What's new inHYPERFINITE FACTORS, PADIC LENGTH SCALE HYPOTHESIS, AND DARK MATTER HIERARCHYNote: Newest contributions are at the top! 
Year 2017 
How to demonstrate quantum superposition of classical gravitational fields?There was rather interesting article in Nature (see this) by Marletto and Vedral about the possibility of demonstrating the quantum nature of gravitational fields by using weak measurement of classical gravitational field affecting it only very weakly. There is also an article in arXiv by the same authors (see this). The approach relies on quantum information theory. The gravitational field would serve as a measurement interaction and the weak measurements would be applied to gravitational witness serving as probe  the technical term is ancilla. Authors claim that weak measurements giving rise to analog of Zeno effect could be used to test whether the quantum superposition of classical gravitational fields (QSGR) does take place. One can however argue that the extreme weakness of gravitation implies that other interactions and thermal perturbations mask it completely in standard physics framework. Also the decoherence of gravitational quantum states could be argued to make the test impossible. One must however take these objections with a big grain of salt. After all, we do not have a theory of quantum gravity and all assumptions made about quantum gravity might not be correct. For instance, the vision about reduction to Planck length scale might be wrong. There is also the mystery of dark matter, which might force considerable motivation of the views about dark matter. Furthermore, General Relativity itself has conceptual problems: in particular, the classical conservation laws playing crucial role in quantum field theories are lost. Superstrings were a promising candidate for a quantum theory of gravitation but failed as a physical theory. In TGD, which was born as an attempt to solve the energy problem of TGD and soon extended to a theory unifying gravitation and standard model interactions and also generalizing string models, the situation might however change. In zero energy ontology (ZEO) the sequence of weak measurements is more or less equivalent to the existence of self identified as generalized Zeno effect! The value of h_{eff}/h=n characterizes the flux tubes mediating various interactions and can be very large for gravitational flux tubes (proportional to GMm/v_{0}, where v_{0}<c has dimensions of velocity, and M and m are masses at the ends of the flux tube) with Mm> v_{0}m_{Pl}^{2} (m_{Pl} denotes Planck mass) at their ends. This means long coherence time characterized in terms of the scale of causal diamond (CD). The lifetime T of self is proportional to h_{eff} so that for gravitational self T is very long as compared to that for electromagnetic self. Selves could correspond subselves of self identifiable as sensory mental images so that sensory perception would correspond to weak measurements and for gravitation the times would be long: we indeed feel the gravitational force all the time. Consciousness and life would provide a basic proof for the QSGR (note that large neutron has mass of order Planck mass!). See the article How to demonstrate quantum superposition of classical gravitational fields? or the chapter Quantum criticality and dark matter. 
Anomalous neutron production from an arc current in gaseous hydrogenI learned about nuclear physics anomaly new to me (actually the anomaly is 64 years old) from an article of Norman and DunningDavies in Research Gate (see this). Neutrons are produced from an arc current in hydrogen gas with a rate exceeding dramatically the rate predicted by the standard model of electroweak interactions, in which the production should occur through e+p→ n+ν by weak boson exchange. The low electron energies make the process also kinematically impossible. Additional strange finding due to Borghi and Santilli is that the neutron production can in some cases be delayed by several hours. Furthermore, according to Santilli neutron production occurs only for hydrogen but not for heavier nuclei. In the following I sum up the history of the anomaly following closely the representation of Norman and DunningDavies (see this): this article gives references and details and is strongly recommended. This includes the pioneering work of Sternglass in 1951, the experiments of Don Carlo Borghi in the late 1960s, and the rather recent experiments of Ruggiero Santilli (see this). The pioneering experiment of Sternglass The initial anomalously large production of neutrons using an current arc in hydrogen gas was performed by Earnest Sternglass in 1951 while completing his Ph.D. thesis at Cornell. He wrote to Einstein about his inexplicable results, which seemed to occur in conditions lacking sufficient energy to synthesize the neutrons that his experiments had indeed somehow apparently created. Although Einstein firmly advised that the results must be published even though they apparently contradicted standard theory, Sternglass refused due to the stultifying preponderance of contrary opinion and so his results were preemptively excluded under orthodox pressure within discipline leaving them unpublished. Edward Trounson, a physicist working at