An Enigma machine. (Photo: Wikimedia Commons)

All week long we'll be posting stories about randomness and how poorly we tend to deal with it. Check back tomorrow for more.

Pick a number. Any number, one through 100. Got one? OK, so how did you pick it?

Humans are bad at creating and detecting randomness. Perceiving patterns has proven a great survival mechanism—the giant, spotted cats eat my children; this berry doesn’t make me sick—so we have evolved to be good at it. Perhaps too good. We misinterpret data all the time as a result of this desire for order. We believe that when a coin comes up heads five straight times, we are “due” for a tails, or we think that the stock market is predictable. It’s maybe unsurprising, then, that humans aren’t very good random number generators. And because of that, we’ve had to make some.

If you Google “Random Number Generators,” you’ll find several on the first page that are perfectly capable of mimicking a random process. After specifying a range, they will return a number. Do so 100 or 1,000 or 10,000 times, and you won’t find any discernible pattern to the results. Yet despite the name, the results are anything but random.

Once you learn about pseudo-randomness, it’s easy to see the world through Democritus’ eyes. Rolling dice isn’t random. Instead, the dice are governed by specific, mathematical laws, and, if we knew the exact contours of the desk and the force applied to the dice, we could calculate which sides would come to rest facing upward.

Computers are hyper-logical machines that can only follow specific commands. As explained by a BBC Radio broadcast from 2011, some of the random number generators you’ll find on Google follow something called the “Middle Squares” method: start with a seed number, which can be any number. Square that number. You’ll now have roughly twice as many digits. Take a few of the digits in the middle of that number and square that. Repeating this process is like shuffling a deck of cards. Still, if you know three basic pieces of information—the seed number, the number of digits taken from the middle of each square, and how many times the process will be repeated—you can calculate this supposedly “random” number every single time without fail.

Mathematicians have a word for this kind of randomness. They cleverly call it “pseudo-randomness”: the process passes statistical tests for randomness, yet the number itself is completely determined. On the BBC Radio broadcast, professor Colva Roney-Dougal of the University of St. Andrews says, “I can never prove that a sequence is random, I can only prove that it looks random and smells random.”

All of which brings us to this: Given the limits of human knowledge, how can we ever know if something is truly random?

A FEW ANCIENT THINKERS, known as Atomists, fathered a line of thought, which claims that, in fact, randomness doesn’t exist. The most deterministic among them, Democritus, believed the entire state of the universe could be explained through cause and effect. In other words, he was only interested in how the past dictated the present and future.

Once you learn about pseudo-randomness, it’s easy to see the world through Democritus’ eyes. Rolling dice isn’t random. Instead, the dice are governed by specific, mathematical laws, and if we knew the exact contours of the desk and the force applied to the dice, we could calculate which sides would come to rest facing upward. The same is true of shuffling cards. If we knew the exact height the cards were lifted, the exact force with which they were released, and the distance from each other, it’s completely feasible to calculate the order of the cards, time and time again. This is true for every game of chance, which are governed by Newtonian, or classical, physics. It all appears completely deterministic.

A lack of true randomness would be a huge problem, just like it was for the Germans during World War II with their revered but ultimately doomed Enigma enciphering machine. With its 150 quintillion different settings, many Allied cryptologists believed the code was unbreakable. Yet, because it was a mere matter of rotor settings and circuitry—or put simply, completely deterministic—the Allies were able to crack the code.

Since Newtonian physics has proven resistant to true randomness, cryptologists have since looked to quantum physics, or the rules that govern subatomic particles, which are completely different than Newtonian physics. Radioactive materials spontaneously throw off particles in a probabilistic manner, but the exact time when each particle will be discarded is inherently random. (We think.) So given a small window of time, the number of radioactive particles discarded can act as the seed for the random number generator.

Every time you buy something with a credit card, you’re relying on your information to be transmitted safely across a perfectly accessible network. This is where the difference between random and pseudo-random becomes vastly important. Pseudo-random patterns, like the ones created by the Enigma machine, are messages begging to be read. Random patterns are the cryptic ideal.

A company called PDH International is one of the patent-holders for Patent US6745217 B2, or “Random Number Generator Based on the Spontaneous Alpha-Decay,” the very process described above. PDH International, with an annual revenue of $10 to $25 million, specializes in the “fields of Privacy Protection, Authentication, Encryption and Electronic Document Protection.” PDH comes up with ways to safely encrypt data using true randomness from quantum physics.

BUT BACK TO THAT number you picked.

As with randomness, the more we learned about the precise nature of brain functions, we began to question whether free will was possible. If everything is the result of precise causal chains like the rolling of dice or shuffling of cards, some wondered how we can really be making genuine choices. However, as we’ve learned more about quantum physics, the possibility of genuine choice has been revitalized due to the break in the causal chain. In a way, quantum physics introduced a giant, unsolvable question mark, and question marks are good for free-will theorists. Ironically, quantum physics simultaneously undermines this line of thought, since randomness is bad for the idea that we are actually making rational choices.

So pick a number, any number. Maybe it is random after all.