Reflections on Jim Holt's When Einstein Walked With Godel: Excursions to the Edge of Thought

When Einstein Walked with Godel: Excursions to the Edge of Thought is a collection of 24 full length essays plus several shorter pieces written by Jim Holt, the author of the thought-provoking 2013 book Why Does the World Exist? Holt discusses a wide range of subjects that relate to at least one of three categories: "our most general conception of the world (metaphysics), how we come to obtain and justify our knowledge (epistemology), and even on how we conduct our lives (ethics)" (p. x). 

When Einstein Walked with Godel: Excursions to the Edge of Thought is a fascinating book. I will not review each essay, but I will single out a few of my favorites to whet your appetite to read them all.

The book begins with the title essay. It is a fun fact that two of the greatest geniuses of all-time regularly took walks together, and it is touching that Einstein once said that he went to his office at the Institute for Advanced Study "just to have the privilege of walking home with Kurt Godel." I don't take Einstein's statement as false modesty--like most, if not all, geniuses, Einstein was quite aware of his capabilities--but rather as a genuine statement of affection and admiration for his friend Godel. 

Einstein and Godel were not only geniuses but also--regardless of the fame and acclaim that both received--outsiders. Holt notes that after Einstein initially failed to receive his doctorate in physics he gave up on pursuing an academic career, declaring "the whole comedy has become boring." Einstein worked as a patent clerk, but he followed closely the scientific questions of the time, and he read with interest about what Henri Poincare termed the three greatest unsolved questions: (1) the photoelectric effect, (2) Brownian motion, and (3) the nature of the "luminiferous ether" which had yet to be detected experimentally but was supposed to be the medium through which light waves traveled. Holt explains, "Working alone, apart from the scientific community, the unknown junior clerk rapidly managed to dispatch all three" questions in a series of papers published in 1905, when Einstein was just 26 years old (p. 5). Einstein received the 1921 Nobel Prize in physics for his work on the photoelectric effect, but his equation E=MC² forever transformed our understanding of space, time, and energy.

Einstein had already finished most of the work for which he would be most remembered prior to Godel's birth: "In 1906, the year after Einstein's annus mirabilis, Kurt Godel was born in the city of Brno (now in the Czech Republic). Kurt was both an inquisitive child--his parents and brother gave him the nickname Herr Warum, 'Mr Why?'--and a nervous one. At the age of five, he seems to have suffered a mild anxiety neurosis. At eight, he had a terrible bout of rheumatic fever, which left him with the lifelong conviction that his heart had been fatally damaged" (p. 8).

Godel developed two incompleteness theorems that had profound implications for mathematics and epistemology. The first incompleteness theorem is that no logical system can capture all the truths of mathematics; within any mathematical system there will always be at least one statement that cannot be proven or disproven within that system. The second incompleteness theorem is that no mathematical system can be proven, within its own devices, to be free from inconsistency. When Godel first presented his theorems, few people understood them, and some of the people who understood vigorously objected because they disliked the implications about the nature and limitations of knowledge.

The nature of time is one of the subjects that Einstein and Godel discussed. For Einstein's 70th birthday, Godel presented to him a gift: a solution to Einstein's General Relativity equations demonstrating the theoretical possibility of time travel in a rotating universe. Einstein did not like the idea of a rotating universe in which time travel is possible, but he found no flaws in Godel's math. Holt notes that Godel presented the solution as proof that, in Holt's words, "time itself is impossible. A past that can be revisited has not really passed. And the fact that the universe is expanding, rather than rotating, is irrelevant. Time, like God, is either necessary or nothing; if it disappears in one possible universe, it is undetermined in every possible universe, including our own" (p. 13).

The unanswered and perhaps unanswerable question is that if time is impossible then why do we feel its passage so intensely and so vividly? That question leads to other unanswered and perhaps unanswerable questions. Is everything that we consider to be real and to be meaningful an illusion, or a collective delusion/hallucination? If so, what is the purpose of such a grand deception?

Einstein and Godel could not answer those questions, but that did not stop them from walking, talking, and thinking together.

"The Riemann Zeta Conjecture and the Laughter of the Primes" begins with a discussion of the "Copernican Principle": the "Copernican Principle," first formalized as a mathematical equation by astrophysicist J. Richard Gott III in 1993, postulates that at any given time we are not privileged observers of an event, which in simple terms means that when you see something you are not in the first 2.5% of observers and you are not in the final 2.5% of observers. In other words (to borrow Holt's example from pp. 36-37), if you are attending a play that has had n showings then there is a 95% chance that the play will have no more than 39 x n showings and a 95% chance that the play will have no fewer than n/39 showings. Something that has already existed for a long time is statistically more likely to continue to exist for a long time than something that has only existed for a short time.  

Holt demonstrates that laughter and numbers are things that we share with species who have a common ancestor with us several million years ago. Since laughter and numbers have already existed for millions of years, based on the "Copernican Principle" it is more likely than not that laughter and numbers will exist one million years from now. 