the Naval Ordnance Laboratory repeated the experiment and again gained successful results but they too, were not published. One cannot avoid the question, what physics would look like today, if Sternglass had published or managed to publish his results. One must however remember that the first indications for cold fusion emerged also surprisingly early but did not receive any attention and that cold fusion researchers were for decades labelled as next to criminals. Maybe the extreme conservatism following the revolution in theoretical physics during the first decades of the previous century would have prevented his work to receive the attention that it would have deserved. The experiments of Don Carlo Borghi Italian priestphysicist Don Carlo Borghi in collaboration with experimentalists from the University of Recife, Brazil, claimed in the late 1960s to have achieved the laboratory synthesis of neutrons from protons and electrons. C. Borghi, C. Giori, and A. Dall'Olio published 1993 an article entitled "Experimental evidence of emission of neutrons from cold hydrogen plasma" in Yad. Fiz. 56 and Phys. At. Nucl. 56 (7). Don Borghi's experiment was conducted via a cylindrical metallic chamber (called "klystron") filled up with a partially ionized hydrogen gas at a fraction of 1 bar pressure, traversed by an electric arc with about 500V and 10mA as well as by microwaves with 10^{10} Hz frequency. Note that the energies of electrons would be below .5 keV and nonrelativistic. In the cylindrical exterior of the chamber the experimentalists placed various materials suitable to become radioactive when subjected to a neutron flux (such as gold, silver and others). Following exposures of the order of weeks, the experimentalists reported nuclear transmutations due to a claimed neutron flux of the order of 10^{4} cps, apparently confirmed by beta emissions not present in the original material. Don Borghi's claim remained unnoticed for decades due to its incompatibility with the prevailing view about weak interactions. The process e^{}+p→ n+ν is also forbidden by conservation of energy unless the total cm energy of proton and the electron have energy larger than Δ E= m_{n}m_{p}m_{e}=0.78 MeV. This requires highly relativistic electrons. Also the cross section for the reaction proceeding by exchange of W boson is extremely small at low energies (about 10^{20} barn: barn=10^{28} m^{2} represents the natural scale for cross section in nuclear physics). Some new physics must be involved if the effect is real. Situation is strongly reminiscent of cold fusion (or low energy nuclear reactions (LENR), which many main stream nuclear physicists still regard as a pseudoscience. Santilli's experiments Ruggero Santilli (see this) replicated the experiments of Don Borghi. Both in the experiments of Don Carlo Borghi and those of Santilli, delayed neutron synthesis was sometimes observed. Santilli analyzes several alternative proposals explaining the anomalyn and suggests that new spin zero bound state of electron and proton with rest mass below the sum of proton and electron masses and absorbed by nuclei decaying then radioactively could explain the anomaly. The energy needed to overcome the kinematic barrier could come from the energy liberated by electric arc. The problem of the model is that it has no connection with standard model. Both in the experiments of Don Carlo Borghi and those of Santilli, delayed neutron synthesis was sometimes observed. According to Santilli: According to Santilli: " A first series of measurements was initiated with Klystron I on July 28,2006, at 2 p.m. Following flushing of air, the klystron was filled up with commercial grale hydrogen at 25 psi pressure. We first used detector PM1703GN to verify that the background radiations were solely consisting of photon counts of 57 μR/h without any neutron count; we delivered a DC electric arc at 27 V and 30 A (namely with power much bigger than that of the arc used in Don Borghi's tests...), at about 0.125" gap for about 3 s; we waited for one hour until the electrodes had cooled down, and then placed detector PM1703GN against the PVC cylinder. This resulted in the detection of photons at the rate of 10  15 μR/hr expected from the residual excitation of the tips of the electrodes, but no neutron count at all. However, about three hours following the test, detector PM1703GN entered into sonic and vibration alarms, specifically, for neutron detections off the instrument maximum of 99 cps at about 5' distance from the klystron while no anomalous photon emission was measured. The detector was moved outside the laboratory and the neutron counts returned to zero. The detector was then returned to the laboratory and we were surprised to see it entering again into sonic and vibrational alarms at about 5' away from the arc chamber with the neutron count off scale without appreciable detection of photons, at which point the laboratory was evacuated for safety. After waiting for 30 minutes (double neutron's lifetime), we were surprised to see detector PMl703GN go off scale again in neutron counts at a distance of 10' from the experimental set up, and the laboratory was closed for the day." TGD based model The basic problems to be solved are following.
