Thanks, that's very useful advice. I've usually done the stream-of-conciousness approach because my blogwriting began as a recreational thing, but I'll be sure to try and work harder on brevity and structure as I keep writing.
I was inspired to write my own blog post to better articulate what I'm getting at in this comment :)
https://medium.com/@couldbewrong/reconciling-left-and-right-from-the-bottom-up-3227eb1c0b47
I think the right way to look at this is that Public Positions are the output of top-down processes, and Private Guts are the output of bottom-up processes. Private Guts are obtained by taking a heap of concrete data and abstracting something out of that, for example taking the sense data obtained from smelling an orange and abstracting out a quality you find unpleasant. The reason it's hard to communicate Private Guts, and the reason they are Private, is that it's unlikely two people will be running their bottom-up processes on the same set of data (sense data in the case of smelling an orange). This is why art is so alluring: it presents us a distilled set of (usually visual) data from which we can use bottom-up processes to abstract away something that we couldn't easily communicate to another person verbally let alone identify ourselves in our everyday experiences due to the amount of noise that might make it hard to identify whatever it is that the artwork is telling you.
Top-down reasoning is more about having a goal (highly abstract) and working down towards concrete implementations on how to achieve that goal (e.g. prove a hypothesis). The reason the outputs of top-down processes become our Public Positions is partially because it doesn't take much data to communicate, but moreso because it is not dependent on a contextual dataset from which the Public Position originated.
It is not a prerequisite that you need to have a generative understanding of something (e.g. what makes a tiger a tiger?) for you to be able to infer its traits from a data set like an image (I've seen other things like this and they were allegedly tigers, so this is a tiger). Knowing something is 'like' something else is useful enough for us, and is why we have bottom-up processes. But this does not lend itself well to communication because the bandwidth of words is so low. Lizards don't have public positions because their brains are mostly purposed towards bottom-up processing. Top-down processing is mostly the domain of humans, and no doubt our language developed alongside that processing because concepts originating in the abstract are easy to communicate.
The reason humans are currently better than algorithms at proving theorems is that we can switch between top-down and bottom-up reasoning as we please. We can start with a top-down expression of the theorem we're trying to prove, and take a few valid steps in the direction of proving it, and once we can't see how to go any further down, we switch to bottom-up processes where we look at the stuff we've written down so far and say 'This part here has a likeness to some other things I've seen, maybe the same logic that worked with those other things will work with this thing as well'. And so on.
I think this is the best model for viewing Public Positions vs Private Guts
Please forgive some minor plot holes: I optimised for humour over realism! Figured it was worth posting this here as it has plenty of concepts familiar to LessWrongers