What is the Riemann Zeta Conjecture and what does it have to do with any of this? The Riemann Zeta Conjecture is a hypothesis about prime numbers. If Bernhard Riemann was correct, then prime numbers have a hidden harmony, but if he was not correct then the provisional proofs of thousands of theorems "conditioned" on the correctness of his conjecture will be falsified and, as Holt puts it, "the part of higher mathematics that is built upon it will collapse" (p. 43). In layman's terms, the distribution of prime numbers seems at first sight to be random, but Riemann suggested that when one considers the full (i.e., infinite) set of prime numbers then order emerges from what looks to be chaos. The Riemann Zeta Conjecture has been one of the great unsolved math problems for more than 160 years. Applying the Copernican Principle, Holt suggests that there is a 95% chance that it will be solved within the next six millenia. Holt further argues that once the secret of prime numbers is understood then mathematics will be revealed to be, as Bertrand Russell proposed, "as trivial as the statement that a four-footed animal is an animal." Or, put another way, Holt believes that laughter has a better chance of being an integral part of human existence a million years from now that mathematics does. One could object that his opinion is based too much on speculation, but if you read the entire chapter you will be intrigued even if you remain skeptical.

In "Benoit Mandelbrot and the Discovery of Fractals," Holt, in his typical engaging style, describes Mandelbrot's eventful life, and Mandelbrot's inquisitive spirit that enabled him to find order where others saw only disorder and chaos. Benoit Mandelbrot discovered the Mandelbrot set, and demonstrated that things that had been thought to be rough or chaotic--such as clouds and shorelines--actually have a "degree of order." Mandelbrot coined the word "fractal" (derived from the Latin word for broken) to describe self-similar forms, phenomena that are visible not only in physical objects such as clouds and shorelines but also in the behavior of financial markets. Orthodox thinkers in both mathematics and economics bristled at Mandelbrot's ideas but Mandelbrot was stubborn and undeterred.

Academic tenure eluded Mandelbrot--or he eluded it--until he was 75, but his unorthodox way of thinking about mathematics found a home for many years at, of all places, IBM; for a lengthy period of time, the computer manufacturing giant decided to fund pure research. "We can easily afford a few great scientists during their own thing," the director of research told Mandelbrot (p. 98), and those words were music to Mandelbrot's ears. He worked for IBM from the late 1950s until 1987, when IBM decided it no longer wanted to pay great scientists to do their own thing. Six years later, IBM posted $8 billion in losses, at the time the largest such total in U.S. corporate history. Did IBM stop funding geniuses because it ran out of money, or did it run out of money because it stopped funding geniuses?

Fractals are not only beautiful to observe, but they exist at the nexus of science, math, and art. Here is an example of a fractal:

"The Ada Perplex: Was Byron's Daughter The First Coder?" methodically debunks attempts to elevate Lord Byron's daughter Ava from a person who struggled to learn basic mathematics to someone who supposedly was a pioneering scientific figure. It is important to give proper credit to anyone--man or woman--whose accomplishments merit recognition, but it is dishonest and harmful to rewrite history for the purpose of heaping honor on an individual who is not worthy of such recognition. Holt's effort to set the record straight is important, and hopefully will not only result in a widespread reassessment of Lord Byron's daughter but also inspire a thorough and thoughtful examination of other historical figures who are given too much--or too little--credit.

Holt's curiosity, smooth writing style, and active engagement with any subject that he tackles would probably enable him to communicate engagingly even about uninteresting subject matter, but it is a treat to read his writing about the fascinating subjects briefly described above, as well as the other topics addressed in When Einstein Walked with Godel: Excursions to the Edge of Thought.

Further Reading:

Albert Einstein the Man (December 13, 2015)

Kurt Godel: Mathematician/Philosopher Extraordinaire (August 25, 2016)

Kurt Godel: Mathematician/Philosopher Extraordinaire

If you have heard the name Kurt Godel at all, you probably heard it in connection with Douglas Hofstadter's masterful (and massive) Gödel, Escher, Bach: An Eternal Golden Braid. Unless you read and remember the contents of that more than 30 year old book, you probably have no idea who Godel was and why his work is so significant.

John W. Dawson's article Godel and the Limits of Logic provides a sensitive and perceptive glimpse at the accomplishments and inner life of one of the most eminent mathematicians of all time. Dawson explains that Godel was a Platonist: "he believed that in addition to objects, there exists a world of concepts to which humans have access by intuition. For Plato, who lived around 400 BC, concepts such as truth were not products of the human mind which can change according to the thinker's point of view, as some philosophers believe, but existed independently of the human observer. Thus, a statement could have a definite 'truth value'--be true or not--whether or not it had been proved or could be empirically confirmed or refuted by humans. Gödel subscribed to this philosophy, and, in his own view, this was an aid to his remarkable mathematical insights."

Mental illness plagued Godel for much of his life and ultimately led to his untimely demise but Godel nevertheless made an indelible impact on mathematics, logic and philosophy. Dawson declares:

Gödel proved that the mathematical methods in place since the time of Euclid (around 300 BC) were inadequate for discovering all that is true about the natural numbers. His discovery undercut the foundations on which mathematics had been built up to the 20th century, stimulated thinkers to seek alternatives and generated a lively philosophical debate about the nature of truth. Gödel's innovative techniques, which could readily be applied to algorithms for computations, also laid the foundation for modern computer science...