TGD explanation (see this) could be the same for Tesla's findings, for cold fusion (see this), Pollack effect (see this) and for the anomalous production of neutrons. Even electrolysis would involve in an essential manner Pollack effect and new physics. Could this model explain the anomalous neuron production and its strange features?

Nonlocal production of photon pairs as support for h_{eff}/h=n hypothesisAgain a new anomaly! Photon pairs have been created by a new mechanism. Photons emerge at different points! See this. Could this give support for the TGD based general model for elementary particle as a string like object (flux tube) with first end (wormhole contact) carrying the quantum numbers  in the case of gauge boson fermion and antifermion at opposite throats of the contact. Second end would carry neutrinorighthanded neutrino pair neutralizing the possible weak isospin. This would give only local decays. Also emissions of photons from charged particle would be local. Could the bosonic particle be a mixture of two states. For the first state flux tube would have fermion and antifermion at the same end of the fluxtube: only local decays. For the second state fermion and antifermion would reside at the ends of the flux tubes residing at throats associated with different wormhole contacts. This state in state would give rise to nonlocal twophoton emissions. Mesons of hadron physics would correspond to this kind of states and in oldfashioned hadron physics one speaks about photonvector meson mixing in the description of the photonhadron interactions. If the Planck constant h_{eff}/h=n of the emitting particle is large, the distance between photon emissions would be long. The nonlocal days could make the visible both exotic decay and allow to deduce the value of n! This would how require the transformation of emitted dark photon to ordinary (same would happen when dark photons transform to biophotons). Can one say anything about the length of fux tube? Magnetic flux tube contains fermionic string. The length of this string is of order Compton length and of the order of padic length scale. What about photon itself  could it have nonlocal fermionantifermion decays based on the same mechanism? What the length of photonic string is is not clear. Photon is massless, no scales! One identification of length would be as wavelength defining also the padic length scale. To sum up: the nonlocal decays and emissions could lend strong support for both flux tube identification of particles and for hierarchy of Planck constants. It might be possible to even measure the value of n associated with quantum critical state by detecting decays of this kind. For a summary of earlier postings see Latest progress in TGD. Articles and other material related to TGD. For details see the chapter Quantum criticality and dark matter. 
Hierarchy of Planck constants, spacetime surfaces as covering spaces, and adelic physicsFrom the beginning it was clear that h_{eff}/h=n corresponds to the number of sheets for a covering space of some kind. First the covering was assigned with the causal diamonds. Later I assigned it with spacetime surfaces but the details of the covering remained unclear. The final identification emerged only in the beginning of 2017. Number theoretical universality (NTU) leads to the notion of adelic spacetime surface (monadic manifold) involving a discretization in an extension of rationals defining particular level in the hierarchy of adeles defining evolutionary hierarchy. The first formulation was proposed here and more elegant formulation here. The key constraint is NTU for adelic spacetime containing sheets in the real sector and various padic sectors, which are extensions of padic number fields induced by an extension of rationals which can contain also powers of a root of e inducing finiteD extension of padic numbers (e^{p} is ordinary padic number in Q_{p}). One identifies the numbers in the extension of rationals as common for all number fields and demands that imbedding space has a discretization in an extension of rationals in the sense that the preferred coordinates of imbedding space implied by isometries belong to extension of rationals for the points of number theoretic discretization. This implies that the versions of isometries with group parameters in the extension of rationals act as discrete versions of symmetries. The correspondence between real and padic variants of the imbedding space is extremely discontinuous for given adelic imbedding space (there is hierarchy of them with levels characterized by extensions of rationals). Spacetime surfaces typically contain rather small set of points in the extension (x^{n}+yn^{2}=z^{n} contains no rationals