Reflections on Mathematics as a foundation for Reality
by R.A. Herbst
Mathematics as champion of the sensate world view
Sociologist Pitiram Sorokin sees “systems of truth” as a socially agreed upon construct. In his four volume classic Social and Cultural Dynamics, he postulates a cyclic alternation between two cultural values: ideational, which professes that truth lies beyond the material world (and is thus not in the domain of science or scientists), and sensate, which asserts that truth is in the senses; observable matter (and therefore via Einstein, energy) alone is real. (and thus is in the domain of science and scientists) Ideational and sensate values can be traced back at least to classical Greek civilization, with the ideational philosophy of Plato on the one hand, and the sensate philosophy of Aristotle on the other. 
Thomas Kuhn, science historian and philosopher, implicitly concurs with Sorokin’s sociological definition of truth, or reality. The term "Paradigm Shift" was introduced in his 1962 book, The Structure of Scientific Revolutions. According to Kuhn a “Paradigm Shift” is a distinctively new way for a society to think about “reality”. A valid scientific idea may exist for years, without a corresponding societal paradigm shift.
The Copernican concept that the earth revolves about the sun rather than vice versa is often given as an example of a paradigm shift. The heliocentric theory had some unofficial support in Copernicus’ time, but was not recognized formally for many years. Yet this was not solely due to the influence of the Catholic church.
According to some, astronomy in the time of Copernicus was taken as a mathematical discipline which at best was a model. The reality of the physical world, on the other hand, was established through causal investigation in natural philosophy, not mathematics. Thus, many believed that Copernicus had not proved that heliocentrism was physically true, but that he had provided a more accurate mathematical model, which was perhaps useful for making better calendars. 
What appears to have changed then, in the gradual societal acceptance of the heliocentric theory, was the increasing credibility of mathematics in people’s minds as not only describing the world, but representing the reality of it. This trend to see mathematics as the final arbiter of sensate reality continued in western civilization until it collided with Quantum Mechanics in the 1920s.
In 1960, Eugene Wigner remarked in his book The Unreasonable Effectiveness of Mathematics in the Natural Sciences, that amazingly, most of the time when physicists see a pattern in the natural world, and they pick up a pattern from mathematics, the pattern from mathematics usually fits what is going on in the natural world with amazing accuracy.
Mathematics developed for one particular application often turns out to be applicable to other applications. For example, trigonometry, originally developed in the study of astronomy, finds application in the modeling of a vibrating spring, heat flow, and electromagnetism. Trigonometric functions are solutions to James Clerk Maxwell’s equations of electromagnetism, to name a few. Electromagnetic radiation is transmitted by sinusoidal waveforms.
A mathematical model often also suggests ways to go deeper into the physical reality.
mathematical physics progressed, it was found that
Quantum Mechanics as dissolver of the sensate universe
Even as early as the 17th century, we see indications of the unsuspected trajectory that physics and mathematics were taking, which would prove the undoing of the sensate world view. In 1801, the British physicist Thomas Young appeared to prove light was a wave from the results of his “Double Slit Experiment”, which showed that multiple light sources produce interference patterns; yet in 1839, it was first shown that light waves falling on metal caused the emission of electrons, which suggests that light has particle properties.
Louis de Brogli generalized wave particle duality by associating a wave length not only with mass-less photons, but also electrons, and in fact to any material body. Validity of the de Broglie hypothesis has been confirmed for macromolecules, as well as molecules, atoms, and subatomic particles. 
Max Plank produced a formula in an “act of desperation” which allowed matter to absorb radiant energy only in discreet amounts, or quanta. He is considered the founder of Quantum Theory, and his discovery is considered the beginning of modern science.  Einstein completed the coup in 1905 by asserting that radiation itself comes in discreet packets, now called “photons”. 
Quantum Mechanics was developed in the 1920s, and has been highly successful at explaining many phenomena, including spectral lines, the Compton effect and the photo electric effect, where electromagnetic radiation causes a current of electrons. Multiple logically consistent mathematical representations of Quantum Mechanics helped to cement its credibility. 
In the early 20th century, it was natural to speak of the elementary particles as being the “building blocks” of matter. At that time matter was believed to consist of atoms made up of a nucleus surrounded by a cloud of electrons. As the internal structure of the nucleus was probed, the number of “elementary particles” grew to a veritable zoo: 
Werner Heisenberg, originator of Quantum Mechanics, argued that what was truly fundamental in nature was not the particles themselves, but the symmetries, or patterns that lay beyond them. These fundamental symmetries could be thought of as the archetypes of matter and the ground of material existence. The particles themselves would simply be the material realizations of those underlying abstract symmetries. These abstract symmetries, normally only ascertainable through mathematics, could be taken as the scientific descendents of Plato’s ideal forms. 
thought experiment was devised by Einstein Podolsky and Rosen in an attempt to
discredit the new quantum physics. This thought experiment said that if quantum
theory were correct, a change in spin of one particle in a two particle system
would effect its twin simultaneously, instantaneously,
even if the two had been widely separated in space. A mathematical proof of
this was produced by JS Bell in 1964, and experimentally confirmed in 1982. At
In the mid 1860s, James Clerk Maxwell integrated the basic equations of
electromagnetism into a coherent whole,  a
Grand Unified Theory of Electromagnetism.
