick review of it, but I intend to go back to it this year and read it one chapter at a time again. Really, there are at least five great reasons to read this book.
1. You'll learn how the spirals in the head of a sunflower grow at an exact rotation of a specific degree and angle.
2. You'll find out how petal and leaves of specific flowers and plants form at specific number combinations and alternate patterns.
3. You'll learn about viruses from a fourth dimention.
4. Darwin is going to be described in whole new light.
5. Variety of mathematical approaches from sequences, networks, cellular and topological theories, as well as multi-dimentional geometries.
If you're a scientist, of someone who has been surrounded by the field of science and biology, this is definitely one of those books you HAVE to read. I am absolutely intrigued by how mathematics integrates in every aspect of our lives, to the very cellular level of our existence. This book not only covers our own world, but the whole sets of worlds on our planet. It connects every realm of existence through mathematics.
As I mentioned before, though. I will be reading it again. I think you'll either read this book once and that's it, or you'll read it once and you'll crave to go back and revisit some concepts that didn't quite settle with you.
How do you feel about mathematical theories being part of every aspect of our lives?
1. You'll learn how the spirals in the head of a sunflower grow at an exact rotation of a specific degree and angle.
2. You'll find out how petal and leaves of specific flowers and plants form at specific number combinations and alternate patterns.
3. You'll learn about viruses from a fourth dimention.
4. Darwin is going to be described in whole new light.
5. Variety of mathematical approaches from sequences, networks, cellular and topological theories, as well as multi-dimentional geometries.
If you're a scientist, of someone who has been surrounded by the field of science and biology, this is definitely one of those books you HAVE to read. I am absolutely intrigued by how mathematics integrates in every aspect of our lives, to the very cellular level of our existence. This book not only covers our own world, but the whole sets of worlds on our planet. It connects every realm of existence through mathematics.
As I mentioned before, though. I will be reading it again. I think you'll either read this book once and that's it, or you'll read it once and you'll crave to go back and revisit some concepts that didn't quite settle with you.
How do you feel about mathematical theories being part of every aspect of our lives?
November 8, 2024
Título engañoso y que no ha cumplido mis expectativas. El 80% del libro es un repaso general y muy básico de los grandes temas de la biología: evolución, genética y demás, sin mucho nuevo que aportar. La parte dedicada a las matemáticas es escasa y en muchos casos también trillada para aquél que guste de estos temas (la vida artificial, la serie de Fibonacci...)
Total: si nunca has leído algo sobre biología, te puede ofrecer una buena visión general. De matemáticas, poca cosa...
Total: si nunca has leído algo sobre biología, te puede ofrecer una buena visión general. De matemáticas, poca cosa...
April 18, 2018
Excellent book! Worth reading if you have biology or math interest. My only complaint is the on the chapter on aliens ... a bit unnecessary to say the least.
June 10, 2017
Las matemáticas de la vida «celebra la rica variedad de conexiones existentes entre matemáticas y biología«. Es, de todas formas, un libro con mucha más biología que matemáticas, y solo podemos entrever la aparición de esta última; el punto de vista se sitúa casi siempre en la biología y es a través de ese prisma como vemos a las matemáticas extenderse. De hecho, durante aproximadamente el primer tercio del libro prácticamente no aparecen, pues el autor empieza estableciendo el trasfondo biológico, y solo a partir de ahí desarrolla la escala matemática. Las ramas que de esta última toca son variadas: probabilidad, teoría del caos, simetría, redes, mecánica elasticidad o teoría de nudos.
Ian Stewart comienza explicando que aunque la biología solía tratar sobre plantas y animales, cinco grandes revoluciones cambiaron el modo en que los científicos piensan sobre la vida. Esas revoluciones fueron el microscopio, la clasificación taxonómica, la teoría de la evolución, la genética y la estructura del ADN. Como decía antes, la primera parte del libro es solo biología, está dedicada a ampliar estos cinco temas.
En opinión de Stewart, la sexta gran revolución de la biología está en camino, y consiste en «aplicar el modo de percibir las cosas en matemáticas a los procesos de la biología». Y a ella dedica el resto del libro, exponiendo y comentando distintas cuestiones de la biología en las que se ven involucradas las matemáticas. Algunas de ellas son las siguientes:
- Los virus, pues en modelos de su estructura aparecen poliedros regulares. A lo largo de ese capítulo trata también sobre otros conceptos matemáticos como la geometría multidimensional, pues argumenta que los conocimientos actuales justifican que la geometría abstracta en dimensiones grandes puede aportar información sobre los virus reales en tres dimensiones.
