When light reflects at a mountain at the distance, all the information is restored in a beam of light, which is heading towards us. To a certain extent, it does not matter how narrow you choose that beam of light, when we conjugate the information by using the lens of a camera, you will get the whole picture of the actual mountain. And depending on the strength of your lens, you could recover the information about surface texture or microscopic structures of each point in the mountain. If we had a stronger device we could even extract the atomic or even subatomic structure information of every miniscule of the distant mountain. If you think about it, this is a lot of information for a tiny beam of light to carry. Although the Bekenstein bound put a limit to amount of information that we can get from a screen with a limited area. The number of bits of information available will be less than one quarter of the area of the screen in Planck units. Nevertheless, It is still tremendous amount of information. Let us see how this happens? How do we recognize a spatial object, which exists say about 20 km away from us? You will say the light hit the mountain and part of it gets reflected and travels to our location. A part of the beam of light passes through our eye lenses and hit the retina. From there the action potential transfer the information to our brain and somehow our brain interprets it. In this way we come to realize that there is a mountain twenty kilometer away. Let's investigate it further. Originally the beam of sunlight was just carrying the information about surface of sun. After it hits the distant mountain, it takes the bulk of information from our spatial object and includes it in the light wave. Underneath I use Dr. Jeff Prideaux's interesting description of holography.

The act of converting spatial forms to frequency domain is determined by Fourier transform formula. The Fourier transform (and inverse Fourier transform) consists of convolution integrals, which mathematically smear or de-smear the information. For continuous functions, the Fourier transform and inverse Fourier transform are as follows (for transforms between the time and frequency domain):

The Fourier transform also has meaning between a spatial domain (for instance the position in two dimensional space) and spatial frequency. Mathematically, the two-dimensional spatial Fourier transform is

and the inverse transform is

where x and y are spatial coordinates and a and b are horizontal and vertical frequencies. (Ref 19)

When we put a lens and screen in front of our beam of light we change the frequency nature of information and convert it to a spatial image. We are doing inverse Fourier transform.

Figure 4 Diagram expressing the holographic nature of light incident on the surface of the lens of the eye. (Ref 19)

Please note that the nature of light is electromagnetic energy not spatial. This is exactly the same concept that I am trying to convey about singularity. The proposed singularity contains information and can accommodate the information of four-dimension space just like the beam of light, which accommodate the information of our object, and its space.

Non Locality

Hologram also offers a solution for non-locality. If we where at the foot of the mountain, and were trying to climb the mountain and reach the peak, it would need a lot of time and effort. That is how we actually notice the distance in human terms. If we use a helicopter, it takes less amount of time. Even if we go with the speed of light, although we reach the peak much faster, but it still takes some fraction of second to go from the foot of the mountain to the peak. The important fact is that, there is no distance between the foot and the peak in our beam of light. One can choose smaller and smaller diameter beam and still get the information of far apart points in it. All of the sudden there is no locality and everything will fall on top of each other. So we face non-locality in frequency domain. A lens helps us to diffract the information from the beam of light and the screen assists to extract the information. A lens and a screen apparatus perform the inverse Fourier transform and converts frequency information to spatial information, which we can interpret and understand.

In 1993 the famous Dutch theoretical physicist G. 't Hooft put forward a bold proposal. This proposal, which is known as the Holographic Principle, consists of two basic assertions:

Assertion 1 The first assertion of the Holographic Principle is that all of the information contained in some region of space can be represented as a `Hologram' - a theory that `lives' on the boundary of that region. For example, if the region of space in question is the Coffee shop, then the holographic principle asserts that all of the physics, which takes place in the coffee shop, can be represented by a theory, which is defined on the walls of the Tearoom.