Einstein showed that Maxwell’s
equations worked perfectly through Lorentz’s transformation, but
Einstein wanted to expand his general theory of gravity to
include Maxwell’s Equations. For the last 20 years of his life, he secluded
himself in a modest house in
Physicists have come to understand that the known universe is governed by the four forces of gravity, electromagnetism (EM), and the weak and strong nuclear forces. The strong nuclear force holds the protons and neutrons of the nucleus together; the weak nuclear force allows neutrons to turn into protons, giving off radiation in the process. The atomic bomb releases the power of the strong nuclear force. Physicists since Einstein have been trying to understand gravity, and to reduce the expressions for the four forces of the universe to a single equation. 
Astronomers have discovered regions in space with enormous gravitational pull. Most believe these regions are under the influence of black holes, which are points, or singularities, so massive that gravity prevents even light from escaping. Further, as already noted, the vacuum fluctuations in energy density at every point in space are also enormous. However, Einstein’s General Theory, today’s standard theory of gravity, deals with large spaces and demands smooth variations in space time. Currently science has no equations that can be used to describe something that is both very massive, where normally the General Theory would apply, and very small, where normally quantum mechanics would apply. 
According to Professor Alex Filippenko, unification of the electro-weak and strong nuclear force will require a Grand Unified Theory (GUT), while unification of the electro-weak and strong nuclear force with gravity will require a more difficult Theory Of Everything (TOE). 
The search is on to develop the TOE, and some think a primary contender is the next iteration in particle physics. “String” theory, or “Super String” theory.
In 1967, Murray Gell-Mann was lecturing on the striking regularities in data pertaining to the collisions of protons and neutrons. An Italian grad student, Gabriele Veneziano, became intriguged, and found a simple math function that would describe the regularities. Why this function worked was presented in 1970 in the work of Leonard Susskind and Yoichiro Nambu. They found that Veneziano’s mathematical function would arise from the underlying theory if you modeled the protons and neutrons not as points, but as tiny vibrating strings. 
In 1984, John Schwarz and Michael Green resolved the last major inconsistency in string theory. This did not make the theory any easier to solve, but it convinced many leading physicists- especially Edward Witten- that the theory had too many miraculous properties to ignore. String theory then jumped from laughingstock to hottest thing in physics. 
String theory asserts that all phenomena are made up not of tiny particles, but of very tiny strings of energy, which vibrate in varying ways. Edward Witten showed that the original 5 different versions of string theory were merely different perspectives on the same thing. His mathematical theory, called “M” theory, requires 11 dimensions, and also predicts multiple universes. 
What is so alluring about String Theory? Its mathematical elegance; its aesthetics; some scientists think that certain relationships are so appealing that they must be correct. 
Leonard Susskind states that String Theory is based on Quantum Mechanics and describes a system of elementary particles similar to those in our universe. However, unlike quantum mechanics, there is no experimental data in support of string theory.
What kind of experimental data could support it? Evidence of proton decay would do. The predicted rate of decay is very small; significant proton decay would be detrimental to our existence, and, perhaps fortunately, no evidence of proton decay has been found to date. 
The notion of a holographic principle in the universe pops up in String Theory. Susskind notes “There is something crazy about string theory that I first came across in 1969, but it is so crazy that string theorists don’t even want to think about it… the mathematics of string theory implies an absurdly violent case of quantum jitters [zero point fluctuations], with fluctuations so ferocious that the pieces of an electron would spread out to the ends of the universe… String theory … places every bit of information, whether in black holes or black newsprint, at the outer edges of the universe … To most physicists, including string theorists, that seems so crazy that it is unthinkable.”  The appearance of this information at the outer edges of the universe for Susskind constitutes a “holographic principle”; a peculiar type of non-locality arrived at apparently independently from David Bohm’s holographic concept.
Vlatko Vedral notes that in the invention of optical holography, Dennis Gabor showed that two dimensions were sufficient to store all the information about three dimensions. Three dimensions are able to be represented due to light’s wave nature of forming interference patterns. “Light carries an internal clock, and in the interference patterns, the timing of the clock acts as the third dimension.“ He also notes that Susskind proposed to call the relationship between entropy (information) and surface area the holographic principle. The key property behind this is quantum mutual information, which is defined as the area interfacing any particular partition in the universe, say an electron or an atom, and the rest of the universe. 
It seems that Quantum Mechanics’ dissolution of the material world left mathematics, and equations, as the only reality for some physicists. By subsuming the very large, the very small, and the very fast under one “TOE” equation, scientists of the Four Force Particle school would claim a major intellectual victory. However, Just as most people would agree there is really much more to reality than Newtonian descriptions of the motions of celestial bodies, most people would agree there is more to reality than a mathematical relationship between the four forces.
Did Quantum Mechanics really dissolve material reality? What about the middle scale, of biological organisms? What about consciousness? What is the scale of consciousness?