for n>2!). Hence one expects a discretization with a finite cutoff length at spacetime level for sufficiently low spacetime dimension D=4 could be enough. After that one assigns in the real sector an open set to each point of discretization and these open sets define a manifold covering. In padic sector one can assign 8:th Cartesian power of ordinary padic numbers to each point of number theoretic discretization. This gives both discretization and smooth local manifold structure. What is important is that Galois group of the extension acts on these discretizations and one obtains from a given discretization a covering space with the number of sheets equal to a factor of the order of Galois group, typically equal to the order of Galois. h_{eff}/h=n was identified from the beginning as the dimension of polysheeted covering assignable to spacetime surface. The number n of sheets would naturally a factor of the order of Galois group implying that h_{eff}/h=n is bound to increase during number theoretic evolution so that the algebraic complexity increases. Note that WCW decomposes into sectors corresponding to the extensions of rationals and the dimension of the extension is bound to increase in the long run by localizations to various sectors in self measurements (see this). Dark matter hierarchy represents number theoretical/adelic physics and therefore has now rather rigorous mathematical justification. It is however good to recall that h_{eff}/h=n hypothesis emerged from an experimental anomaly: radiation at ELF frequencies had quantal effects of vertebrate brain impossible in standard quantum theory since the energies E=hf of photons are ridiculously small as compared to thermal energy. Indeed, since n is positive integer evolution is analogous to a diffusion in halfline and n unavoidably increases in the long run just as the particle diffuses farther away from origin (by looking what gradually happens near paper basket one understands what this means). The increase of n implies the increase of maximal negentropy and thus of negentropy. Negentropy Maximization Principle (NMP) follows from adelic physics alone and there is no need to postulate it separately. Things get better in the long run although we do not live in the best possible world as Leibniz who first proposed the notion of monad proposed! For details see the chapter Quantum criticality and dark matter. 
Time crystals, macroscopic quantum coherence, and adelic physicsTime crystals were (see this) were proposed by Frank Wilzek in 2012. The idea is that there is a periodic collective motion so that one can see the system as analog of 3D crystal with time appearing as fourth lattice dimension. One can learn more about real life time crystals here. The first crystal was created by Moore et al (see this) and involved magnetization. By adding a periodic driving force it was possible to generate spin flips inducing collective spin flip as a kind of domino effect. The surprise was that the period was twice the original period and small changes of the driving frequency did not affect the period. One had something more than forced oscillation  a genuine time crystal. The period of the driving force  Floquet period was 7475 μs and the system is measured for N=100 Floquet periods or about 7.47.5 milliseconds (1 ms happens to be of same order of magnitude as the duration of nerve pulse). I failed to find a comment about the size of the system. With quantum biological intuition I would guess something like the size of large neuron: about 100 micrometers. Second law does not favor time crystals. The time in which single particle motions are thermalized is expected to be rather short. In the case of condensed matter systems the time scale would not be much larger than that for a typical rate of typical atomic transition. The rate for 2P → 1S transition of hydrogen atom estimated here gives a general idea. The decay rate is proportional to ω^{3}d^{2}, where ω= Δ E/hbar is the frequency difference corresponding to the energy difference between the states, d is dipole moment proportional to α a_{0}, a_{0} Bohr radius and α∼ 1/137 fine structure constant. Average lifetime as inverse of the decay rate would be 1.6 ns and is expected to give a general order of magnitude estimate. The proposal is that the systems in question emerge in nonequilibrium thermodynamics, which indeed predicts a masterslave hierarchy of time and length scales with masters providing the slowly changing background in which slaves are forced to move. I am not a specialist enough to express any strong opinions about thermodynamical explanation. What does TGD say about the situation?
For details see the chapter Quantum criticality and dark matter. 
