Chess is a relatively simple game. The board can fit on a small table and only has sixty-four squares in eight rows of eight. There are only thirty-two total pieces, and the pieces always begin in the same positions. The rules can be written on one page and learned in one sitting.
Though simple, chess offers a dazzling array of possibilities. At the beginning of the game, the player controlling the white pieces can choose any one of twenty legal moves to start. The player controlling the black pieces can likewise respond with any of twenty moves. So after each player has moved once, 400 unique possible board setups exist (twenty times twenty). This number is still relatively small, but further moves lead to an exponential explosion of the games that are possible to play. After each player has made two moves, more than 150,000 possible games exist. After three, the number of possible games is more than 100 million. The possibilities only climb from there.
For any human, no matter how intelligent, chess offers possibilities that cannot possibly be exhausted in a lifetime. If one had the capability, interest, and speed to play a new chess game every second for 100 years straight, one would play fewer than 10 to the power of 10 games. If one could do that for a billion billion lifetimes of 100 years each, one would play fewer than 10 to the power of 30 games. The total number of possible chess games is a topic of some debate, but it certainly dwarfs that number. One estimate, assuming that games last only 40 moves, and that only three choices are “sensible” for most moves, is that there are about 10 to the power of 40 possible chess games. This would mean that after those billion billion lifetimes, one would have played less than one billionth of the total number of sensible games.
In fact, chess games can go much longer than 40 moves, and there are often many more than 3 sensible choices for each move. One commonly cited estimate for the number of possible unique chess games of normal length is 10 to the power of 120, a number much larger than common estimates of the total number of atoms in the observable universe.
These facts should cheer up anyone who feels bored with life – one chess board and a friend, or just a free computer chess program, can more than fill all of the idle hours of anyone’s mortal lifetime without ever repeating a game. For our finite lives, chess is more than enough to keep us busy and constantly surprise us. It may not appeal to everyone, but our good fortune is that chess is only one of the many thousands of things to which we can apply our intellect and will during our relatively short lives in this world. We can all find something like chess with seemingly endless possibilities to explore and discover.
Music is another pursuit with an enormous range of choices to explore. A piano has 88 keys, which are all different octaves of just 12 notes from A to G-sharp. If we limit ourselves to the basic 12 notes and only five different note durations (whole, half, quarter, eighth, sixteenth), there are 60 (twelve times five) choices a composer has for just the very first note of a new piece. So even with these limitations there are 3,600 (60 times 60) unique two-note compositions, and 216,000 (60 to the power of 3) unique three-note compositions. The number of possible compositions shoots into the millions and billions after adding a few more notes, and continues to grow from there. Orchestration and tempo choices multiply the possibilities even further, not to mention octaves and other variations like fermatas and grace notes. Like chess, music offers possibilities that could never be exhausted during a normal human lifespan.
For those who believe in it, eternal life offers a chance to dig deeply into these possibilities. Winston Churchill famously said “when I get to heaven I mean to spend a considerable portion of my first million years in painting, and so get to the bottom of the subject.” Someone may similarly plan to spend a million or a billion years mastering chess, composing music, thinking about the Riemann Hypothesis, or naming all the stars in the universe. Of course, if life is eternal, one could do each of those things in succession, and still have an infinite length of time left to try other things. After all, infinity is larger than any number, however large.
This banal fact, that infinity dwarfs all numbers, leads to a discomfiting possibility: eternal boredom. Even though the number of unique chess games of 40 moves is dizzyingly large, it is still finite. An eternal being, after many trillions of years, would play all of them, and have no surprises or new experiences left in store on the chess board. It would be the same for music. A composer with eternal life could eventually write every possible combination of ten thousand notes, and thus exhaust the (huge but finite) possibilities of musical composition, at least of pieces of normal length.
The same idea applies to language. With a finite number of words to choose from, the number of possible combinations of any length is immense but finite. So an eternal poet could eventually write every possible page-long poem, and have none left to write. A comedian with eternal life could tell every possible one-line joke, and his audiences would then be bored by him forever. More disturbing still, each person with eternal life could easily have every possible thousand-word conversation. How depressing it would be to think that all your future conversations would be repeats of your previous conversations. Could it be that every possible diversion or activity in the afterlife could be exhausted by an eternal being, who would then be doomed to repeat his past forever?