- El sistema nervioso, «la instalación eléctrica escondida que hace que el cuerpo funcione». Trata aquí el análisis numérico, y asegura que «la neurociencia es una de las áreas más activas de la biología matemática».
- Topología en el estudio del ADN a través de la teoría de nudos. Resulta útil porque el ADN se hace nudos a sí mismo. Dentro de la teoría de nudos, aplica los "enredos" de John Conway a un problema sobre el ADN llamado recombinación específica de sitio.
- La geometría de las manchas de los animales, cuyo estudio inició Alan Turing. Esto lleva a la morfología, forma y patrón.
- A partir de los lagartos utas norteamericanos explica la aplicación de la la teoría de juegos iniciada por Von Neumann y diserta sobre la especiación, o divergencia de una única especie en dos.
- Con el moho del fango llega la teoría de redes.
- La paradoja del plancton consiste en que si dos especies compiten por el mismo nicho entonces la selección natural implica que una de ellas ganará... y sin embargo en el caso del plancton los nichos son pocos pero la diversidad es enorme. En este capítulo se tratan modelos para el crecimiento de poblaciones, ya sean humanas o no, y se introducen sistemas caóticos, que se presentan como totalmente naturales. Es el caos precisamente el que resuelve la paradoja del plancton.
Citando un pasaje del libro, «la complejidad de los sistemas biológicos, a menudo presentada como un obstáculo insuperable para cualquier análisis matemático, realmente representa una oportunidad muy importante. Las matemáticas, usadas de manera adecuada, pueden hacer los problemas complejos más simples. Lo hacen tan solo centrándose en lo esencial, no reproduciendo fielmente todas las facetas del mundo real».
- ¿Qué es la vida? La biología es la ciencia que estudia la vida, y ya cerca del final del libro Stewart se extiende en las distintas caracterizaciones que podemos dar de la vida. Una interesante aparición matemática en este capítulo es el Juego de la Vida de John Conway.
- Stewart se extiende después en la posible existencia de vida extraterrestre, sobre la que afirma «el modo de entender las probabilidades que habría de vida extraterrestre [...] confundiendo suficiencia con necesidad, como es típico, que solo estas condiciones son adecuadas para la vida». Necesidad y suficiencia, conceptos que nos ofrecen una lección sobre lógica.
Con todo esto, esta sexta revolución que presenta no lo es porque nadie hubiese usado antes las matemáticas para resolver problemas, lo revolucionario consistiría en la amplitud de los métodos usados y la medida en que estos están empezando a ser aplicados en algunas áreas de la biología. Aunque el mismo Ian Stewart duda que las matemáticas lleguen a nunca a dominar el pensamiento biológico en el sentido en el que sí le ocurre a la física, está convencido que su papel se está convirtiendo en esencial.
Ian Stewart comienza explicando que aunque la biología solía tratar sobre plantas y animales, cinco grandes revoluciones cambiaron el modo en que los científicos piensan sobre la vida. Esas revoluciones fueron el microscopio, la clasificación taxonómica, la teoría de la evolución, la genética y la estructura del ADN. Como decía antes, la primera parte del libro es solo biología, está dedicada a ampliar estos cinco temas.
En opinión de Stewart, la sexta gran revolución de la biología está en camino, y consiste en «aplicar el modo de percibir las cosas en matemáticas a los procesos de la biología». Y a ella dedica el resto del libro, exponiendo y comentando distintas cuestiones de la biología en las que se ven involucradas las matemáticas. Algunas de ellas son las siguientes:
- Los virus, pues en modelos de su estructura aparecen poliedros regulares. A lo largo de ese capítulo trata también sobre otros conceptos matemáticos como la geometría multidimensional, pues argumenta que los conocimientos actuales justifican que la geometría abstracta en dimensiones grandes puede aportar información sobre los virus reales en tres dimensiones.
- El sistema nervioso, «la instalación eléctrica escondida que hace que el cuerpo funcione». Trata aquí el análisis numérico, y asegura que «la neurociencia es una de las áreas más activas de la biología matemática».
- Topología en el estudio del ADN a través de la teoría de nudos. Resulta útil porque el ADN se hace nudos a sí mismo. Dentro de la teoría de nudos, aplica los "enredos" de John Conway a un problema sobre el ADN llamado recombinación específica de sitio.
