The main character in the film Pi (1998), named Max, is searching for a number (perhaps a solution to a mathematical equation) that holds the key to understanding fundamental truths. The film itself never makes clear what kind of truths are waiting to be discovered (scientific? religious? philosophical? abstract? Etc.), although we do learn that at least two groups of individuals are interested in acquiring/stealing whatever information Max has discovered, one for religious purposes and the other to make money predicting changes in the stock market.
This is a fascinating film, seemingly full of obscure big ideas and mysteries, but also fun to watch, especially trying to figure out whether Max’s search represents a virtuous quest for truth or delusional thoughts of an insane person. However, my purpose in writing this commentary is not to try to make sense of the film itself. I simply want to use the film as a springboard to discuss one of the big issue questions lurking implicitly in the film’s plot: What is the ultimate source of truths about the fundamental nature of the universe? 1
One common view about the origins of truths can be traced back to Aristotle. His empirical method emphasized the importance of making systematic observations of the physical world as a means to understanding the nature of reality. Using the empirical method in modern times, scientists typically try to discover truths in a three-step sequence along the lines: 1. Make observations and manipulations of some specific part of the physical world (physicists put atoms into atom smashers, chemists pour solutions into beakers, psychologists put clients on a couch and ask them to talk, etc.); 2. Then construct theories that try to explain what was observed, emphasizing causal relationships; 3. Finally, try to express the main elements of theories very precisely by using mathematical equations.
Use of this empirical method implies a belief that an ultimate source of scientific truths comes from the physical universe that is being observed. Mathematics is simply a tool that can express the scientific truths that are discovered with more precision than words, but mathematics is not itself the source of the truths.
However, the way scientific truths are actually discovered is sometimes in the opposite order from this scenario. Sometimes theoretical scientists working in isolation from the physical world, simply trying to solve mathematical equations, come up with solutions that, it is discovered later, describe actual properties of the physical universe. This second approach to discovering truths also has a long history. Its origins can be traced back at least to the pre-Socratic Pythagorean School where it was taught that ultimate reality is to be found in the realm of perfect mathematical ideas. Somewhat later Plato also argued that ultimate reality exists in the realm of ideas. He considered the relationship between the physical world and ultimate reality to be analogous to dim shadows projected from the outside world onto the walls of a cave where they are seen by people confined inside the cave. It only appears to those people that these dim shadows are reality because that is all they can see. But ultimate reality actually exists in the outside world that is casting the shadows.
Theoretical physicists working in more modern times have also sometimes made arguments that the truthfulness of scientific ideas can be evaluated based on thinking about them rather than by empirical evidence. Einstein, for example, was quoted on more than one occasion as stating that he was convinced that some of his theories about relativity were correct because when thinking about them he found them to be “beautiful”, long before there was any empirical evidence to support them.2 There are numerous other examples in the history of modern science where theoretical physicists arrived at mathematical solutions to equations that were later discovered to be accurate descriptions of physical reality. Sometimes mathematical solutions were initially considered to be too bizarre to apply in the actual physical world, but later turned out to reflect physical as well as mathematical reality.3
Examples like these seem puzzling and mysterious. Our universe appears to be obeying some kind of independently existing rules (sometimes referred to as Laws of Nature) that are articulated in the language of mathematics. This leads to an obvious question, Where did the non-physical mathematical truths that govern our physical universe come from? One answer is provided by a religious perspective that attributes these laws to a preexisting God who created the physical universe.
It is easy to get hung up on the names of things, especially when the names have been associated historically with movements or policies with which one does not want to be associated. This is one of the reasons many scientists profess to be atheists or agnostics – They simply do not want to be associated with much of what has been done historically “in God’s name.” However, if one changes the name from “God” to “order”, the reluctance frequently dissipates. Many scientists, even those who profess atheism, would agree with a statement along the lines, “there is order in the universe, order that can be expressed in the mathematical equations that underlie quantum physics, and that has been present since at least as long as the big bang event that created our universe” (and perhaps before that as I will elaborate next).
If one can get past knee-jerk prejudices and look at deeper concepts, religious perspectives and modern scientific theories are sometimes not as far apart as it might appear. St. Augustine wrote that time was created when God created the universe. Modern physics asserts that time did not exist until 10-43 seconds after the big bang. The scientific concept that the universe was created from some sort of “order” present at the moment of the big bang is consistent with an account of creation told in the Christian New Testament Book of John.4
In a previous essay I summarized some of the current scientific views about the origin of the universe, including the somewhat bizarre sounding theory that our universe paradoxically sprung into existence out of “nothing”. This is because the primordial quantum foam that gave rise to our universe is not made of physical particles that exist in the dimensions of time and space. We know this based on some mysterious numbers that crop up in the mathematics that underlie quantum theories of physics. One is Plank distance, the smallest measure of length that can be said to exist. Another is Plank time, the smallest unit of time that can be said to exist. Times or distances less than these amounts have no existence in time or space. Physical materials whose spatial dimensions are smaller than these distances can accurately said to be nothing (“no thing”). The elements of the primordial quantum foam out of which our universe was created fall within these dimensions. But this quantum foam, although not part of the dimensions of time and space in our physical universe, is real, and it contains order, order that governs the Laws of Nature, and order that can be described using the language of mathematics, and perhaps also be called, appropriately, by the name “The Mind of God, The Creator of the Universe”.5
 The theme for our discussion films this month is The Universe in Three Acts, and each of our three films illustrate different approaches to trying to understand some of the fundamental truths about the universe in which we live. In this commentary, I discuss an approach to discovering fundamental truths depicted in the fictional film Pi (1998): mathematics. In separate essays I discuss the empirical approach taken by scientists as depicted in the documentary, Particle Fever (2013). and metaphysical approaches in the form of a religious fable in, Le Quattro Volte (2010).
Abraham Pais, Subtle is the Lord: The Science and the Life of Albert Einstein, Oxford University Press, 1982.
Walter Isaacson, Einstein: His Life and Universe, Simon and Schuster, 2007.
 In a previous essay I gave some examples. One was Dirac’s negative solutions to equations that were considered to be too bizarre to apply to the physical universe, until anti-matter was discovered. Another was Einstein’s insertion of a cosmological constant into his equations describing general relativity because of his initial inability to accept the implications of the equations that the universe was unstable. These and other examples are described in a rather remarkable small book:
Christopher Potter, You Are Here: A Portable History of the Universe, Harper, 2009
Another fascinating example taken from this same book also involves Einstein. The physicist Maxwell had earlier formulated some equations to describe properties of light, but discovered that these equations could only be solved mathematically if light was considered to be invariant across certain conditions. This idea was so counter-intuitive to common sense that Maxwell assumed this had to be simply a statement of mathematical truth, not a statement about the true nature of the physical universe. Einstein took the truths expressed by those equations as being descriptions of the physical world and gave us the scientific theory of special relativity, describing a bizarre world where clocks run at different speeds depending on how fast they are traveling through space.
 “In the beginning was the word…”, where “word”, as commonly translated from the Greek “logos”, is actually better translated as “order”.
 According to Potter [see Note 3], current theories of physics allow the current universe to have emerged from only about 20 pounds of quantum stuff. This opens the possibility that it might be possible for a scientist to someday create a brand new universe working with only a few pounds of quantum foam in a laboratory.