the empirical standard of knowing - faith misplaced · the empirical standard for knowing - faith...

Exploring the limits in physics, complexity theory and mathematics. The empirical tenets

of faith contradict our shared personal experience and deny the obvious mystery and intentionality of the universe. A new symbiosis of spiritual and empirical inquiry as pathways to

knowing is needed.

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The Empirical Standard for Knowing - Faith Misplaced

By George R. Gantz Based on a presentation at the 2016 Annual Conference of the Institute for Religion in

an Age of Science (IRAS), Star Island, New Hampshire, June 25, 2016 Abstract: Humans have always sought to understand the world. Originally, understanding was derived from direct personal experience, intuition, imagination and shared cultural knowledge. In time, measurement and codification of regularities in nature added to human understanding. Natural philosophy (empirical science) became a key partner with human aspirations, leading to vast accumulations of physical goods and gratifications. As human economic progress exploded, particularly in the 20th century, our culture became increasingly secular and materialist. Pathways to knowing other than the empirical are often viewed as outmoded and sometimes ridiculed. This shift fails to acknowledge the hard limits to empirical knowledge and the implicit tenets of faith that ground the empirical enterprise. We explore the limits in physics, complexity theory and mathematics, and conclude that the empirical tenets of faith contradict our shared personal experience and deny the obvious mystery and intentionality of the universe. A new symbiosis of spiritual and empirical inquiry as pathways to knowing is needed. 1. Introduction The challenge we face in seeking to understand the world is analogous to the challenge we face in grasping the Goblet Illusion image provided in Figure 1. Is this a picture of a goblet, or an image of two faces staring at each other? The answer is, of course, that it is both, yet it is extremely difficult for our human brains to fully comprehend both at the same time. I suggest that scientific knowledge is like the foreground image, the goblet, prominent and immediate to our senses. Spiritual knowledge is more elusive, like the faces in the background, and requires greater imaginative effort to keep in focus. Figure 1 - The Goblet Illusion. Weisstein, Eric W. "Goblet Illusion." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/GobletIllusion.html

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The image of the two faces also offers a referent for the primary thesis of this paper, that the interrelated phenomena of consciousness, awareness, attention, reflection, contemplation and intention inevitably give rise to paradox and mystery. While we will never be able to fully comprehend and know the world, we can seek to transcend the paradoxical and the mysterious with a higher level of understanding incorporating both empirical and spiritual influences. 2. The Purpose of Knowing

The human story is wonderfully rich and complex, and that story has been the subject of study for a vast array of thinkers, philosophers, poets and theologians since before the dawn of recorded history. One key thread of that story involves the apparently unique capacity of humans for reflective consciousness - the ability to observe and create conceptual models for the patterns and regularities that we experience in the world around us. This consciousness - the activity of engaging with and theorizing about the world - is characterized by an inherent dualism between the embodied conscious self and the objectified world of which we are a part and with which we interact. We seek to understand and to bend that world to our purposes: purposes that include survival, the pursuit of pleasure, the avoidance of pain and the maximization of personal fulfillment in its many forms. We have come to name this understanding of the world and the mastery it confers as “knowing”. Knowing is at its core a personal and subjective enterprise. We each absorb and interpret our direct experience of the world and seek to make sense of it, to bring order to it. We learn to use our hands, to build tools and to master complex skills. We are also provided with powerful mental capacities that assist our learning – intuition, imagination and creativity. Our minds are predisposed to seek out and interpret patterns, whether they are the locations and seasons for edible foods, the behaviors of predators and prey, the fleeting and subtle expressions on the faces of our companions or the abstract meaning of symbols and sounds. We order, structure, interpret and engage with the world as animate and purposeful. At the same time, we are fundamentally social creatures. We are inextricably embedded in a human community by birth, by sociality and by language. We share and communicate our feelings, our experiences and our ideas about the world. This process builds a complex shared culture of stories, ideas, myths and revelations guiding our relationships with each other and our interactions with the world – a collective knowing that enriches and vastly expands our personal knowing. If this personal and collective knowing is successful in leading us to well-being and mastery, to personal and collective thriving, then we invest it with a special quality as “truth” and pass it on to future generations and across cultures. This process of adjusting, refining, redefining and reinventing human knowledge is evolutionary. Over time, humanity discovered and developed increasingly sophisticated observations, useful technologies and complex institutions that led to expanded knowledge and its application to the management and control of our physical and social environment. Agriculture, trade and empire became possible. Human civilization accelerated and knowledge expanded. Superfluity created the opportunity for specialists