- La geometría de las manchas de los animales, cuyo estudio inició Alan Turing. Esto lleva a la morfología, forma y patrón.
- A partir de los lagartos utas norteamericanos explica la aplicación de la la teoría de juegos iniciada por Von Neumann y diserta sobre la especiación, o divergencia de una única especie en dos.
- Con el moho del fango llega la teoría de redes.
- La paradoja del plancton consiste en que si dos especies compiten por el mismo nicho entonces la selección natural implica que una de ellas ganará... y sin embargo en el caso del plancton los nichos son pocos pero la diversidad es enorme. En este capítulo se tratan modelos para el crecimiento de poblaciones, ya sean humanas o no, y se introducen sistemas caóticos, que se presentan como totalmente naturales. Es el caos precisamente el que resuelve la paradoja del plancton.
Citando un pasaje del libro, «la complejidad de los sistemas biológicos, a menudo presentada como un obstáculo insuperable para cualquier análisis matemático, realmente representa una oportunidad muy importante. Las matemáticas, usadas de manera adecuada, pueden hacer los problemas complejos más simples. Lo hacen tan solo centrándose en lo esencial, no reproduciendo fielmente todas las facetas del mundo real».
- ¿Qué es la vida? La biología es la ciencia que estudia la vida, y ya cerca del final del libro Stewart se extiende en las distintas caracterizaciones que podemos dar de la vida. Una interesante aparición matemática en este capítulo es el Juego de la Vida de John Conway.
- Stewart se extiende después en la posible existencia de vida extraterrestre, sobre la que afirma «el modo de entender las probabilidades que habría de vida extraterrestre [...] confundiendo suficiencia con necesidad, como es típico, que solo estas condiciones son adecuadas para la vida». Necesidad y suficiencia, conceptos que nos ofrecen una lección sobre lógica.
Con todo esto, esta sexta revolución que presenta no lo es porque nadie hubiese usado antes las matemáticas para resolver problemas, lo revolucionario consistiría en la amplitud de los métodos usados y la medida en que estos están empezando a ser aplicados en algunas áreas de la biología. Aunque el mismo Ian Stewart duda que las matemáticas lleguen a nunca a dominar el pensamiento biológico en el sentido en el que sí le ocurre a la física, está convencido que su papel se está convirtiendo en esencial.
March 24, 2016
Leí la traducción al español titulada "Las matemáticas de la vida". Probablemente mi evaluación de 3 estrellas se deba más a mi falta de capacidad para comprender en su totalidad el texto y las técnicas matemáticas descritas en él, que a otra cosa. Admito que hubo párrafos enteros que escaparon a mi entendimiento. Mi parte favorita fueron las analogías, como la que el autor utiliza para explicar la diferencia entre la mitosis y la meiosis: "Si piensas en un organismo como un pastel, entonces la mitosis parte el pastel en dos trozos. La meiosis copia la receta del pastel y la guarda en un cajón, para usarla cuando necesite hornear un nuevo pastel. Pero estos pasteles pueden crecer y la receta está guardada dentro del pastel".
Dejando de lado los tecnicismos... ¡es un libro inspirador! Definitivamente hace evidente la importancia -y potencial- de la integración de las matemáticas con las diferentes ramas de la biología. Me hace querer regresar a la preparatoria, y aplicarme, por ejemplo, en geometría, ahora que sé que muchos virus son icosaédricos y la utilidad de este conocimiento: "Un modo de atacar virus es interferir con su proceso de ensamblaje, y la geometría del virus completamente formado proporciona pistas sobre sus potenciales puntos débiles en este proceso".
También, amplía mi perspectiva sobre la complejidad de la naturaleza y reparar en ocurrencias que, de otra forma, nunca habría notado: "Muchas margaritas tienen 34 pétalos, si no, normalmente tienen 55 u 89. En general, raras veces verás una margarita con 37 pétalos y si ves una con 33 es probable que se le haya caído un pétalo. Los girasoles, los cuales pertenecen a la familia de las margaritas, normalmente tienen 55, 89 o 144 pétalos". Y me maravillo todavía más al saber que hay una explicación matemática para ello (aunque no la haya comprendido completamente).
