Author John L. Casti characterizes The One True Platonic Heaven as "scientific fiction." Neither simply fiction nor nonfiction, scientific fiction intermixes fiction and fact to convey important ideas in science. While the story in The One True Platonic Heaven revolves around the prestigious Institute for Advanced Study at Princeton in 1946, the important scientific ideas have to do with the limits of scientific knowledge. For example, in light of Gödel's Incompleteness Theorem and Turing's work on the decision problem, are there questions about the world that are logically beyond the scientific method?
These issues and more are debated by characters representing the intellectual giants of the twentieth century who were at the IAS in 1946 — Albert Einstein, Kurt Gödel, J. Robert Oppenheimer, John von Neumann and a host of others. Their discussions at teas, committee meetings, and parties take center stage as the Institute for Advanced Study wrestles with two issues. First, should the IAS make Kurt Gödel a full professor? His Incompleteness Theorem was a crowning achievement, but there are concerns about his behavior. Second, should von Neumann's proposal to build a computer at the IAS be approved? From today's perspective, it is difficult to imagine opposing someone who played an integral role in legitimizing scientific computing, but the book presents the computer project as a challenge to the "One True Platonic Heaven."
The Platonic heaven of the title refers both to the IAS as an idyllic setting in which to do research and to philosophical ideas dating back to Plato. Located in pastoral Princeton, New Jersey (but not affiliated with Princeton University), the IAS is dedicated to the advancement of pure knowledge. With no teaching duties and few obligations, scholars are free to think and pursue their interests. There are several schools at the IAS but few laboratories, so that work is dedicated to intellectual activity — research that must be done abstractly in the Platonic world of ideas and ideals rather than in the "real" world. In this light, von Neumann's computer project is seen as an application, a mere engineering project, without the facilities to support it. (In fact, when the IAS computer project was terminated in the late 1950's, a resolution was passed to never have an applied project at the IAS again.)
Even though they are embellished in the book, the problems of the day are described in an interesting and useful way. Einstein broods about the uncertainty of quantum physics as he searches for a grand unified theory. Gödel talks of using special relativity to envision a universe in which time travel is possible. Von Neumann lays out a vision for the computer's use in such areas as weather forecasting as he proposes that information will become the focal point of science.
There are liberties taken. For instance, Oppenheimer was not the director of the IAS until 1947, and Gödel's promotion took place in 1953. However, such liberties can be taken because "scientific fiction" is not bound by the conventions of the historical novel or by what is historically known about the thoughts and motives of the individuals. The book can then focus on the ideas. At least this is what is proclaimed by the prefaces of The One True Platonic Heaven and The Cambridge Quintet, Casti's first attempt at scientific fiction. Whether or not such claims are accepted, a work like this is a terrific way to creatively explore profound concepts as long as it:
- Motivates further exploration into what is actually known.
- Acknowledges that it is a work of fiction.
The One True Platonic Heaven makes it very clear that it is not a work of historical scholarship. One hopes that its readers will take this to heart.
In addition to exploring the limits of scientific knowledge, The One True Platonic Heaven focuses on a second conflict, described in the preface: that between human personalities and intellectual accomplishments. This secondary conflict embodies the tension of writing a book that attempts to popularize difficult material. How does one keep the writing interesting for a general audience while communicating complex concepts? It would be very tempting to exaggerate Gödel's struggles with mental illness or Oppenheimer's role in the development of the atomic bomb and his subsequent "red scare" humiliation. The title, The One True Platonic Heaven, is taken from a book by science writer Ed Regis about the IAS, Who Got Einstein's Office? While entertaining, much of that book focuses on the eccentricities and the infighting at the IAS. It is commendable that Casti keeps these from overshadowing the big ideas in The One True Platonic Heaven.
Unfortunately, the results are not always interesting. To put it crudely, only academics are likely to really appreciate a plot based on a committee's decision on faculty promotion or project funding. Furthermore, much of the book takes place in conversations and thoughts that seem stilted and unnatural. To provide exposition, people remind others of previous events that would normally go unmentioned in actual conversations. A cameo appearance by T. S. Eliot is meant to bring in a humanities perspective but seems artificial. What Casti is trying to do is a delicate business: interpreting the views of great minds by putting words that sound real into their mouths, while at the same time providing context to neophytes.
On the other hand, it is unrealistic to expect this to be a literary masterpiece or a John Grisham novel. The book does well in introducing important figures and questions in the fields of mathematics, physics, and computer science. The historical and leading edge contributions within the last century, not to mention their relationship to other fields, are often not considered in an undergraduate education. The One True Platonic Heaven is a relatively short book free of the ponderous prose of a philosophy text while at the same time introducing profound questions:
- Does Gödel's Incompleteness Theorem have any bearing on our scientific understanding of reality?
- Is our scientific knowledge directly tied our the ability to carry out scientific computations?
- What are the social responsibilities of scientists?
- How are the limits of our scientific knowledge related to the limits of mathematical models?
- What are some of the implications of quantum physics? Does something come into existence only when it is observed?
These issues are not resolved in The One True Platonic Heaven, only introduced. The book could be recommended to someone who even has a passing interest in science or mathematics. College instructors could use it as a companion text to any course that introduces logic, quantum physics, or the questions of scientific or mathematical knowledge. Some follow-up will be necessary, since much of the context had to be omitted and the lines between fiction and fact are blurred. For these very reasons, the book encourages further study.
Books mentioned in The One True Platonic Heaven:
- Aspray, William, John von Neumann and the Origins of Modern Computing, MIT Press, Cambridge, MA, 1990.
- Casti, John, The Cambridge Quintet: a work of scientific speculation, Addison-Wesley, Reading, MA, 1998.
- Casti, John, and DePauli, Werner, Gödel: A Life of Logic, Perseus Books, Cambridge, MA, 2000.
- Casti, John, Karlqvist, Anders, and Robbins, Jeffrey (eds.), Boundaries and Barriers. Addison-Wesley, Reading, MA, 1996.
- Dawson, John, Logical Dilemmas: The Life and Work of Kurt Gödel. A.K. Peters, Wellesley, MA, 1997.
- Davis, Nuel Pharr, Lawrence and Oppenheimer, Simon and Schuster, New York, 1968.
The Institute for Advanced Study:
- The Institute for Advanced Study homepage, http://www.ias.edu/.
- Jackson, Allyn. "The IAS School of Mathematics." Notices of the AMS September 2002: pp. 896-904. http://www.ams.org/notices/200208/fea-ias.pdf.
- Regis, Ed, Who Got Einstein's Office? Eccentricity and Genius at the Institute for Advanced Study. Addison-Wesley, Reading, MA, 1987.
- IQ, Paramount Pictures, Hollywood, 1994. Starring Meg Ryan, Tim Robbins, Walter Matthau, Charles Durning. Directed by Fred Schepisi. Note: This mindless romantic comedy takes place at the IAS as Einstein and Godel play matchmaker. It has little to do with reality, but it might be a fun math club event.
Jeremy Case is an Associate Professor of Mathematics at Taylor University in Upland, Indiana. He is interested in mathematical themes in literature and theatre.