Randomness might seem to dominate the world around us: falling leaves, the movement of trees in the wind, where the next raindrop will fall. Yet, attaching numbers to randomness is an unsolvable problem to which researchers in various disciplines get closer as they develop new and more accurate methods.
Is the order of cards in a well-shuffled deck random? There are always patterns such as consecutive numbers or three of the same suit, but is the deck “perfectly shuffled”? How could one know?
A random number is one that is drawn from a set of equally probable values. In a sequence of random numbers, each number must be statistically independent of the others.
You can usually find a sequence such as three numbers in a row or three of the same suit, but how could you know whether the deck was truly random?
One way might be to compare the order against a computer-generated list of random numbers. In most cases this would be sufficient, but is that list of computer-generated numbers truly random?
Why do we care about random numbers? Random numbers are used for data encryption keys, to simulate and model complex phenomena and to select random samples from larger data sets. Literature and music have used random numbers aesthetically, and they are essential for games and gambling.
When an online site sends a six-digit PIN to verify an identity, the chance of someone guessing the PIN on the first try is 1 in a million. However, what if the PIN the site sends is not truly random?
Most computers use pseudo-random number generators, known as PRNGs, but they are not truly random because, as it turns out, it is impossible to produce an arbitrarily long string of random digits and prove it is truly random. How close to truly random is close enough?
PRNGs are efficient because they can produce many numbers in a short time. They are deterministic, meaning that a given sequence of numbers can be reproduced later given the same starting conditions and inputs. PRNGs are also periodic, which means that the sequence of numbers will eventually repeat itself. While periodicity is never desirable, modern PRNGs have a very long period, so it is not important for most practical purposes.
The truly random number is a philosophical problem, and “What does it mean to be random?” is the crux of the philosophical analysis. For example, we assume that radioactive decay is random, but we are not certain whether it is due to a pattern we have not yet figured out.
Einstein famously said of quantum theory that God does not play dice with the universe because he believed that there must be internal processes within the atom that controlled the decay.
Niels Bohr, a contemporary of Einstein and one of the framers of quantum theory quipped, “Einstein, stop telling God what to do.”
Security personnel are always looking for ways to generate cryptographically secure nondeterministic random numbers. Several, which rely on some external source of entropy, are now online and open to the public. Although not truly random, these are as as close as we can get.
One such way is the randomness beacon of the U.S. National Institute of Standards and Technology. The institute begins with output from two commercial PSRGs that rely on electronic noise in circuits. Then it increases the unpredictability by combining them in a mathematical operation that reduces underlying bias.
Another is Chile’s beacon that combines circuit noise with other disorderly data such as Twitter posts, earthquake measurements, radio streams and cryptocurrency transactions.
Researchers are working on perfecting and upscaling quantum computers, which operate on the weird quantum condition where a bit can be either a zero, a one or both at the same time.
Richard Brill is a professor of science at Honolulu Community College. His column runs on the first and third Fridays of the month. Email questions and comments to brill@hawaii.edu.
