b. 'remote viewing' - when one person's mind obtains significant amounts of accurate information about a location previously unknown to him or her, that also is too distant for the perceiver to see with their eyes, and furthermore is blocked from their eyes by many barriers including walls, buildings, mountains, etc.

c. 'precognition and presentiment' - when one person's mind (cognition) or body (sentiment; feeling) registers information accurately about an event before that event has taken place ('non-locality' across time).

a. Accepting Maxwell's original equations' inclusion of terms describing magnetic monopoles and the flow of such monopoles as a magnetic current taking place in at least some portion of space-time (Harmuth 1986; Barrett 1988; Seiberg & Witten 1994), Tiller proposes that human minds can, through concentration and meditation, move into a state of coherence greater than U(1) and approaching SU(2) gauge symmetry in which they can impress upon such magnetic currents the information content of their mental images. These information modulated magnetic currents then can radiate outwards at speeds faster than light (up to c²) , and can be sensed – and their content can be read – by other human minds.

b. Tiller envisions these magnetic currents as traveling in a particular region of space-time which includes the quantum vacuum (into which particles have empirically been observed to disappear and from which they have been observed to emerge).

c. And Tiller cites the laboratory measurements of humans radiating high electrostatic charge at will (Green 1991) as indicative of the possibility of such a 'broadcasting' telepathic mechanism.

a. All objects in the Universe contain information at the quantum level regarding their current as well as their past states (their "event histories"), because waves impinging upon each object are partly absorbed, partly reflected, and partly de-flected, thus conveying outwards detailed indications about the structure and character of that object (much as macro-level radar and sonar operate, including "nature's own sonar" evolved by bats, dolphins, and whales).

b. Such specific alterations in the amplitude – and especially in the phase - of quantum-level waves returning from an object are already used routinely nowadays to extract detailed information from human tissues, through devices the public knows as "magnetic resonance imagers" (MRIs) (Schempp 1998 & Schempp 1992).

c. Mitchell's team proposes that the human mind can similarly compose meaningful images of even far-away objects by focusing its attention toward those distant locales, because when we "attend to" a specific object or location, we are actually – they propose – sending outwards a quantum wave which establishes a standing-wave interference pattern with quantum waves emitted by the distant object or location. Mitchell et al. call this the establishment of a "phase-conjugate adaptive resonance" with the object. And they cite as possible indications of such outward-going mental waves the telekinetic laboratory demonstrations of Schmidt, Jahn and Dunne (Schmidt 1970; Jahn & Dunne 1987; Princeton Engineering Anomalies 2007).

d. So long as that vibratory resonance is maintained, they argue, the individual's neural structures can apprehend holographic information about distant objects available through quantum entanglement. And this holographic information is converted by the brain through the known, neurological Discrete Fast Fourier Transform process (De Valois 1990; Pribram 1991 & Pribram 2004), into visual imagery and other conscious sensations.

a. Extending relativity theory's Einstein-Minkowski 4-dimensional space-time into eight dimensions, they conceive of the four additional dimensions as counterparts, being three additional space dimensions and one additional time dimension.

b. Mathematically, the four new dimensions are designated by multiplying the original dimensions (x, y, z and t) by the square root of -1 (conventionally symbolized as the coefficient i).

c. This has the consequence that between any two points in the 8-dimensional universe there is always a path that has zero units of separation. (In near-layman's language, non-locality is thereby demonstrated to be true of time, not just of space.) Thus any two points in time can become adjacent; for instance, something that will happen in the future we can be aware of now (as the laboratory experiments on presentiment and precognition seem to confront us with [Biermann & Radin 1997; Biermann & Scholte 2002; Honorton & Ferrari 1989]).

d. Rauscher and Targ's eight-dimensional space-time metric does not violate any of the equations of Maxwell, Einstein, or Schrodinger. The "transactional" interpretation of quantum mechanics by John Cramer (Cramer 1986; Price 1996) might even require the kind of attention to connections between the 'future' and the present which Rauscher and Targ have explicated. Likewise, Polish theoretical physicist Bialynicki-Birula insists:

"The very structure of all quantum theories suggests…that two copies of spacetime, rather than one, are the proper arena for all quantum processes. … Every set of equations and formulae in quantum theory, from which all the transition amplitudes are determined, may always be written in two equivalent forms, differing by complex conjugation. We obtain one set from the other by reversing the sign of the imaginary unit i." (Bialynicki-Birula 1986).

a. More fully, Schild represents conventional spacetime (which Tiller called "Direct" subspace) and Frequency sub-spacetime via the following mathematical expressions:

Conventional (or Direct) spacetime:

The line element describing any infinitesimal interval in conventional space-time has the minus sign before the spatial component, requiring all real solutions to be "time-like".

