OK, with this new-found agreement, let's revisit the original issue:

You claimed that my categorization of language (and, specifically, the cognitive processes involved in understanding linguistic communication, which is what I was discussing in the post you replied to) as high-level, was contrary to professional usage, where it is, you claim, regarded as a low-level capability. In support of that claim, instead of doing the obvious -- offering some citations (as I had done) -- you present, as the accepted way to make the distinction, a test: language is lower-level than mathematics because you can have a conversation while doing mathematics in your head.

Or should that be that you can do mathematics in your head while having a conversation? The first problem with this test is its symmetry: in itself, it does not rank the one thing over the other, as you can switch them around (for that matter, it cannot even establish that they are at different levels.) To try and get around that problem, you insist that mathematics is a high-level one, and so language must be low-level.

Implicit in this move is the corollary that, by definition, one can do at most one high-level task at a time. I suppose that when people refer to a cognitive capability as high-level, that is explicitly what they mean (though I doubt it), but if so, it is an assumption that should be possible to verify empirically (and you should do so, if you want to make use of it.)

Therefore, your claim that mathematics is the high-level capability is begging the question, as, through the corollary of the previous paragraph, it is tantamount to an a priori claim that language comprehension is the lower-level one. You have not shown that language comprehension is lower level; you have asserted it.

To try to avoid the problem that mathematics is not feasible concurrently with all conversations, you next modified the claim to include only simple conversations. Not only does this render the test moot, as it excludes language in general (the observation that a simple conversation is easier than calculus is trivial and uninformative in the general case), it is also a tendentious move; for one thing, you have not made a similar bifurcation of mathematics. Also, as you acknowledge at one point, it implies that, in your way of looking at the issue, simple language comprehension (or, for that matter, simple mathematics) is on a different cognitive level than difficult language comprehension or mathematics (note that there is a four-way comparison to be made there.) Again, maybe most people think that is how the concept of cognitive levels are to be understood, but I doubt they do -- and if they do, then it is sufficient for the point I was making in my original post.

Now you have come to say that complicated conversations are so cognitively demanding that it is not possible to do any sort of math while engaged in one, while math is not so cognitively demanding that you can't have a simple conversation concurrently. From the corollary of your position (as explained three paragraphs up), that would make mathematics lower-level than language comprehension! This follows from your own position because the latter is capable of excluding the former, but not vice-versa.

This just goes to show that your test is not achieving what you think it does. It is possible that you are coming from some actual science, but if so, it is getting lost in your insistence on defending this test. More relevantly, it is possible that people working in the field do, in fact, regard language comprehension as a low-level cognitive capability, but this is not the way to show they do.