So if equations such as in celestial mechanics have no interpretative (or synergistic) origins, dimensions, how did we manage to use them to send spacecraft to Mars, Mercury, Venus? This is a question I reckon Mr. Chater can't answer any more than Mr. Rosenberg. (But Chater does agree, p. 146, "automatic processes can go on at the same time") The problem, of course, is that working through multi-body interactions in celestial mechanics requires a skill beyond use of automatic processes).
Rosenberg bases his claims on documented experiments, such as those by Lüder Deecke and Hans Helmut Kornhuber in 1964, showing that all human actions precede conscious decisions to perform them. For example, Rosenberg argues, in his discussion concerning neural time delays, that a simple action like flexing a wrist can’t be done at the instant one consciously thinks of doing so. Instead, there’s an inevitable time delay of about 200 milliseconds from conscious willing to wrist flexing and finger pressing. He adds that the cortical processes responsible commence 500 ms before that! The obvious implication: Consciously deciding to do something is not the cause of doing it. This is pretty well the conclusion Chater arrives at as well (Ch. 6, 'Manufacturing Choice'). In Chater's case (p. 131) we are "making up our preferences as we go on", finally opting for one - then forget it as the next thought or choice displaces it. But it comes to the same thing, i.e. deciding to do something is not the cause of doing it.
The point is humans aren't equipped to gain real time access to anything in their world! What actually happens in vision, for example, is that the brain must perform tricks to first erect an image that appears inverted on the retina. The process takes time and processing via the optic nerve is also needed. Thus, in Rosenberg’s parlance, vision turns out to be hindsight not foresight. Rosenberg’s inescapable conclusion is that because of this we are victims of a monumental illusion condemned to live our lives through rear sight, not foresight. This transfers to his Chapter Eight, in which we are shown The Brain Does Everything Without Thinking About It At All.
Chater, for his part, is not far behind in delivering similar gobbledygook. Thus (p. 51), we only have an "illusion of explanatory depth", such as in the computed perturbations of one celestial object by another. Hence, "the verbal accounts we give of our knowledge turn out to be flimsy improvisations, invented after the fact." There is in reality 'no there, there' so we are "being spectacularly fooled even about our own sensory experience." Which again is not that different from what Rosenberg claims.
But what are the implications of such radical baloney? I suspect they are the same whether one adopts Chater's arguments, or Rosenberg's. Hence, if either or both of these guys is correct, it's hasta la vista to any mode of introspection or knowledge. Shakespeare’s work, The Tempest? Doggerel and drivel! Einstein’s original paper on special relativity? A product of excess brain improvisations of prior single thoughts based on previous improvisations. Jean-Paul Sartre’s Being and Nothingness? A delusional, solipsistic voyage that could as well have been produced from LSD ingestion! Basically, all our fine cogitating, ruminating and writing translates to a torrent of meaningless effluent. Or in Chater's parlance: "a historical collection of momentary thoughts out of which no coherent theories ever materialized."
All our millions and billions of volumes of books, e-books and scientific or other journals amount to culminations of massive forest destruction or wasted bytes. With no introspection, the products of human thought have no interpretative dimensions. They’re merely elaborate chemical-physical automatons operating under the illusion of genuine personhood. Human history follows suit, reduced to the simple retelling of all our accidents, and nonsense. Philosophy is reduced to nothing more than assemblies of chaotically processed, random signals input to our neurons, then output.
As for mathematics? It's effectively reduced to a mere series of backward looking "improvisations" with no coherence or creativity. But as mathematician Jordan Ellenberg points out : 'How Not To Be Wrong: The Power Of Mathematical Thinking, p. 436;
"Every mathematician creates new things, some big, some small. All mathematical writing is creative writing. And the entities we create mathematically ae subject to no physical limits."