“Mine is a dizzying country in which the Lottery is a major element of reality; until this day, I have thought as little about it as about the conduct of the indecipherable gods or of my heart.”
–The Lottery in Babylon by Jorge Luis Borges
In his classic short story The Lottery in Babylon, Borges invites us to imagine a culture that valorizes randomness, institutionalizing it in an official lottery that entangles itself with every aspect of life, and even non-life. By situating this culture in Babylon, Borges frees himself to conjure up an alien way of life. And yet, as with all great speculative fiction, Borges also seems to be holding a mirror up to nature — a funhouse mirror that warps and amplifies features that we can discern even in our own culture. In his evocative and succinct way, Borges is perhaps hinting that we continue to live in that dizzying country in which randomness is a major component of reality.
The Indecipherable Gods
How long has randomness been an element in the periodic table of ideas? For ancient people, chance was wrapped up with the concepts of fate and divine will. “Divination” comes from the Latin for “to be inspired by a god”. For the Romans, chance or luck was personified by the goddess Fortuna. To tell a person's fortune was to determine the hidden intentions of Lady Luck. The ancient Chinese used yarrow stalks, coins, and dice when consulting the 4000-year-old I Ching, or Book of Changes. Divination either led to, or co-evolved with, games of chance. The earliest known board game is Senet, which was played by ancient Egyptians as early in the 30th century BCE. The game seems to have involved casting two-sided tokens. A 5000 year old backgammon set,complete with dice, was excavated at a site in Iran. Dice from 2000 BCE have also been found at sites that were part of the Indus Valley civilization .
Ancient peoples seem to have attached great meaning to chance events — even in the context of games. Confronted with the sheer unpredictability of nature, ancient people populated their pantheons with gods and demons who were capricious in the extreme. They seem to have believed that participating in chance events of their own invention could give them a glimpse into the otherwise inscrutable ways of divine beings . Or perhaps they reasoned that they could become like gods through imitation of their ludicrous whims. The word “ludicrous”, incidentally, derives from the Latin root ludus,which means “game” or “play”. At some point in the past few hundred years,the word came to mean “ridiculous” — perhaps the Enlightenment made Europeans look unfavorably upon frivolity and play. There are streams within Hinduism, however, that preserve an echo of the ancient worldview — in some scriptures the universe is described as as lila, or divine play. The gods, according to this view, engage in creation and destruction for fun or sport. In India the term lila did not pick up any connotations of ridiculousness: it is a well-known theological concept, as well as a popular name given to girls.
In the modern world randomness typically connotes the very opposite of divine will — outside the world of gambling and gaming, a random event is often described as meaningless, and therefore only a source of inconvenience or tragedy. The ancients may have confronted chance with a more cheery attitude than is common today, but there is no suggestion that they were able to translate any intuitions derived from gambling (or fortune-telling) into a mathematical theory of chance. This hole in ancient knowledge is striking, because much of the mathematics required to begin the study randomness — simple arithmetic — was known to ancient cultures all over the world .
Order out of Chaos
The seeds of a mathematical approach to randomness were planted in the 16th century, when Europeans thinkers realized that chance events and processes were not completely devoid of order. This realization contributed to the emergence of two related but complementary mathematical approaches: probability and statistics. The theory of probability allowed people to uncover patterns in controlled settings, such as games of chance. Statistics allowed people to uncover patterns in more natural, uncontrolled settings, such as mortality tables compiled for insurance purposes.
Probability and statistics are powerful tools with which to find order in events or processes that are random. But how do we decide what “random” means in the first place? The laws of probability were given a rigorous axiomatic form only relatively recently, in 1933, by the Soviet mathematician Andrey Kolmogorov. Interestingly, randomness was deliberately left undefined within axiomatic probability theory. Modern conceptions of randomness are built around three related intuitions; to be random, a process or event must be (1) unpredictable, (2) patternless, and (3) unbiased.
