I have been trying (like lots of others) to better understand complexity. And it struck me that we often speak of a given object as being both simple and complex. For example:
*My TV is simple to operate, but really complex to set up.*
*This application is simple to install, but complex to upgrade.*

To investigate this insight further, I did what I always do: Google. I googled "complexity is relative". One of the first results was this amazing paper entitled: *Entropy as a fixed point*. Apparently it was just published in February 2003. Given my previous post suggesting that complexity evolves to maximize entropy, I was amazed to see this connection to entropy in the title of the paper!

I was even more amazed when I read the abstract:

*We study complexity and information and introduce the idea that while *__complexity is relative to a given class of processes, information is process independent: Information is complexity relative to the class of all conceivable processes. __In essence, the idea is that information is an extension of the concept algorithmic complexity from a class of desirable and concrete processes, such as those represented by binary decision trees, to a class more general that can only in pragmatic terms be regarded as existing in the conception. It is then precisely the fact that information is defined relative to such a large class of processes that it becomes an effective tool for analyzing phenomena in a wide range of disciplines.

*We test these ideas on the complexity of classical states. A domain is used to specify the class of processes, and both qualitative and quantitative notions of complexity for classical states emerge. The resulting theory is used to give new proofs of fundamental results from classical information theory, to give a new characterization of entropy in quantum mechanics, to establish a rigorous connection between entanglement transformation and computation, and to derive lower bounds on algorithmic complexity. All of this is a consequence of the setting which gives rise to the fixed point theorem: *__The least fixed point of the copying operator above complexity is information. __

While I don't understand the formal discussion (yet), I am encouraged to see someone dealing formally with my intuition that complexity is relative to the process involved with (an) information (structure). This also reinforces my intuition that process and information are a duality.

## Recent Comments

Robert K. Logan:The link in See this paper for confirmation of... | more »Nick Gall:William, Thanks for your comment. Do you have ... | more »William Nelson:The entropy of the earth is increasing.. It is... | more »