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Negentropy Maximization Principle updated
by Dr. Matti Pitkänen / March 4, 2010
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Conscious existence is a continual recreation of the Universe.
My own humble contribution to this magnificent activity is endless updating of the chapters of the books about TGD. During this particular cascade of quantum jumps, I updated the chapter "Negentropy Maximization Principle" of TGD-inspired Theory of Consciousness so that Zero Energy Ontology and causal diamonds, hierarchy of Planck constants, and the vision about Life as something in the intersection of real and p-adic worlds (which is nothing but number theoretical criticality) are taken into account from the beginning. I managed to build a vision about what it means mathematically to be in this intersection and what it means for U-matrix.
I also found an expression for U-matrix as a collection of M-matrices so that these 2 matrices are not independent of each other as I had erratically thought. Unitarity of U states the orthogonality for the zero energy states defined by M-matrices. Very beautiful.
Number theory enters into game strongly. For instance, different algebraic extensions of rationals are regarded formally as quantum states and there is unitary dispersion in this space. Also the notion about leakage between different number fields at the level of partonic 2-surfaces leads to amplitudes expressible in terms of points of partonic 2-surface belonging to the algebraic extension of rationals. A kind of number theoretic Quantum Field Theory emerges naturally.
For the first time, I encountered really naturally infinite collection of commutative diagrams which mathematicians have used since the days of Adam and Eve. We theoretical physicists are rather slow in our reactions. I attach the abstract of the updated chapter below.
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In the TGD Universe, the moments of consciousness are associated with quantum jumps between quantum histories. The proposal is that the dynamics of Consciousness is governed by Negentropy Maximization Principle which states the information content of conscious experience is maximal. The formulation of NMP is the basic topic of this chapter.
Negentropy Maximization Principle (NMP) codes for the dynamics of standard state function reduction and states that the state function reduction process following U-process gives rise to a maximal reduction of entanglement entropy at each step.
In the generic case, this implies at each step a decomposition of the system to unique unentangled subsystems and the process repeats itself for these subsystems. The process stops when the resulting subsystem cannot be decomposed to a pair of free systems since energy conservation makes the reduction of entanglement kinematically impossible in the case of bound states. The natural assumption is that self loses consciousness when it entangles via bound state entanglement.
There is an important exception to this vision based on ordinary Shannon entropy. There exists an infinite hierarchy of number theoretical entropies making sense for rational or even algebraic entanglement probabilities.
In thiscase, the entanglement negentropy can be negative so that NMP favors the generation of negentropic entanglement which need not be bound state entanglement in standard sense. Negentropic entanglement might serve as a correlate for emotions like "love" and experience of "understanding". The reduction of ordinary entanglement entropy to random final state implies Second Law of Thermodynamicsat the level of ensemble.
For the generation of negentropic entanglement, the outcome of the reduction is not random. The prediction is that second law is not a universal truth holding true in all scales. Since number theoretic entropies are natural in the intersection of real and p-adic worlds, this suggests that Life resides in this intersection.
The existence effectively bound states with no binding energy might have important implications for the understanding the stability of basic bio-polymers and the key aspects of metabolism. A natural assumption is that self experiences expansion of consciousness as it entangles in this manner. Quite generally, an infinite self hierarchy with the entire Universe at the top is predicted.
The identification of Life as a number theoretically critical phenomenon is also consistent with the idea that the transformation of intention to action corresponds to a U-process inducing leakage between different sectors. This leakage makes sense in the intersection where same mathematical expression defines both real and p-adic partonic 2-surfaces which are the fundamental objects in TGD framework. What these statements really mean requires a construction of number theoretical variant of quantum theory applying in the intersection of real and p-adic worlds.
Besides number theoretic negentropies, there are also other new elements as compared to the earlier formulation of NMP. Zero Energy Ontology modifies dramatically the formulation of NMP since U-matrix acts between zero energy states and can be regarded as a collection of M-matrices which generalize the ordinary S-matrix and define what might be called a complex square root of density matrix so that kind of a square root of thermodynamics at single particle level justifying also p-adic mass calculations based on p-adic thermodynamics is in question.
The hierarchy of Planck constants is a further new element having important implications for Consciousness and Biology. Hyper-finite factors of type II1 represent an additional technical complication requiring separate treatment of NMP taking into account finite measurement resolution realized in terms of inclusions of these factors.
NMP has important implications for Thermodynamics. In particular, one must give up the standard view about the Second Law and replace it with a formulation taking into account the hierarchy of causal diamonds assigned with Zero Energy Ontology and dark matter hierarchy labeled partially by the values of Planck constants as well as the effects due to negentropic entanglement. Specifically in the case of living matter breaking of Second Law in standard sense is expected to take place and be crucial for the understanding of evolution.
Self hierarchy having the hierarchy of causal diamonds as imbedding space correlate leads naturally to a thermodynamical description of the contents of consciousness and quantum jumps is very much analogous to quantum computation. This leads to a vision about the role of bound state entanglement and negentropic entanglement in the generation of sensory qualia.
