In the summer of 1975, lying on my back in the Stanford University quad, looking up at the blue sky through the fronds of a palm tree, I realized that I would NOT find the meaning of life by pursuing more academic study. I would have to actually live life. This was a turning point in my journey. In the six years leading up to that moment, I had earned a BS in Mathematics while studying physics and the humanities, and taken graduate courses in philosophy. I also played in a rock band, raced bicycles and worked in a pizza parlor, activities which offered no vocational track. So I set this all aside, including my passion for big questions, moved back east closer to family, secured a job, got married, bought a house and had kids. I was living life.
At the same time, I followed developments in the fields I had left behind. The last quarter of the 20th century brought mesmerizing advances in many areas of math and science. I had last studied physics just after quarks had been theorized, but by the end of the century the standard model of particle physics, quarks and all, was nearly complete. While the integration of quantum and classical physics continued to elude the best minds, the new theoretical frontiers of string theory and supersymmetry were flourishing, and continued progress in cosmology was bringing us closer to understanding the big bang. Physics, popularized by the likes of Stephen Hawking, Brian Greene and others, offered hope for a unified Theory of Everything (TOE).
Mathematics, always a key partner with physics, had also advanced on many fronts. Information theory and computer tools vastly increased the speed and scope of analytic inquiry; key developments in set theory, topology, chaotic systems, fractals and game theory generated considerable excitement. At the same time, progress in the life sciences, medicine, and genetics had exploded. New and exciting findings were routinely promoted in the popular press. Big questions were being answered!
It seemed that things were too good to be true.
The World Falling Apart
We’re all familiar with Aristotle’s hackneyed phrase “The whole is greater than the sum of the parts.” The corollary is that something separated into parts is less than the whole. The puzzle has no picture if the pieces are strewn on the floor. A machine will not function if it is disassembled. A life that consists only of separate pieces has no meaning. Fifteen years into my life plan towards the goal of finding the meaning of life, the process derailed. I had the pieces of a life – the job, the wife, the kids, the mortgage, and all the rest. But the pieces were not integrated into a whole. My marriage no longer held the spark of love. Job and life were separated by more than a long commute. I felt alienated and disconnected. I could find no unifying whole from which to draw meaning. Things were in parts. My life was not working.
So too, my progressive optimism in the inexorable, integrated progress of physics, mathematics, and other fields, was faltering. The intuitive concept of Newtonian space and time as a fixed background had already unraveled as Einstein’s special and general relativity theories took hold. Physicists continued to tell us that time is just an illusion, contrary to our immediate experience. The intractable puzzles of quantum mechanics, including wave-particle duality, the paradox of Schrodinger’s Cat, the phenomena of paired particles and the observer problem, had never been resolved, but merely ignored under the Copenhagen Interpretation. The reality of Quantum Physics continued to challenge the very comprehensibility of the physical world. Cosmologists grappled with the inscrutable properties of the Big Bang and Black Holes, infinitely dense and impenetrable discontinuities in the fabric of space and time, and puzzled over the apparently missing quantities in the universal physical balance, now named Dark Energy and Dark Matter. Even Hawking finally gave up on the TOE: “…there is no picture or theory-independent concept of reality.” It seemed that as we pulled the physical universe apart into ever more discrete and fine-grained components, we found the pieces could not be integrated into a whole
Surely mathematics, unsullied by the need for empirical validation, would be different? Math has always held a privileged position in the pantheon of human knowledge, at least since the time of Pythagoras, as it relied on deductive proof rather than inductive generalization. Yet novel findings in chaos and complexity theory confirmed that much of the world, and life, was, of necessity, uncertain. Very small changes in the initial conditions of dynamic systems lead to wildly different outcomes; in truth, very little can be modeled or predicted with any accuracy. In mid-century, Alan Turing had first proved the feasibility of the Universal Computing Machine and founded the computer revolution, but then also proved that the Halting Problem could not be solved. It is impossible to know if a computer will complete a calculation in a finite amount of time. This was the first of an infinite variety of “undecidable” problems. At about the same time, Kurt Gödel published his Incompleteness Theorems, proving that logic itself had holes in it. In any formal logical system (such as arithmetic, or set theory, for example), we can demand consistency: a statement and its negation cannot both be true. However, if we demand completeness, meaning that we can prove the truth or falsity of any statement, then we have to abandon consistency – we cannot have it both ways. The consistency of mathematics is essential, and the consistency of our reality is a strongly held metaphysical position that can be traced to Aristotle’s second principal of logic, the law of non-contradiction. Based on Gödel’s proof, then, we have to conclude that there are true mathematical theorems that will never be proved and true facts about reality we will never discern.
Fractal images are not always pretty.
The End?
The whole of mathematics is greater than the sum of its provable theorems. The whole of what we seek to know is beyond computation. The whole of our universe is awash with uncertainty. The whole of our reality transcends the laws of nature.
Nor can the meaning of our own lives be comprehended in the various pieces scattered across our personal timeline.
Continue to Episode 3 – Minding the Gaps
Return to Episode 1 – Sources of Faith