Although Gödel's work irrefutably proves that "undecidable" statements do exist within number theory, not many examples of such statements have been found. One example comes from the sentence:

This statement is unprovable
You can see why this is a prime candidate: if you could prove this statement to be true, then it would be false! It is true only if it is unprovable, and unprovable only if it is true. As it stands, this is not a statement about the natural numbers. But Gödel had devised an ingenious way to assign numbers to English-language phrases like this one, so that finding whether the statement is true or not translates to solving numerical equations. He proved that, within the axioms of number theory, it is impossible to prove whether or not the equation corresponding to the sentence above holds true, thus confirming our "common-sense" analysis.

In a similar way, Gödel translated the statement

The axioms of this theory do not contradict each other
into numerical code, and again proved that the translation is unprovable. Any proof that the axioms do not contradict each other--that they are consistent-- must therefore appeal to stronger principles than the axioms themselves. 

The latter result greatly dismayed David Hilbert, who had envisioned a program for securing the foundations of mathematics through a "bootstrapping" process, by which the consistency of complex mathematical theories could be derived from that of simpler, more evident theories. Gödel, on the other hand, saw his incompleteness theorems not as demonstrating the inadequacy of the axiomatic method but as showing that the derivation of theorems cannot be completely mechanized. He believed they justified the role of intuition in mathematical research.

The concepts and methods Gödel introduced in his incompleteness paper are central to all of modern computer science. This is not surprising, since computers are forced to use logical rules mechanically without recourse to intuition or a "birds-eye view" that allows them to see the systems they are using from the outside. Extensions of Gödel's ideas have allowed the derivation of several results about the limits of computational procedures. One is the unsolvability of the halting problem. If you have ever written a computer program, you will know that a programming mistake can cause it to enter an infinite loop: it will run forever and never end. The question is if there can be an algorithm that can examine any computer program and decide whether it will eventually halt or whether it will keep running forever. This is the halting problem and the answer is "no."

Another result that derives from Gödel's ideas is the demonstration that no program that does not alter a computer's operating system can detect all programs that do. In other words, no program can find all the viruses on your computer, unless it interferes with and alters the operating system.

Godel's concepts have wide-ranging implications not only for mathematics, physics and computer science but also for philosophy and metaphysics. David Goodman, writing in First Things, describes Godel's impact as both a mathematician and someone who thought seriously about theological matters:

Kurt Gödel was a believer--or, at least, a knower--whose engagement with God included a reworking of the ontological proof of God’s existence. Born in 1906, Gödel was arguably the great mathematician of his time. Certainly no twentieth-century thinker did more to show that the human mind cannot be reduced to a machine. At twenty-five he ruined the positivist hope of making mathematics into a self-contained formal system with his incompleteness theorems, implying, as he noted, that machines never will be able to think, and computer algorithms never will replace intuition. To Gödel this implies that we cannot give a credible account of reality without God. But Gödel’s God is not the well-behaved deity of the old natural theology, or the happy harmonizer of the intelligent-design subculture. Gödel’s God hides his countenance and can be glimpsed only in paradox and intuition. God is not an abstraction but “can act as a person,” as Gödel once wrote, confronting those who seek him with paradox, uplifting man through glorious insights while guarding his infinitude from human grasp. Gödel’s investigations in number theory and general relativity suggest a similar theological result: that God cannot be reduced to a mere principle of the natural world. Gödel may have seen himself as a successor to Leibniz, whose critique of Spinoza’s atheism set a precedent for much of Gödel’s work.

Rebecca Goldstein's book-length biography Incompleteness: The Proof and Paradox of Kurt Godel further explains Godel's significance: "This man's theorem is the third leg, together with Heisenberg's uncertainty principle and Einstein's relativity, of that tripod of theoretical cataclysms that have been felt to force disturbances deep down in the foundations of the 'exact sciences.' The three discoveries appear to deliver us into an unfamiliar world, one so at odds with our previous assumptions and intuitions that, nearly a century on, we are still struggling to make out where, exactly, we have landed" (p. 22).

Positivists and postmodernists cite Albert Einstein, Kurt Godel and Werner Heisenberg as three figures who destroyed the concept of objective reality but Einstein and Godel rejected this interpretation of their work. In Goldstein's words, "Einstein interpreted his theory as representing the objective nature of space-time, so very different from our human, subjective point of view of space and time" (p. 42). Similarly, Godel's "commitment to the objective existence of mathematical reality is the view known as conceptual, or mathematical, realism. It is also known as mathematical Platonism, in honor of the ancient Greek philosopher whose own metaphysics was a vehement rejection of the Sophist Protagoras' 'man is the measure of all things'" (p. 44). In layman's terms, "For Godel mathematics is a means of unveiling the features of objective mathematical reality, just as for Einstein physics is a means of unveiling aspects of objective physical reality" (p. 45). Einstein and Godel did not believe that they had thrown the world into chaos but rather that they had used their intellect to decipher the true nature of, respectively, space-time and mathematical reality.

