A Magic-Coin Toy Model: Visualizing the Limit of Anonymity (0, 1, 2) and the Denial of Hidden Variables

A tabletop magic toy model that visualizes, before any formula, two claims from section 0.5 of the related report (On the Logarithmic Map of Scale and the Separation of Scale and Quantization): (1) the limit of anonymity = 2, namely that in the system-interior 0 and 1 cannot be distinguished and 2 and 2-or-more cannot be distinguished; and (2) the denial of hidden variables, namely that even when everything inside is shown there is no clue to separate the count. The apparatus is a semi-translucent frosted cup on a digital scale (the exterior, additive conserved total) next to a CRT monitor that displays the image filmed by cameras attached to each coin, where a camera cannot film itself and films only the others (the interior, anonymous viewpoint). Four scenes (0, 10, 20, 30 g) show: 0 indistinguishable from null; 1 indistinguishable from 0; difference standing at 2; and 2 indistinguishable from 2-or-more via a slightly offset cheated stack that appears as a double edge on the monitor. This is an intuitive illustration, not a rigorous proof; the denial of hidden variables here is not in the sense of Bell's theorem.