A GUT, as opposed to a TOE, does not include gravity in its definition. Physicists willing to avoid unification of gravity see in Quantum Mechanics, and alternatively the Holographic Universe, and Zero Point Field, mathematics which dissolves the material universe at one level, but then unifies it at a deeper level. All three theories account for biological processes to varying degrees, are sympathetic with the idea of consciousness, and are ultimately related to one another. They very likely may be thought of as three mathematical “lenses” which are focused on our “reality”, each of which reveal different aspects of that reality.
The Zero Point Field
Quantum Mechanics and the Zero Point Field are the most obviously related, as they are mutually interdependent for their existence.
To quantum physicists attempting to model the electron mathematically, the vacuum, or Zero Point Field was seen as an annoyance which introduced infinities into their equations. In Paul Davies words: “The presence of infinite terms in the theory is a warning flag that something is wrong, but if the infinities never show up in an observable quantity we can just ignore them and go ahead and compute.”  To their delight, physicists found that not only could these infinities be subtracted out mathematically, but the resulting theory of Quantum Electrodynamics proved highly successful.  This theory states that interaction between electrons is mediated by virtual photons from the quantum vacuum (ZPF). Electrons feel each other by exchanging virtual photons.
However, the very success of QED itself provided a clue to the profound importance of the Zero Point Field. This theory says that fluctuations of this Zero Point Field are really occurring and effect the structure of atoms. In 1947, Willis Lamb found that the energy levels in the hydrogen atom are not exactly where you would expect them to be based on classical physics. The mismatch is called the Lamb Shift, which is explained by QED: unless you include the effects of the virtual particles, you will not get the classically expected values. The vacuum is also manifest macroscopically, as seen in the Casimir effect, in which two thin plates placed on one another experience a net attraction. 
There is some controversy regarding the energy density of the Zero Point Field, or quantum vacuum.  The vacuum or quantum fluctuation theory, also known as the cosmological constant theory is among the major contenders in accounting for “dark energy”, which makes up 70% of the universe, and which is causing an acceleration in the expansion of the universe.  From astronomical considerations, many believe the vacuum energy density to be close to zero.
However, empty space may turn out to be a writhing sea of energy. The quantum vacuum itself obeys Heisenberg’s Uncertainty Principle: the smaller the distance and time the larger the uncertainty in energy. Even though space time is considered discrete at the Plank scale, (10 -33rd cm) the vacuum fluctuations in energy density are still enormous, being calculated variously as 1096 kilograms per cubic meter.  Richard Feynman, who made major contributions to QED ,  noted that the energy in one cubic meter (variously one teaspoon) of empty space contains enough energy to boil all the oceans of the world.  These large vacuum fluctuations, as we have previously seen, make unification of Quantum Mechanics and gravity very difficult.
Seen in this perspective, physical matter can be seen more as a froth appended to the churning sea. 
The combined theories of kinetic theory of gasses, thermodynamics, and Maxwell’s equations seemed to indicate that all of the kinetic energy of molecules should long ago have been radiated away, leaving a cold dead universe.
Quantum physicists struggled with the question of why an electron orbits around a proton, like a planet orbiting around the sun. In the atomic world, any moving electron, which carries a charge, would eventually radiate away its energy and spiral into the nucleus, causing the entire atomic structure to collapse. 
The hidden mechanism which prevents atomic collapse appears to be the Zero Point Field. In 1987, Hal Puthoff was able to demonstrate in a paper published by Physical Review, that the stable state of matter depends on the dynamic interchange of energy between the subatomic particles and the sustaining Zero Point Energy field.  In quantum field theory, the individual particles are transient and insubstantial. The only fundamental reality is the underlying entity- the Zero Point Field itself . 
Interestingly, Timothy Boyer and Hal Puthoff showed that if you take into account the Zero Point Field, you don’t have to depend on Bohr's Quantum Mechanical model. One can show mathematically that electrons loose and gain energy constantly from the ZPF in dynamic equilibrium, balanced at exactly the right orbit. Electrons get their energy to keep going because they are refueling by tapping into these fluctuations of empty space
Puthoff showed that fluctuations of the ZPF drive the motion of subatomic particles and that all the motion of all the particles generates the ZPF.
Timothy Boyer showed that many of the weird properties of subatomic matter which puzzled physicists and led to the formulation of strange quantum rules could easily be accounted for in classical physics, if you include the ZPF: uncertainty, wave-particle duality, the fluctuating motion of particles all had to do with interaction of the ZPF and matter.
Gravity has remained a mystery to physicists, being billions of times weaker than the other of the four forces. Even Einstein, who was able to describe it thru his general theory of relativity, could not explain where it came from or how to relate it to the other fundamental forces.
Puthoff, with the help of Bernie Haisch and Alfonso Rueda, demonstrated mathematically that gravitational and inertial effects were entirely consistent with zero point particle motion. Tying gravity to Zero Point energy solved a number of problems that had troubled physicists for centuries. It answered why gravity is weak and can’t be shielded (the ZPF can’t be shielded). it also explained why we can have positive mass and not negative mass . 
The paper The Origin of Inertia, by James F. Woodward, discusses in a lucid way, many concepts of physics and quantum mechanics. In particular, it offers an interesting perspective on and critique of Zero Point Field theory of inertia put forward by Haisch, Rueda, and Puthoff in 1994, and popularized by Lynn McTaggart’s book The Field. 