Godel was a member of the famous Vienna Circle of intellectuals who regularly met in the 1920s and 1930s but most of the Vienna Circle's members believed in logical positivism while Godel was a Platonist. However, Godel rarely spoke during these meetings and he was one of the younger members of the group, so it appears that the other members did not even realize that Godel opposed their views. Godel first presented his revolutionary Incompleteness Theorem during a 20 minute talk on "Epistemology of the Exact Sciences" during the second day of a scientific conference in Konigsberg. Godel's work was later described as an "amazing intellectual symphony" but because of his mild-mannered presentation and because of the complexity of his ideas it was not immediately apparent even to the esteemed attendees of this conference that Godel had accomplished something monumental.

On the third day of the conference, Godel summarized the meaning of his Incompleteness Theorem: "One can (assuming the [formal] consistency of classical mathematics) even give examples of propositions (and indeed of such a type as Goldbach and Fermat) which are really contextually [materially] true but unprovable in the formal system of classical mathematics." Goldstein describes this sentence as "meticulously crafted, a miniature masterpiece" (p. 157) but adds, "Godel was always disappointed by the abilities of others to draw the implications he had scrupulously prepared for them, and his experience at Konigsberg must have been a magnificent disappointment, for the response was a resounding silence."

The only person present who grasped the implications of what Godel had said was another towering genius, John von Neumann. Von Neumann spoke with Godel afterwards and Von Neumann later informed Godel--who was then still finishing his doctoral studies--that the implication of what Godel had said was that it is impossible to formally prove the consistency of a system of arithmetic within that system of arithmetic. Godel drily replied that not only did he realize this but he had already drafted the mathematical proof of it (this is known as Godel's second Incompleteness Theorem).

After Godel emigrated to the United States, he shared a close friendship with Einstein, despite being separated in age by nearly 30 years. Einstein so enjoyed their daily walks together on the grounds of the Institute of Advanced Study that toward the end of Einstein's life he told the economist Oskar Morgenstern that his own work did not matter much anymore but he came to the Institute primarily for the privilege of walking alongside Godel each day. Einstein was an outgoing, mentally stable (though highly unconventional) person, while Godel was introverted and battled mental illness throughout his life but they shared in common immense genius and insatiable curiosity: Einstein once said, "The most important thing is to not stop questioning," while Godel was known as "Mr. Why" when he was a child because he constantly asked questions.

In A World Without Time: The Forgotten Legacy of Godel and Einstein, Palle Yourgrau notes that Godel provided a mathematical solution for Einstein's General Theory of Relativity that demonstrated that in a relativistic universe time travel is theoretically possible. If Godel is correct, then this means that time does not exist, at least not in the linear way that we humans subjectively perceive it, because what is past is not actually past.

Yourgrau laments that mathematicians and physicists have essentially ignored or dismissed Godel's solution even though no one has found any flaw with Godel's math; Einstein disliked the idea that time travel might be possible but he could find no mistakes in Godel's calculations and Einstein admitted that "the problem here involved disturbed me at the time of the building up of the general theory of relativity."

Einstein further stated, "Kurt Godel's essay constitutes, in my opinion, an important contribution to the general theory of relativity, especially to the analysis of the concept of time." However, Einstein questioned whether Godel's model was physically plausible even though it was mathematically and conceptually sound; Godel's theoretical universe rotates and for the remainder of his life after he proposed this solution Godel had a keen interest in whether or not our universe rotates (to this day, astrophysical observations have neither confirmed nor refuted the possibility that our universe may in fact conform to Godel's hypothetical model).

In his younger days, Einstein had questioned other interpretations of general relativity--including the possibility that black holes exist and the possibility that the universe is expanding--on the grounds of being physically implausible only to later be proven wrong. Godel's relentless logic led Godel inexorably to the conclusion that if time does not exist in a theoretically possible universe (such as the rotating universe postulated in his solution to Einstein's General Relativity equations) then it stands to reason that time does not exist in any universe to which General Relativity applies. Physicists and philosophers have mocked Godel's concept for decades but have yet to actually disprove it. We humans subjectively perceive the passage of time but that does not mean that our subjective perception is accurate; Einstein's theory accurately predicted that time passes more slowly as an object is accelerated and thus there is not one universal "now" but rather only various frames of reference, so Godel's suggestion that the passage of time is an illusion is perhaps not so radical a notion as it seems (though, if correct, it does raise an interesting philosophical or perhaps theological question of why our brains are designed/have evolved to believe in the passage of time if the passage of time is actually illusory).

The Einstein-Godel friendship survived any disagreements about theoretical or practical matters and it endured despite differences in age and temperament. While Einstein enjoyed his celebrity status and used his fame as a platform to publicly speak out about a variety of issues, Godel shunned the spotlight and at times seemed stunningly oblivious to anything that did not directly relate to mathematics; during the late 1930s, he innocently asked a refugee scientist who had recently fled the Nazis what had brought him to America. Not surprisingly, many people were not charmed by Godel's singular focus on mathematics to the exclusion of just about anything else. Godel avoided conflict and in time avoided human contact in general (other than with his wife, Einstein and very few others) by utilizing his full-proof escape method: agree to meet a person at a particular place and time and then not show up, thus ensuring that he avoided contact/conflict.