Negentropic entanglement leads to a vision about cognition. Negentropically-entangled state consisting of a superposition of pairs can be interpreted as a conscious abstraction or rule. Aegentropically-entangled "Schrödinger cat" knows that it is better to keep the bottle closed. A connection with fuzzy qubits and quantum groups with negentropic entanglement is highly suggestive.
The implications are highly non-trivial also for quantum computation which allows three different variants in TGD context. The negentropic variant would correspond to conscious quantum computation-like process.
Comments
1. At 2:46 AM, Matti Pitkanen said...
Terminology is always bound to me misleading, whatever one does. It would be logical to talk about TGD-inspired theory of Awareness but who would take this kind of theory seriously;-).
Maybe it would be useful to talk about Consciousness only when one has negentropic entanglement: positive information, knowledge. Otherwise awareness.
I think that emotions are very high-level consciousness unlike often thought. They provide summaries about the hole and it would be natural to assign them to negentropic fusions of a large number of mental images giving rise to stereo consciousness.
I would not assign real-p-adic dichotomy with brain hemispheres. Right-left brain dichotomy might relate more to the kind of mental images resulting in the state function reduction cascade. On the left-hand side, the process goes to smaller details and "smaller" mental images. At right-hand side would stop to much larger mental images with negentropic or bound state entanglement.
Right brain signs - Left brain talks reflects thisdifference nicely. Frequencies (singing) are a global notion related to time. Rhythms (speech) are a local notion. People who have lost the ability to speak and understand speech still have ability to sign and communicate in this manner. Time-like entanglement in long time scale. Perhaps this characterizes right brain. Wasn't memory assigned with singing in the mythology of ancient Greece?
2. At 2:43 AM, Matti Pitkanen said...
I have felt a deep shame for my mathematically primitive games with preferred frequencies (cyclotron frequencies, Josephson frequencies) assignable to what I call "topological light rays". A "real" theoretician would have constructed a supercomputer model performing heavy simulations irrespective of whether it would have made sense or not.
More than decade ago, I proposed the notion of "spectroscopy of Consciousness" which contained many unrealistic interpretational elements (in particular, the assignment of qualia to frequencies).
I also proposed the notion of neural window: neurons connected by flux tubes along which light represented as topological light-rays propagated. For instance, the poorly understood quite too rapid communication of auditory input to cortex could be possible in this manner.
It seems that the idea makes sense in terms of frequencies assignable to connections between subsystems (say the biological body and magnetic body in the case of EEG and its predicted fractal variants) rather than in terms of qualia.
In the case of cyclotron frequencies, the variation of the magnetic field strength would realize the knob tuning the frequency to a desired one characterizing the net of subsystems in communication. These frequencies would define sub-webs (and subselves and thus mental images) of the Indra's net formed by systems (molecules, neurons) connected by flux tubes.
3. At 8:29 PM, Matti Pitkanen said...
Thanks to "anomalous" for an excellent video about what neuroscience can say about self and enlightment experience. This is a really enjoyable lecture.
The main message is that neuroscience supports what can be seen as common for the teachings of Buddhism, Jainismi, and Hinduism. There is no self. There is no permanent self/there is no ego.
You can choose from the list and try to interpret.
The lecture also contains a lot of known facts for anyone who wants to get more precise view about the brain than right-left/good-bad association gives.
For instance, the fact that right amygdala is specialized on fear (yes --right!) and related negative feeling and left amygdala to positive feelings. It would be really fascinating to interpret this theoretically.
The basic message conforms with TGD. I would, however, talk about moments of consciousness first. Consciousness is not a property of matter but something which you cannot catch. One of the ancient teachings stated it as "not here, not here, not here....". Each quantum jump replaces universe with a new one and consciousness is in this moment of recreation and cannot be put neatly in box. Every attempt to describe contents of consciousness or monitor it changes it.
Ulla mentioned magnetic body. Biological body and magnetic body are those regions of space-time from which the information content of consciousness are from. This is quite different from saying that biological body or magnetic body is conscious. It is practical to use this expression (for instance, I talk about magnetic body as intentional agent). But it is not in principle true.
In TGD framework, selves exist but change all the time since it is an integrated sum of experiences defined by quantum jump. Self has subselves experienced as mental images. They come and disappear. Self is mental image of higher level self and comes and disappears (if we really lose our consciousness when we fall asleep).
Another manner to say this is that there is no unique objective reality. Quantum states as objective realities obeying laws of Physics are replaced with new ones all the Subjective-Time.
Ego - -in contrast to self -- could be defined as a collection of those mental images (subselves) which end up to unentangled and thus isolated state with full autonomy in each quantum jump. Generation of negentropic entanglement removes this autonomy and fuses mental images to larger ones. This means expansion of consciousness. One gets rid of ego and fuses to ocean of consciousness. The difference between bound state entanglement and negentropic entanglement is the difference between meditative state and sleep. Meditators love to spend their time in the intersection of real and p-adic worlds.