In the 1960s, Paul Dirac showed that fluctuations in fields of material particles produces a polarization of the ZPF whereby it in turn affects the particles mass, charge, spin, or angular momentum. About the same time, Andrei Sakharov proposed that the slowing of clocks and shrinkage of lengths near the speed of light are the result of effects induced in the vacuum “due to the shielding of the ZPF by charged particles. 
The existence of the Zero Point Field implies that all matter in the universe is interconnected by waves. 
Robert Jahn notes that current science deals not only with matter and energy, but also information. According to the Apollo astronaut Edgar Mitchell, information and energy are the stuff of the universe. “The quantum vacuum”, Mitchell said, “is the holographic information mechanism that records the historical experience of matter.”  Ervin Laszlo contends that  the Zero Point Field is in fact a super dense information field which in addition to retaining a record of all events, holds the universe together and accounts for literally “everything”.
How could the quantum vacuum convey the “historical experience of matter”? The German physicist Hartmut Mueller has found that pressure waves may propagate through the ZPF, and claims that the observed dimensions of atom as well as galaxies is determined by pressure waves in the ZPF. These pressure waves may superimpose, creating standing waves. These waves determine physical interactions by setting the values of the electromagnetic, gravitational, weak and strong nuclear forces. By means of resonance they amplify some vibrations and suppress others, and are thus responsible for the distribution of matter through the universe. 
The Russian physicists G.I. Shipov and A.E. Akimov et al proposed the “torsion wave “ theory, which has been elaborated upon by European and US scientists. This theory shows how the vacuum can link physical events through space time. The torsion waves act at one billion times the speed of light. Particles that have “spin” also have a specific magnetic momentum, which is registered in the vacuum in the form of minute vortices made up of virtual bosons. Hungarian Laszlo Gazdag has argued that these vortices carry information, much the same as magnetic impulses on tape or a computer disk. These vortices interact with each other to form interference patterns that integrate the strands of information. An analog is the sea and the way waves from objects in the sea interact. The persisting wave patterns are the memory of the objects that moved in the water. 
It makes sense, says Laszlo, to name this ZPF information field of the universe the “A-Field”, after the Indian philosophical concept of the Akashic Chronicle, the record of everything that has happened in the universe.
Laszlo arrives at his ZPF as the explanation for everything by way of a grand generalization in assuming that the ZPF is the mechanism producing the well documented property of non-locality of quantum mechanics. He then notes that living tissue, being a Bose- Einstein condensate, may be considered a quantum system. He then goes on to assume that the coherence of biological systems, the linkage of organisms to one another and the environment in evolution, and the connection of individual consciousness to a larger awareness are all due to the ZPF. Information is carried by superimposed vacuum wave interference patterns that are equivalent to holograms.
“No Particle” theories: The Spherical Standing Wave Theory and the Holographic Theory
Erwin Schrödinger apparently was not happy with Max Born's statistical / probability interpretation of waves that became commonly accepted in Quantum Theory. He believed waves were real, and the “particles” in wave-particle duality were merely an artifact.
The Spherical Standing Wave Theory of matter 
Milo Wolff believes that spherical “in and out-waves” remove the need for a separate particle, as the wave-center of the spherical waves creates the particle effect. He found that when one spherical standing wave was moving relative to another the Doppler shifts gave rise to BOTH the de Broglie Wavelength (y=h/mv) and the Mass increase of Albert Einstein's Relativity (E=hf =mc2). Other contemporary alternative physicists also argue for a non holographic no particle universe.  This theory is subject to several technical problems, and does not seem to be taken seriously in the physics community 
The Holographic Universe
His alternative theory to Quantum Mechanics assumes that elementary particles do not actually have a wave particle nature, but are particles with considerable internal complexity. In the more advanced version, this particle is represented by fluctuations within a quantum field. Bohm postulates a “Quantum Potential” which acts on an elementary particle, in addition to the conventional EM, strong, and weak nuclear forces. The Quantum Potential, unlike the other forces of nature, does not reduce with increasing distance. Because of this, even remote objects can have a profound effect. Also, the Quantum Potential does not push or pull like other forces, but acts more like a guide wave, or like a radar signal received by a ship at sea. This is analogous to the way a morphic field would work. Although the amount of energy in the signal is negligible, the information it provides has a formative effect, as the radar information could be used by a ship at see to steer. The Quantum Potential carries information about the environment of the quantum particle and thus informs and effects its motion. Since the information in the Quantum Potential is very detailed, the resulting particle trajectory appears chaotic or indeterminate. Bohm’s causal interpretation suggests that matter has orders that are closer to mind than to a simple mechanical order.
His holographic theory, developed between 1970 and 1980, yields numerical results that are identical to conventional QM, but has not been examined in a serious way by the physics community.
In the quantum field version of the theory, the elemental particles themselves become a manifestation of the quantum field. Active information is responsible for the way quantum processes unfold out of the quantum field. For this reason, the inner structure of elementary particles may be of unlimited complexity, for they are an expression of the entire universe.