Godel was burdened from an early age with serious psychological problems. He suffered rheumatic fever as a child and when he was a child his research about rheumatic fever revealed that it often causes permanent heart damage. Therefore, Godel concluded that logic dictates that he suffered permanent heart damage, so he spent most of his adult life taking pills for a non-existent heart ailment. Godel also convinced himself that poisonous fumes were emanating from his air conditioner's ducts.

A deep pessimism clouded Godel's thoughts and moods. "We live in a world in which ninety-nine percent of all beautiful things are destroyed in the bud," he lamented. Godel did not believe in the concept of historical progress but instead felt that humanity was regressing: "The world tends to deteriorate. Good things appear from time to time in single persons and events...but the general development tends to be negative."

Taking this concept to what seemed to him to be a logical conclusion, Godel was convinced that there was a conspiracy to rid the world of logical-thinking people and that--as perhaps the foremost logician in the world--he was one of the targets of this conspiracy. Thus, Godel was constantly afraid that his food would be poisoned. Godel's wife Adele allayed those fears by sampling his food first; not long after Adele became too ill to perform this task for him, Godel died of starvation because he refused to eat.

Godel's paranoia is similar to the paranoia exhibited by the great chess champion Bobby Fischer in the sense that both men excelled in disciplines that require the rigorous application of logic and yet, paradoxically, logic failed them in areas outside of their expertise. However, Goldstein does not find Godel's paranoia paradoxical: "Paranoia isn't the abandonment of rationality. Rather, it is rationality run amuck, the inventive search for explanations turned relentless. A psychologist friend of mine put it this way: 'A paranoid person is irrationally rational...Paranoid thinking is characterized not by illogic, but by a misguided logic, by logic run wild" (p. 205).

Goldstein asks a haunting question about Godel that applies equally to Fischer and to other supergeniuses whose strict dedication to misguided logic led them to very dark places: "How can a person, operating within a system of beliefs, including beliefs about beliefs, get outside that system to determine whether it is rational? If your entire system becomes infected with madness, including the very rules by which you reason, then how can you ever reason your way out of your madness?" (p. 204). This is clearly a formidable task even for some of the most brilliant people who ever lived; neither Fischer nor Godel ever figured out how to reason their way out of their particular versions of madness: Fischer's logic extrapolated from the truth that the Soviet Union cheated at chess to create in his mind a vast conspiracy centered on anti-Jewish thought that reached bizarre (but to Fischer completely logical) conclusions such as every single move in every single Kasparov-Karpov game was prearranged; Godel's logic extrapolated from some truths about his early childhood illnesses to some unfounded beliefs about his health and about supposed conspiracies to poison him.

Fischer was only officially the World Chess Champion from 1972-75 but more than 40 years later many people still consider him to be the greatest chess player of all-time. Similarly, Godel published relatively little during his lifetime but because of the depth, quality and influence of what he did publish he has been called the greatest mathematician of the 20th century and perhaps the greatest logician since Aristotle. Godel postulated that the passage of time may be illusory but as long as we humans perceive the passage of time he should and will be remembered as someone who shed some light on the mysteries of the universe.

Further Reading:

1) Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid has been described as "simply the best and most beautiful book ever written by the human species."

In the 20th anniversary edition of his Pulitzer Prize winning book, Hofstadter explains his original goals and intentions:

GEB is a very personal attempt to say how it is that animate beings can come out of inanimate matter...GEB approaches [this question] by slowly building up an analogy that likens inanimate molecules to meaningless symbols, and further likens selves... to certain special swirly, twisty, vortex-like, and meaningful patterns that arise only in particular types of systems of meaningless symbols. It is these strange, twisty patterns that the book spends so much time on, because they are little known, little appreciated, counterintuitive, and quite filled with mystery [that] I call..."strange loops"...

...the Godelian strange loop that arises in formal systems in mathematics... is a loop that allows such systems to "perceive itself," to talk about itself, to become "self-aware," and in a sense it would not be going too far to say that by virtue of having such a loop, a formal system acquires a self.

2) A World Without Time: The Forgotten Legacy of Godel and Einstein by Palle Yourgrau focuses on Godel's mathematical solution to Einstein's General Theory of Relativity and the implication of that solution, namely that in a universe governed by the General Theory of Relativity time travel is possible. As Godel realized, if the past is accessible then this means that the past is not really past and therefore time cannot exist as anything other than an ideal concept in such a universe (i.e., in such a universe there is no real distinction between past, present and future).

3) Incompleteness: The Proof and Paradox of Kurt Godel by Rebecca Goldstein is a very readable yet informative account of Godel's life, though it apparently contains some errors in its descriptions of Godel's work (see below; as I do not have formal, higher level mathematical training I must defer to the experts on this issue).

4) The Incomplete Godel is a review of Yourgrau's book and Goldstein's book by Gregory Moore, a professor of mathematics at McMaster University in Canada. Moore prefers Yourgrau's book to Goldstein's because of several errors he notes in Goldstein's attempts to explain Godel's mathematical work but he states that the definitive Godel biography is Logical Dilemmas: The Life and Work of Kurt Gödel (A K Peters, 1997), by John W. Dawson, Jr.

5) Time and Causation in Godel's Universe describes some of the practical implications of Godel's concept of a universe in which time travel is possible.

