Winston Ewert, Bill Dembski, and Bob Marks have recently published a new peer-reviewed paper in the journal IEEE Transactions on Systems, Man, and Cybernetic: Systems, titled “Algorithmic Speci?ed Complexity in the Game of Life.” The purpose of the paper is to develop the concept of algorithmic specified complexity as a new and improved method of measuring biological (and other forms of) information.

They start by observing that “Neither fundamental Shannon nor Kolmogorov information models are equipped” to measure “meaningful” information. As I recently explained, “the purpose of Shannon information is to help measure fidelity of transmission of information. What the transmission says doesn’t matter” and:

Kolmogorov information is not necessarily tied to likelihood. In fact, higher Kolmogorov bits could mean more randomness. In that regard, it’s not useful for distinguishing functional information from non-functional.

Complex and specified information (CSI) has long been cited as an improved method of measuring the functional meaning of information. But recently the team at the Evolutionary Informatics Lab has developed a new variation on CSI, algorithmic specified complexity (ASC), to measure the degree to which information is meaningful. As they put it:

We propose an information theoretic method to measure meaning. Fundamentally, we model meaning to be in the context of the observer. A page ?lled with Kanji symbols will have little meaning to someone who neither speaks nor reads Japanese. Likewise, a machine is an arrangement of parts that exhibit some meaningful function whose appreciation requires context. The distinguishing characteristic of machines is that the parts themselves are not responsible for the machine’s functionality, but rather they are only functional due to the particular arrangement of the parts. Almost any other arrangement of the same parts would not produce anything interesting. A functioning computational machine is more meaningful than a large drawer full of computer parts.

They explain why Shannon Information and Kolmogorov-Chaitin-Solomonoff (KCS) measures of information don’t help measure functionality:

The arranging of a large collection of parts into a working machine is highly improbable. However, any arrangement would be improbable regardless of whether the configuration had any functionality whatsoever. For this reason, neither Shannon nor KCS information models are capable of directly measuring meaning. Functional machines are specified — they follow some independent pattern. When something is both improbable and specified, we say that it exhibits specified complexity. An elaborate functional machine exemplifies high specified complexity. We propose a model, algorithmic specified complexity (ASC), whereby specified complexity can be measured in bits.

ASC is similar to KCS in that it assumes a computer environment where we can describe some event, object, or scenario in terms of computer programming commands. This can allow, as they put it, a “quantitative measurement of specified complexity.” To show how it works, they use Conway’s famous “Game of Life.”

The “Game of Life” is a computer simulation that’s meant to mimic living systems by creating a grid in which some cells on the grid are “alive” and some are dead. A series of rules based upon the number of alive or dead neighboring cells determine whether a given cell will remain alive, remain dead, or come to life, or die, after each successive generation. They describe the rules as follows

1) Under-Population: A living cell with fewer than two live neighbors dies.
2) Family: A living cell with two or three live neighbors lives on to the next generation.
3) Overcrowding: A living cell with more than three living neighbors dies.
4) Reproduction: A dead cell with exactly three living neighbors becomes a living cell.

If you deliberately create certain patterns in the Game of Life, they can do unexpected things, like “gliders” which can move across the screen, or a really complicated pattern called “Gemini” that can make copies of itself every 33.6 million generations. Ewert, Dembski, and Marks use these features of “Game of Life” to apply ASC:

Our goal is to formulate and apply specified complexity measures to these patterns. We would like to be able to quantify what separates a simple glider, readily produced from almost any randomly configured soup, from Gemini — a large, complex design whose formation by chance is probabilistically minuscule. Likewise, we would like to be able to differentiate the functionality of Gemini from a soup of randomly chosen pixels over a similarly sized field of grid squares.

A highly probable object can be explained by randomness, but it will lack complexity and thus not have specified complexity. Conversely, any sample of random noise will be improbable, but will lack specification and thus also lack specified complexity. In order to have specified complexity, both components must be present. The object must exhibit a describable functioning pattern while being improbable.

They find that some of these patterns in the Game of Life are “simple enough that they arise from random configurations of cell space,” but “[o]thers required careful construction.” They measured the ASC in these patterns, and then asked whether the patterns are known to appear randomly, or whether they require intelligent design. Their model predicts that high ASC patterns would arise only by design, and that patterns that are known to appear randomly would always have low ASC. They found that their method is generally a good predictor of whether low ASC patterns can appear at random or require design:

We have merely calculated the probability of generating the pattern through some simply random process not through the actual Game of Life process. We hypothesized that it was close enough to differentiate randomly achievable patterns from one that were deliberately created. This appears to work, with the exception of the unix pattern. However, even that pattern was less than an order of magnitude more probable than the bound suggested. This suggests the approximation was reasonable, but there is room for improvement.

We conclude that many of the machines built in the Game of Life do exhibit significant ASC. ASC was able to largely distinguish constructed patterns from those which were produced by random configurations. They do not appear to have been generated by a stochastic process approximated by the probability model we presented.

In other words, many of the high ASC patterns that appear in Game of Life don’t appear at random. But is that surprising? After all, the Game of Life is a computer program created by intelligent agents that’s designed to mimic living systems — systems that also have high ASC. As they conclude, “Our work here demonstrates the applicability of ASC to the measure of functional meaning.”

Image credit: aussiegall (Laceflower abstract) [CC BY 2.0], via Wikimedia Commons.