In all things there are two different kinds of characteristics: quality and quantity. While quantity is relatively easy to define, quality is difficult to define or specify. Consider an apple. It is easy to grasp what is the difference between one apple, two apples, three apples… only an integer number changes, representing the amount of apples. Differently, it becomes hard to define in detail what an apple is, what are its essential properties and its intrinsic attributes, ─ in a single word ─ what is its quality, which distinguishes it from anything else. This is more true more the thing investigated is complex and rich of information and organization.
Often a quality of a thing is related to its shape. Shape, form, position, topology imply qualitative attributes, which cannot be reduced in principle to numbers, let alone to a single number. This is the reason why in engineering, which deals with complex things, to describe them, one uses, yes, numbers but also uses words, symbols, drawings, charts, diagrams, pictures, etc. Consider a simple example: a spring. What distinguishes a spring from a straight steel wire and gives the spring the properties and functionalities the latter lacks? Aside from the fact that just the material must have specific qualities, the helical shape has a major role in making a spring. One could object that this shape can be described by an equation with three variables related to the three dimensions of space. Ok, but an equation is not pure quantity, is not a single number.
Sometimes the quality of a thing is related to its dynamic behaviour. Processes, events, evolutions, transitions, movement, state sequences are qualitative things. They entail time, which is even more qualitative than space. This is the reason why usually dynamic systems are more complex than static ones, and, consequently, more difficult to model and describe. Consider the example of a watch. Its dynamics transcends quantity and cannot be reduced to a number.
In some advanced cases the quality of a thing is related to the levels of abstractness it involves. Symbols, codes, words, languages, instructions are qualitative things. They entail meanings, which have high qualitative rank. This is the reason why information processing systems are among the more complex dynamic systems. Consider the example of a computer. It is made of matter, but this matter is support of an information processing that transcends matter. A computer transcends quantity, while being able to compute quantity.
Have you noted how many measures of complexity have been invented in system theory and in the complex systems field? All experts admit that no measure is perfect. A kind of complexity measure is good for a family of systems but is bad for another. Again, this is due indeed to the strict relation between true complexity and quality.
Quality and quantity are incomparable and irreducible. Total quantification, reduction of a thing to a single number, is a chimera. Quantification would be fine for us, because numbers are what is easier to deal with (not by chance, computers are good at crunching numbers but bad at grasping meanings). Unfortunately, to perfectly reduce quality to quantity is impossible in principle. As a direct consequence, perfect measures of complexity don’t exist. Expressed in a single number, what is the information content, the degree of organization, of a spring, of a watch, of a computer? Intuitively we feel they are in increasing order of complexity, but of how much?
What all this has to do with intelligent design?
It has a lot to do, and explains why so many discussions, also here at UD, arise about the concepts of CSI, FSCI, functional information, complexity and organization. We can consider a design as a thing containing “much” quality (but where this “much” cannot be properly quantified, so to speak). Roughly speaking, in the ID concept of CSI (complex specified information), the “complex” is somewhat related to quantity (it is a probability), while the “specification” is somehow related to quality (it is in relation with the functional description of the system). It easy to see here how quality, when we expel it from the front door, comes back through the back door. We would like a purely quantitative measure of complexity, nevertheless CSI seems to contain a qualitative part. In fact we can, yes, count the bit/bytes of the system description but this number will never perfectly represent the deep meaning of the description, what the system is. We may have two fully different systems with the same description length or even the same CSI.
What is the CSI of a mousetrap (Behe’s intuitive example of irreducible complexity)? What is the amount of information contained inside a mousetrap? The shapes of its parts matter and positional constraints about them are necessary so that the mousetrap work. Besides, the mousetrap implies a mechanism causing a short but effective dynamic event, when it catches the mouse. So consider how just this little example of design is difficult to quantify, how it is difficult to measure it by means of a single number. Go figure systems much more complex and organized than a mousetrap!
That being said, I do not mean the metrics of complexity and the measures of information proposed so far are useless. They can give an idea of what a system is, an hint about how much is more complex than another, how difficult is to design and produce it. Often, especially for specific, not extremely complex, types of systems, the measures of complexity are particular apt to characterize it, to provide an approximate metric.
Of course what said here doesn’t at all undermine ID. Quite the contrary, in a sense it reinforces ID, because dignifies more the role of design, in so far as eminent container of quality. Here what matters for me is the principle question, i.e. something we should be aware conceptually, while practically we can well use quantitative methods and tools, if they serve to get some result. After all also defective tools can be useful.