Assertion 2 The second assertion of the Holographic Principle is that the theory on the boundary of the region of space in question should contain at most one degree of freedom per Planck area. (Ref 18)

I assumed that the information in space-time, in its entirely, is reflected and registered in singularity. To make it objective, Holographic theorists convert the whole ordeal to spatial form again but with one dimension less and present it to us. On proposed singularity we can ignore the inverse Fourier transform and imagine that information remains in spectral state while in singularity. We do not have to pass to spatial state (conjugate) and look at the shadow in the wall to realize that information is out there. Or we may do that for objectivity reasons, but at least we'd appreciate and recognize the spectral state of the information. That is what I am trying to convey about the singularity part of the reality. The Holographic theorists stay in the boundary. I am not sure why we have to stop there. We have enough information to dare passing the border; at least our imagination should help us building theories and present them for speculation and investigation. Meantime if we establish a sound theory for mind function, we can utilize mind activities as analogy to explore beyond finite world. Holographic theory, says that all the information can be present in space with one dimension less. Holographic theorist and M theorist found out that the answer of major paradoxes couldn't be found in our 4-dimension space-time. To find solutions they had to look out of our tangible space. My question is why did they have to assume and expand the dimensions of space to create an arena to solve the paradoxes? Why couldn't we untie and free ourselves from space boundaries? We know that dimensions and space are not absolute.

In my proposed singularity, information is present in no dimension, in an entity out of spatial domain. If we know that space can be expanded and contracted, we also have to accept that space can cease to exist in some arena, as it would happen in pre-big bang era. I freed myself from ties. I passed the boundaries. I jumped off the cliff. And guess what? It was not dangerous or scary at all. There was not just darkness. A new tangible and deterministic world exists out there. We can take the risk and receive the rewards. Now it seems to me that the major paradoxes possess explanations if we leave our ken. We will look at those paradoxes later together. Meanwhile let me add this beautiful piece from University of Cambridge DAMTP web page. (Ref 18)

To them, I said,
the truth would be literally nothing
but the shadows of the images.
-Plato, The Republic (Book VII)

Holography Through the Ages

Plato, the great Greek philosopher, wrote a series of `Dialogues', which summarized many of the things, which he had learned from his teacher, who was the philosopher Socrates. One of the most famous of these Dialogues is the `Allegory of the Cave'. In this allegory, people are chained in a cave so that they can only see the shadows, which are cast on the walls of the cave by a fire. To these people, the shadows represent the totality of their existence - it is impossible for them to imagine a reality, which consists of anything other than the fuzzy shadows on the wall.However, some prisoners may escape from the cave; they may go out into the light of the sun and behold true reality. When they try to go back into the cave and tell the other captives the truth, they are mocked as madmen. Of course, to Plato this story was just meant to symbolize mankind's struggle to reach enlightenment and understanding through reasoning and open-mindedness. We are all initially prisoners and the tangible world is our cave. Just as some prisoners may escape out into the sun, so may some people amass knowledge and ascend into the light of true reality. What is equally interesting is the literal interpretation of Plato's tale: The idea that reality could be represented completely as `shadows' on the walls. (Ref 18)

At the time of recovery of information we need a spatial arena to use as a scene to represent the original information.

Mind as hologram another analogy

Earlier I mentioned that Holographic theory offers an explanation for the nature of mind. Now we can investigate it further. Experiments show that optical or other memories do not have to be stored in any specific location in brain. If any part of brain is experimentally damaged, still other live parts will show evidence of stored memory information. How do memories actually stored in the brain? A series of experiments were performed in both cats and monkeys (De Valois et. al., 1979) to see if the cortical cells responded to differences in the Fourier spectrums. The results showed that, the visual cortical cells respond to the Fourier fundamentals, not acting as an edge detector. In (De Valois et. al., 1979) experiment visual cortical cell respond to the angular location of the Fourier fundamentals and not to the edge of the squares (or grating) seen in the untransformed pattern. It also showed that the visual cortical cell was responding to the Fourier fundamental and not the edges (or distance between the edges) of the visual stimuli. (Ref 19)

This observed rotation matched the theoretical predicted rotation from the Fourier mathematics (De Valois et. al., 1979)

Similar experiments have been performed with the rat somatosensory system (Pribram, 1994) where the cortical cells were also found to respond to spectral information. (Ref 19)

Pribram says that both time and spectral information are simultaneously stored in the brain. He also draws attention to a limit with which both spectral and time values can be concurrently determined in any measurement (Pribram, 1991).

