As almost a third of English words do, “random” stems from Old French. However, the original noun “random” had a meaning closer to “speed” or “impetuosity”. Over time the sense of haste embedded in the word wrought new meanings like “careless”, “unforeseen”, and ultimately the sense we accept today – that of something bizarre, unplanned, or strange.
Random is a useful word. It peppers our everyday conversations, emphasising the sheer craziness, excitement and unpredictability of our lives, and seems to just roll off the tongue when talking about those moments where, for example, the author of a randomness article randomly began by talking about English etymology, or the fact that he has randomly interrupted this article to shuffle into the third person.
However, true randomness is far rarer than the everyday usage of the word leads us to expect. Pulling short straws, rolling dice, flipping coins – these are some of the many time-tested methods used to generate randomness and preside over fair contests. Ignoring irregularities of the sort discovered by researchers at the Akademia Podlaska in Eastern Poland, who claimed the embossed design on the Belgian €1 coin causes the coin to land on heads more so than tails, we can take it as given that a single coin flip is random. We know intuitively, though, that while one coin flip is random, many coin flips become predictable and will tend towards a fairly even 50/50 split.
So, how well does our intuition serve us when it comes to other puzzles of probability? Were you really listening in maths class? How well-based are your assumptions? The truth is – maybe less so than you thought.
Consider the following scenario. 22 people have signed up to a new Probability and Statistics module and are walking into the tutorial room on campus for the first time, oblivious that after a single class their brains will have melted and oozed out onto the linoleum floor. The teaching assistant strolls through the door once all the students are done filing in, bringing the room count to 23. What are the odds that a pair of people in the room share the same birthday? The bemused students shuffle around the room, perhaps approaching the problem by organising into January rows, February rows, etc. Soon, they discover that the odds are not as long as they originally thought – in fact, virtually the same odds as flipping a (non-Belgian?!) €1 coin and watching it land on heads. How can this be?
From a group of 23 people, there are in fact 23C2 possible pairs – 253 pairs, to be clear. This turns out to be well over half the amount of days in a year – 182.5 or 183. Mathematically, it is easier to calculate the probability that two people don’t share the same birthday, and then subtract this from 1 to find the probability that they do. Back in our stuffy room, the teaching assistant grabs a student at random and asks them what their birthday is. Ignoring leap years, this student has the luxury of 365 options, as they are the first to be asked. Moving on to the next student, they still of course have 365 possible birthdays, but if they don’t want to break the not-having-the-same-birthday streak, they must not repeat the first birthday and thus have 364 options. Moving on again, the students are getting a bit impatient, but after asking everyone in the room and crunching the numbers ( 365⁄365 × 364 ⁄365 × … × 343 ⁄365 ), then subtracting this number from 1, we find that the chance of any two people in the room sharing a birthday is in fact 0.507297, or just over 50%. Repeat the experiment in a larger lecture hall of 70 people, and the odds soar to 99.9%. Try it yourself!
This sort of confusion arises from several irreducible human factors. Over many tens of thousands of years, the human brain has learned that the best way to deal with the stunning amount of information presented by our surroundings is to make predictions and seek patterns. The brain is upset by pattern-devoid input. As the Ganzfeld experiment famously shows, participants who sit in a comfortable chair for half an hour with halved ping-pong balls over their eyes and a constant red light shone towards them, with nothing but white noise playing out through their headphones, will have starved their brains of patterns for just enough time to undergo mild hallucination. Sensory stimulation is like oxygen to the human brain; the confiscation of this basic need is what makes solitary confinement such a malevolent method of punishment and what makes people shock themselves rather than sit idle in a room (as entertainingly demonstrated in Michael Stevens’ Pain vs Boredom experiment uploaded to one of YouTube’s most popular science channels, Vsauce).
The pendulum, however, swings both ways. Input that is indecipherably random can be as jarring as no input at all. Comedians like Andy Kaufman and Eric André consciously challenge the threshold at which something passes from the hilarious into the haphazard – leaving punchlines undelivered, flitting between personalities, or even walking onto a crowded New York subway wearing pyjamas and an Elizabethan dog collar, pouring milk everywhere and eating Froot Loops (looking at you, Mr André). The greatest works of art successfully toe this line between structure and disarray, forte and piano, action and inaction. They strike the optimum balance in our brains – enough pattern to satisfy and enough randomness to subvert.
