Hello Bob,
Thank you for the comment and the inquiry. In order to respond to you, this reply may be a little philosophical in nature.
First of all. There is nothing mathematics about any of the social stuff that I blog about. Sociology, even with the most academic exposition, is fundamentally not an axiomatically rigorous with definitions and logical deduction. It is an field based on observation and summarization. So what I offer here is merely a perspective. There are many perspectives out there, like the Conversation Prism mentioned in this post. And there are many if you want to look into the academic literatures.
Second, the difference I mention are not meant to be taken a definition. There are always exception. With systems that is merely as complex as biological system, scientist already knew that any strict definition simply don’t work, because there are too many exceptions. Human and social system are even higher order complex systems, so I wouldn’t even try to put forth a rigorous definition.
So what can we do. We build models! No models are perfect, some models are more useful than others in some cases. Especially in social system, you have to take a look at what question you are trying to address and what problem you are trying to solve and pick the model that is just complex enough to help you, but not anymore complex. That doesn’t mean that the model is correct, right, or true by any means.
You can certainly treat Facebook as a community too. It just won't help you. Because if you do, then everything is just a big social network and every platform is a community too. This is like highlighting everything in a book. It provides no information as if you didn’t highlight anything at all. If everything is the same as everything else, you don’t get any benefit from those perspective. That is not to say that they are wrong or anything, They are in fact the ultimate truth. They are call tautology in mathematical logic. Undisputable, obvious truth, with absolutely no exception. But they tautological truth are not very useful.
I decided to use this model / framework, not because they are undisputably correct. It is because it allows me to understand the science of relationship (see My Chapter on Relationships: The R in Social CRM). This is just the very first post. If you adopt this view, then you can get the rest of the insights I wrote about in the 13 articles linked in the chapter above. If you don’t accept this perspective, you may get some of those insights elsewhere too. There are many ways to understand the world. And you are free to pick and choose what works for you.
So if you don’t think this model is sufficient for you, pick a different model. There is no perfect models out there. So as a scientist, when I disagree with someone else, I always first question myself, "Is it because I didn't see their perspective? What is the benefit from adoption that perspective vs. ignoring it and adopting a different perspective?" Life is full of choices, that is what make it interesting ;-)
BTW, if you want to be rigorous, I’m happy to talk real math with you.
Thanks again for the comment and see you nex time.