variation, evolution, and heredity than ever before. The extent of this data and the type of inquiries it supports means that research such as the kind popularized by Wells cannot be conducted without mathematics. Its necessity is evidenced by the emergence and coalescence of a number of mathematical subfields in modern biology—such as bioinformatics, molecular genetics, population genetics, biostatistics, and statistical genetics—dedicated to meeting the needs of a quantitative science (Templeton). Researchers in bioinformatics, for example, devote their efforts to developing databases, algorithms, and statistical and computational techniques for analyzing and managing massive data sets. With the complete sequencing of the human genome and other important organisms, the amount of genetic data that needs to be organized and synthesized has grown. The human genome, for example, has between twenty and twenty-five thousand genes and other functional elements, with an estimated three billion base pairs. To collect this data set, the institutions working on the Human Genome Project collaboratively sequenced genes for fifteen years. Computer scientists in bioinformatics employ their mathematical skills to develop more powerful algorithms for ensuring that data on this scale can be properly stored and retrieved for scientific research.
Whereas some biomathematical researchers devote their talents to managing data, others use their mathematical skills to develop formulae to pose and solve important questions about variation, evolution, and heredity, such as how closely species are related and how diseases have emerged and developed over time. Molecular geneticists, for example, might test hypotheses about the degree of relatedness between organisms by developing genetic taxonomies or gene trees. These trees require special algorithms designed to calculate the proximity of organisms to one another based on their genetic divergence in some physical trait. For example, a molecular geneticist might compare the order of amino acids in the red blood cells of humans, pigs, mice, and chickens. Using one or more of a handful of standard mathematical methods for calculating relatedness between organisms, he/she would conclude that, evolutionarily speaking, humans are closer to pigs than chickens (Hartl and Jones 612–13).With these methods, molecular geneticists are beginning to provide better insight into relations of descent between organisms, including ones that would have likely eluded qualitative taxonomists, such as the water lily’s (Nuphar polysepalum) position as the genetic progenitor of the oak tree and all other seed-bearing plants (National Science Foundation).
Along with molecular biologists, population geneticists also use established mathematical algorithms to describe changes in organic populations. They rely, for example, on the algebraic Hardy-Weinberg principle as a model for the distribution of genes in a population under random mating conditions. In this endeavor, mathematics plays a central role because it is used to define a hypothetical baseline for change in the rate of alleles (the different possible gene types at a specific location on a chromosome) in a population against which the effects of natural selection, population size, mutation, migration, and random drift can be assessed. Calculations like these are essential to a number of modern applications, such as scientific breeding programs, assessments of the efficacy of screening for genetic disease factors, and the estimation of biodiversity.
Finally, a discussion of the importance of mathematics to modern investigations of variation, evolution, and heredity would be incomplete without mentioning the general value of statistics and probability in the day-to-day pursuit of scientific research. In modern biological research, investigations regularly begin and end with statisticians or biostatisticians carefully assessing the methods and results of experiments. Trained in statistics and probability, these members of a research team provide guidance to laboratory scientists on how to structure their experiments so that they limit the influence of factors which might bias their outcomes. For example, a lab’s biostatistician might advise geneticists working in disease research on techniques for random sampling to ensure that they have a data set from the general population for a genetic trait that might be used comparatively to identify genetic disease markers in a population of interest. After the tests are run and the data are collected, statisticians and biometricians are also tasked with calculating the reliability of the results and assessing the data to determine whether, if any, significant patterns emerge. These duties are so important to modern genetic research that Eleanor Feingold, a quantitative geneticist at the University of Pittsburgh, explained, “a lab of any reasonable size would have a biostatistician, a quantitative geneticist, or a statistician attached to it.”
A behind-the-scenes investigation of operations of modern research into variation, evolution, and heredity reveals: (1) that these phenomena cannot reasonably be investigated without mathematics and (2) that because of the increasing size and availability of data on these phenomena, the importance of mathematics will continue to grow. For these reasons, understanding both the role of mathematical argument in science and how that role came to be established, which are the subjects of this book, should be considered important topics of exploration.
Rhetoric, Mathematics, and Science
Although modern research in variation, evolution, and heredity would be impossible without mathematics, there was a time when these phenomena were explored largely without it. The focus of this book is the one hundred-year period between the publication of The Origin of Species and the emergence of modern programs of population and quantitative genetics in the nineteen fifties and sixties. During this critical period of development, mathematics and its capacity to generate reliable knowledge about organic populations was disputed. The goal of this text is to explore some of the reasons why mathematical argument was resisted in these early periods, and how it was advocated for either successfully or unsuccessfully by natural researchers who wanted to advance its credibility and explore the possibilities for its use.
To examine the use of and debates about mathematics in this formative period, this investigation turns to the methods and tools of rhetoric, a field of research and analysis devoted to the study of human communication, argument, and persuasion. With the aid of concepts and methods from this field, the book examines choices in language, organization, and argument in discourse located within specific social, epistemological, and cultural/historical contexts. Examining these dimensions of discourse in context permits characterizations of the goals and beliefs of arguers, the perceptions they have of their audiences, and the suitability of their choices in argument and communication. By investigating these facets of argument and persuasion, this book aims to better understand mathematical argument in a scientific context as well as explore what this relationship reveals about the practical value of rhetorical tools and concepts in understanding it.
Although the text is written primarily with philosophers, historians, sociologists, and rhetoricians of science in mind, every effort has been made to accommodate a broader educated audience of readers. Non-specialist readers who follow the subjects of mathematics, genetics, and evolution will likely find their interests reflected in the choice of topics and figures being investigated in this book. Well-known researchers such as Darwin and Mendel will be discussed, and fresh perspectives on their work as mathematical argument will be examined. Chapter 3, for example, explores in detail not only Mendel’s mathematical arguments in his famous paper, “Experiments in Plant Hybridization,” but also the historical context in which he makes these arguments. Assessing these dimensions of Mendel’s work reveals his reliance on the mathematics of probability as a source of invention for his pea experiments as well as his overconfidence that by using mathematical arguments he could persuade his audience to accept the general validity of his hereditary law.
Chapter 2 looks at Darwin’s work from a seldom–examined, mathematical perspective and reveals the extent to which the self-proclaimed mathematical bumbler relied on quantitative evidence and arithmetically informed arguments to invent and support some of his central conclusions in The Origin of Species. An examination of Darwin’s letters, diaries, his “big species” book (the original manuscript from which The Origin of Species was abstracted), and his arguments in The Origin of Species reveal that Darwin hoped to place biology on par with the physical sciences by giving it a solid, mathematical foundation. Other chapters in the book are devoted to less-well-known—but no less important or interesting—figures such as Francis Galton, Karl Pearson, and R.A. Fisher, all of whom play important roles in the development