Why metabolism and what happens in biocatalysis?TGD view about dark matter gives also a strong grasp to metabolism and biocatalysis  the key elements of biology. Why metabolic energy is needed? The simplest and at the same time most difficult question that innocent student can make about biology class is simple: "Why we must eat?". Or using more physics oriented language: "Why we must get metabolic energy?". The answer of the teacher might be that we do not eat to get energy but to get order. The stuff that we eat contains ordered energy: we eat order. But order in standard physics is lack of entropy, lack of disorder. Student could get nosy and argue that excretion produces the same outcome as eating but is not enough to survive. We could go to a deeper level and ask why metabolic energy is needed in biochemistry. Suppose we do this in TGD Universe with dark matter identified as phases characterized by h_{eff}/h=n.
Biocatalysis is key mechanism of biology and its extreme efficacy remains to be understood. Enzymes are proteins and ribozymes RNA sequences acting as biocatalysts. What does catalysis demand?
Hydrogen atom allows also large h_{eff}/h=n variants with n>6 with the scale of energy spectrum behaving as (6/n)^{2} if the n=4 holds true for visible matter. The reduction of n as the flux tube contracts would reduce n and liberate binding energy, which could be used to promote the catalysis. The notion of high energy phosphate bond is somewhat mysterious concept. There are claims that there is no such bond. I have spent considerable amount of time to ponder this problem. Could phosphate contain (dark) hydrogen atom able to go to the a state with a smaller value of h_{eff}/h and liberate the excess binding energy? Could the phosphorylation of acceptor molecule transfer this dark atom associated with the phosphate of ATP to the acceptor molecule? Could the mysterious high energy phosphate bond correspond to the dark atom state. Metabolic energy would be needed to transform ADP to ATP and would generate dark atom. Could solar light kick atoms into dark states and in this manner store metabolic energy? Could nutrients carry these dark atoms? Could this energy be liberated as the dark atoms return to ordinary states and be used to drive protons against potential gradient through ATP synthase analogous to a turbine of a power plant transforming ADP to ATP and reproducing the dark atom and thus the "high energy phosphate bond" in ATP? Can one see metabolism as transfer of dark atoms? Could possible negentropic entanglement disappear and emerge again after ADP→ATP. Here it is essential that the energies of the hydrogen atom depend on hbar_{eff}=n× h in as hbar_{eff}^{m}, m=2<0. Hydrogen atoms in dimension D have Coulomb potential behaving as 1/r^{D2} from Gauss law and the Schrödinger equation predicts for D≠ 4 that the energies satisfy E_{n}∝ (h_{eff}/h)^{m}, m=2+4/(D4). For D=4 the formula breaks since in this case the dependence on hbar is not given by power law. m is negative only for D=3 and one has m=2. There D=3 would be unique dimension in allowing the hydrinolike states making possible biocatalysis and life in the proposed scenario. It is also essential that the flux tubes are radial flux tubes in the Coulomb field of charged particle. This makes sense in manysheeted spacetime: electrons would be associated with a pair formed by flux tube and 3D atom so that only part of electric flux would interact with the electron touching both spacetime sheets. This would give the analog of Schrödinger equation in Coulomb potential restricted to the interior of the flux tube. The dimensional analysis for the 1D Schrödinger equation with Coulomb potential would give also in this case 1/n^{2} dependence. Same applies to states localized to 2D sheets with charged ion in the center. This kind of states bring in mind Rydberg states of ordinary atom with large value of n. The condition that the dark binding energy is above the thermal energy gives a condition on the value of h_{eff}/h=n as n≤ 32. The size scale of the dark largest allowed dark atom would be about 100 nm, 10 times the thickness of the cell membrane. For details see the chapter Quantum criticality and dark matter. 
NMP and selfThe preparation of an article about number theoretic aspects of TGD forced to go through various related ideas and led to a considerable integration of the ideas. In this note ideas related directly to consciousness and cognition are discussed.
The view about Negentropy Maximization Principle (NMP) has coevolved with the notion of self and I have considered many variants of NMP.