Bohm made use of the idea of a holograph to illustrate the concept of enfoldment of an implicate order. In holography, light from each part of the object is folded over the whole photographic plate, so each part of the photographic plate contains information about the whole object.  Bohm later identified the deeper level as the “implicate order”, a holofield where all the states of the quantum are permanently coded. Observable reality emerges from this field by constant unfolding of the “implicate order” into the “explicate order:” These correspond to the holographic plate and holograph in optical holography.
“In the enfolded [or implicate] order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the "explicate" or "unfolded" order, which is a special and distinguished form contained within the general totality of all the implicate orders”. 
As F. David Peat notes, instead of science reducing nature to the material, the whole notion of the “material” has been extended into the regions of indefinite intangibility.
As we have seen, the concept of the holographic nature of “reality” has been introduced in connection with string theory and Zero point field/Quantum Mechanics theory, as well as Bohm’s theory.
The concept of a “holographic universe” has been supported
by the results of an investigation into gravity waves by a German team. Their
gravity wave detector had been plagued by an inexplicable noise. According to a researcher at Fermilab in
The Middle Scale: Biological Systems
Fritz -Albert Popp showed that all living things emit a permanent current of photons. The higher on the evolutionary scale, the more complex the organism, the fewer photons are emitted.  Bernhard Ruth, working in conjunction with Popp, developed a machine that could count photons. 
In quantum physics, coherence means that subatomic particles are linked by bands of common electromagnetic fields, so they can 'communicate'. They are like a multitude of tuning forks that all begin resonating together. As they get into phase, they begin acting like one giant wave. Usually this level of coherence , called a Bose-Einstein condensate, is only observed in superfluids and superconductors, a few degrees above absolute zero.
Perfect coherence corresponds to an optimal state between total randomness and total order. In total randomness cells become disordered. Cancer patients were found to lack biophoton coherence. Too much order prevents flexibility. Multiple sclerosis patients were found to have too much order, and too many biophotons. This led Popp to think of biophotons emissions as a sort of correction by a living system to the fluctuations of the Zero Point Field. Photon emission may be a compensatory measure to maintain equilibrium.
Popp found that molecules in the cells would respond to certain frequencies and that a range of vibrations from the photons would cause a variety of frequencies in other molecules of the body. From experiment, Popp showed that one of the most essential sources of biophoton emission was DNA.
The conventional theory of how molecules communicate in the body requires some direct contact. This theory is too dependent on chance, and also requires a long time duration, and can’t account for rapid emotional changes. According to Jacques Benveniste's theory, which has been supported by experiment, molecules rely on electromagnetic signaling at low frequencies (between 20hz and 20 khz) Each molecule has its own signature frequency, and can resonate with other molecules.
Robert O. Becker and Cyril Smith had conducted extensive experiments on EM frequencies in living things. Jacques Benveniste's contribution was to show that molecules and atoms had their own unique frequencies by using modern technology both to record this frequency and to use this recording itself for cellular communication. 
Herbert Frohlich was among the first researchers to suggest that waves or vibration allow proteins to cooperate with one another and carry out instructions from DNA. He predicted certain frequencies, now called “Frohlich frequencies” could be excited in the cell by vibrations in the proteins. He showed that once energy reaches a certain level, molecules begin to vibrate in unison, until they reach a high level of coherence, when they may take on certain properties of quantum mechanics, including non-locality.  One might wonder how the de Broglie frequency, discussed above, might be related to Frohlich frequencies.
Benveniste and Frohlich’s work has been ignored or attacked by the status quo.
Just as some scientists see quantum effects in the behavior of biophotons, other scientists see Quantum Mechanics at work in the biology of living tissue, and see it as a key in unraveling the mysteries of the human mind and consciousness. The Japanese physicist Kunio Yasue, the American physicist Gordon Globus and others claim that brain substrates uphold second-order quantum fields. 
In the 1960s Carl Pribram encountered the concept of holography and realized he had found the explanation for the location of memory that brain scientists had been looking for. Pribram believes memories are encoded not in neurons, or small groupings of neurons, but in patterns of nerve impulses that crisscross the entire brain in the same way that patterns of laser light interference crisscross the entire area of a piece of film containing a holographic image. In other words, Pribram believes the brain is itself a hologram. Pribram's theory explains how the human brain can store so many memories in so little space. It has been estimated that the human brain has the capacity to memorize something on the order of 10 billion bits of information during the average human lifetime (or roughly the same amount of information contained in five sets of the Encyclopaedia Britannica).
Pribram's belief that our brains mathematically construct "hard" reality by relying on input from a frequency domain has received a good deal of experimental support.
Phil Anderson, a Nobel Prize winner in condensed matter physics, disagrees strongly with the reductionistic science of the Four Force Particle school, which asserts that "fundamental" particles hold all the secrets and are the most important. He supports the Emergent Properties school, which says that the whole is greater than the sum of the parts; i.e. unexpected behaviors "emerge" from large numbers of component parts. 
Biological systems are the supreme example of self organizing structures, and provide many examples of emergent properties, such as metabolism, blood and oxygen circulation, nerve stimulation and transmission. Although mathematics may be applied to the emerged structures, it has little to say about their emergence. It is conceivable that quantum fields may exhibit emergent properties related to the generation of biological systems.
