Dear Dr. Gerlach,

It is a great pleasure to read your papers. May I share with you some thoughts prompted by your observation that "to exist means to have specific properties" [Ref. 1].

It seems to me that we can grasp an entirely new mathematical object which can be described, in psychological terms, as the UNspeakable,

http://members.aon.at/chakalov/Vecchi.html

I believe the UNspeakable reflects a peculiar mode of *physical reality* of things being 'neither true nor false', hence they become UNspeakable. In psychology, we call it 'context',

http://members.aon.at/chakalov/Bushara.html

It is like a virtual dough of potential values of physical quantities kept in the Holon,

http://members.aon.at/chakalov/faq.html

If all this is correct, the implications could hardly be exaggerated.

As to the problems with the quantum formulation of the *source* of gravitation [Ref. 2], I believe we should start from the tacit presumption that there is 3-D space in classical GR,

http://members.aon.at/chakalov/Zeh.html#falsifiable

I dare to challenge this presumption, since I believe it is the Holon which creates 3-D space, but there is no room for it in present-day classical GR.

I will highly appreciate your professional comments.

With kind regards,

Dimi Chakalov
http://members.aon.at/chakalov
--
Dead matter makes quantum jumps; the living-and-quantum matter is smarter.
 

References

[Ref. 1] Ulrich Gerlach, LINEAR MATHEMATICS IN INFINITE DIMENSIONS, 2003-04-06, Preface,
http://www.math.ohio-state.edu/~gerlach/math/BVtypset/node1.html

"The effectiveness and the power of mathematics (and more generally of logic) in this regard arises from the most basic fact of nature: to be is to be something, i.e. to be is to be a thing with certain distinct properties, or: to exist means to have specific properties. Stated negatively: a thing cannot have and lack a property at the same time, or: in nature contradictions do not exist, a fact already identified by the father of logic^11 some twenty-four centuries ago. [Footnote 11: Aristotle, the Greek philosopher, 384-322 B.C]

"Mathematics is based on this fact, and on the existence of a consciousness (a physicist, an engineer, a mathematician, a philosopher, etc.) capable of identifying it. Thus mathematics is neither intrinsic to nature (reality), apart from any relation to man's mind, nor is it based on a subjective creation of a man's consciousness detached from reality. Instead, mathematics furnishes us with a quantitative link that connects reality to our consciousness. Mathematics allows our consciousness to grasp, in numerical terms, the microcosmic world of subatomic particles, the macrocosmic world of the universe and everything in between.

"Linearity is as fundamental to mathematics as it is to our mind in forming concepts. The transition from recognizing that  x + y = y + x  to the act of grasping that  a + a = 2a  is the explicit starting point of a conceptual consciousness grasping nature in mathematical terms with linearity at the center. Thus it is not an accident that linear mathematics plays its pervasive role in our comprehending the nature of nature around us. In fact, it would not be an exaggeration to say that "Linearity is a *sine qua non* in our grasping of nature in conceptual terms".
 

[Ref. 2] Ulrich Gerlach, Quantum Mechanical Carrier of the Imprints of Gravitation, 1998-02-20, Phys. Rev. D 57 4718-4723 (1998),
http://www.math.ohio-state.edu/~gerlach/qm_carrier_imprints_la/index.html

The Wider Perspective,
http://www.math.ohio-state.edu/~gerlach/qm_carrier_imprints_la/node11.html

"We comprehend gravitation in two stages. First we identify the agent which carries the imprints of gravitation. In Newton's formulation this agent is the set of particle trajectories, in Einstein's formulation the set of particle world lines, and in the quantum formulation the set of correlations between the wave amplitudes in a pair of oppositely accelerating Rindler frames.

"In Newton's formulation the imprints consist of the bending of the particle trajectories, in Einstein's formulation they consist of the deviations of the geodesic world lines, and in the quantum formulation they consist of the deviations of the correlations away from the "Planckian" and the "fluctuation" spectral values given by Eq. (13).

"The second stage of our comprehension consists of relating these imprints to the source of gravitation. In Newton's formulation this relation is the Poisson equation, in Einstein's formulation the field equations of general relativity, and in the quantum formulation we do not know the answer as yet."