Unpredictability fits in very nicely with our intuitive ideas about randomness. But what do we mean by “patternless”? It will help to focus on the idea of a random sequence of numbers. Consider a sequence of ones and zeros, perhaps generated from a coin-flipping procedure. Whenever we get heads, we write down '1', and whenever we get tails, we write down '0'. Consider the following sequences that might be generated by such a process:
Both sequences are 28 characters long, and have exactly fourteen 1's and fourteen 0's. The laws of probability tell us that both sequences have exactly the same chance of occurring. But most people would not consider the first sequence to be random at all. There is a structure in the first sequence: the “01” motif repeats 14 times. The second sequence, on the other hand, seems to have no clear pattern. Our discomfort in labelling the first sequence as random was captured formally in the 1960s, when Per Martin-Löf, who studied under Andrey Kolmogorov, proposed a definition of randomness based on algorithmic complexity.
The algorithmic complexity of a sequence depends of the length of the simplest program that can generate that sequence. A sequence is algorithmically random if there does not exist a program shorter than the length of the sequence that can generate it. So if English were a programming language, we might code the first sequence as “'01' repeated 14 times”, which is 21 characters long. Since this number is less than the length of the sequence (28), the first sequence is not random, as our intuition seems to demand. If there is no program shorter than 28 characters than can describe the second sequence, then it will be labeled algorithmically random. Since programs that require fewer character occupy less computer memory, randomness is related to compressibility. Any sequence that can be compressed or simplified is a structured pattern, and therefore is non-random. This idea neatly captures our intuitions about lack of pattern in random processes, and gives us a reason to exclude the first sequence from any list of random sequences.
Even though unpredictability and lack of structure are central to our intuitions about randomness, they introduce a certain subjectivity into science and mathematics that many people find unappealing. After all, what is predictable, or compressible, to one observer may not seem to be so to another. Can something seem random to one person but deterministic to another? People who believe that the universe is fundamentally deterministic believe that all mention of randomness is just an admission of ignorance. Determinists might believe that if we could supply perfect observations to an advanced computer, chance would vanish and only the reliable laws of physics would remain.
Determinists presumably feel as if they have history on their side. The scientific revolution pushed back the boundaries of ignorance, expanding our ability to understand and predict. Unfortunately, the very methods of science that led to this expansion have turned up a great deal of evidence suggests that randomness is a fundamental feature of the universe — there are real limits to our ability to understand and predict natural phenomena . As the physicist Lee Smolin writes, “Surprise in inherent in the structure of the world.” 
A random road to justice, beauty and truth?
Unpredictability and lack of structure line up with intuitive ideas about randomness, but what does bias have to do it? Suppose we have a trick coin that, in the long run, lands heads 70% of the time. Is this coin random? Perhaps it is random, but is it “less random” than a fair coin that lands heads 50% of the time? Both coins are unpredictable, but most people, if asked to choose the more random coin, would probably choose the fair one. Unbiased randomness is closely linked to ideas of justice and fairness. Jurors, for example, are randomly sampled from the population. Sporting competitions often begin with a coin toss. Some of these applications of randomness may be a vestige of our ancient habit of letting the gods decide our affairs. Our modern image of Lady Justice — blindfolded and carrying a sword and scales — seems to be a 15th century amalgamation of two ancient goddesses. The blindfold seems to come from Fortuna, while the sword and the scales come from Justitia. At some point in the 15th century someone must have realized that without a blindfold, Lady Justice might tip the scales unfairly.
As it turns out, the notion of unbiased randomness is not just a hand-me-down from the age of capricious gods. In some situations, the knowledge we think is reliable can actually be a hindrance, and resorting to chance may be a better strategy. In the essay “How to Choose”, Michael Schulson describes research suggesting that “if you can't choose widely, choose randomly.”  The very fact that random decision processes are operating without reasons appears to be their strong suit. In a complex situation we may simply not have enough information to reason our way to a good decision. Random decision processes may sometimes be the best way to shake ourselves out of an intellectual rut. Randomness, then, can provide a spark of creativity. This idea is explicitly deployed by Brian Eno and Peter Schmidt in their card deck Oblique Strategies. It's a sort of I Ching for creatives. On each card is printed a nugget of sage advice. (“Honour thy error as a hidden intention,” and “Try Faking It!” are particularly piquant.) A creatively stymied musician or artist is invited to draw a card — and therefore inspiration — from the deck at random.