6) The theoretical possibility of time travel presents us with the confounding Grandfather Paradox, which Robert Heinlein memorably explored in his classic short story "'--All You Zombies--.'"

Jim Holt's Why Does the World Exist? Takes the Reader on a Thought-Provoking Intellectual Journey

When Bill Moyers asked Martin Amis about the origins of the universe, Amis replied,  "I'd say we're at least five Einsteins away from answering that question." Jim Holt took Amis' response as a worthy challenge and decided to look for those Einsteins and glean some insights from them. Holt's book Why Does the World Exist? is a compilation of speculations, insights and hypotheses gathered from some of the world's foremost scientists and philosophers.

Why Does the World Exist? is similar in style to Harold T.P. Hayes' Three Levels of Time--both books tell a personal narrative intermixed with grand thematic narratives and both books largely consist of material gleaned from interviews with prominent thinkers--but the subject matter is different; Hayes focused on how the universe was created, how life began and what humanity must do as a species to avoid extinction, while Holt focused less on "how" questions and much more on "why" questions. Holt describes Why Does the World Exist? as an "existential detective story" and the questions he raises about the nature and meaning of existence are profound.

Holt notes that any purely technical description of the universe's creation is inherently limited: "A scientific explanation must involve some sort of physical cause. But any physical cause is by definition part of the universe to be explained. Thus any purely scientific explanation of the existence of the universe is doomed to be circular. Even if it starts from something very minimal--a cosmic egg, a tiny bit of quantum vacuum, a singularity--it still starts with something, not nothing. Science may be able to trace how the current universe evolved from an earlier state of physical reality, even following the process back as far as the Big Bang. But ultimately science hits a wall. It can't account for the origin of the primal state out of nothing. That, at least, is what diehard defenders of the God hypothesis insist" (p. 6).

Holt mentions that Stephen Hawking's "no-boundary" model of the universe "is completely self-contained, without beginning or end." It does not require a God to start the process of creation. Yet, even Hawking does not find this answer alone to be completely satisfying. Hawking wonders, "What is it that breathes fire into the equations and makes a universe for them to describe? Why does the universe go through all the bother of existing?"

Atheists are content to just shrug their shoulders and say that the existence of the universe is a "brute fact" that does not require explanation but Holt writes (p. 7) that "intellectually this feels like throwing in the towel. It's one thing to reconcile yourself to a universe with no purpose and no meaning--we've all done that on a dark night of the soul. But a universe without explanation? That seems an absurdity too far, at least to a reason-seeking species like ourselves." Holt rejects the "brute fact" view by invoking Leibniz' Principle of Sufficient Reason (at least one source says that Baruch Spinoza articulated this concept before Leibniz did, though Leibniz is credited with actually naming the principle): Nothing happens without a reason. "And if the Principle of Sufficient Reason is valid," Holt adds (p. 7), "there must be an explanation for the existence of the world, whether we can find it or not."

Leibniz declared that this is the best of all possible worlds, created by God in His infinite wisdom, and that God exists because His existence is necessary. Not everyone was convinced by Leibniz' reasoning; Voltaire's satire Candide is a withering critique of the idea that our world is the best of all possible worlds--and the billions of people who are starving, ill and/or experiencing other forms of suffering also have a right to question if this really is the best of all possible worlds. Frankly, if this is the best possible world, I would hate to see the worst possible world, a world that has horrors worse than those experienced by the victims of the Holocaust.

After outlining the basic questions he will attempt to answer, Holt begins his philosophical inquiry on a light note, examining the cheeky concept that the universe could have been created by a "hacker." Andrei Linde's "chaotic inflation" theory posits that a hundred-thousandth gram of matter is all that is needed to create a universe teeming with billions of galaxies. If Linde is correct--and he readily admits "There are some gaps in my proof"--then, as Linde puts it, "...we can't rule out the possibility that our own universe was created by someone in another universe who just felt like doing it." Holt acknowledges that a religious believer can respond to Linde's speculation by asking, "Who created the physicist hacker?"

Even if Linde is right about a possible method for creating a universe, his theory does not answer the larger question of why there is something rather than nothing; Holt points out that this question reflects a Western way of thinking, deeply influenced by early Judeo-Christian concepts: most of the ancient creation stories/myths described a universe/world that was created out of something and no explanation was provided for the origins of that something--but Christianity posited creation ex nihilo and that idea permeates Western philosophy, leading modern scientists, philosophers and theologians to ponder how it is possible that something could emerge from nothing.

Thinking about this becomes much like the process of opening up a Russian doll only to find a smaller Russian doll inside--except that eventually one can find the smallest Russian doll, whereas each new scientific discovery or philosophical approach only brings to mind more unanswered questions.

Holt's interview subjects run the gamut from defiantly atheistic to deeply religious. Adolf Grunbaum, who Holt describes as "arguably the greatest living philosopher of science," rejects Holt's entire premise: "There is no mystery of existence," Grunbaum declares in a letter to Holt. Holt met with Grunbaum at the University of Pittsburgh and Grunbaum explained his perspective, which Holt cogently summarizes (pp. 68-69):

He was not content to observe that what he called the Primordial Existence Question rested on dubious premises. He wanted to show that these premises were just plain false. There is no reason, in his view, to be astonished, puzzled, awed, or mystified by the existence of the world. None of the virtues claimed for Nothingness--its supposed simplicity, its naturalness, its lack of arbitrariness, and so on--made it the de jure favorite in the reality sweepstakes: such was his conviction. In fact, if we look at the matter empirically--the way modern, scientifically minded people ought to--we'd find that the existence of a world is very much to be expected. As Grunbaum himself put it, "What could possibly be more commonplace empirically than that something or other exists?"

