The most basic phenomenon, the link between mind and brain, becomes in this sense, an integral part of the paranormal and, I believe, can be analyzed as the starting pont for the study of other paranormal manifestations such as psychokinesis which has a very obvious connection with the link.

We will consider that the total quantity of information H_tot in an isolate process, i.e., one that does not exchange energy with the exterior, be it through matter or through a field, remains constant in time, that is H*_tot = 0  (1).  Generally we can define for a given instant, that H_tot is the sum of syntactic H_i, semantic H_e, and esthetic H_s type information: (2):

H_i + H_e + H_s = H_tot

In this study we will consider, in accordance with the theories of the significant and the signification (3), that esthetic information is a non-linear function of the other types of information.  Therefore we can reduce the previous equation to

H_i  +  H_e  = H_tot

or even, as conjectured:

H*_i  +  H*_e  = 0

2.  NEURONAL PROCESSES HIGHLY SIMPLIFIED

3.  INFORMATION

In 1877, Boltzmann defines entropy, which had previously been deduced by Clausius, from the thermodynamic point of view, that is as being proportional to the probability P of the state of a system of particles:

S = in P

Nearly 60 years later, Shannon and Wiener (5) respectively dedicated to the study of information and communication, observed that the quantity of information H, according to the theory of measurements, could be practically defined as the inverse of entropy.  Thus, a measurement being made in the interval (a, b), within an interval (0, 1) containing the former, the probability P of the measurement is:

        measurement (a, b)
P =
        measurement (0, 1)

In the above observation, the quantity of information H was practically defined as:

H = - in P

Extending the definition to the density of probability functions, or the f distribution functions, instead of simples measurements we see that, as certain distribution will always be normalized, then:

Thus Neumann reasonably considered that in this case of the distributions,

Finally, it is interesting to see that while a change in entropy results in an isolated system tending towards a chaotic state of equilibrium, the supposed physical variation, of information following the inverse of the principle of growth, reduced itself over time in the same manner.  However, here we are dealing with material, physical or energetic systems.  Non-syntactic systems, as we shall see, tend to subvert these principles, shedding light on the obscure mind-brain enigma.

4.  PSICONS AND THE MIND

Previously we posited that semantic information He was related to mental processes.  A question remains, however.  What does one understand by the mind?

Without foolishly trying to materialize the mind, we call the quantum of the semantic particle a (6) psicon so that the associated wave, because of the duality particle/wave, is ψ_P where ψ_P is the well known function of the plane quantum wave, without, however, any interference from material particles:

ψ_P = e ^{i (kx -ωt)}

This function, where k, wave number, non-indeterminately, is related to the length of the wave and where ω, also non-indeterminately, is related to the frequency of the wave, is commutative when faced with the operator of uncertainty:

This means that Heisenberg's principle of uncertainty of no longer valid when the result of commutation produces an imaginary velocity:

with Ћ being Dirac's constant, v the velocity, and m the mass related to ψ_P.  Thus as m is real, and without damaging the equation for relativistic mass, one arrives at the imaginary superluminous velocity:

We have the same concept as Popper (7) for whom the destruction of uncertainty results from the knowledge of theory, that is from semantic information.  The possibility of absolute knowledge of two non-commutative quantities in the physics of the world presupposes that k and ω respectively related to the amount of movement and the amount of energy, are perfectly determinable, in such a way that

∆ x = ∆ t = ∞

signifying that the psicon is an imaginary vacuum, that is, the total  P_P probability

As the exact probability is

this makes ( 8 ) the chain of probability for non-interactive particles:

meaning a cluster of particles with (superluminous) velocity.

5. SEMANTIC INFORMATION H_e

In possession of a physical mathematical description of purely mental processes and taking these isolated processes to be related to semantic information He one finds, as foreseen, that:

where P_P is the probability of a given psiconic state.  Taking the definition of psiconic waves in an interval x one will get for n particles

The temporal variation of

This equation will always be negative because the numeric term is always positive, expressed in the number of psiconic particles per interval  of time.

6. HORTA  SANTOS'S INFORMATIONAL HYPOTHESIS FOR THE BENDING OF METALS BY PSYCHOKINESIS (PKMB)

One of the most important, recent paranormal phenomenon is the bending of metals through psychokineis.  It would appear to be a phenomenon based on energy as pieces of hard metal are bent, possibly by using energy.  However, there are cases in which the pieces of metal are very thick and it would only be possible to bend by using machines capable of applying inhuman force.  As sometimes there is a softening of the metal just a small effort can make it bend, or it can even bend without the use of any force, that is, by itself.  This non-chemical softening of various sections of the piece, led Dr. Horta Santos to suggest (9) that the bending of metals did not take place through the use of energy, but rather through a process using information and probabilities.

His hypothesis briefly described is as follows.  As we know, metals, when formed by a net work of crystals, give off electrons from the outer wave bands of energy producing an ionic network and a cloud of free electrons which are responsible for the metallic union.  These electrons, in the form of gas, move with a certain amount of ease through the ionic network, and with very low probability, might become incorporated into the incomplete paths, as if there had been a return to an earlier state but with a significant increase in information.  The completion of the outer layers of the atoms during this return, would result in a lack of metallic cohesion in some parts of the piece of metal, making it plastic.  In this case, a small effort, or even the internal tensions resulting from the structure's modification, would easily bend the piece owing to the improbable reduction in its cohesiveness.

To verify the validity of Horta Santos's hypothesis, he, together with a team of parapsychologists from ABRAP and paranormal Antonio Alves Ferreira adopted the following experimental procedure, drawn out below

If, after placing the above circuit under the influence of the paranormal, a return of the electrons forming valance bands was to occur together with the softening of the piece, the electrical resistance would increase causing a voltage drop.  The test failed because the paranormal did not manage to set off the process.  Or in the language that we are using, the link between the paranormal's mind and the metallic structure was not established.  However, Dr. Horta Santos's hypothesis has the great value of being testable experimentally and can consequently validate the theory that we are presenting, given that, if, as already seen, H* e is negative, then H* i is positive:

H* i > 0

that is, the variation of syntactic information in time will be positive if the link is established.

7.  BEHAVIOR OF THE SYNTACTIC DISTRIBUTIONS DURING THE LINK

Adopting Von Neumann's concept of information, for distribution ƒ of elementary particles, one finds that (10):

being  the vector speed found for distribution  ƒ.  If  is the number of particles  which in the time t respectively have a speed and position in  d³ v e d³ x,  then

Let us say, for the purpose of unity, that  Hi = ∫ ƒ1n ƒd³ v  which gives the volume density of the syntactic information, when no spatial gradients exist to influence the distribution of the particles.

Generally (Boltzmann), in the case of   type particles, differentiating the ƒ distribution given previously, in relation to time:

in which the term on the right, (unopened), is the term of collision between the particles and "a" represents the acceleration coming from external forces.

At this point, I would like to stress that the macromolecular neuronic structures, principally the pyramidal, basal and cerebellar ones, must always reflect some micro distribution of elementary particles, of the generic type , of the type that we are dealing with (for example: electrons).  This being the case, the neuronal configurations in the brain, basically digitized, are the result of microphysical distributions, ultimately responsible for the motor activity efferent to the brain.

Supposing that there are no external forces, or spatial gradients, the unopened term of the collision, in number per interval of time, that is, the flow, will be (10)