The thoughts preceding are pivotal to what comes next.. they became evident as I searched for the answer to a question posed by finding a small tincture bottle while walking. I guessed the bottle would be about a 100 years old by its imperfections and the air bubble locked into the unevenly molded sides, but it was instantly recognizable as a man made artifact, a design. I asked the question: how much information is contained in that bottle compared with an irregular blob of glass the same size? I thought of what it would take to make a copy to within a certain tolerance (ie minimum dimensional error acceptable) but the bubble was an error, a random unspecified part of it. It soon became apparent it would take just as much information to copy the blob of glass as it would to copy the bottle! So that does not answer the question concerning the difference between the two.
The information required to copy the bottle is the same as the information to create it in the first place (including the tolerance) but the blob of glass was not designed or specified beforehand it just happened. The key lay in another type of descriptor.. complexity.
We could relate complexity to the size or amount of material in an object.. call it 'numerical complexity' but given the same minimum tolerance (say .01mm) the two are the same. We may talk about the shape and call that 'geometric complexity' but with the lack of symmetries on the blob of glass it would probably have a higher geometric complexity than the bottle. That is it would take more information to correctly describe the shape to the tolerance specified than for the bottle. Then I realized the bottle was designed with a purpose in mind.. it had what may be called 'functional complexity', of which the blob of glass had absolutely none! So the bottle is in what may be called a 'functionally complex' state of matter. The only problem now was how to measure it??
Have a nice day..
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