I was bowled over by your comment, and not just because of the praise at the beginning. (Answering questions here has been a delight because I do so enjoy discussing such topics. I'm also fascinated that a lot of the questioners appear to be adults, on this site aimed at high school kids.)
Your comment was so deep that I barely know where to begin. I'm afraid that I cannot answer it in the way it deserves as I am currently in Palo Alto, attending a workshop at the American Institute of Mathematics and am very busy indeed.
I think that you have identified a very deep and important aspect of the scientifico-mathematical enterprise which is certainly a part of what I was discussing here, although not something I had emphasised in the article. How do we define our basic unit? This seems to me to be (a) partly arbitrary, (b) non-algorithmic, and (c) always wrong, although hopefully useful.
It is almost certainly impossible to define the "edge" of a human on a quantum scale, or even an atomic scale, yet this "unitisation" of human-scale objects lies at the heart of what so many consider to be "natural" about the natural numbers. So I certainly agree that there is something about our visual perceptions which define units, and hence the natural numbers, and hence counting - we discretise the world and call it natural. This only seems to deepen the mystery of why a system of thought which develops from such crude beginnings should be able to uncover the depth of quantum mechanics and more besides.
I would be keen on discussing these matters in a more formal way, so do please feel free to contact me at dr dot phil dot wilson at gmail dot com