One
Introduction: Overview of Proving Darwin
Like many pure mathematicians, I like giving “chalk” talks: improvised talks given on a blackboard or white- board using a minimum of technological assistance. Another strategy is for me to fill the board with what I want to cover just before I start to lecture, while people are still coming in, so that they can take in all the key ideas at a glance. In a large auditorium, however, a projector is necessary, or nobody will see anything.
On the facing page you can see me giving an overview of this book in a large auditorium at the Federal University of Rio Grande do Sul in southern Brazil. The four slides I prepared are on pages 5 and 6. They summarize Chapters 2 to 4, which outline my strategy for making biology mathematical. After you finish reading these chapters, you should review the slides. Then they will make more sense.
You’ve heard people refer to DNA as a computer program? Well, that’s the whole idea: to make this metaphor into a mathematical theory of evolution. In fact, it turns out that the mathematical tools for doing this were already available in the 1970s. More precisely, we will treat evolution as a random walk in software space. Random walks are an idea that mathematicians feel comfortable with, although the space we are walking around in at random is bigger than usual.
I call this proposed new field “metabiology” because it is a highly simplified version of real biology—otherwise I wouldn’t be able to prove any theorems. These theorems are presented in Chapter 5, which is the climax of the book, and was a talk that I gave at the Santa Fe Institute. Chapters 6 to 8 discuss the broader significance of metabiology, theological, political and epistemological. And then there are two appendices.
In the first appendix you can read the crucial section on self-reproducing automata in John von Neumann’s far-seeing “DNA = Software” paper that influenced Sydney Brenner, who in turn influenced Francis Crick—a remarkable fact that I only discovered while working on this book. And the second appendix gives some additional mathematical details that may be of interest to experts.
Finally, I give a short list of suggested further reading, some books and a few articles that are important if you want to really understand metabiology. These are the books and articles that helped me the most to come up with a strategy for making biology mathematical, plus a few more related items that I threw in just for the fun of it. Enjoy them all!
“One of the great ideas men of mathematics and computer science.” —New Scientist
“Strange and marvelous. . . Disarmingly funny, but also thrillingly clear.” —The Guardian
“[Chaitin’s] enjoyment of the topics of his own research is infectious.” —The Times Higher Education Supplement
“Call him Omega Man. . . . In the rarefied world of pure mathematics, Gregory Chaitin is indeed something of a venerated superhero.” —Waterloo Region Record
“[Chaitin is] enthusiastic and extremely readable. . . . Amazing. No wonder [he] chose mathematics over physics.” —New Scientist
“The musings of a great mind on a subject beyond most of us.” —Ottawa Citizen
“Provocative. . . . Stimulating. . . . Credit the author for a lively style, lots of useful historical references and an appendix that includes von Neumann’s prescient essay on self-reproducing automata.” —Kirkus Reviews
"Gregory Chaitin has devoted his life to the study of mathematics. . . . A great mind.” —The Victoria Times Colonist
“[Chaitin] is a creative genius.” —Tucson Citizen
One
Introduction: Overview of Proving Darwin
Like many pure mathematicians, I like giving “chalk” talks: improvised talks given on a blackboard or white- board using a minimum of technological assistance. Another strategy is for me to fill the board with what I want to cover just before I start to lecture, while people are still coming in, so that they can take in all the key ideas at a glance. In a large auditorium, however, a projector is necessary, or nobody will see anything.
On the facing page you can see me giving an overview of this book in a large auditorium at the Federal University of Rio Grande do Sul in southern Brazil. The four slides I prepared are on pages 5 and 6. They summarize Chapters 2 to 4, which outline my strategy for making biology mathematical. After you finish reading these chapters, you should review the slides. Then they will make more sense.
You’ve heard people refer to DNA as a computer program? Well, that’s the whole idea: to make this metaphor into a mathematical theory of evolution. In fact, it turns out that the mathematical tools for doing this were already available in the 1970s. More precisely, we will treat evolution as a random walk in software space. Random walks are an idea that mathematicians feel comfortable with, although the space we are walking around in at random is bigger than usual.
I call this proposed new field “metabiology” because it is a highly simplified version of real biology—otherwise I wouldn’t be able to prove any theorems. These theorems are presented in Chapter 5, which is the climax of the book, and was a talk that I gave at the Santa Fe Institute. Chapters 6 to 8 discuss the broader significance of metabiology, theological, political and epistemological. And then there are two appendices.
In the first appendix you can read the crucial section on self-reproducing automata in John von Neumann’s far-seeing “DNA = Software” paper that influenced Sydney Brenner, who in turn influenced Francis Crick—a remarkable fact that I only discovered while working on this book. And the second appendix gives some additional mathematical details that may be of interest to experts.
Finally, I give a short list of suggested further reading, some books and a few articles that are important if you want to really understand metabiology. These are the books and articles that helped me the most to come up with a strategy for making biology mathematical, plus a few more related items that I threw in just for the fun of it. Enjoy them all!
“One of the great ideas men of mathematics and computer science.” —New Scientist
“Strange and marvelous. . . Disarmingly funny, but also thrillingly clear.” —The Guardian
“[Chaitin’s] enjoyment of the topics of his own research is infectious.” —The Times Higher Education Supplement
“Call him Omega Man. . . . In the rarefied world of pure mathematics, Gregory Chaitin is indeed something of a venerated superhero.” —Waterloo Region Record
“[Chaitin is] enthusiastic and extremely readable. . . . Amazing. No wonder [he] chose mathematics over physics.” —New Scientist
“The musings of a great mind on a subject beyond most of us.” —Ottawa Citizen
“Provocative. . . . Stimulating. . . . Credit the author for a lively style, lots of useful historical references and an appendix that includes von Neumann’s prescient essay on self-reproducing automata.” —Kirkus Reviews
"Gregory Chaitin has devoted his life to the study of mathematics. . . . A great mind.” —The Victoria Times Colonist
“[Chaitin] is a creative genius.” —Tucson Citizen
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All reading communities should contain protected time for the sake of reading. Independent reading practices emphasize the process of making meaning through reading, not an end product. The school culture (teachers, administration, etc.) should affirm this daily practice time as inherently important instructional time for all readers. (NCTE, 2019) The Penguin Random House High
Translanguaging is a communicative practice of bilinguals and multilinguals, that is, it is a practice whereby bilinguals and multilinguals use their entire linguistic repertoire to communicate and make meaning (García, 2009; García, Ibarra Johnson, & Seltzer, 2017) It is through that lens that we have partnered with teacher educators and bilingual education experts, Drs.
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