Roy,
Thanks for that response.
Yes, by presenting every assumption in the order that he makes them, I've somewhat overstated the number because of redundancy. I'm not sure it shrinks to 2 however.
I see his assumptions [2..4] as a leap of faith. Assumption [4] is probably the weakest, since as I remarked, the mass/area relations can be found with no mention or use of the concept of information. If then the fact that both mass and entropy are additive is used to assume some equivalence that leads to the Holographic Principle, this may or may not be appropriate.
We may misunderstand each other on the issue of 'territory from a map". You seem to view it as an 'inverse mapping': "a full 'map back to the territory' ...would require further information such as physical composition to be specified." But I am not referring to a "map back to the territory"; that implies that both territory and map exist and are somehow isomorphic. I am referring to what I interpret as an increasing tendency to start only with a map and use this to 'produce' the territory [versus starting with territory and producing a map.]
It seems that many are starting with information and trying to create physical reality. Tegmark's "Mathematical Universe" may be a prime example of this. Some seem to expect symmetries to give rise to particles, rather than the other way around. Maybe I'm misinterpreting them. Anyway, what I am objecting to is any attempt to create physical reality from information. Korzybski was addressing such confusion between representation and reality, imo. To expect to derive physical reality from info is as if physics is saying "In the beginning was the Word".
The map is figuratively and literally derived from the territory. The territory can never be derived from the map. One can't start with a Texaco map and create the Rocky Mountains and the Great Lakes.
And even if information is understood to be 'about' things, it is very hard for me to swallow Verlinde's fourth assumption: "info about particle location is stored in discrete bits on a screen", with or without assumptions [5] and [6].
In trying to understand where these ideas come from, they seem to be a generalization of Cauchy's integral formula
f(a) = (1/ i 2pi) Contour_integral [ f(z)dz / (z-a)]
which applies to "conservative" potentials. That may be why it is necessary for Verlinde to begin by introducing an 'effective' force that is conservative macroscopically. Cauchy shows that every interior point can be determined by the points on the boundary.
Susskind, in "Black Hole War", claims that "the entropy of a black hole is about equal to the area" and also that "hidden information is proportional to the total length of a string" and, since "the mass and entropy of a string are proportional to its length" [then] "entropy must be proportional to the mass" [later mass^2].
If, per Verlinde, both entropy and mass are additive, then an increase in mass might be made to imply an increase in entropy. Whether this is physically meaningful inside a black hole is questionable, especially so if it depends on the existence of strings, and even more so if [Susskind:Cosmic Landscape] "the quark ends [of the string] are most likely to be found far away *at the very edge of the universe* [his emphasis].
In The Automatic Theory of Physics I discuss a Monte Carlo Random Walk procedure that, in walking from an arbitrary point f(a) to a boundary, pretty much reproduces Cauchy's integral formula. To go from these connections to strings is a very big step.
I believe that by mistakenly assigning physical reality to information, sometimes treating it like a particle, sometimes as energy, and assuming things like [5], physicists are building castles in the air or perhaps a house of cards. In my opinion 'qubits' may be less a physical reality than a consequence of the incredibly complex 'apparatus' used to prepare them--without this apparatus, there may or may not be 'qubits'.
The more physics comes to depend on 'out of this world' ideas, such as the Multiverse and the insides of black holes, the farther out on a limb it climbs. In the worst case, like Climate-gate, there will be a crash of public confidence in such outlandish theories, that come to be seen as indistinguishable from other religions.
Edwin Eugene Klingman