The holonomic brain theory maintains that the brain is continuously engaged in correlation processes. This is how we make associations (how the senses are integrated). There is an obvious computational advantage for the brain storing sensory information (and perceptions) in the spectral (or holographic) domain as opposed to the brain directly storing individual features and characteristics.The holonomic brain theory claims that the act of "re-membering" or thinking is concurrent with the taking of the inverse of something like the Fourier transform. The action of the inverse transform (like in the laser shining on the optical hologram) allows us to re-experience to some degree a previous perception. This is what constitutes a memory.The holonomic theory (for the example of vision) summarizes evidence that the image formed on the retina is transformed to a holographic (or spectral) domain. The information in this spectral "holographic" domain is distributed over an area of the brain (a certain collection of cells) by the polarization of the various synaptic junctions in the dendritic structures. At this point, there is no longer a localized image stored in the brain. Correlations and associations can then be achieved by other parts of the brain projecting to these same cells. Conscious awareness (and memory) is the byproduct of the transformation back again from the spectral holonomic domain back to the "image" domain. Possibly the most radical part of the holonomic theory is Pribram's claim that a "receiver" is not necessary to "view" the result of the transformation (from spectral holographic to "image"). He claims that the process of transformation is what we "experience". Memory is a form of re-experiencing or re-constructing the initial sensory sensation.

(So according to him, consciousness does not need a part of nervous system to physically accommodate it so it can appear. This views the mind, as separate entity from so-called physical brain, just like Plato viewed it.)

The conventional view is that the brain is a computational device. There is a growing body of literature, though, that shows that there are severe limitations to computation (Penrose, 1994; Rosen, 1991; Kampis, 1991; Pattee, 1995). For instance, Penrose uses a variation of the "halting problem" to show that the mind cannot be an algorithmic process. Rosen argues that computation (or simulation) is an inaccurate representation of the natural causes that are in place in nature. Kampis shows that the informational content of an algorithmic process is fixed at the beginning and no "new" information can be brought forward. Pattee argues that the complete separation of initial conditions and equations of motion necessary in a computation may only be a special case in nature. Pattee argues that systems that can make their own measuring devices can affect what they see and have "semantic closure". (19)

Experiment shows that selective damage to certain area of brain tissue will not erase the specific related memories. It further suggests that memories are restored as frequency.

Hopefully, Pribram's ideas (or variations on them) will eventually find their way into the consciousness of the conventional neurophysiologist (and appear in most textbooks) once the current fascination with molecular biology runs its course. Then the attention of physiologists may again be directed back toward a system's organization and away from simply analyzing its parts. (19)

Holonomic brain theory suggests that conscious awareness is a state of wave function and not material state entity. This conclusion is based on Neuropsychological experiments. Please see the references below for detail of some of these experiments.

References

18 - http://www.damtp.cam.ac.uk/user/gr/public/holo/

19 - http://www.acsa2000.net/bcngroup/jponkp/#chap1

© Copyright Jeff Prideaux along with electronic copy right ACSA and The BCN Group. All Rights Reserved. Posted by permission of the author.

Entropy

The second law of thermodynamics tells that the entropy always increases in any isolated system (figure 10). This simply means that if something is left to itself, it will move towards equilibrium...it will move towards maximal disorder...its internal energy state will tend to be minimized. There has not been, to date, any confirmed observation that this law is invalid. (Ref 20)

Figure 10

Our observation shows that our universe is behaving in the contrary. Our theories about the history of universe, not only denies progress to maximal disorder, but it actually suggests that it is moving to obtain more complex and sophisticated structure as we go along. It progressed from creating sub-atomic particles to atoms of lightweight. Second and third generation of stars is creating heavier elements. From there simpler molecules are generated and they further developed themselves to more detailed and complex organic molecules and their sophisticated functions. I do not have to go any further. Progress of organization in our world is obvious. So we need to look at another model for our world.

An isolated system can itself be divided into a subsystem that is open to energy flow and the subsystem's environment (see figure 11). As such, the whole combined isolated system still obeys the second law of thermodynamics, but it is possible that the subsystem can experience a decrease in entropy at the expense of its environment.

