What if "quantum" basically means "meeting" (the idea of generalised "2" in math?); and "relativity" basically means "meeting a meeting" or "3" in math say?
Einstein's geometry treated "time" differently from space; so was a 1 + 3 geometry.
Having ALREADY separated quantum (meeting) from relativity (meeting meeting) by saying 1 meets 3 (quantum that is two-ness where "1" meets (is "two with") "3") so having used a geometry that seems to separate "three-ness" (relativity) from "1 meets something" (quantum): Einstein could not define these as fully separate in his geometry as that would clash.
So Einstein's geometry echoes the famous double-slit experiment: you cannot pin down a quantum theory with a relativity theory at the same time: as they are defined into his very geometry as different times.
Now how does Dr. Dick's simple 4-geometry achieve defining relativity and defining quantum mechanics without clashing?
By ALREADY using a geometry which mixes these together (it doesn't say which in the "4" is "3" (that is: relativity) and which in the "4" is "1 meets something, say e.g. "1 meets 3" (that is: "a quantum" ("meeting").
So having CLASHED quantum mechanics and relativity ALREADY in his simple 4-geometry: Dr. Dick is able to DEFINE them at the same time (because they are free to share the same time in his 4-geometry?)
However; the price paid is "time" gets muddled (cause and effect get to seem swappable say?).
And Dr. Dick's system naturally projects 4-ness (so in Chap. 5 he writes of rotations of n-dimensional polygon).
By using a non-specified "4"; he can construct a 3-space (relativity theory) and a "1 meets 3" space (quantum electrodynamics). "1 meets 3" redefined gives a potential swapping of roles of what does "1" refer to and what does "3" refer to.
In two cycles of seeing the 4-geometry of Dr. Dick; you can get "4th axis virtual particle exchange as QED" ("particle" I call here "1 meets group").
Stephen Hawking's work fits in neatly; the idea of "imaginary time" is a partial transcribing of Einstein's "3 + 1" geometry into Dr. Stafford's "4" geometry by using "3 + 1; alternative 3 + 1" geometry?
Fischer sampling: I don't know about this but my guess is the "samples" are "chunks of 4-ness" (layered 4-ness e.g. 4 to power of 4) taken from a geometry of "imaginary matter" where you have "4 + 4" geometry?
Doesn't sound quite right? Trouble is I don't know about Fischer sampling except what Yanniru said about it being said to be like Dr. Dick's system...
So an idea might be: they have double-defined Dr. Dick's system to get a sampling system; just as Hawking-Hartle maybe double-defined Minkowski geometry to get a cake-projection (instead of sampling a cake; they project a cake because they have generalised "sample" as "two-ness" or time + imaginary time?)
Lot of guessing in my comments re: Fisher sampling!
(Mississipi John Hurt: you heard him sing / play guitar? He sometimes leaves out words in the lyrics but keeps on going with the music. Maybe my physics style....?)