Dejando de lado los tecnicismos... ¡es un libro inspirador! Definitivamente hace evidente la importancia -y potencial- de la integración de las matemáticas con las diferentes ramas de la biología. Me hace querer regresar a la preparatoria, y aplicarme, por ejemplo, en geometría, ahora que sé que muchos virus son icosaédricos y la utilidad de este conocimiento: "Un modo de atacar virus es interferir con su proceso de ensamblaje, y la geometría del virus completamente formado proporciona pistas sobre sus potenciales puntos débiles en este proceso".
También, amplía mi perspectiva sobre la complejidad de la naturaleza y reparar en ocurrencias que, de otra forma, nunca habría notado: "Muchas margaritas tienen 34 pétalos, si no, normalmente tienen 55 u 89. En general, raras veces verás una margarita con 37 pétalos y si ves una con 33 es probable que se le haya caído un pétalo. Los girasoles, los cuales pertenecen a la familia de las margaritas, normalmente tienen 55, 89 o 144 pétalos". Y me maravillo todavía más al saber que hay una explicación matemática para ello (aunque no la haya comprendido completamente).
July 7, 2011
Did you know that there are 300,000 species of plants, 30,000 species of fungi and 1.25 million species of animals of which 1.2 million are invertebrates (lack a backbone)or that the majority of viruses are icosahedral(20 sided)or helical in shape. Ian Stewart has sprinkled these knowledge nuggets throughout his book, The Mathematics of Life. In the first third of this book he also provides a well done capsule history of biology by discussing the five revolutions in biology: the microscope,classification,evolution,genetics and DNA structure. The remainder of the book discusses areas of mathematics such as Fibonacci and Lucas sequences,geometry,topology,probability theory,group theory, network theory and mathematical modeling and their application to numerous topics in biology. Topics such as spiral patterns in sunflowers and pineapples, the shape of DNA and protein molecules,genetics,the structure of viruses,evolution and even hallucination patterns. This was primarily an easy read except for a couple of chapters like the one on viruses where subjects like group theory and Penrose tiling require a little more intellectual digestion and maybe a re-read. I particularly enjoyed reading the chapter entitled "Is Anybody Out There?" which discusses what alien life forms should look like.
November 25, 2013
This book was tricky. 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.
This is a book that will take more than one reading—and most likely research on the side—to understand. Stewart has a great writing style and a slew of other books that compliment this one, I’ll be reading more of him soon.
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.
This is a book that will take more than one reading—and most likely research on the side—to understand. Stewart has a great writing style and a slew of other books that compliment this one, I’ll be reading more of him soon.
April 30, 2012
I thought this was an amazing piece of non-fiction. I would very highly recommend this book to just about anyone.
Why? Stewart is one of those people who's real calling in life is too teach, and it permeates every chapter of this book. Although I am not a biologist, I felt like I could follow and understand the basic biology concepts used in this book after freshman year biology. However, I can not attest to accuracy in a lot of his claims on biology for that reason also - it would be nice to have an evolutionary biologist weigh in on a lot of the topics he addresses.
As for the Mathematics part, Stewart keeps it straight forward and does an excellent job of explaining a lot of the mathematical concepts and terms. Most of them are patterns, like the Fibanacci Sequence, and are easy for just about everyone to understand if explained properly. There were only a few times in this book that I felt a little bogged down and lost, which, quite frankly, is impressive for a non fiction about math and biology.
If you have a chance or you are interested in applied mathematics, I think this would be a fantastic read for you, and it comes with my highest recommendation. You will definitely learn and few new things and maybe even see the world a litte differently.
Why? Stewart is one of those people who's real calling in life is too teach, and it permeates every chapter of this book. Although I am not a biologist, I felt like I could follow and understand the basic biology concepts used in this book after freshman year biology. However, I can not attest to accuracy in a lot of his claims on biology for that reason also - it would be nice to have an evolutionary biologist weigh in on a lot of the topics he addresses.
As for the Mathematics part, Stewart keeps it straight forward and does an excellent job of explaining a lot of the mathematical concepts and terms. Most of them are patterns, like the Fibanacci Sequence, and are easy for just about everyone to understand if explained properly. There were only a few times in this book that I felt a little bogged down and lost, which, quite frankly, is impressive for a non fiction about math and biology.
If you have a chance or you are interested in applied mathematics, I think this would be a fantastic read for you, and it comes with my highest recommendation. You will definitely learn and few new things and maybe even see the world a litte differently.