When we hit shuffle on our music library, we expect a roundabout trip through discographies, eras, and genres, and can be left frustrated if five songs from the same artist come up in a row. After complaints from begrudged customers, iTunes decided to alter their shuffle function for this very reason, “making it less random to make it feel more random”, in the words of erstwhile CEO Steve Jobs. Of course, a random system with such a large user base can be reasonably expected to serve up an oddly specific string of similar content from time to time – for example, with over 120 billion videos on YouTube, it is not that surprising that one random broadcast snippet from a Greek radio show contains the word “Hello” in its randomly generated URL.
“Rolling dice and flipping coins are serviceable means of generating randomness, but when it comes to national sweepstakes, data encryption, drug screening, military drafts, and university entrance lotteries we obviously need to seek out the highest quality, crème de la crème randomness.”
All this is to say that what looks random to the human eye often isn’t. The odds of showing 3, 1, 6, 4, 5, and 2 upon six rolls of a die is the exact same as the odds of showing 1, 2, 3, 4, 5, and 6, despite the former looking a lot more random. Genuine randomness is hard for us to understand. An experiment carried out by Dr Christopher Wetzel of the Rhodes College Department of Psychology asked participants to create a list of 100 coin flip results from thin air, and to make the results seem as random as possible. Subsequent analysis showed that humans are surprisingly incapable of behaving randomly. It’s not that we as humans lack the imagination; more often than not, we will actually overcompensate. We will create chaotic lists that flit around unpredictably, just like the roundabout iTunes shuffle that sounded more pleasantly random to our ears. True randomness, like serving up those five Bob Marley songs in a row, will occasionally hit a “run” of similar results, creating an illusion of order that contradicts our understanding of randomness.
The subtle difference between chaos and randomness has lain at the heart of the debate of what counts as true randomness. Rolling dice and flipping coins are serviceable means of generating randomness, but when it comes to national sweepstakes, data encryption, drug screening, military drafts, and university entrance lotteries such as those used by the Irish Central Applications Office (which must sometimes revert to randomly selecting new entrants among equally qualified candidates), we obviously need to seek out the highest quality, crème de la crème randomness.
Computers, to begin with, are terrible at producing truly random numbers. Most programming languages rely on Pseudo-Random Number Generators (PRNGs), which vary in implementation but rely on formulae and algorithms to produce strings of random numbers. The trouble is, these formulae are deterministic and require a term zero or seed to get the ball rolling. From this starting point, the same subsequent randomness will always be reproduced. They are also periodic, in that the sequence of random numbers will eventually repeat itself. Dr Mads Haahr, founder of Random.org, identifies simulation and modelling as suitable use cases for PRNGs, owing to their efficiency. However, to acquaint computers with true randomness, we must get them to listen to external phenomena.
True Random Number Generators (TRNGs) are the sort of computer systems we must use if we want the fairest and highest quality randomness demanded by some of the lottery and encryption situations mentioned earlier. A popular approach is to observe large-scale, chaotic systems. In fact, Random.org uses this very approach – the service is based on randomness generated by atmospheric noise, which is picked up by radios and is caused by all sorts of natural phenomena, including thunderstorms. If you have ever been foolish enough to hinge your plans on the suggestions of the weatherman, you’ll realise that despite truly awe-inspiring leaps in technology over the past few decades, weather forecasts still get it spectacularly wrong. If you wanted to know exactly what the weather was going to do over the coming days and weeks, you would have to know the position and status of every single molecule in the earth’s atmosphere at any given moment in time, and extrapolate into the future based on a set of laws that describes nature predictably 100% of the time. A quote from French polymath Pierre-Simon Laplace deserves to be reproduced in full:
“We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.”
At a time when solar eclipses and planetary movements can be accurately predicted hundreds and even thousands of years into the future, you could be led to believe the scientific cause has been edging ever closer to such an overarching “intellect”. However, if such an intellect truly existed, we would not only know whether or not we ought to wear our wellies and raincoat when we leave the house tomorrow morning, but for the morning after as well, and the morning after that, and, well, every morning ever until the sun stops rising.