Here was a man who thought Why is there something rather than nothing? was as much of a cheat as the question When did you stop beating your wife?

The laws of physics as currently understood break down at the instant of the Big Bang; there literally is no spacetime prior to the Big Bang, at least not in the sense that we understand/perceive spacetime. Thus, Grunbaum tells Holt that even though the universe is finite in age it has always existed, at least in terms of the spacetime history that we know about. Holt explains how this understanding of cosmology shapes Grunbaum's philosophical world view (p. 75):

If there was never a transition from Nothing to Something, there is no need to look for a cause, divine or otherwise, that brought the universe into existence. Nor, as Grunbaum observes, is there any need to worry about where all the matter and energy in the universe came from. There was no "sudden and fantastic" violation of the law of conservation of mass-energy at the Big Bang, as his theistically minded opponents have claimed. According to the Big Bang cosmology, the universe has always had the same mass-energy content, from t = 0 right up to the present.

Holt calls Grunbaum's reasoning "admittedly formidable" but says that ultimately it "did not leave me convinced that the quest should be abandoned. There is nothing I dislike more than premature intellectual closure" (p. 78).

Richard Swinburne occupies the opposite end of the belief spectrum from Grunbaum, asserting that the universe was created by a God who takes great personal interest in what happens. Perhaps the biggest moral/philosophical challenge to this idea is the daunting presence of great evil in the world but Swinburne tells Holt how he reconciles God's love/goodness with the hate/darkness that exists (p. 102):

I have a theodicy--a view of why God should allow evil to happen. I think he allows it to happen because it's logically necessary if certain goods are to be possible, the goods arising from our possession of free will. God is omnipotent. He can do anything that is logically possible to do. And it isn't logically possible for him to give us free will and yet to ensure that we always use it the right way.

In an abstract sense, that sounds very logical and refined--a perspective that can be debated at a cocktail party over drinks and hors d'oeuvres--but Swinburne's theodicy crumbles in the presence of Auschwitz' crematoria, Cambodia's killing fields and dozens of other atrocities that fill the human race's blood-stained history. How can an all-good and all-powerful being permit innocent children to be slaughtered in the name of the exercise of free will? Perhaps this is philosophically valid at some intellectual level but in the face of immense human suffering such lofty words sound obscene and indefensible; in our legal system, a person who has information about a murder and does not report it is an accessory after the fact, even if he did not directly participate in the crime. What can be said of a being that has the power to prevent millions of murders and does not act? A theologian would reply that the ways of God cannot be understood by people but that answer is not very comforting.

Another perspective about the nature of the universe is provided by Hugh Everett's "many worlds" interpretation of quantum mechanics; this theory proposes that an infinite number of parallel universes branch off every time a quantum wave function collapses: Schrodinger's infamous cat is alive in one universe and dead in another universe. At first glance, this may sound like a joke or a fantasy but the mathematics underpinning the theory are very solid and many eminent physicists support Everett's approach (sadly for Everett, his ideas were ridiculed during his lifetime and have only recently gained traction, many years after he passed away). From this point of view, the reason that there is something rather than nothing is that the collapse of the quantum wave function requires that everything that is possible eventually happens in some universe or other; the problem is that we only have access to our universe and thus there is no way to prove whether or not these other theoretical universes exist (James P. Hogan's novel The Proteus Operation is a fascinating alternate history story that utilizes Everett's theory as a major plot point, though in Hogan's version it is possible to travel back and forth between different timelines).

Perhaps the universe consists of, as Holt describes it (p. 188), "one great relational web: all structure, no stuff. The entities making up the physical world are like the pieces in a game of chess: what counts is the role defined for each piece by a system of rules that say how it can move, not the stuff that the piece is made of." This is similar to the Platonic idea that mathematical concepts are not human constructions but rather essential to the innate nature of the physical universe; Galileo declared, "The book of nature is written in the language of mathematics" and the great logician/mathematician Kurt Godel said, "I don't see any reason why we should have less confidence in this kind of perception, i.e., in mathematical intuition, than in sense perception."