One resolution to this apparent problem is to forever increase the length of compositions. For example, after a poet had written every possible page-long poem, he could begin the task of writing every possible two-page poem. After the trillions of years required for that, he could start writing three-page poems, and so on. If he continued increasing the length of his poems without end, he could continue writing ever-longer poems throughout eternity. A composer who had exhausted every combination of ten thousand notes could work on every combination of twenty thousand notes, and so on without end. Even the rules of chess allow arbitrarily long games if both parties agree to continue, and so even a chess player could explore games of a thousand moves, then two thousand moves, and so on forever. A conversationalist, after having every possible thousand-word conversation, would start having original, longer conversations with no need to ever cease. If an eternal being had enough endurance and patience, he could stay occupied eternally in this way.
Simply increasing length may not eliminate the specter of eternal boredom, however. Imagine a poet who had written every possible million-page poem, then started writing million-and-one-page poems. He would be creating new compositions, however the first million pages of each million-and-one-page poem would be identical to one of the million-page poems he had already written. Similarly, the final page would be identical to one of the one-page poems he had already written, and that page would also exist in many of his million-page poems. So rather than creating something entirely new, he would be simply rearranging his own previous compositions. That activity may hold excitement and promise for some, but I think I would be dissatisfied with an eternity spent on it.
For a poet seeking eternal occupation, it seems to me that a more promising idea is to expand the language in which he writes. After writing every page-long poem in English, he could turn to Spanish and Malay and Hebrew and Chinese and Iban and every other language that exists. Of course, the number of existing languages that we know of is finite, and each has a finite vocabulary, so he will eventually write every possible page-long poem in each of these languages.
An interesting next step for an eternal being would be to create new languages in which to write. If he is interested in Mandarin Chinese, for example, he will know that each Mandarin word is spoken in one of four vocal tones or a fifth, neutral tone. After exhausting the possible combinations of Mandarin words, he could invent a sixth tone, perhaps with an accompanying meaning or linguistic significance, and thus create thousands more words and have millions more poems that he could write. After writing all of those poems, he could invent a seventh tone, and write poems with new words he created that were spoken with that tone. There is no obvious limit to the number of tones and new words he could add to any language, and this activity could fill eternity with new poems in unimagined new languages. He could also make grammatical adjustments to a language to change and increase the expressive possibilities available to him. Imagine the shades of meaning that we would be capable of if our vocabularies were increased by so much.
We can imagine analogously expanding the possibilities of any activity to give it suitable variety for eternal engagement in it. For chess, we can imagine that after exhausting the possibilities of an eight-by-eight board, we create a nine-by-nine board, or we could add a few new pieces or maybe some new rules (or maybe do all of these at once). This new version of chess would take an eternal chess player some more thousands of years to master. He could then expand to a ten-by-ten board, and so on without any obvious limit and thereby fill eternity with new and surprising chess challenges.
For music, we may imagine creating new notes to increase the available possibilities. A piano’s keys are a half step apart. Occasionally, musicians today explore the possibilities of the quarter tones whose pitch resides halfway in between the pitches of piano keys. After exploring and exhausting the possibilities of piano music, a composer could begin to write quarter tone music. After exhausting those possibilities, he could create eighth-tone music with pitches that resided halfway in between the quarter tones, sixteenth-tone music, and so on with no obvious limit to the number of new notes that could fit between any two piano keys. Or, we could create new instruments without end, mining new materials across the universe to create slightly different timbres and expressive possibilities, once again with no obvious limit to the unique new instruments that could be created.
It could be that there are natural limits to some or all of these ideas, so that infinite variety is not possible. For language, it could be that our vocal cords are not capable of expressing an endless variety of tones like those of Mandarin. Even if we were capable of creating an infinite range of tones, it could be that our ears have natural limitations on the number of tones they can distinguish. It could even be that the physics of our universe doesn’t allow sound waves to propagate at an infinite variety of frequencies, so there are only finite possibilities for the tones that can be created at all.
