Verifier, Voynich and Accidental Complexity

By Gordon Rugg

There’s a widespread belief that complex outcomes are always due to complex causes. The theological argument of Paley’s watch uses this approach, for instance.

http://en.wikipedia.org/wiki/Watchmaker_analogy

There’s a similar belief that complex outcomes are always due to deliberate action (again, as in Paley’s watch).

The reality in both cases is very different. Complex outcomes can easily be due to very simple causes, and complex outcomes can easily be produced completely by accident, or by natural processes without any deliberate agency involved.

It’s an important issue in human error, and I think it’s a common mistake that people make when trying to make sense of the Voynich Manuscript.

This article describes some examples of how complexity can arise by accident or by natural processes.

First example: simple rules, deliberate intention, unpredictable outcomes

One case of complex outcomes occurs when birds or fish move in synch with each other. An example is starlings, as in the YouTube video below (if it doesn’t work for you, a YouTube search for starlings flying in formation will find others).

Starlings flying in formation:

https://www.youtube.com/watch?v=eakKfY5aHmY

This degree of apparent co-ordination has fascinated people for decades, and was often assumed to be the product of some complex and/or mysterious cause, such as telepathy.

In reality, when Artificial Intelligence researchers tried simulating this kind of behaviour, they soon managed to produce outputs that were very similar to the starlings’ behaviour, as in this YouTube video. (If it doesn’t work for you, a YouTube search for boids flocking will find others.)

Boids flocking:

https://www.youtube.com/watch?v=GUkjC-69vaw

The fascinating thing about the simulation is that it’s actually based on just a handful of rules for how each of the simulated birds behaves. Typically, the simulations only need to specify each bird’s preferred distance from its nearest neighbour, its degree of alignment with its neighbour’s direction, its speed, and one or two other similar variables, depending on the particular simulation.

In this example, the complex behaviours have arisen out of deliberate but very simple rules. The rules were produced by a human being who wanted to simulate birds flocking, but that human being wouldn’t be able to predict what the flock of simulated birds would do.

The next example shows how complexity can arise accidentally from simple causes.

Second example: Complex statistical effects arising by accident; humans involved

An important concept in statistics is the distribution of the data being analysed.

One common distribution, for instance, is the Gaussian distribution; a well-known version of this is known as the bell curve. In the Gaussian distribution most of the data cluster in the middle around the average value, with some of the data a bit above or below the average, and a small amount of data being more distant from the average; overall, this forms a shape similar to a bell, if you plot it as a bar chart.

There are a lot of other types of distribution. Here are some examples, from a Google image search for statistical distribution.

One of the interesting things about the Voynich Manuscript is that if you plot the lengths of the words in it as a bar chart, you get a symmetrical distribution similar to a bell curve, known as a binomial distribution. This concept wasn’t known until centuries after the likely date when the Voynich Manuscript was created, some time in the fifteenth or sixteenth century.

This has often been viewed as proof that the Voynich Manuscript couldn’t have been created as a meaningless gibberish hoax, on the grounds that nobody at that time would have had the knowledge needed to produce this distribution.

The reality is very different. This distribution could very easily arise as a completely accidental and un-noticed side-effect of producing a meaningless hoax.  Here’s how that could happen.

There’s a strong case for the manuscript having been produced as a meaningless hoax by combining meaningless gibberish syllables. If you were a hoaxer, how might you produce a set of these syllables?

One thing you’d probably want to do is use the structure that you see in many real languages, where many words consist of a prefix, a root and a suffix – for example un or re as prefixes in English, walk or read as roots, and ed or ing as suffixes.

Another thing you’d want to mimic is that words vary a fair amount in length, such as the variation from a to antidisestablishmentarianism in English. There are various ways that you could do that. One simple way is to vary the syllable length. Here’s a simple example of how you could do that for gibberish syllables, if you’re a tidy-minded sort of person, with a short, a medium and a long syllable for prefixes, roots and suffixes. For simplicity, I’ve only shown one example for each.

	Prefix	Root	Suffix
Short	o	k	y
Medium	ol	ke	dy
Long	olo	kee	ldy

If you now combine these randomly in the strict sense of the word*, you’ll get a variety of word lengths. The shortest will be oky, with three letters; the longest will be olokeeldy, with nine letters. Most words will be somewhere in between; a few shortish ones, such as okey or olky, a few longish ones such as olokedy or okeedy, but most in the middle, such as okeey or oloky or olkedy.

If that distribution sounds familiar, it’s because it is; it’ll be some form of bell curve. It may be a bit flatter or a bit steeper than the familiar bell curve, but it will be the same basic shape. So you’ve produced a recognisable statistical distribution just by combining different lengths of prefix, root and suffix in a tidy-minded manner. Just this sort of symmetrical distribution occurs among the words in the Voynich Manuscript. I’ve argued that this is probably no coincidence, and that it arose in just the way described above.

*The asterisk about randomness is an important point. There are various ways of combining the syllables, some of which are truly random in the strict statistical sense, and others of which are not. It isn’t an either/or choice between truly random and completely predictable; there are other options as well. My proposed explanation for how the Voynich Manuscript could have been produced as a meaningless gibberish hoax involves using a quasi-random way of combining the syllables, not a random way. It’s an important distinction, that’s at the heart of my explanation, and I’ll post an article soon about it.

Depending on just how you put your list of meaningless syllables together, you can get different statistical distributions in the output. Whichever method you use, the statistical distributions will arise naturally from the method you use, without any need for you to predict the distribution, to know the name of the distribution, to have intended it, or even to have the faintest idea what a statistical distribution is.

So, in summary, you can get complex, sophisticated outcomes arising from simple processes, without the creator intending those outcomes, or even realising that they’ve occurred.

The next example involves natural complexity, with no deliberate actions involved.

Third example: Complex statistical effects arising by accident; no living beings involved

The first illustration below shows complex-looking shapes in landscapes. It’s from a Google image search for ice polygons. The shapes were produced simply by expansion and contraction of frozen ground.

The next illustration is from another Google image search, for fractals in nature. Fractals are very complex shapes that arise from a very small number of rules about how often a shape should divide into smaller versions of itself, which in turn will also divide into smaller versions of themselves, and so on. There are many dramatic human-made images of fractals, and many natural processes which produce fractals, such as ferns. Which of the images below are computer generated, and which are produced by nature? I have no idea, apart from one case where I happened to recognise the image.

So, in conclusion, complex outcomes can occur from simple causes, and complex outcomes can occur from deliberate agency or by natural processes with no living beings involved, and it often isn’t possible to tell which of these situations you’re dealing with in a particular case just by looking at the surface complexity.

I’ll be returning to the theme of complexity in a later blog, with particular regard to definitions of complexity and ways of mentioning it.