pi, I always think about Carl Sagan and his novel Contact. During the past year I have mentioned Sagan in about 10% of my blog posts, which is a good measure of my amazingly high regard for his ideas, even though he only ever wrote one novel.
In Contact, Sagan imagined a possible form of evidence that could make a scientist believe that our universe was created by a "designer". Sagan explored the idea that an advanced extraterrestrial intelligence might have shaped the physical laws of our universe and, during the creation process, left a "signature of the designer" in the form of an unusual value for the number pi. As a learning tool, Contact provides an interesting exploration of the difference between science and religion. I'm always pleased when fiction writers manage to slip in some math, science or philosophy.
Does mathematics provide us with tools for describing the universe or is the universe in some way fundamentally mathematical? Albert Einstein wrote, "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." I've been thinking about mathematics while creating The Start of Eternity, a fan fiction sequel to Isaac Asimov's time travel novel. Asimov constructed his Foundation Saga on the idea that it might be possible for mathematical laws to guide the course of human history (psychohistory). Adopting a hint from Asimov, The Start of Eternity position's Asimov's time travel novel firmly within the Foundation Fictional Universe.
In Asimov's time travel novel he introduced the idea that time has momentum. When time travelers go back in time and change Reality the course of history can be deflected, but then it usually returns to its original course after several centuries. In his robot stories, Asimov wrote about the Laws of Robotics existing within positronic brains as a kind of mathematical foundation upon which robot behavior is built.
All of these examples of mathematics in fiction (Sagan's "signature of god inside the value of pi", Asimov's psychohistory, idea of momentum for history and a mathematical foundation for behavior) strike me as fun, but silly. All of these examples seem like the sort of fictional mathematics that a physical scientist might daydream about and have fun incorporating into a story.
Silly? Yes, in the sense of extrapolating ideas that are familiar to physical scientists into the domain of living systems. My favorite example of this kind of extrapolation is how some physicists have explored the idea of quantum consciousness. I'm in favor of letting people "think outside the box", but it gets a little strange when people who are trying to do science are exploring ideas that seem even stranger than Sagan's made-up "signature of god" inside pi.
In the The Start of Eternity I've been trying to apply ideas such as attractors and catastrophy theory to biological systems. I'm still wondering if there is a way to portray psychohistory as a "cover story" for advanced knowledge of future events that is actually obtained by time travel...and feeling a bit odd that I am more comfortable with the absurdities of time travel than I am with psychohistory. Small prayer for pi day: Seldon forgive me for my limited faith in mathematics!
Related reading: Comments on Carl Sagan's novel "Contact"