February 18, 2012
Stewart's primary argument is that mathematics is a revolution to biological sciences on the order of the microscope, DNA, Mendelian genetics, Darwin, and classification of species. The first part of the book, which he spends discussing each of these biological revolutions in turn is well-written and easily followed. The second part of the book is more mixed in its successes. In instances, Stewart takes exceedingly complicated mathematics and explains them in brilliantly simplistic terms for the layperson. There were chapters, however, where I felt that either his arguments were less effective or his explanation of the mathematics was less successful. Regardless, this is still a dense book, but one from which I feel I learned quite a bit.
March 15, 2017
For readers with painful memories of high-school algebra and geometry, this book about mathematics is for you. You'll understand and enjoy Stewart's explanations of population growth, speciation, brain function, chaos, Darwin and evolution, and game theory, networking, symmetry and even the mechanism that produces animal stripes and spots.
All chapters begin with basics, but if you don't have a wee bit of scientific background it can be a struggle to the end. But it is written so well that it is a book you'll want to pick up and read again later. Something I intend to do.
All chapters begin with basics, but if you don't have a wee bit of scientific background it can be a struggle to the end. But it is written so well that it is a book you'll want to pick up and read again later. Something I intend to do.
September 15, 2011
There is very little mathematics in this book about biology. What little there is is not all that interesting. Nevertheless, the topics covered could have been made more engaging and better explained had they been accompanied by animation. The book would have been ideal written in the new Wolfram Research Computable Document Format (CDF). Instead, it only has black and white illustrations that mostly appear after the page cited.
October 11, 2011
Even a giant math nerd like myself found some of this difficult to follow. Appreciated finally learning to understand the Fibonacci connection to flowers, but after that it kinda became way too deep into the applied physics of DNA proteins for me.
October 5, 2011
Awesome. If you like the mating of math and science to explain the complexities of the world around you, you will love this book.
December 8, 2017
Un livre dense, magnifique et difficile that i had enjoyed a lot. Jaurais préféré que l'auteur Ian Stewart parle plus des maths... mais bon je conseille vivement ce p'tit bijou
July 29, 2024
Was educational, some elements are now dated
Did not finish
February 23, 2026"Mi propongo, in questo libro, di dimostrare come i procedimenti matematici e le relative intuizioni ci possano aiutare a capire quali sono i componenti essenziali del fenomeno vita, ma anche i suoi meccanismi, a qualunque livello, da quello delle molecole a quello di tutto il pianeta e, forse, anche oltre." Ian Stewart
Il titolo è forviante. In realtà il libro parla delle principali scoperte scientifiche senza un chiaro filo logico. L’autore ci tiene a riempire i capitoli di nozioni e aneddoti vari. Parte del contenuto non riguarda gli aspetti più importanti in materia ma le ricerche svolte dall'autore stesso nel corso degli anni.
Bisogna aspettare il capitolo 10 per avere testo incentrato sulla matematica. Ad essere precisi sulla geometria. Il libro contiene anche informazioni datate. Ad esempio, l’autore si scaglia contro gli OGM parlando di tecnologie ormai obsolete: “… la modificazione genetica invece spara a caso del DNA alieno nel genoma dell’organismo, permettendogli di allocarsi ovunque capiti.”
Se cercate un libro che vi spieghi come la matematica può rappresentare i principali comportamenti biologici cercate da un’altra parte.
Il titolo è forviante. In realtà il libro parla delle principali scoperte scientifiche senza un chiaro filo logico. L’autore ci tiene a riempire i capitoli di nozioni e aneddoti vari. Parte del contenuto non riguarda gli aspetti più importanti in materia ma le ricerche svolte dall'autore stesso nel corso degli anni.
Bisogna aspettare il capitolo 10 per avere testo incentrato sulla matematica. Ad essere precisi sulla geometria. Il libro contiene anche informazioni datate. Ad esempio, l’autore si scaglia contro gli OGM parlando di tecnologie ormai obsolete: “… la modificazione genetica invece spara a caso del DNA alieno nel genoma dell’organismo, permettendogli di allocarsi ovunque capiti.”
Se cercate un libro che vi spieghi come la matematica può rappresentare i principali comportamenti biologici cercate da un’altra parte.