The purely sensate mode of comprehending reality may embrace mathematics, and may ignore or deny the reality of mind and consciousness, seeing them as merely incidental by-products, or epiphenomena  of physical processes. It is odd however, that the mere epiphenomenon of mind could itself bring forth the tool of mathematics, the final arbiter of today’s reality.
Why, in the indeterminate and probabilistic theory of Quantum Mechanics, are there definite outcomes? Quantum Mechanics researchers have long accepted that the spin of a particle will always be found to point along whichever axis is chosen by the experimenter as his reference. Physicist Eugene Wigner suggested that these definite outcomes, including looking where a wave was and seeing a particle, are produced by the consciousness of the observer acting on the quantum system; “collapsing” the wave function into a well defined state. Somehow the observer’s consciousness is effecting what is observed, and this is certainly a macroscopic effect. Perhaps for this reason, the study of consciousness as a Quantum Mechanical science has moved more towards the mainstream. Of course another issue is location of the seat of consciousness. Is it in the body, and if so, which part?  Can consciousness reside outside of the physical body, and is it restricted in scale? Can the consciousness of individuals merge, like raindrops, into a sea?
David Bohm applied Eugene Wigner type observations directly to functions of the brain and the problem of consciousness. He concluded that mind and matter “are two aspects of one whole, and are no more separable than form or content. …Deep down the consciousness of mankind is one. 
Wikipedia provides a good article on the current spectrum of quantum mind theories. 
Some sensate schools hold that reductionism will eventually explain mind and consciousness in terms of mechanisms of a biological system, such as action potentials, neurotransmitters, etc. Others believe that consciousness is an emergent property, but there is insufficient evidence to support this hypothesis.
In a 12 lecture course, Consciousness and Its Implications,  Professor Daniel Robinson discusses what is called the “Problem of Consciousness”, being an embarrassment to both scientific materialism (physicalism) which assumes only matter, and dualism, which asserts two types of stuff; matter and mind. He dismisses epiphenomenalism and explores the difficulty science has in explaining just how neurobiological processes of the brain gives rise to consciousness, in all of it’s multifaceted glory.
Even assuming a connection between quantum mechanics and consciousness; even assuming the validity of Bohm’s implicate and explicate orders and the great significance of the Zero Point Field; even assuming science succeeds in building a theoretical bridge between matter and mind, science is still at an impasse with regard to “explaining” consciousness in a reductionistic way.
The linkage of Mind and Matter: Consciousness creating reality
Synchronicity is generally seen as a confluence of an individual’s mental experiences; ie consciousness, usually in the form of thoughts or dreams, with that individual’s experiences in daily life. F. David Peat has suggested that the existence of synchronicity shows that both consciousness and matter are linked. Random Event Generator (REG) experiments and the work at the Princeton Engineering Anomalies Research (PEAR) lab also demonstrate a linkage of mind and matter. Peat notes that various attempts to explain how mind and matter relate often preserve features of Cartesian duality. The duality could be resolved if mind and matter could be understood as emerging from a common source.
There is a trend to see consciousness not just as the perception but also the creation of “what is out there”. Roger Sperry, a neuroscientist from Cal Tech, won the Nobel prize for work characterizing the left and right brain. He put his thoughts into a lead article for the 1981 Annual review of Neuroscience titled Changing Priorities. In the article he says we are leaving behind determinism, behaviorism, and the materialism of the science of the past. “we are having to recognize the primacy of inner conscious awareness as a causal reality.”  This is related to Sorokin’s Ideational mode of comprehension.
Consciousness creating reality has been deduced directly from Quantum Mechanics. Bernie Haisch, an astronomer, stated in his book The God Theory: ‘It is not matter that creates an illusion of consciousness, but consciousness that creates an illusion of matter.’ Richard Conn Henry notes that we know from quantum mechanics that our observations create the past, as demonstrated by the famous delayed-choice experiment. 
TTOE: Total Theories Of Everything
A trend in the early years of the twentyfirst century is an attempt to unify TOE contenders. Nassim Haramein, a Swiss-born self-trained scientist, and physicist Elizabeth Rauscher have provided intriguing new studies, integrating not only the four forces, but the ZPF and complexity theory. A 2004 paper which incorporates torque and Coriolis effects in "'plasma dynamics'" interacting with a "polarized geometric structured vacuum".  The paper makes the case that “gravitational forces with spin-like terms may be related to the strong and electroweak forces”, thus providing a new unification of the four forces, otherwise called a “Theory Of Everything” (TOE).
Haramein and Rauscher have also developed a "Scaling Law for Organized Matter",  which characterizes all matter from subatomic to galactic and universal size as various sized black holes. Haramein’s unified field theory and the fractals associated with this scaling law are integral to his concept of a "Holofractographic Universe". Geometry is important to Haramein, and since string theorists claim that Supersymmetry is related to geometry,  he may be onto something.
Haramein’s 2009 paper The Schwarzschild Proton  presents a model in which Vacuum (Zero Point Field) energy is converted to a proton with Black Hole characteristics, such that the “Strong Force” can be seen as gravitational attraction.
Mathematics not only describes, predicts, dissolves, and unifies the material universe. Intriguing correspondences between nature and mathematics continue to be discovered, whose significance is not yet, and may never be, understood.