Number theoretical Shannon entropy can serve as a measure for genuine information assignable to a pair of entanglement systems. Entanglement with coefficients in the extension is always negentropic if entanglement negentropy comes from padic sectors only. It can be negentropic if negentropy is defined as the difference of padic negentropy and real entropy. The diagonalized density matrix need not belong to the algebraic extension since the probabilities defining its diagonal elements are eigenvalues of the density matrix as roots of N:th order polynomial, which in the generic case requires ndimensional algebraic extension of rationals. One can argue that since diagonalization is not possible, also state function reduction selecting one of the eigenstates is impossible unless a phase transition increasing the dimension of algebraic extension used occurs simultaneously. This kind of NE could give rise to cognitive entanglement. There is also a special kind of NE, which can result if one requires that density matrix serves a universal observable in state function reduction. The outcome of reduction must be an eigen space of density matrix, which is projector to this subspace acting as identity matrix inside it. This kind NE allows all unitarily related basis as eigenstate basis (unitary transformations must belong to the algebraic extension). This kind of NE could serve as a correlate for "enlightened" states of consciousness. Schrödingers cat is in this kind of state stably in superposition of dead and alive and state basis obtained by unitary rotation from this basis is equally good. One can say that there are no discriminations in this state, and this is what is claimed about "enlightened" states too. The vision about number theoretical evolution suggests that NMP forces the generation of NE resources as NE assignable to the "passive boundary of CD for which no changes occur during sequence of state function reductions defining self. It would define the unchanging self as negentropy resources, which could be regarded as kind of Akashic records. During the next "reincarnation after the first reduction to opposite boundary of CD the NE associated with the reduced state would serve as new Akashic records for the time reversed self. If NMP reduces to the statistical increase of h_{eff}/h=n the consciousness information contents of the Universe increases in statistical sense. In the best possible world of SNMP it would increase steadily. Does NMP reduce to number theory? The heretic question that emerged quite recently is whether NMP is actually needed at all! Is NMP a separate principle or could NMP reduced to mere number theory? Consider first the possibility that NMP is not needed at all as a separate principle.
Hitherto I have postulated NMP as a separate principle. Strong form of NMP (SNMP) states that Negentropy does not decrease in "big" state function reductions corresponding to death and reincarnations of self. One can however argue that SNMP is not realistic. SNMP would force the Universe to be the best possible one, and this does not seem to be the case. Also ethically responsible free will would be very restricted since self would be forced always to do the best deed that is increase maximally the negentropy serving as information resources of the Universe. Giving up separate NMP altogether would allow to have also "Good" and "Evil". This forces to consider what I christened weak form of NMP (WNMP). Instead of maximal dimension corresponding to Ndimensional projector self can choose also lowerdimensional subspaces and 1D subspace corresponds to the vanishing entanglement and negentropy assumed in standard quantum measurement theory. As a matter fact, this can also lead to larger negentropy gain since negentropy depends strongly on what is the large power of p in the dimension of the resulting eigen subspace of density matrix. This could apply also to the purely number theoretical reduction of NMP. WNMP suggests how to understand the notions of Good and Evil. Various choices in the state function reduction would correspond to Boolean algebra, which suggests an interpretation in terms of what might be called emotional intelligence . Also it turns out that one can understand how padic length scale hypothesis  actually its generalization  emerges from WNMP.
For details see the chapter Negentropy Maximization Principle or the article Reexamination of the basic notions of TGD inspired theory of consciousness. 
WCW and the notion of intentional free willThe preparation of an article about number theoretic aspects of TGD forced to go through various related ideas and led to a considerable integration of the ideas. In this note ideas related directly to consciousness and cognition are discussed.
The original definition of self was as a subsystem able to remain unentangled under state function reductions associated with subsequent quantum jumps. The density matrix was assumed to define the universal observable. Note that a density matrix, which is power series of a product of matrices representing commuting observables has in the generic case eigenstates, which are simultaneous eigenstates of all observables. Second aspect of self was assumed to be the integration of subsequent quantum jumps to coherent whole giving rise to the experienced flow of time. The precise identification of self allowing to understand both of these aspects turned out to be difficult problem. I became aware the solution of the problem in terms of ZEO (ZEO) only rather recently (2014).