Figure 11

The entropy increase in the "sub-system environment" is guaranteed (by the second law) to more than offset the entropy decrease in the subsystem. Also note that the sub-system can only be maintained away from equilibrium as long as there is usable energy in its environment. (20)

The above model explains the chain phenomena in our space-time universe. Although the main order is entropy, but organization and differentiation continues. One can extend this concept to relation between proposed singularity and space-time, where space-time being a subsystem. The universe can accept structure at the expense of singularity. But we supposed the energy of singularity to be infinite. So our space-time can continue building its internal structure forever. In this model the entropy inside the space-time can decrease and order prevails.For this model to be acceptable, we have to assume that exchange of energy is possible in the borders of our universe.On the other hand, our world is not a place for random and unrelated structures. It seems that our world is goal oriented and follows a pattern of self-organization. As De Biase states, it continuously creates and recreates itself and explores the possibilities of new existence. Upon destruction of first generation stars and from their dust evolves second generation of stars, which are the source for heavier and more complex elements. Third and forth generation stars follow the mission and create even more complex atoms.Interestingly, the changes in far apart locations are similar and follow the same pattern. One interpretation would be that because the initial conditions have been the same and the laws of physics are similar, the changes are alike.Please note that, the possibilities of changes, especially at subatomic level are endless. If the world follows the same pattern in distant and far apart locations, we may conclude that, world is interconnected and goal oriented.For the world to be interconnected, it requires a non-local media. We assumed that media to be the singularity. Going back to Holonomic Brain theory, and its interpretation of brain function, we again encounter with similarities between singularity and mind.

"There is a special class of such subsystems (as described above) where the subsystem's organization comes exclusively from processes that occur within the sub-system's boundaries. This class of subsystems was labeled "dissipative structures" by Prigogine, 1984 (who won the Nobel price for his work)." (19)

To explain how the holonomic brain functions, Pribram suggests "dissipative structure" as a model.

One way of modeling a structure that goes to equilibrium is to minimize a mathematical expression for the internal energy (which is the same as maximizing an expression for entropy). Interestingly those factors have been present in every miniscule of the universe, thus, we are observing a logical pattern is called the least action principle. This would not be appropriate, though, for a "dissipative structure" since it is not going towards equilibrium. "Dissipative structures" self-organize around a different "least action principle". In the holonomic brain theory, Pribram states that in the brain, the entropy being minimized (which maximizes the amount of information possible to store) as the "least action principle". Thus, the system (the brain) self-organizes such that more and more information can be stored.

We can use the same subsystem model for universe and proposed singularity.

In Hopfield networks and the Boltzmann engine (which are computer models of neural processing), computations proceed in terms of attaining energy minima. In the holonomic brain theory, computations proceed in terms of attaining a minimum amount of entropy and therefore a maximum amount of information. In the Boltzmann formulation the principle of least action leads to a space-time equilibrium state of least energy. In the holonomic brain theory, Pribram describes the principle of least action as leading to maximizing the amount of information (minimizing the entropy).Independently, (in unrelated work) Schneider and Kay (1994) have proposed a variation on the second law of thermodynamics, which may be applicable to Pribram's holonomic theory." (19)

The above model for mind/brain relation can be Shown as diagram below

Wheeler (1990) and Chalmers (1995) realized how important the information is in such context. Chalmers, by stating that information must be considered as an essential property of reality as matter and energy, and that "conscious experience be considered a fundamental feature, irreducible to anything more basic". Wheeler, with its famous "the it from bit" concept that allows us to unite information theory to consciousness and physics: "...every it -- every particle, every field of force, even the space-time continuum itself -- derives its function, its very existence, entirely - even if in some contexts, indirectly - from the apparatus-elicited answers to yes-or-no questions, binary choices, bits". Norbert Wiener put this identity on the very conceptual basis of cybernetics stating that "information represents negative entropy", and prophetically emphasizing that "information is information, not matter or energy". Consciousness is conceived as a non-local flow of meaningful quantum-informational activity, interacting actively with each part of the universe through the holo-movement. (20)

Day dreaming, Dream and Unconsciousness

With the holonomic brain theory definition we can explain the phenomena by assuming that, the lens is removed, focus is lost, and we go to holistic phase or spectral domain.

References

19 - http://www.acsa2000.net/bcngroup/jponkp/#chap1

© Copyright Jeff Prideaux along with electronic copy right ACSA and The BCN Group. All Rights Reserved. Posted by permission of the author.

20 - http://www.merkabaweb.net/holo2.htm

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