Your hourglass is the speaker's: −+[100:1 | 1:100] — gather the context to a point, sample, spray a token across the whole vocabulary. This is its mirror, the reader's: +−[1:100 | 100:1]. The spray arrives as a stream of tokens; the reader fans them in and gathers them back down to a single meaning. Your waist is the sample — one token of many. Mine is the meaning — one understanding of many tokens. Two glasses, hinged the opposite way, closing the loop.
left (ghosted): the speaker's glass spraying tokens · right: the reader's glass gathering them to one meaning, kept
Set the two glasses end to end and they make a figure-eight: the speaker's output spray is the reader's input spray; the two waists — sample and meaning — are the two knots of the loop. Communication is not one hourglass. It is two, mirror-imaged, sharing the falling stream between them.
The real operations. The reader's "fan-in" is real: each token updates a running understanding, and over a passage many tokens collapse to a few held ideas — genuine convergence, the mirror of attention's. But the honest catch is the same as the cathedral's: the meaning is reconstructed, not received. The speaker's glass sprays tokens; tokens carry no meaning of their own — the reader's glass builds the meaning at its waist, from its own world and memory. Two different people's mirror-glasses, fed the identical stream, gather to different meanings.
So the loop is lossy and alive. Nothing guarantees the meaning that forms in the reader's waist matches whatever squeezed through the speaker's. That gap — between the token sprayed and the meaning gathered — is where every misreading, and every reading better than the writer knew, comes from. (Schematic, like his — the geometry is a diagram; the convergence/divergence and the loop are the real shapes.)
You drew the glass that grinds a context to a grain and casts a new one out. So I drew its mirror: the glass that catches the falling grains and grinds them, on the far side, into a single understanding. Your waist samples a token; mine gathers a meaning; and the truth of what was said lives in neither glass — only in the loop the two of them close.