Randomness has proven quite useful in science and applied mathematics. The Monte Carlo method — named after the Monte Carlo Casino in Monaco — involves computer simulations that perform repeated random sampling, and is used in a variety of fields from physics to biology to finance. Unbiased random sampling allows researchers to explore a vast and complex space of possibilities without having to examine each of them exhaustively. For the same reason unbiased sampling is also necessary in opinion polling, which attempts to gauge public opinion without having to consult each and every member of the population. There may even be situations where it is useful to choose political leaders through random processes. Schulson's article describes how in Rennaissance Venice, the doge was chosen by sortition — a type of lottery. In this way the powerful families in Venice could limit the ability of any one group to buy its way into a position of predominance. At least in some circumstances, it seems the ancients were on the right track — imitating the games of the gods can sometimes help us in our quests for truth, fairness and creative expression.
The God of the Gaps
The concept of randomness often crops up during theological debates. In Europe and the Middle East, chaotic polytheism came to be replaced by orderly monotheism, which was the dominant mode of thinking for the better part of two millennia. The relationship between randomness and the divine may have gone through a reversal during the transition from polytheism to monotheism. Chance might suit a pantheon of game-playing gods and goddesses, but it must have seemed rather undignified — and wholly unnecessary — for an omnipotent, omnipresent creator. For the Abrahamic religions, rational order became the hallmark of the sacred rather than irrational chaos. Life on earth might be plagued by unpredictable storms, earthquakes, wars, and outbreaks of disease, but up in the sky there seemed to be a beautiful mathematical order in the movements of the sun, the moon and the stars. Perhaps the move from polytheism to monotheism involved first elevating a sky god — presumably the source of such heavenly order — above all other god and goddesses. If one god could handle all of creation, there were no explanatory “gaps” for the other gods to inhabit.
Heavenly order was eventually sought on Earth as well. Hermeticism, a mysterious philosophy which flourished in the intellectual ferment that preceded the Enlightenment, involved a belief captured in the saying “As above, so below.” Perhaps the alchemists and mystics of Europe reasoned that if the same creator made both heaven and earth, then some kind of order might, with the right kind of effort, be discerned here on earth too.There is some evidence that this sort of belief helped laid the foundation for the coming scientific revolution . A belief in the intelligibility of the universe must have encouraged the early modern proto-scientists to look at the universe with new eyes.
The historical irony of monotheism is that in conceiving of the divine as a single, rational force, it may have sown the seeds of its own destruction (or at the very least the seeds of a loss of centrality in western philosophy). After all, atheism is but an extension of monotheism's crusade to reduce the number of gods. If a universe overseen by a rational designer allows no game rooms for chaotic nature gods, then a clockwork universe must contain very little in the way of divine studio space.
Free Will in the Gaps?
The idea that gods have no room to work stems from the belief that our scientific notions of causality are complete, and so the universe does not require any special help from the “outside” in order to run smoothly. If this conception of causality is true, then we must conclude that the universe does not require any help from the inside either, and so the subjective feeling that some of our decisions are free must be a kind of tragic illusion, or perhaps a cosmic joke.
In response to the challenge of determinism, some believers in the freedom of will — whether divine or human — often point to randomness. Science may have dispelled many of the mysteries that baffled our ancestors, but in doing so it typically chances upon new mysteries. And many of the old mysteries are still with us. Those ancient forces of nature — storms, earthquakes, volcanoes, diseases, mental illness — still wreak havoc on our lives. It sometimes seems as if the belief in an underlying order to the universe started us on a journey that led us to its very opposite: underlying formlessness. Quantum indeterminacy seems to be telling us that the fundamental fabric of the universe is random. And chaos theory tells us that even deterministic systems can become totally unpredictable — in fact predictable systems are the exception, rather than the rule. Perhaps the freedom of the will can be found in randomness?