Frequency (or Reciprocal) sub-spacetime:

Here it is not yet clear if the algebraic sign should be positive, which creates solutions that can be any arbitrary form. Or should the sign possibly be negative, creating propagating waves for time-like solutions? Because he will be looking for solutions of the Einstein-Maxwell field equations, and because non-propagating solutions will probably be needed to describe quantum wave-forms, Schild tentatively prefers the plus sign.

As these show, Schild emphasizes that Frequency sub-spacetime "is very restricted", i.e., confined to the counterparts of conventional spacetime's x, y, z and t dimensions. Note, however, that such a formulation does not require a further multitude of dimensions beyond the basic Einstein 4; instead it is similar to the Section 4 set of "imaginary" solutions.

b. Further, Schild asks – along with symposium participants Pracna and Bernstein – to what extent events within Frequency sub-spacetime might additionally be well-described by applying the projective algebraic-geometry Cremona transformation discoveries of symposium host Metod Saniga (Saniga 2000, 2002, 2004). Those transformations convert a point in conventional 3D-space into a line, and convert one moment in our conventional time dimension into a conic (parabola, hyperbola, or ellipse, etc) (Saniga 2001). In such "projective space", human experiences can be tracked and differentiated as intersections across those lines and conics, and as meaningful separations from those lines and conics (Saniga 2005).

c. This brought Bernstein to consider whether the transform mentioned by both Mitchell's team and Tiller - namely, the discrete fast Fourier transform that has been shown to play a concrete role in both the human brain's storage of perceived experiences (De Valois 1990; Pribram 1991 & Pribram 2004) and in the hologram's storage of quantum-level information (Mitchell & Staretz, in press) -might also describe the transitions to each other between conventional spacetime and Frequency sub-spacetime, through a complete set of Maxwell's equations. One is strongly led to this question because the transformation accomplished by the Fourier algorithm is exactly a conversion of ordinary spacetime's events into frequency data.

a. One clue might be from Tiller's implication that it is across the sub-spacetime boundary that sub-atomic particles have been observed to 'disappear' into the 'quantum vacuum' (of which Tiller proposes Frequency ("reciprocal") sub-spacetime to be "the coarsest layer"). Perhaps this "disappearance" – to our instruments – occurs when particles' wave nature comes to predominate over their particle-nature? And vice-versa, when particles suddenly appear out of the vacuum, is it perhaps that their wave-nature (which Tiller says predominates in frequency-subspacetime) is becoming overpowered by their particle nature, and therefore we in conventional spacetime can suddenly perceive them? Is the quantum vacuum thus one empirical indication of the actual existence of Frequency sub-spacetime?

b. To what extent does the boundary behave like a 'membrane'?

c. Pracna put forth the idea of the relation between conventional spacetime and Frequency spacetime being encoded in the Cremona transformation (CrT). In this context the question emerges, "What is the relation between the CrT and the discrete Fourier transformation (DFT)?"

d. Pracna further asked Symposium attendees to consider:

e. Similarly, one asks whether the impedance observed at the boundary of the vacuum might be occurring because indeed there is a Frequency spacetime there which, as Tiller proposes, already contains a predominance of magnetic events, and those need to be 'pushed' or curved in order to accept any large electromagnetic input from conventional spacetime?