It could also be that our minds have natural limitations. Among other things, there could be an upper limit on our memory. Maybe languages with a thousand tones are too complex for us to ever master, even if we had eternal life. If so, we would be stuck with a finite number of finite languages that we could work in, and eternal repetition becomes a problem again.
This point highlights a distinction between eternal repetition and eternal boredom. If we have limited memories, after writing (say) a billion poems, we may begin to forget several of the poems we had written long ago, and could write those poems again as if they were completely new. If we forgot our old conversations, we could have those again and repeat them every billion years or so with a sense of surprise every time. We could play every chess game, forget every chess game, and then start again playing every chess game, and repeat for all eternity.
Though this forgetful repetition would solve the problem of the endless feeling of boredom, it would seem to reduce eternal life to something absurd—a constant repetition of the same scenarios over and over again. There would be no progress and no lasting growth. The ancient Greeks might identify this as a protracted version of the story of Sisyphus. In more recent times the idea has been known as “Poincare recurrence” as well as by other names. T.S. Eliot thought about it as well, saying of human life that “we shall not cease from exploration, and the end of all exploring will be to arrive where we started.” Anyway, this fate is endless repetition leading nowhere. Again, it may be that some would be satisfied with such an eternal fate, but I would struggle to find such a repetitious and stagnant life worth living.
With some further thought, maybe there is some idea that could save us from this repetition and forgetfulness… but I will break off my imaginings here. I could continue to speculate, but I fear getting (further) lost in an intellectual maze with this tricky subject. People, including many much cleverer than me, have been pondering eternal life for thousands of years. Nothing indicates that we will fully understand it anytime soon. In our present state we have little chance of knowing with certainty (among other things) whether the universe is infinite in size or duration, or whether our own lives will last forever. So we cannot come to certain conclusions about whether our final destiny will be joyous or dreadful, thrilling or boring, full of growth or full of stagnation.
Before closing, I will briefly address the final dilemma that these speculations lead to. Consider: Though we are not up to the task of understanding eternal life, we cannot avoid taking a position on the topic. Even if we do not explicitly state an opinion on the existence or nature of an eternal afterlife, the way that we conduct our lives is an implicit endorsement of one belief or another. Those who live merely to satisfy appetites are acting as if life is finite and it ends in the grave. Those who put aside this world and eschew lust, greed, and pride, are acting as if they are in preparation for some other world where they will find greater joys and rewards for their diligence. A person’s actions imply a belief about whether or not life is eternal and whether eternal life is desirable, even when he has never thought about his opinion on it.
So our position is difficult—we cannot understand eternal life, and yet we must conduct our lives in harmony with some belief about it. This is a great dilemma of life, and I have spent many long hours trying to resolve it. The only resolution I can come up with is that we must have faith: faith that we are not condemned to eternal torture or boredom or forgetfulness, faith that the suffering that we experience will pale in comparison to the joy to which it will lead, and faith simply that the universe is fundamentally good rather than evil or indifferent.
Advocating faith may seem like a cop-out to some, as if I recommend it as a replacement to rational inquiry. It is true that rational inquiry has dim prospects for ever being able to answer the question of whether the universe is good or evil. But I think of faith as something much higher and more important, not as the excuse of ignorant minds but rather as the passion of curious ones. Personally, I agree with Kierkegaard who had respect for faith and even said that “none come further than faith.”
Many have rejected faith in the past, and many have embraced it. We all must work out for ourselves whether we will have faith, and if so, precisely what we will have faith in. Do we take the imaginative leap of believing that the soul continues infinitely after death? Do we choose to have faith that the universe could be infinite in duration or size, even if it’s unknowable? Do we live on earth according to the impulse of the moment, or in assiduous preparation for the promise of a blissful eternal life? As for me, I am a partisan of the infinite. I love the notion of infinity, and I am keen to learn and accomplish the many things that won’t fit into my brief mortal life. It will take me much longer than Winston Churchill’s million years to master painting, but an infinite afterlife provides time for this and much else besides. This prospect motivates and strengthens my faith. My faith, in turn, adds meaning and purpose to my life, not as an anti-scientific distraction but as a complement and partner to scientific inquiry. To each of the eternal beings reading this, I commend faith to you, and I challenge you to a game of chess.
Books on the topic of this essay may be found in The Imaginative Conservative Bookstore.