December 8, 2019
Livro bastante interessante, onde o autor tenta mostrar como a Matemática se tem tornado uma componente não só importante, como indispensável da Biologia. Stewart, porém, tenta mostrar isto sem entrar em demasiados detalhes, isto é, sem de facto explicar a fundo muitos dos detalhes matemáticos, de forma a poder dar uma visão genérica e não muito massuda sobre os temas abordados. Assim, embora seja uma decisão razoável por parte do autor, o livro por vezes parece tentar resumir em demasia, ficando a exposição pouco clara. A organização do livro também me pareceu no mínimo questionável. Se por um lado os capítulos iniciais e os finais fazem sentido de um ponto de vista estrutural, os do meio parecem ser artigos um pouco desligados do resto. Por outro lado, são esses capítulos do meio que têm de facto a Matemática. Em geral, a componente da Biologia pareceu-me mais bem explicada que a da Matemática. É pena, mas é compreensível.
September 11, 2024
Subtitled Unlocking the Secrets of Existence, this book is a readable tour through the maths of biology and ecology. The book is very accessible for those who don't enjoy too much maths and covers topics such as the Fibonacci series, the maths of genetics, game theory, networking and patterns.
I've got a Botany degree, and so a lot of this felt like revision, but very engaging and sometimes entertaining revision with a new focus on maths. As a student, I had been aware of the importance of statistics in populations studies in ecology and also the importance of mechanics in environmental physics (my least favourite subject, far too much physics!). Reading this book, though, really opened my eyes to the hidden maths, particularly that which determines the pattern and form of living things.
This is an excellent book if you want an overview of the hidden importance of maths to biology, but if you want some serious mathematical investigation, you may need to look elsewhere!
I've got a Botany degree, and so a lot of this felt like revision, but very engaging and sometimes entertaining revision with a new focus on maths. As a student, I had been aware of the importance of statistics in populations studies in ecology and also the importance of mechanics in environmental physics (my least favourite subject, far too much physics!). Reading this book, though, really opened my eyes to the hidden maths, particularly that which determines the pattern and form of living things.
This is an excellent book if you want an overview of the hidden importance of maths to biology, but if you want some serious mathematical investigation, you may need to look elsewhere!
April 12, 2020
There is definitely some good stuff in the middle of this book, but the first half is taken up recapping big moments in biology and it's hard to imagine anyone reading the book not knowing that stuff already, so it probably could have been done much, much quicker. Also, the author seems repeatedly to convince the reader that evolution is a real thing, but -again- who's reading this sort of book without believing in evolution? So if you skip the first third-to-half of the book, there's plenty of cool examples of mathematical usage in biology, generally well-explained in a non-technical manner. But, man, the intended audience is really weird.
June 17, 2020
“What is Life?”
“What is Life?” Is the title of a little book written by Erwin Schrödinger in the early 1940s. It explores the fact that life is a process of negative entropy (as all machines are) in that livings borrow energy from the environment to organise and build their bodies. (In plants, sunlight, in animals, the biological life forms they eat) I was disappointed in the first page through that the Author did not address this issue, an issue I consider crucial to life. It is essentially a mathematical exercise to understand thermodynamics.
“What is Life?” Is the title of a little book written by Erwin Schrödinger in the early 1940s. It explores the fact that life is a process of negative entropy (as all machines are) in that livings borrow energy from the environment to organise and build their bodies. (In plants, sunlight, in animals, the biological life forms they eat) I was disappointed in the first page through that the Author did not address this issue, an issue I consider crucial to life. It is essentially a mathematical exercise to understand thermodynamics.
December 25, 2021
The fibonacci sequences of sunflowers was totally awesome, and the book presented a decent survey of math in biology, including various math topics like networks and game theory and higher-dimension geometry...but never went into real detail about anything beyond the minimum basic info (aka no equations). I was hoping for more real math details, so I felt that it was oriented too much towards "pop science" and "pop math".
August 23, 2020
I feel like this book could have been improved with a different structure. Frontloading biological history without integrating the maths stuff until about halfway through made this book a bit dull at points.
The author also flippantly slags off GTA for no apparent reason. I therefore docked a star from the rating for no apparent reason.
The author also flippantly slags off GTA for no apparent reason. I therefore docked a star from the rating for no apparent reason.
February 13, 2022
Mathematics is everywhere. It is amazing to see that something so simple that we take for granted and assume just happens, like the arrangement of petals on a flower, is actually deeply rooted in a mathematical formula that provides the most efficient results for the plant. A great read for fans of mathematics and people wanting a more in-depth understanding of nature.
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