Lakoff & Nunes entitle their book, “where mathematics comes from” by which they mean, metaphors we use in regular life. That is, we manipulate physical objects, and what we learn from these, we apply to the abstract space of maths.

I can’t help but think of this as a kind of reductionism, but I cover this in a previous post. It is useful, no doubt, to ground the abstraction of mathematics in a more familiar territory. Indeed, it explains how we can make sense of maths at all. At least, that’s what the authors hope to do.

Last night I was quite active in my sleep, and kept waking. I didn’t rise to record a mind flow, but vestiges of the thoughts come to me. If mathematics is a pure language, like this plate of glass I keep imagining, and science is the projection of it into the physical realm, then L&N’s account seem to me to be magnifications of the boundary between them. The details on how makes sense, in terms of physical things.

I think of XQ as being the reflected side of maths. It is not to do with physical reality. And neither does it bare much resemblance to the way L&N discuss their cognitive science. There is no metaphor, but a direct account of our mental processes. And I think there is an equivalent magnification at the boundary on the XQ side of maths.

It all comes down to how we… capture?… represent?… experience time. The objectification, the mensuration in seconds and minutes etc bears little relevance to our own subjective experience.

I imagined the mind as composed of cycles, some micro-seconds long, others an hour long, all circulating around the same point, more or less. This derives the “discreteness” of the self, as it travels through time, like a soliton wave. The Lorenz attractor shows how another circulation at an angle to this interacts in such a way that the outer most cycle influences the inner most of the other. I know this is not explaining anything, and this is more a note for myself…

XQ proposes that counting is the marking of time. There is no discreteness except in the mind’s capacity to bound things, including itself both in the ordinary sense of naming as well as the special case of its self-conscious twist.

I don’t think I have captured it… perhaps I should have got up and recorded it. What I am hunting for is something along the lines that Leon asked for, Applied XQ, and at the boundary of maths and the XQ direction, to reflect L&N’s work. And it has to do with time.

OK. I shall meditate on it. Sorry, bit of a gasbag of a post.