In TGD framework, the conceptually most economical proposal is that self and quantum jump are actually one and same thing. This seems to make sense in Zero Energy Ontology. There exists a fractal hierarchy of quantum jumps==selves with contents of consciousness coming from space-time regions with increasing size. Even the human lifecycle at a certain level would represent a single quantum jump: U process creating superposition of possibilities and state function reduction cascade selecting from these. This is what Life seems to be at this age when not too many choices are left.
3. At 8:49 PM, Matti Pitkanen said...
40 Hz waves are assigned by a Finnish neuroscientist Antti Revonsuo ("Is synchronization the direct neural correlate of visual consciousness?", 1998, )whose name decided to escape my attention to the situations when something new emerges. I think he studied these pictures which look like complete visual noise. But when you stare at them for a sufficiently long time, you finally get it -- a beautiful 3-D pattern emerge representing something familiar.
The interpretation would be that 40 Hz waves are associated with the emergence of a completely new holistic pattern from chaos. A possible interpretation is that a negentropic entanglement between large number of neutrons representing details about the picture emerges and manifests itself as a synchronous firing.
This fits also with the fact that oxidative metabolism is low during synchronous firing. Negentropic entanglement indeed means low dissipation and breaking of second law in appropriate time scale.
[Also magnetic body with size 0.75*107 km would be involved. By the way, the age of the Universe would define causal diamond containing the magnetic body of a system with size about 10-4 meters -- the size scale of a large neuron!]
40 Hz resonances occurs also in the beginning of meditative states and the interpretation would be in terms of a generation of negentropic entanglement between neurons also in this case.
4. At 3:30 AM, Matti Pitkanen said...
There is large number of cyclotron frequencies of biologically important ions in the vicinity of 40 Hz for B=0.2 Gauss (which is the value of magnetic field explaining the quantal looking effects of ELF em fields on the brain). This magnetic field is not same as Earth's magnetic field (with nominal value of B=0.5 Gauss). The proposed interpretation is as a dark magnetic field containing dark matter.
Iron could relate to the"seeing" the flux tubes of Earth. This could help animals to navigate along field lines to their birth place.
EEG synchrony and negentropic entanglement
by Matti Pitkanen / March 4, 2010
Postal address:
Köydenpunojankatu 2 D 11
10940, Hanko, Finland
e-mail:
URL-address:
(former address:)
"Blog" forum:
In the discussion related to the previous posting (above), someone turned my attention to 40 Hz synchrony. If one accepts the vision about Life as something in the intersection of real and p-adic worlds, 40 Hz EEG synchrony can be interpreted as a correlate for the generation of negentropic entanglement between cortical neurons.
Before proposing this interpretation, let us first describe the experimental findings of a Finnish neuroscientist Antti Revonsuo (see his article "Binding and the Phenomenal Unity of Consciousness").
Findings
The interpretation for 40 Hz EEG frequency inspired by the binding hypothesis is as a synchronizing frequency necessary for the generation of unified percepts. This hypothesis has been studied using auto-stereograms. There was no detectable difference in the power spectrum at 36-44 Hz range in the situation when auto-stereogram was experienced as a set of random dots as compared to the situation when it was perceived as a coherent, symmetrical gestalt. The situation was same also in 8-13 Hz and 13-20 Hz beta bands.
On the other hand, when the conscious percept was transformed from a random set of points to a coherent gestalt, there was a detectable increase in 40 Hz power in the occipital and right posterior sites for EEG electrodes in a time window 300-500 ms before the unified percept was reported. There could be also some time lapse between the unified percept and the report about it but probably this cannot explain the entire lapse.
No increase of power in beta bands was detected. This might be due to the fact that the widths of the measured bands are much wider than the widths ofthe narrow sub-bands reported masked by other EEG activity according to Nunez (Behavioral and Brain Sciences, 23, 2000). Note that in the model for a hierarchy of EEGs based on dark matter hierarchy beta band correspond to data communicated to the magnetic body (see this).
That the change in activity is associated with the emergence of a new percept suggests that the temporary increase of the EEG power could be assigned to the communications of the forming percept to the magnetic body.
Interpretation in terms of a generation of a Negentropic Entanglement
A fresh view about what really happens during 40 Hz synchrony came with the realization that negentropic entanglement is possible in the intersection of real and p-adic worlds. The generation of negentropic entanglement between 2 subselves means that the corresponding mental images are fused (see see this and this).
The process is experienced by the fusing subselves as an expansion of consciousness whereas consciousness is lost when bound state entanglement is generated. Also, the meditative states begin with enchanged 40 Hz activity and interpretation would be same.Quite generally, the generation of negentropically entangled neuron groups could be a correlate for the emergence of a new idea or a new holistic pattern emerging from a chaos.