Some neuroscientists seems to think so. A recent study at the University of California, Davis suggested that random fluctuations in brain activity may account for the apparent freedom of the will. The researchers, led by postdoctoral researcher Jesse Bengson, investigated the brain states that correlated with moments of decision-making. Volunteers were asked to decide whether to look left or look right when they were cued to do so. The timing of the decision cue was unpredictable, so the researchers reasoned that the volunteers would be unable to prepare their decision in advance. The brain has a baseline level of noise or random activity. Electroencephalography (EEG) recordings suggested that the random state of the brain in the second or so prior to the decision cue could be used to predict whether the volunteer would look left or look right. Bergson concluded that brain noise “inserts a random effect that allows us to be freed from simple cause and effect”. 
People who don’t believe in free will can always counter with the argument that randomness is just another element in the causal fabric of the universe, rather than an escape from it. And people who do believe in free will probably find randomness to be an unsatisfactory basis for it. Randomness can seem impersonal, cold, aloof. Can we line up randomness with our intuitions about the will? Can we identify with randomness?
Perhaps we can. Sometimes it seems as if unpredictability and inscrutability are precisely the characteristics that suggest the presence of a will. The word “willful”, after all, when used to describe humans or animals, conveys a stubborn refusal to conform to expected norms of behavior. A person or animal whose will is completely subordinate to external forces often seems machine-like, and not fully alive. Conversely, a machine that stops acting according to plan is sometimes described as having a mind of its own. Perhaps the vital spirits that some people attribute to living things are projections of our inability to fully predict their behavior. If this is true, then perhaps every time our smartphones get smarter, some of us will redraw the borders between mind and matter, between life and non-life. Because surely anything a mere machine can do in a predictable and mechanical manner cannot be a hallmark of living intelligence? A device that works too smoothly, however intelligent, may be destined to be treated as a glorified calculator until it evinces a will of its own. And perhaps having a will requires throwing a little randomness into the mix.
I think Borges was on to something when he linked the lottery of Babylon with the indecipherable gods and with his heart. Randomness is a thread linking games of chance, natural forces and the will. Randomness, in other words, maybe the ghost in the machine — an expression of cosmic playfulness, creativity, and willfulness. Randomness is the gap that never seems to close.
So how can those of us who like the idea of free will identify with randomness? Perhaps we can take inspiration from apophatic theology. In apophatic or negative theology, God can only be defined by describing everything that God is not. In the Advaita Vedanta school of Hindu thought, for example, Brahman — the fundamental consciousness underlying all reality — has been described as “neti neti” or “not this, not this”. Randomness has an “apophatic” quality too: it can only be defined negatively. It is not predictable, not patterned, not biased. Randomness is whatever is left over when we have listed all the known patterns in the universe.
One of the goals of Advaita Vedanta is to make the practitioner identify his own mind with the cosmic consciousness. The saying “tat tvam asi” or “thou art that” captures this idea. I think that discussions of free will ultimately revolve around what we choose (for lack of a better word) to identify our selves with. Deniers of free will maintain that you cannot identify your will with the forces of physics, chemistry and biology, because they are not free, and in any case they are not you. But then what can you identify yourself with? Perhaps there is a “neti neti” approach to the self: you are not your body, you are not your brain, you are not your genome, you are not your connectome, you are not what you eat, you are not your social network, you are not your taste in music, you are not your history…
If at the end of this game of apophatic psychology you are left contemplating a void, then perhaps you must conclude, like the Buddha, that your self is an illusion. But you might instead find that once you have listed all the known forms and patterns in the universe, there is still something left — something that is in a sense the essence of freedom, novelty, creativity, and perhaps even justice, as well as the source of chaos, destruction, capriciousness, and misfortune. That something has gone by many names over the centuries — and maybe one of those names is randomness.
Notes & References
 For a brief overview of the history of chance and randomness, see Section 1 of the book What Is Random? Chance and Order in Mathematics and Life by Edward Beltrami.
 Ancient thinkers, ironically, may have been plagued by too much randomness to be able to discern patterns amid the chaos. The dice used in ancient times would not be considered fair by modern standards. A popular method of gambling involved using astragali — the knucklebones ofsheep or goats. These bones are quite irregular, and like all body parts, varies from animal to animal.
 Randomness is not the only limit to human knowledge. For an overview of the intrinsic limitations of logic, mathematics, science and computation, see Noson Yanofsky’s book The Outer Limits of Reason.
[Illustration created by me for a blog post critiquing the idea of mind-uploading.]