Back to iTunes – where previously the dice had been rolled afresh between every song, the new system that Steve Jobs was going on about took a starting point, or “seed” song, and generated the entire playlist there and then, determining from the beginning what song would be the 10th, 20th, or 30th, in the list, for instance. If the universe were truly deterministic, as if someone pressed play on a certain song at the exact moment of the Big Bang and everything that has ever happened since has been the slow shuffle through a predetermined playlist, then nothing could ever be truly “random”. The atmospheric noise providing randomness for Random.org must have come from somewhere.
Perhaps if we could find the butterfly that beat its wings somewhere halfway across the globe, the little “seed” that triggered the series of whispers, breezes, winds, gales, and storms that caused the atmospheric noise in the first place, we could open up Random.org in front of a friend and gobsmack them by accurately predicting every next number that came up on the screen. Yet, when we are talking about such chaotic systems as the weather, we know the odds of anyone ever being able to do this are vanishingly small, so it is safe to say these numbers are about as bloody random as it is going to get.
Some, however, prefer to peer closer and look at the seemingly random behaviour of electrons and other subatomic particles. Heisenberg’s Uncertainty Principle tells us that there are some things about these minute particles that can never be truly known – the corresponding position and momentum of a particle at any given moment in time, for example – and implies that it is not always possible to predict the value of a quantity or the behaviour of a subatomic particle with full certainty, even if we did possess Laplace’s “intellect” and knew the precise starting conditions. As with many questions of quantum mechanics, the jury is still very much out on this one – Einstein himself was sceptical of true randomness and tried reaching around for proof of a deterministic universe, maintaining that “God does not play dice”.’
“Although the belief that everything unfolds from the whims of omniscient, bloodthirsty deities has gone a bit out of fashion over the years, the relentless search for meaningful patterns seems to be as much a preoccupation of the human mind as ever.”
The question is whether this behaviour, along with others, is truly random, or whether we simply have not glimpsed the underlying pattern yet. There was a time when someone who claimed that on 7 September 2993, there would be a solar eclipse for exactly 5 minutes and 33 seconds would have been laughed out of the room, sent to a psychiatric hospital, or worse. But hundreds of years of scientific enquiry later and here we are. Human civilisations have been obsessed with randomness, for better or for worse, for as long as we can tell. Surviving Roman frescoes show men playing at dice, and examinations of hordes of ancient cultures reveal the very human obsession with the determinism debate, manifested in ritual sacrifice and offerings, art and sacred texts, and the reverence laid upon oracles, prophets, and seers.
Although the belief that everything unfolds from the whims of omniscient, bloodthirsty deities has gone a bit out of fashion over the years, the relentless search for meaningful patterns seems to be as much a preoccupation of the human mind as ever. In 1898, American author Morgan Robertson released a novella entitled Futility, within which he introduces an enormous, 800-foot long vessel named Titan, the largest of its day. As the Titan progresses through the North Atlantic in mid-April, it hits an iceberg and, carrying only the minimum legal quota of lifeboats, many of the passengers are doomed to an icy death. Fourteen years later, and firmly outside the domain of fiction, the RMS Titanic sets sail across the North Atlantic, destined for Newfoundland. The ship is 882ft long, the largest of its day. Tragically, the ship hits an iceberg in mid-April and, carrying only the bare minimum quota of lifeboats, proceeds to sink into the midnight depths, dooming all but the most blindly fortunate passengers to an icy death.
On such a large playing field as the earth, such bizarre coincidences will of course eventually happen, just like how the word “hello” can be reasonably expected to be nestled in the random URL of at least one of those 120 billion videos on YouTube. Morgan Robertson is no more or less prescient than your neighbour down the road boasting that it was their superior knowledge and insight that led them to bet on the winning horse at the races last weekend, rather than blind, startling luck.
So, take a moment to pause and question yourself the next few times you throw around the word “random”. True randomness is not bizarre, wacko, out of the blue, unplanned, or strange. It is just random. That’s it. Trying to look further into it, to take it in your hands and declare dominion over it is a fruitless exercise. That being said, what is fruitless can still be revelatory. Gazing into the abyss and seeing little fictions unfold is as strong an affirmation of your humanity and the power of your pattern-hungry brain as you will likely ever experience. True randomness is neither beautiful nor ugly, neither predictable nor chaotic, neither provocative nor banal, neither jarring nor soothing, neither human nor robot, and it is for precisely these reasons that you ought to be more in awe when you come across it.