For details see the chapter Negentropy Maximization Principle or the article Reexamination of the basic notions of TGD inspired theory of consciousness. 
Anomalies of water as evidence for dark matter in TGD senseThe motivation for this brief comment came from a popular article telling that a new phase of water has been discovered in the temperature range 5060 ^{o}C (see this ). Also Gerald Pollack (see this ) has introduced what he calls the fourth phase of water. For instance, in this phase water consists of hexagonal layers with effective H_{1.5}O stoichiometry and the phase has high negative charge. This phase plays a key role in TGD based quantum biology. These two fourth phases of water could relate to each other if there exist a deeper mechanism explaining both these phases and various anomalies of water. Martin Chaplin (see this ) has an extensive web page about various properties of water. The physics of water is full of anomalous features and therefore the page is a treasure trove for anyone ready to give up the reductionistic dogma. The site discusses the structure, thermodynamics, and chemistry of water. Even academically dangerous topics such as water memory and homeopathy are discussed. One learns from this site that the physics of water involves numerous anomalies (see this ). The structural, dynamic and thermodynamic anomalies form a nested in densitytemperature plane. For liquid water at atmospheric pressure of 1 bar the anomalies appear in the temperature interval 0100 ^{o}C. Hydrogen bonding creating a cohesion between water molecules distinguishes water from other substances. Hydrogen bonds induce the clustering of water molecules in liquid water. Hydrogen bonding is also highly relevant for the phase diagram of H_{2}O coding for various thermodynamical properties of water (see this ). In biochemistry hydrogen bonding is involved with hydration. Biomolecules  say aminoacids  are classified to hydrophobic, hydrophilic, and amphiphilic ones and this characterization determines to a high extent the behavior of the molecule in liquid water environment. Protein folding represents one example of this. Anomalies are often thought to reduce to hydrogen bonding. Whether this is the case, is not obvious to me and this is why I find water so fascinating substance. TGD indeed suggests that water decomposes into ordinary water and dark water consisting of phases with effective Planck constant h_{eff}=n× h residing at magnetic flux tubes. Hydrogen bonds would be associated with short and rigid flux tubes but for larger values of n the flux tubes would be longer by factor n and have string tension behaving as 1/n so that they would softer and could be loopy. The portional of water molecules connected by flux tubes carrying dark matter could be identified as dark water and the rest would be ordinary water. This model allows to understand various anomalies. The anomalies are largest at the physiological temperature 37 C, which conforms with the vision about the role of dark matter and dark water in living matter since the fraction of dark water would be highest at this temperature. The anomalies discussed are density anomalies, anomalies of specific heat and compressibility, and Mpemba effect. I have discussed these anomalies already for decade ago. The recent view about dark matter allows however much more detailed modelling. For details see the chapter Dark Nuclear Physics and Condensed Matter or the article The anomalies of water as evidence for the existence of dark matter in TGD sense. 
About number theoretic aspects of NMPThere is something in NMP that I still do not understand: every time I begin to explain what NMP is I have this unpleasant gut feeling. I have the habit of making a fresh start everytime rather than pretending that everything is crystal clear. I have indeed considered very many variants of NMP. In the following I will consider two variants of NMP. Second variant reduces to a pure number theory in adelic framework inspired by number theoretic vision. It is certainly the simplest one since it says nothing explicit about negentropy. Second variant says essentially the as "strong form of NMP", when the reduction occurs to an eigenspace of density matrix. I will not consider zero energy ontology (ZEO) related aspects and the aspects related to the hierarchy of subsystems and selves since I dare regard these as "engineering" aspects. What NMP should say? What NMP should state?
The notion of entanglement negentropy
State function reduction as universal measurement interaction between any two systems
NMP as a purely number theoretic constraint? Let us consider the possibility that NMP reduces to the number theoretic condition tending to stabilize generic entanglement.
For background see the chapter Negentropy Maximization Principle. or the article About number theoretic aspects of NMP. 