Cosmologist John Leslie believes in what he calls "extreme axiarchism," a term that Holt explains is based on the Greek words axia ("value") and archein ("to rule"). "Extreme axiarchism" is developed from Plato's idea that, as Leslie puts it, "the ethical requirement that a good universe exist was itself enough to create the universe"; Leslie is also influenced by Spinoza and, in Holt's words, "Like Spinoza, Leslie sees all individual things as ripples on the sea of a unified divine reality." Leslie's universe is, Holt writes, "fundamentally made out of consciousness." Holt describes an analogy that Leslie uses (pp. 201-202):

Just as an infinite mind contains many universes, the Louvre contains many artworks. One of these artworks--say, the Mona Lisa--is the best. But if the Louvre contained nothing but perfect replicas of the Mona Lisa, it would be a less interesting museum than it actually is, with its vast number of inferior artworks adding to the variety. The best museum on the whole is one that contains, in addition to the very best works of art, all lesser works, as long as those lesser works have some redeeming aesthetic value--as long, that is, as they are not positively bad. Similarly, the infinite mind is one that contemplates all cosmic patterns whose net value is positive, ranging from the very best possible world on down to worlds of indifferent quality, where the good barely outweighs the evil. Such a variety of worlds, each of which is, on the whole, better by some positive margin than sheer nothingness, is the most valuable reality overall--the one that might leap into existence out of a Platonic requirement for goodness.

Leslie had answered one obvious objection to his cosmic scheme: the problem of evil. Our own world is decidedly not the Mona Lisa. It is blemished by cruelty, suffering, arbitrariness, and waste. Yet, even with all its ethical and aesthetic defects, it manages to contribute a little net value to reality as a whole--just the way a mediocre painting by a second-rate artist might contribute a little net value to the collection in the Louvre. Our world is thus worthy to be part of that larger reality: worthy, that is, of contemplation by an infinite mind.

Holt says that in order to support Leslie's "extreme axiarchism" you have to buy three premises: "(1) value is objective, (2) value is creative, and (3) the world is good" (p. 210). Even if one accepts that value can be objectively defined and that such value has the ability to create a universe as the product of a collective consciousness, the third point is problematic for many philosophers. Holt writes (pp. 212-213):

Leslie himself concedes the existence of evil. He admits that "many items in our universe are far from splendid"--ranging from headaches to mass murder to the destruction of entire galaxies through false-vacuum fiascoes. Yet he purports to render the problem of evil manageable by making our world a tiny part of a much greater reality--a reality consisting of an infinite number of infinite minds, each of them contemplating everything of value. As long as the world around us contributes at least a little net value to this infinite reality, its existence is sanctioned by the abstract need for goodness. It may not be perfect, but--with its causal orderliness, its congeniality to life, and its conduciveness to more happy states of consciousness than unhappy ones--it's good enough to merit inclusion in a maximally valuable reality.

Holt admits that it is "tempting to join the sunny Spinoza-Leslie consensus" but he cites a number of thinkers, philosophers and poets who have a much darker perspective (pp. 213-214): 

Schopenhauer said it in the nineteenth century: reality is overwhelmingly a theater of suffering, and nonexistence is better than existence. So did Byron, in his lines, "Sorrow is knowledge: they who know the most/Must mourn the deepest o'er the fatal truth..." More recently, Camus declared that the only genuine philosophical problem is suicide and E.M. Cioran epigrammatized endlessly about the "curse" of existence. Even Bertrand Russell, despite his professed admiration for Spinoza's character, could not accept the Spinozist view that individual evils are neutralized by absorption into a larger whole. "Each act of cruelty," Russell insisted, "is eternally a part of the universe." Today, the most uncompromising opponent of cosmic optimism may be Woody Allen. In an interview he gave in 2010 (to a Catholic priest, curiously enough), Allen spoke of the "overwhelming bleakness" of the universe. "Human existence is a brutal experience to me," he said. "It's a brutal, meaningless experience--an agonizing, meaningless experience with some oases, delight, some charm and peace, but these are just small oases." There is no justice to it, Allen maintained, and no rationality either. Everyone does what one can do to alleviate "the agony of the human condition." Some distort it with religion; some chase money or love. Allen himself makes films--and whines. ("I do get a certain amount of solace from whining.") Yet in the end "everyone goes to his grave in a meaningless way."

What is Holt's worldview? Holt objectively presents the strengths and weaknesses of several different philosophical/religious/scientific perspectives and he does not extensively discuss his personal beliefs but on page 34 he parenthetically notes, "A useful compromise between the Christians and the Gnostics might be my own position: that the universe was created by a being that is 100 percent malevolent but only 80 percent effective." Near the end of the book, Holt approvingly paraphrases some ideas expressed by a Buddhist monk on a French television show (pp. 278-279):

Things don't really have the solidity we attribute to them. The world is like a dream, an illusion. But in our thinking, we transform its fluidity into something fixed and solid-seeming. This engenders le desir, l'orgueil, la jealousie. Buddhism, by correcting our metaphysical error, thus has a therapeutic purpose. It offers un chermin vers l'eveil--a path of enlightenment. And it also resolves the mystery of being. When Leibniz asked, Pourquoi quelque chose plutot que rien? his question presupposed that something really and truly exists. And that's an illusion.

Why Does the World Exist? is well-edited, with one exception: on page 10 Holt declares that Philo "comes closest to being a stand-in for Hume himself" in Hume's Dialogues Concerning Natural Religion but when he discusses Hume's Dialogues on page 85 Holt asserts that Cleanthes "comes closest to being the author's mouthpiece."

The "true believers" in a scientific, religious, Platonic or other explanation for why the world exists will not be swayed by any information that Holt presents that contradicts their convictions but any open-minded person who is interested in reading a wide-ranging and well-balanced examination of diverse perspectives about the nature and meaning of existence will enjoy Why Does the World Exist?