Here are some of my thoughts that could clear up the creationist's questions about complexity and information.
What is information? It correlates to the entropy of a system. A messy space has a lot of information in it. This can be stressful to people who like things neat because they must process all that information to model their space. Failure to model it properly could result in getting a stubbed toe or eaten. It is useful to things which hide because the searcher is less likely to find the hidden information in the competing rush. While organizing someone is actively using energy to transport entropy out of the local system.
The image of the clean office contains 0.87 times the amount of information in the image of the dirty office. You can check this yourself by saving the two halves as separate jpegs and then comparing the file sizes. Most image file types have built in compression.
Information entropy has the same formula as physical entropy. A disordered string such as 110100 has more information than orderly strings such as 000000 or 101010. The universe began very hot and simple, and is now cold and complicated as random processes leave evidence of their action.
This definition seems to defy the common sense idea that information must be meaningful. Meaningful information is information with somehow corresponds to another structure. Database experts have terms which make a distinction between information and meaningful information but I won't state them here because they are parochial and not informative.
The creationist's question might then be rephrased; how do natural processes create meaningful information? To the extent that a system is internally structured it can be said to model itself. A tree ring contains meaningful information about the weather. That information was already there, in the environment. Evolution also uses information that is already present in the environment. The process of it's accrual is more tortuous though.
Yet this information is less readily understood. It has a richer internal organization. Tree rings are obvious but more structured organization seems to need a designer to some people.
Here I present a rather tenuous taxonomy of modelling processes. Criticism is welcomed.
All editing processes involve two different classes of operation; correction and compression. Compression includes organization of objects, organization of ideas, removal of duplication and uninformative wordiness, and throwing out garbage. Compression always reduces the total information needed to express the meaningful information. Compression requires no insight to perform. An editor can copy edit a document with no knowledge of the subject. The editor must only know how to parse the encoding. A program can compress a file without any regard to what it represents (noise, a picture, a book). Correction includes fact checking, on a lower level of encoding, correcting spelling, or otherwise making your model more accurate. Correction requires insight to perform. An editor must have access to the system being modelled in some way in order to make corrections. A spell checker is a corrector with recourse to a set of data concerning spelling. A fact checker would verify using an outside source.
Care must be taken to be clear about what metric you are compressing by. If you are compressing visually, you would line up the columns of text in a source program so that they all appear to be a single entity. If you were compressing for space in a source program you would remove all the white space. If you are compressing by physical space, you would jam everything you could into your backpack. This would increase the visual complexity of the system.
When adding information, meaningless information can be added by injecting noise or disordering the model or duplicating parts of it. Meaningful information can be added by a process akin to correction.
Evolution never compresses. It adds noise and it corrects. It does so blindly, by trial and error, with the model slowly accreting meaning as it interacts with the environment. An organism can be said to contain information about its environment. By looking at an animal out of it's normal context, one can infer many facts about where it lived. The lack of compression gives genomes their horribly messy, profuse, and disorderly nature. To the extent that the genome IS the environment this rule is violated.
The normal human way to edit is to verify with the environment for meaning and then add the information. Evolution adds the information, and then checks with the environment for meaning.
