Does the act of organizing information (e.g. categorization) reduce entropy? I am fascinated by the relationship between entropy and life. From the Wikipedia article of that name, to the science fiction series "Three Body Problem" characterizing human-like lifeforms across the universe as simply 'low entropy beings'. However, entropy can be a tricky concept to grasp my mind around (I am an earth scientist, not pure physicist, by training). So I come to ask: does the act of organizing information (e.g. categorizing or identifying patterns) reduce entropy?
My understand is yes, because 'organizing information' is creating information about information, and the creation of information (or 'knowledge'?) reduces the randomness of (or at least uncertainty about) the states of things.
This question could seem ambiguous or nonsensical since entropy is used in a thermodynamic sense and an information science sense, and I'm asking about changes in information but am not necessarily asking about information entropy only. Citing sci-fi might not help, but I think this has a sound basis even if it's far out: consider the concept of humanoids being 'low entropy beings'. Humans in particular and life in general does seem to reduce entropy locally, at the least by simply keeping a warm body and therefore working to prevent the entropy of one's body from increasing. In that context - thermodynamic entropy in the physics of life - does the act of gaining knowledge (organizing information) reduce entropy? Again I'd think yes, in a simplest sense because when I have information organized I can spend more of my energy on actually doing work efficiently.
 A: Sensing and learning information clearly reduces entropy in the observer, who pays a corresponding or bigger physical entropy cost to perform these actions. 
Imagine a system (a robot, human, alien) observing another system (a rock, say). This paper shows that the sensor device cannot be at equilibrium in order to detect things. Indeed, it needs to produce some entropy to work, because otherwise it will just fluctuate uselessly. Now, the information gained by this process may reduce entropy in the memory of the observer - a probability estimate representing whether there is a rock there or not goes from a uniform distribution to a tighter distribution (or, you can imagine a discrete RockIsThere bit being set to a 0 or 1 value, for a more rigid design). Having a memory can also increase the ability of the sensor to acquire information (with some trade-offs). 
So when the observer knows something, it has reduced the entropy of its internal probability distributions (epistemic entropy, what Jaynes was talking about), or we can say it has literally physically reduced the entropy of the RockIsThere bit by setting it to a definite value. In the later case there was the Landauer cost $k_B T \ln(2)$ J that had to be paid in the form of waste heat - the local entropy reduction  had to be balanced with increasing global entropy. I suspect one can show that even the epistemic entropy reduction calculation will require a Landauer cost, since it erases past uncertain knowledge with more certain knowledge, but things can get messy if one has extra memory to store old results in (essentially it acts as a cold heat bath one can dissipate entropy into "for free" until it fills up).
Categorisation is trickier to analyse. It basically corresponds to searching for short descriptions that efficiently describe large amounts of data. It turns out that one can erase unwanted information more cheaply if one has knowledge of its internal structure, so the observer that figures out that X,Y,Z are actually one thing A can now (in principle) free up memory at a lower cost than was originally used to write X,Y,Z into their memory - the entropy "win" will be this compression efficiency minus the entropy cost of coming up with A (which might be small if the observer is a reversible computer; for such an agent interacting with the world is the main entropy cost).
I would not say organising information decreases entropy in the large - there is a lot of computation and writing/erasing memory going on - but locally inside the organising agent memory it seems like it does.
A: Entropy is anthropic.
In a famous paper, E.T. Jaynes shows that entropy represents human information. To him, it is known since 1875 with Gibbs that entropy has, his terms, an "anthropomorphic nature": it is not a purely objective property of a physical system: it is a measure of the information we human have about the system that help us get work from it. We have to be able to distinguish thermodynamic degrees of freedom to make use of them. 
So in a sense you are right, there is a deep link between classification and entropy: entropy as a measure needs classification. And if the classification changes, in Jaynes' paper when imaginary superkalic elements are discovered, then entropy also changes along with our capacity to make new kind of tools, superkalic pistons, and effectively use the newly acquired knowledge, while on the objective physical side of the situation, nothing changed.
When new qualitative distinctions are available for the description of a system, its entropy can be seen to decrease, because effectively we can see more order than before. 
