Engines of Our Ingenuity

No. 2862: RANDOMNESS

by: Krešimir Josić

Today, let’s talk about how to pick random numbers out of thin air. The University of Houston Mathematics Department presents this program about the machines that make our civilization run, and the people whose ingenuity created them.

We all have an intuitive notion of randomness. Think of a list of random numbers between 1 and 10. You may come up with something like 3, 5, 2, 1, 7, and so on. Show this string to a friend and they will likely agree that it looks random. But we humans are very bad at both recognizing and generating random numbers: In your string you most likely did not choose the same number twice, let alone three times in a row. But avoiding repetition introduces subtle patterns and makes the sequences less than truly random. Think also of the shuffle function on your music player. If it resulted in a truly random sequence of songs, you would likely get more repeats than you expect.

Randomness is a fundamental aspect of many processes in nature. Evolution is driven by random mutations. Mutations result in diversity, and occasionally produce a mutant that is better adapted to the environment. Randomness is why we are here.

Many scientists studied such random processes experimentally, and developed theoretical models to describe them. Such models of random events are used to decide which drugs are beneficial and safe. These models can be complex, and we frequently need computers to fully understand them. And here is a big problem: like humans, computers are not great at generating random numbers. Computers are designed to provide a precise answer to mathematical questions. Variability or randomness in their output is a sign of bad design.

So can a machine designed to provide reliable output generate random numbers? Well, almost. Some processes follow precise mathematical rules and result in outputs that look random. Think of the number pi. Its sequence of digits is well defined. You can use a computer to generate as many of the digits of π as you please — and every time you do so you will get the same sequence. The beginning of the sequence will be familiar: 3.14159 and so on. However, if you grab a string of digits from a location further downstream they will look random. You will see strings that look like 93993751.

letter of Pi in mosaic pattern in concrete
the letter pi [Wikipedia]

Random number generators based on such principles are good enough for most applications. But it is important to remember that the resulting sequences are not truly random — they were created according to exact mathematical rules.

To generate truly random numbers scientists have looked to natural processes. Some have generated random numbers out of nothing. According to quantum mechanics, vacuum is not truly empty. It is filled with subatomic particles that pop in and out of existence. And this spontaneous creation and annihilation is truly random. Scientists in Australia were able to harness these fluctuations to produce billions of random numbers per second. Amazingly, one of the best ways to generate random numbers is to pick them out of thin air.

Some physicists think that our entire universe popped into existence out of nothingness. Thus everything around us could be just another event in the ultimate random number generator.

photo of quantum random number generator
quantum random number generator [ANU Quantum Optics]

This is Krešo Josić at the University of Houston, where we are interested in the way inventive minds work.

(Theme music)


Here is a very interesting discussion of randomness. You can follow the links on the website to see an analysis on whether mass shootings, or the pattern in which the German V-1 bombs hit London during WW2 were truly random.

Here is an interesting exception to the general idea that humans are very bad at generating random numbers.

For a more detailed discussion of how random numbers can be generated from vacuum, you can look here.

For a fascinating discussion of how the universe may be result of a quantum fluctuation, you can read Lawrence Krauss’ book. Here is a lecture by Prof. Krauss on the subject.

Krešimir Josić's Blog or follow kjosic on Twitter.

This episode was first aired on February 20, 2013



The Engines of Our Ingenuity is Copyright © 1988-2013 by John H. Lienhard.