Why Did I Write This Book?

logic of Nature, and there are so many of us that it is beginning to show. Just one example: most human economic systems are wedded to material growth without bounds and the idea that whatever is desired to maintain this growth can be freely taken. I have never seen a serious politician run on a platform of a stable, as opposed to a materially growing, economy. There are several futures for us that are mathematically, scientifically, socially, economically, historically and politically possible. One reason I wrote this book is to avoid a future “Age of Cannibalism.” The Alferd Packer Grill, at my university, has the slogan: “Have a friend for lunch.” Al Packer (1842–1907) was convicted in Colorado of manslaughter, for allegedly1 killing and eating his companions after they became snowbound one winter in the Rocky Mountains without (other) sources of food. Human cannibalism has been documented in the prehistoric American Southwest [689],2 not far from where I am writing, as well as in places such as Europe in historic times [546, 282]. When food is scarce, and even when it is not, eating fellow humans is not without precedent. Thus it remains a possibility in the future—that I would like to avoid. I would even like to avoid “financial cannibalism,” a few people consuming the life savings of others. I would like to avoid “slavery-lite” where the few rule and greatly limit society’s possibilities. Given the self-organizing generosity that whole populations exhibit from time to time, removing rule by a few would likely lead to happier communities.

At the other end of a spectrum of possible futures is one where everyone has enough to eat without resorting to cannibalism. In fact, it seems possible that all, or at least most, of us could have a reasonably enjoyable, peaceful existence, sustainable for many generations. In between the extremes we humans may muddle through to a mixed future with a few, or possibly massive, casualties. My contention is that what we humans do today will largely determine our possible tomorrows, and that elementary mathematics can help us make informed choices now that will lead us to at least a tolerable future. Parts of this book deal with things that elementary mathematics strongly suggests we do in order to have a future we will enjoy. At the very least a compelling, persuasive argument is required before we ignore what mathematics tells us. For example, the laws of mathematics and physics predict that jumping out of an airplane at 10,000 meters (about 32,808.3 feet) unassisted by some device, leads to a grim future—rather soon. Whereas, a jump with a parachute can be enjoyable, at least for some.

While gravity and its implications are obvious without doing many calculations, mathematics has less obvious but similarly fundamental things to say: about conditions that are necessary for a financial system to be stable and not collapse; about pollution and its e ects; about the growth of populations

1Packer claimed that Shannon Wilson Bell was the true cannibal, whom he shot in self defense.

2This number in brackets refers to a reference in the list of references near the back of the book.

or their decline and extinction; the progression of diseases such as the flu or HIV; about our food supply; our ecological support systems and many other subjects.

There is another reason I wrote this book. From time to time I have taught “College Algebra” and “Math for Liberal Arts,” and while such courses have much merit, for me something was missing. Most of the students I have had in these courses were interested in and talented in some area: history, dance, art, music, car mechanics, journalism, literature, poetry, economics, business, anthropology, psychology, philosophy, politics, social science, science, even mathematics. Most, however, were trying to avoid mathematics entirely; and they had been successful until a dreaded math requirement caught up with them. In all of the abovementioned areas of interest that held my students’ attention I could/can see some mathematics—real math, not made up math. Couple this with the fact that a mathematical perspective can help us solve some of the major problems that we all face or may face in the near future, and I ended up designing the course: “Mathematics for the Environment.” Over a period of ten to fifteen years I wrote various versions of this book for that course. This book is for those who may consider themselves not very mathematically talented, but are at least curious or concerned about some of the topics already mentioned above—and would like to know a bit about how mathematics could possibly be relevant—or even be of help. I have had students of just about every political persuasion. If a student uses what they have learned to help them act in their own self-interest the course(book) has been a success, since a great many people are persuaded by propaganda to act against their own self-interest. Of course, the course(book) is an even greater success to the extent that it helps us all work together to accomplish things we could not accomplish individually.

Finally, I would have been somewhat surprised over a decade ago when I started this project to see how it turned out. It is clear that this book must be interdisciplinary. However, over the years my interaction with other disciplines led me to realize the importance of certain principles/concepts with mathematical content which would not have so starkly stood out had I remained completely within pure mathematics. Among these are: fuzzy logic; the Bio-Copernican Axiom (humans are not the center of the biosphere); the Connection Axiom; cycles and feedback; multiplier e ects; the Dunbar Number, 147.8 (a biological constraint on the number of people to whom one person can be “strongly connected”); and others I will cover in this book. Of course, such topics as fractions and logarithms come up, but this is no surprise!