Complexity

Below are two images I created using algorithms.   Which image is more complex, A or B?   Or are they equally complex?

AB

Now here are two more images.   Which is more complex, C or D?   Or are they equally complex?

CD

For the first question I assume that most people will choose B.   For the second question I assume that most people will choose D.   There is a certain sense within which the second question could be answered in that manner, but not when paired with the first question, and I will explain why in a moment.

More and more I am noticing an ambiguity in the use of the idea of complexity.   I have observed it in both average joes and in the most venerated of scholars.   They will use the word "complex" to refer to very different ideas, sometimes within the very same sentence.   This is not a good, for this vague inconsistency is allowing irrational propositions to sound sensible.

I created the quiz at the beginning of this essay to demonstrate that inconsistency.   In the first question, B is clearly more complex than A.   But the second question is not as straightforward.   In one sense the images look very different.   And yet they were built with identical algorithms.   The only difference is that with image D the range of the equation was greater.   You could increase the scope of the algorithm to encompass millions of pixels and the pattern would never really change.   In essence, compared to the first image, the second image is just more of the same.

If you were to reduce images A and B to their most simple definitions, (the equations used to generate them), B would still be more complex than A.   But if you were to reduce C and D to their simplest definitions, their complexity would be identical. (  Note that while what I am talking about is similar to the idea of Irreducible Complexity, it is not the same thing.) 

I am not going to try to define complexity in this essay.   That is a vast and complex subject.   I am simply bringing attention to a particular slice of complexity.   I will however, note that usually definitions of "complexity" involve the idea of multiple parts connected to each other.   What I am showing in this essay is that there is an important distinction between a system comprised of many identical parts and a system that is comprised of many parts with different essential attributes.   To better explain this I will return to my example of the images.

AB

Most people would say that image B is more complex than image A, and yet the images themselves contain the exact same number of pixels.   To relate that idea to my last paragraph, they have the same number of parts.   And yet when the human mind perceives image A it can summarize it as simply "a square comprised of pixels all of the same color", while the human mind cannot summarize image B into such a neat package.

Another way to illustrate this would be to take a car and glue hundreds of small random objects onto its surface.   In one sense that car would become more complex because it would be comprised of many more parts than it had been, but since none of those parts would actually be essential to the car's functionality of getting its occupants from point A to point B, in that sense the system of that car would not be any more complex than it had been.

This ties back to my last post on how Process = Product.   When I created the algorithms that generated those images, I could have had one of those algorithms additionally check my email and defrag my hard drive, which would have made the algorithm much more complex but as far as the image that it generated, the image would not have changed.   Within the context of the generated image those additional functions would be superfluous.   Mathematically, that would have been the equivalent of taking the following equation:

x = 5

and changing it into:

y = 1
x = 5 + y - 1

In one sense the second equation involves more parts, but in another sense it is just as simple as the first equation.

So in summary, all I am doing in this essay is trying to define and describe these two different dimensions of complexity.   Ideally I should have a term to describe the first type and a term to describe the second type but I don't yet have any good terms for these ideas.   I'm hoping that perhaps a reader of this essay will know of terms for these ideas that already exist and inform me of those terms.