§1. The difference is in how we understand the purpose of and thereby design representations: on the computationalist picture, these are the basic elements of reasoning; each step of reasoning (or computation) involves the manipulation of symbolic representations. And so it follows that our tools for thought should be repositories of these representations, should present symbolic representations in such a manner that they can be drawn with sufficient completeness into the computational structures "in one's head" where they might be manipulated further.
§2. In the alternative picture we question that reasoning consists in passing around of representations, as if it were a sophisticated and less amusing version of the game of telephone. — I'll stop here before I fall into a theoretical weeds that aren't totally relevant to my project; the nature of reasoning will not influence the design of a tool for understanding — only now, having written the entire sentence, do I see that this is an absurd thing to say. Look at what is going on here though, it isn't the manipulation of representations, but a co-ordination between technology (writing), medium (note editor), and mind and the great constants of the cosmos (logic) which nudge us toward truth. An enactment.
§3. Reasoning in the sense in which I understand it may only have significance in literary or textual cultures. We have not moved beyond such a culture just yet of course, but it might be useful to think about what it would mean to do so. Syllogisms and parables and myths were guide rails to truth (as understanding?) in oral cultures just as logic is in textual cultures. The defining character of our age is parataxis, however, and in this sense we are not so distant from the ancients. These are controversial theses my friend.
§4. To return to Pond's vision, its promise: Pond is an instrument to help you see greater detail in the world. Why is this so important—more than aiding reasoning, whether computational or not? I think 'greater detail' may be the wrong framing; Pond aids in making sense of the great detail of the world, in seeing clearly. And making sense of the world is not necessarily (or primarily) reasoning about it in isolation, but relating it to features of the world understands and is close to (in a phenomenological sense of closeness).