a. Initially, we were discussing it as if phenomena which first occurred in conventional spacetime would perhaps have to approach a fixed boundary, and then cross over that, in order to get into frequency spacetime:

b. Subsequently, Pracna introduced a diagram which places conventional spacetime within a 'larger' field of Frequency spacetime which also expresses an implication that Frequency spacetime might be the more fundamental, and even in some sense the "pre-existing" or "sourcing" ground of, our conventional spacetime:

c. In subsequent discussions this concept was further refined to the Frequency spacetime existing as 'parallel' to conventional spacetime, the two being mutually interconnected by the discrete Fourier transform or by the Cremona transformation:

e. Schild agreed with such an "omni-presence" of frequency spacetime, but he strengthened the reasoning underlying such a model by recalling to us the postulate that had initially moved the Symposium into this exploration of two spacetimes; namely, that conventional and frequency spacetimes participate in a common set of eight dimensions. In Schild's words:

"What's necessary is to grasp the fact that every point in our conventional (x,y,z,t) spacetime has a superposition of four more dimensions in which quanta of something else (information) exist at all times."

Although picturing 8 dimensions on a piece of flat paper requires compromises, an illustration of one point with its 8 dimensions is offered below.

f. Pracna cautions that there may not be such a simple one-to-one correspondence of origin points in the two spacetimes as shown in Fig. 3. So he urges us to consider the revised diagram presented in Fig. 4.

a. Tiller's writings emphasize that this other spacetime region is characterized much more by magnetic forces, and much less by electric events, than is conventional spacetime. He therefore offers the label "magneto-electrism" for that region's main force, to contrast with conventional spacetime's electro-magnetism, although he emphasizes that these two forces remain closely related to each other.

Likewise, Tiller suggests that the wave-particle duality observed in conventional spacetime is probably inverted in Frequency spacetime, in that wave-nature is much more present in that alternate spacetime than is particle-nature.

b. Schild proposes that waves in Frequency spacetime might be quadrupole, rather than dipole as they are presumed to be in conventional spacetime.

He also suggests that "dark energy" might be characteristic of Frequency spacetime, and that such energy might be increasing over time due to the growing number of living organisms in the Universe. He further notes that empirical observations already made of dark energy traveling faster than the speed of light (Salart 2008) accord with Tiller's view of Frequency space-time allowing for magnetic currents to travel at speeds up to c².

c. Pracna proposes that time in conventional spacetime only emerges (i.e., can be measured, and can be used to relate accelerations to forces) because of the existence of bound systems, and that time might not exist as an independent fundamental property. It is the frequency (in other words, the periods) of internal motions (vibrations) of constituents in a bound system that defines the unit of time relevant for that system, and for that system's interactions with other bodies (again considered as bound systems) in conventional spacetime. Timescales shorter than the periods of internal motions of the bound system are meaningless to it, unless the constituents of the bound system have themselves an internal structure in which there are motions having even shorter periods (higher frequencies).

Each such bound system represents a special level of hierarchy in which certain physical properties emerge. For example, specific heat or conductivity are not properties of individual atoms, but only of atoms bound into a crystal lattice.

From this also follows the question, "What is the counterpart of such hierarchy in Frequency spacetime -- not only in its 'frequency' (time) dimension but also in its 'spatial' dimensions?" Together with that, we may ask whether a fundamental property like inertial mass might not emerge at a deeper level of hierarchy, or in some so-far-unconceived hierarchy within Frequency spacetime.

d. This led Bernstein to suggest that such a possibility for time differences between conventional and frequency spacetimes might make possible the >c velocities of magnetic currents within Frequency spacetime that Tiller has derived.

e. Pracna notes, additionally, that rotational degrees-of-freedom of bound systems like molecules and their symmetry are qualitatively different from vibrational degrees-of-freedom and symmetry. Should rotational behavior demand our special attention here in light of Schild's observation of the centrality of spirals or coils as significant forms of energy propagation in living ("sentient") – and sometimes even crystalline – systems?

f. Neslušan proposes that at its most fundamental level, our Universe might be composed of certain 'waving' elements, which give rise to the waves and particles we observe in conventional spacetime once their amplitudes are at a sufficient level, but which are not always apparent to us because as they continually oscillate they also participate in Frequency spacetime. To describe them mathematically seems to require both the real and imaginary components of complex numbers.

ii. Does perturbation of the quantum hologram occur? ( e.g., does the sharpness of its content deteriorate?).

iii. What is the attribute of mass that causes mass to curve conventional spacetime?

iv. If the wave associated with a particle is actually evanescent, what is producing the resistance of spacetime that results in the decrease of a wave's amplitude with increasing distance from the center of 'waving'?