For example, , Georg F.B. Riemann added an improvement to an early formula for determining prime numbers which gives the “steps” we see in the actual distribution of prime numbers. The improvement consisted of adding waves at certain frequencies. Rieman’s guess of frequency values needed is called “Rieman’s hypothesis”, and also “the music of the primes” as well as the “zeros of the Rieman Zeta function”. These waves are the key to the successful prediction of prime numbers. Quantum systems have discrete energy levels, corresponding to waves vibrating at certain frequencies. Likewise the distribution of prime numbers is encoded in a discrete set of wave frequencies: the “magic frequencies” Amazingly, Rieman’s frequencies look like the frequencies of a “quantum chaotic system”.
There is some undiscovered chaotic system whose quantum counterpart would hold the secret to the music of the primes. Chaos, atoms, and prime numbers all connected. The Prime numbers of our mental world are connected to the atoms of reality, and the link between them is chaos. 
Although mathematics can describe, predict, dissolve, and unify aspects of our material universe, or offer tantalizing hints of connection, some mathematics appears to offer no connection. Is there one? [examples]
 Pitirim Sorokin Social and Cultural Dynamics (4 vol., 1937–41; rev. and abridged ed. 1957)
Social and Cultural Dynamics: A Study of Change in Major Systems of Art, Truth, Ethics, Law and Social Relationships (1957 Cloth (reprinted 1970) ed.).
Revised edition: S.M. Stern Transaction Publishers 1985:
http://books.google.com/books?id=fbZyka2W_1cC&pg=PA292&lpg=PA292&dq=Pitirim+Sorokin+Social+and+Cultural+Dynamics+idealistic&source=bl&ots=l3anLMUyXC&sig=KnypcML5QpDT-gJJ06sw_O883cE&hl=en&ei=UoBASvOZNIPOsgOD9oCiDw&sa=X&oi=book_result&ct=result&resnum=4 p. 226. f.
He also identifies an idealistic cultural mentality, which synthesizes the premises of sensate and ideational into one inwardly consistent and harmonious unity. Sorokin finds that reason and logic, particularly “rationalistic” philosophy can provide such synthesis.
The main concern of medieval scholasticism, for example, exemplified by the Suma Theologica of Thomas Aquinas, was to reconcile faith and reason. http://www.hps.cam.ac.uk/starry/coperbooks.html
 Paul Davies, Superforce, p. 57 f.
 The Man Who Changed Everything: The Life of James Clerk Maxwell p. 182
 Matrix Quantum Mechanics was proposed by
Werner Heisenberg, who won the 1932 Nobel Prize in Physics
for creation of "Quantum Mechanics". Heisenberg also postulated the Uncertainty Principle:
The more precisely the position of a particle is determined, the less precisely the momentum is known.
If the variability of particle position is represented by
Wave Quantum Mechanics was proposed by Irwin Schrodinger, known for his Wave Equation.
Transformation Quantum Mechanics was proposed by Paul Dirac, who showed that wave and matrix QM amounted to the same thing. Dirac found that a math description of an electron's wave using quantum theory is consistent with Einstein's Relativity Theory. The math allows a "+" and "-" solution, which predicts the existence of anti-electrons; ie antimatter
 F. David Peat Synchronicity: The Bridge Between Matter and Mind. p. 94
 F. David Peat Synchronicity: The Bridge Between Matter and Mind p. 94 f.
 Diverse perspectives on the significance of non-locality: http://www.physlink.com/Education/askexperts/ae634.cfm
Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.
Gauss's law for magnetism is one of Maxwell's equations, the four equations that underlie classical electrodynamics. It states that the magnetic field B has divergence equal to zero, in other words, that it is a solenoidal vector field. It is equivalent to the statement that magnetic monopoles do not exist. Rather than "magnetic charges", the basic entity for magnetism is the magnetic dipole. (Of course, if monopoles were ever found, the law would have to be modified, as elaborated below.)
Faraday's law of induction describes a basic law of electromagnetism, which is involved in the working of transformers, inductors, and many forms of electrical generators. The law states
The induced electromotive force or EMF in any closed circuit is equal to the time rate of change of the magnetic flux through the circuit.
Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the integrated magnetic field around a closed loop to the electric current passing through the loop.
 According to Leonard Susskind, by the 1950s, Richard Feynman, Julian Schwinger, Sin-Itiro Tomanaga and Freeman Dyson had laid the foundation for a synthesis of special relativity and quantum mechanics called Quantum Field Theory. [Leonard Susskind, The Black Hole War p. 7].The first and most successful expression of QFT was Quantum Electrodynamics (QED).
The EM and weak forces have been unified. In high energy interactions, we can’t tell the EM force from the Weak force. Steven Weinberg et al got Nobel Prize for his development of “electro-weak” in 1979. [Notes on Teaching Company Understanding the Universe: An Introduction to Astronomy 2nd edition
Prof Alex Filippenko. Cosmology sections Lecture 89.]
According to Paul Davies, in 1973, Sheldon Glashow and Howard Georgi published a theory in which the new electroweak force was merged with the strong gluon force to form a “grand unified force,” the first Grand Unified Theory. Davies, Superforce, p. 130.
