Interactivity: the extent to which something is interactive; the extent to which a computer program and human being may have a dialog.
Interactive: Acting or capable of acting on each other.
Interactivity, to me at least, is more than the generic “American Heritage Dictionary” definition given above. To be interactive, a thing must change, and respond based on your input and/or actions. It must have a response to your action on it, otherwise you could say that a rock is interactive. I can act on a rock and it can act on me, but that doesn't make it interactive, and if it does, it is only interactive in the sense that we can do each other harm. You can't choose options and have it respond. That's where interactivity comes in. Depending on the definition you use, you may be able to interact with a rock, but there is no interactivity. If you use the right command (the only kind a rock responds to... hit it with something harder than itself), you can get the rock to break for you, but that is really the only command to which your rock will respond. The interactivity of the rock, however, is severely limited, as it has only one “response” to pretty much just one “command” (It responds to my hitting it with a hammer the same way it responds to me hitting it with another rock)... it just breaks. To be truly interactive, you need more than this. To make our trusty rock more interactive, we would need to imbue it with the ability to react to many commands and produce a unique response for each one. A rock is not the best model for interactivity after all even if we can act on it and it can act on us. A much better model for this is the game Zork. Zork formulates responses based on my input and does much more than just break. I can say “kill troll with elvish sword” and sure enough, troll is dead. If I used that command on a rock, or even our other example of interactive fiction, “The Cup of Death,” it would not be able to respond. In order to have interactivity, one must also establish a way to interact with the object or system. “The cup of death” doesn't really respond to your input, but rather, your changing the pages based on its suggestions shapes the outcome of the story. Based on your desires and “input,” the story can change, but only to a limited degree (you can only chose a predetermined outcome built into the system). Even our game Zork can only respond based on a a very complicated series of predetermined “if, then, else” statements. What then, does it mean to be interactive? Neither Zork, nor the book can actually “interact” because you ultimately control how you read the story line. Some would say that that is interactivity, but choosing an alternate ending (that is located somewhere not directly after the last line you read) does not necessarily make something “interactive.” Any story can be interactive. The only difference is that the author didn't intend for it to be. I could read only every other paragraph or skip a few pages here and there (just like the cup of death had us doing) and the story would be vastly altered. That is me inputing my choice and the book is responding to that. It is predetermined and we both (sort of) impact each other, just like in the dictionary definition. The only difference is that this particular book wasn't meant to be read that way... but it's still interactive and its interactivity is decreased only because we may not get as desirable an outcome as we would with a book that was meant to be “interactive.” Zork is really no different in this regard. All the outcomes are there in the coding and our responses are equivalent to us turning the pages of this “interactive narrative.” Zork is slightly more interactive, however, because I can make (almost) infinitely more decisions that end with coherent results (responses). That is only possible, however, due to the difference in the amount of information available in the system. We are still choosing how the story reads, but the whole story is still in there and it is up to us as the reader to determine our own way to finish it... instead of just going on to the next line, we can go to a completely different one and still get a coherent story.
On the other hand, we also have to be able to respond based on its input. It says “turn to page __ if you want to call the cops or turn to page __ if you think you can handle it yourself,” so we respond to the book by choosing one of its suggested outcomes. In this sense, it is more interactive that a common book because I respond to it. Zork is pretty much the same, except it can give error messages (For instance, I type "do jumping jacks," it says "what is 'jumping,'" or I say "take platinum bar," it says "bar bar ..."), instead of a real command so I need to not only respond, but fix my previous response so that it can give me more text (to which I will continue to respond), making it even more interactive in a way. A rock or a normal book will not ask for a response on my part so that rules both out as "interactive." Zork and "The Cup of Death" can make me respond to them, but I can't make it respond to me, so it is not technically interactive... no matter how many times it suggests I should “turn to page __.”
Definitions taken from Dictionary.com and American Heritage Dictionary, respectively.