Probability and randomness has proved to be a popular and controversial topic on this blog. So I am pleased to introduce a guest post by Barbara Jolie, whose by-line occurs at the end of the piece, musing on the question “Does randomness exist?”. As ever, comments are encouraged! |

Randomness is one of the most interesting mathematical concepts I’ve ever considered. The way people view randomness in different ways is fascinating in how it easily turns from a concept rooted in context and perception to an affirmation either for or against determinism. Sometimes free will gets wrapped up in the mix of thought about randomness too.

### Definitions … if you dare

I’ve come to realize that the majority of blown-out, philosophical ramblings (or discussions) about the nature or existence of randomness tend to disagree on semantics. It seems that random is a word that has several shades of meaning and various amounts of depth attributed to its various definitions.

Let’s take a look at how the Oxford English Dictionary defines random: “Having no definite aim or purpose; not sent or guided in a particular direction; made, done, occurring, etc., without method or conscious choice; haphazard.”

From this definition, we can tell that randomness is determined on a contextual basis. Determining whether an action or thing has “no definite aim or purpose” really puts the burden of proof on the one labeling something random. From a limited enough context, everything might seem random, so discerning randomness can be somewhat problematic.

### Looking Through Different Contexts

There are several different fields of study that use randomness on a pragmatic basis; most of them involve science or mathematics. Different studies have different uses for randomness as well as ways to describe it, so I think it is interesting and valuable to consider and compare these different uses and descriptions of randomness.

#### Statistics

In probability and statistics, randomness arguably serves its most valuable role. Statistics describes a random process as a repeating process with outcomes that follow no discernable deterministic pattern but do follow a probability distribution (so that relative probably of an occurrence can be calculated). One of the most basic examples of a random process is a two-sided coin of equal weight; you can’t predict the outcome or a coinflip (making it a random process), but you can determine the probability of it landing on one side.

Random processes are often used in statistics to signify well-defined statistical properties within a study, such as a lack of bias. Randomness is most commonly used to create random samples by means of drawing from a hat or using a random digits chart (which is a large table with digits 0-9 at an even but random distribution.

#### Mathematics

Obviously mathematics shares the same theories on probability and probability distribution. Of course mathematics goes a bit further into the study of what constitutes a random sequence with algorithmic information theory (a subfield of information theory and computer science). This information theory studies complexity measures on strings, which are sequences of characters.

Essentially, algorithmic information theorists determine whether a string of characters is complex by means of describing the string in a length shorter than the string itself (for example, “abababab” would be considered less complex than “f8ef1r30” because it can be described as “ab 8 times”). A random string is an “incompressible” string, meaning that it cannot be described by a program whose length is shorter than the string itself.

#### Biology

Biology is an interesting mesh of determinism and randomness. Some characteristics of an organism (such as freckles) are determined by genes and environment (the density of freckles) while simultaneously distributed randomly on the organism (the location of freckles).

Randomness also plays a role in the theory of evolution, as changes to an organism have so far only been described as random. However, within the scheme of natural selection, some random changes to an organism give it a non-random improved chance of survival and reproduction. While a mutation may be random at first, it can ironically serve a great purpose for that species and be favorable within natural selection, which is an interesting concept of randomness to consider. Granted, who knows if (in the next hundred or so years) we can actually find causes and make predictions to mutations, thus not making them random.

### Back to Randomness

We can state that randomness implies a lack of predictability. This lack of predictability is usually dictated by entropy or complexity. Calling something random just because we do not fully understand its process may seem like jumping the gun to some. However, sometimes we just need to call things random for the sake of randomness (and the practicality of randomness).

While there may be a huge, outstanding number of conditions that affect the outcome of a thrown 6-sided dice, we cannot control, measure, or understand these conditions well enough to say that the dice throw is not random. So there seems to be a fine, sometimes extremely sensitive line between what we can and can’t call random.

Determining whether randomness exists is about as impossible as determining the cause of everything in existence. I would say that we cannot prove randomness anymore than we can prove determinism, simply because we lack information. We can however describe randomness well enough to use it for practical purposes such as to diminish bias in a selection process intended to be random.

#### By-line:

This guest post is contributed by Barbara Jolie, who writes for online classes. She welcomes your comments at her email Id: barbara.jolie876@gmail.com.

This guest post is effectively a form of spam. Shady organizations like the one employing the guest blogger operate by recruiting students for online, for-profit education. In order to build links from reputable sites (for search engine optimization purposes), they hire people to write guest posts on blogs that link back to their site. They do indeed provide legitimate guest posts, but generally ones of no interest at all. In today’s post, we learn that “we cannot prove randomness anymore than we can prove determinism” and that the random distribution of freckles is an interesting application of probability theory in biology.

Now that you’ve agreed to publish one of these guest posts, I suspect you’ll get lots of other offers from prospective guest bloggers. I hope you won’t take them up on it: the posts are inevitably boring, and the links actually make the world a slightly worse place.

The most interesting aspect of this is the economics. Someone is paying these bloggers, and I imagine this content costs a couple of dollars, so these links are actually worth something.

I posted this partly because I was curious to see the reaction. Nobody forced you to click on the link.

The harm doesn’t come from readers being tricked into clicking on the link (anyone who reads the post and then clicks on a site labeled “online classes” should know perfectly well what they are clicking on). Instead, the harm comes from effectively endorsing the site, by giving search engines the impression that lots of reputable bloggers think it is worth linking to, so they’ll decide it’s where they should send anyone looking for online classes. I wouldn’t care so much about the search results, since I’m not seaching for online classes anyway, except for two things: they take advantage of unsophisticated students by steering them towards institutions just one step up from diploma mills, and I don’t like seeing lousy guest posts (so I hope the blogs I enjoy won’t help or encourage the spammers).

I’m a little annoyed, since I’m normally very interested in your blog, so I’m always pleased to see a new post. When I saw this was a suspicious-looking guest post, I was disappointed, but I thought that just maybe it would actually be good (after all, you seemed to think it was worth posting).

By the way, if you want to render the link harmless, you can add rel=”nofollow” to the HTML. Then humans will still be able to click on it if they like, but search engines will be told to ignore it.

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