 In preparing groundwork for such equations, and a TOE,
Nobel prize winner Sheldon Glashow and colleague
Andrew Cohen, of
 [Filippenko lecture 89 ]
 Leonard Mlodinow Feynman’s rainbow Warner books 2003, p. 99.
 Feynman’s Rainbow p. 169.
 Paul Davies Superforce
 Filippenko lecture 89 Interestingly, Susskind, with the publication of his latest books, The Cosmic Landscape and The Black Hole War is at the epicenter of current thinking about the nature of the universe. The Cosmic Landscape review: http://www.nyas.org/publications/readersReport.asp?articleID=48
 Leonard Susskind The Black Hole War p. 293 f.
 Vlatko Vedral Decoding Reality: The Universe as
 Paul Davies Superforce p. 109 f. also The Field p. 109
 Paul Davies Superforce p. 111 f.
 Filippenko lecture 87
 Filippenko lecture 86 and 87.
 The application of quantum mechanics to fields rather than single particles, resulting in what are known as quantum field theories, began in 1927. Early contributors included Dirac, Wolfgang Pauli, Weisskopf, and Jordan. This line of research culminated in the 1940s in the quantum electrodynamics (QED) of Richard Feynman, Freeman Dyson, Julian Schwinger, and Sin-Itiro Tomonaga, for which Feynman, Schwinger and Tomonaga received the 1965 Nobel Prize in Physics. QED, a quantum theory of electrons, positrons, and the electromagnetic field, was the first satisfactory quantum description of a physical field and of the creation and annihilation of quantum particles. http://en.wikipedia.org/wiki/Quantum_electrodynamics
 [The Field p. 23 f. ]
 [???? the field???]
 Lynn McTaggart The Field p. 24f.
 The Field p. 24, also note 14 p.230: Physical Review D 1987, 35: 3266-70
 The field p 23 Fritjof tao of physics.
 Lynn McTaggart The Field p. 25.
 Laszlo, Science and the Akashic Field: An Integral Theory of Everything: Inner Traditions, 2004 p. 47f
 The field p. 24f.
 Laszlo p. 51
 Ervin Laszlo, Science and the Akashic Field: An Integral Theory of Everything: Inner Traditions, 2004
 Laszlo p. 49.
 Laszlo p. 51
 Physics forum comments on the work of Milo Wolff do not take his work very seriously:
the physics forum thread above notes that
“The Physics of Bruce Harvey” also seems to suggest that particles are really a
wave phenomena. However,
 David Bohm, Wholeness and the Implicate Order 1980. Google preview:
According to Ervin Laszlo, various versions of Bohm’s theory are being developed today by theoretical physicists who are unwilling to accept the mathematical formalisms of quantum physics as an adequate explanation of the real world. They account for the behavior of the quantum in reference to its interaction with a deeper dimension that has replaced the luminous ether of the 19th century. Ervin Laszlo Science and the Akashic Field Inner Traditions. 2004. p. 73.
 F. David Peat Synchronicity: The Bridge Between Matter and Mind p. 168 f.
 Wholeness and the Implicate Order p. xv.
 Lynn McTaggart, The Field p. 42 f.
 The photomultiplier detected coherent photons of high intensity from cucumber seedlings and potato sprouts grown in the dark.
 Lynn McTaggart, The Field p. 60f.
http://www.scaruffi.com/mind/yasue.html : book review
Globus, Gordon Quantum Consciousness is Cybernetic [not random]:
 Mitchell Waldrop Complexity. George Cowan was administrator at Los Almos during the development of the atomic bomb under the Manhattan Project. He became director of the Santa Fe Institute, which was dedicated to the study of non-linear science. Cowan observed that science in the 20th century has typically been reductionistic: to do science, you must dissect the world into smaller and smaller pieces. This leads to fragmentation of science and the overlooking of opportunities. Real world problems demand a more holistic approach.
 The heart has been associated with intelligence and consciousness in ancient Chinese and Egyptian cultures, as well as in most religions. Heartmath is a modern scientific institution which has been re-exploring the heart as seat of consciousness. http://www.unitycenter.net/id31.html
 Daniel Robinson: Consciousness and Its Implications CD The Teaching Company, 2007
 Daniel Robinson: Consciousness and Its Implications CD The Teaching Company, 2007. see also Daniel N. Robinson, Consciousness and Mental Life, Columbia University Press, 2007, 264pp. Several reviews of his paper appear at http://ndpr.nd.edu/review.cfm?id=14906, including a review by a proponent of monistic materialism.
 Willis Harman, Global Mind Change p. 9.
 The Origin of Spin: A consideration of Torque and Coriolis Forces in Einstein’s Field Equations and Grand Unification Theory, http://www.theresonanceproject.org/research.html#torque.
 Davies, Superforce p. 145 f.
 http://theresonanceproject.org/pdf/schwarzschild_proton_a4.pdf. In 1916, German astronomer Carl Swarchfield (Schwarzschild) proposed what we now call black holes. He postulated these would arise in cases where the mass was so concentrated that gravity was strong enough to prevent even light from escaping.
 Steven Strogatz Chaos DVD The Teaching Company 2008