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– priests and philosophers – to dedicate their lives to codifying and exploring knowledge for its own sake. Religion, art, architecture, literature, ritual and performance became increasingly sophisticated, woven deeply into human culture and life. Humans thrived. In recent centuries - roughly the last thousand years - humans learned techniques and invented tools for precisely measuring and categorizing the regularities of the natural processes in the world. Natural philosophy (empirical science) was born and became a key partner with human aspirations. The resulting technological and material development, particularly in the past few centuries, created the conditions for human thriving on a vastly expanded scale. This includes a current worldwide human population of about 7.5 billion, and an immense and complex infrastructure for the production and accumulation of a vast array of physical goods, comforts and gratifications. We have, indeed, bent the world to our purposes. 3. The Success of Empirical Knowing The scale of human achievement is demonstrated in Figure 2, a graph showing a measure of the global standard of living from the year 0 C.E. to the year 2000 - two millennia of human progress. The figure shows estimates from the respected researcher Angus Maddison of the average annual per capital worldwide gross domestic product - essentially a measure of the totality of goods and services produced by all humans. The values in Figure 2 are adjusted for inflation to US dollars - and the vertical scale is logarithmic, which means that the increases you see in the graph are exponential! We recognize that Figure 2 is showing an average, and that goods and services are NOT equally shared among humans. In any period, some are fabulously wealthy and some are desperately poor.

Figure 2. World Per Capita GDP Year 0 - 2000 CE Reproduced from William Bernstein, The Birth of Plenty Chapter One, Figure 1-2) For the first 1000 years, humanity averaged a little over $400 a year per capita, and in this year the population also grew slightly to about 250M (Maddison p. 264). In about

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the year 1000, the line jumps upward. Changes in worldwide trade and technology provided opportunities for significant increases in resource exploitation, and commerce. In the roughly 800 years that followed, per capita GDP nearly doubled. In this same period the human population also tripled, according to Maddison. After 1800, the graph shows the impact of the scientific and industrial revolution - in the last two centuries, per capita GDP increased almost ten-fold - a full order of magnitude. Population also increased by nearly an order of magnitude, to 6B. This means that total global production of goods and services (factoring in both population and per capita GPD) increased at a level approaching two orders of magnitude (a hundred-fold) in two centuries. It is no wonder, then, that this extraordinary success, derived from advances in empirical science and material technology, has been accompanied by a growing empirical ethos. As human economic progress exploded, particularly in the 20th century, our shared culture has become increasingly secular and materialist. Why should we pay attention to moral, spiritual, mythological, poetic, aesthetic, spiritual or religious impulses, experiences or teachings when science and its exclusive preoccupation with the empirical regularities of the physical world has proven so powerful and effective at meeting our needs and satisfying our desires? To many, empirical science appears to be the only knowledge - indeed the only truth - that we would ever need. To some, any suggestion that there are categories of knowing beyond the empirical is derided as delusion, hallucination or superstition. 4. The Limitations of Empirical Knowing Setting aside the question of physical limitations to the resource exploitation that underlies our two centuries of explosive materialism, there are fundamental epistemological limits to the empirical worldview and its various manifestations --- materialism, physicalism, reductionism, determinism, scientism or commercialism. The empirical worldview fails to acknowledge these limits. That failure has resulted in a denial of other dimensions of human knowing and the impoverishment of the human experience. Scientific truth is fundamentally limited in two distinct ways. First, the enterprise of science itself is grounded on first principles that cannot be proved - they are articles of faith. By “proved” in this context, I mean proved by deduction, beyond the possibility of doubt. Proof by induction or generalization, in contrast, is always subject to possible dis-proof from a single counter-example. These tenets of faith include the general principles that:

1. the regularities we observe in the physical world are reliable, consistent and enduring

2. these regularities are rational and comprehensible 3. mathematics is the language by which we can best explore and describe

these regularities I have no real disagreement with these articles of faith. Faith in the regularity and comprehensibility of the physical world is a necessary condition to knowing of any kind. But we need to recognize that these are not provable truth claims. Empirically, we have no way of proving that the world tomorrow will exhibit the same regularities as the world

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today - and no way of knowing that these regularities will be comprehensible to us, or be amenable to the tools of mathematics. We also cannot prove WHY these principles (and not others) work. Renowned physicist Eugene Wigner in a famous 1960 paper titled “The Unreasonable Effectiveness of Mathematics in the Natural Sciences” stated, for example: “The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.” We also need to recognize that the above tenets of faith do not exclude religion. It is entirely consistent to have deep faith in a creator God while holding fast to a belief in empirical science. Most of the great scientists through history including Newton and Einstein have, indeed, seen the order and beauty revealed by empirical science as manifestations of God. Yet modern secular science has tended to discard a faith in God or in any universal --- and has adopted certain additional tenets of faith, ones that I argue impose unwarranted metaphysical conditions that prohibit many reasonable hypotheses from consideration. These include the following:

4. the world is fundamentally random - there is no purposeful intentionality or agency involved in its functioning.

5. the world is causally determined, from small to large, from past to future -- reductionism is methodologically exclusive

6. the physical world is all there is - there are no non-physical causes, no miracles and, to some, no mystery.

These additional three principles, like the first three, are not scientific laws and they cannot be proven, even though many scientists believe them to be true. In fact, they are articles of faith. Moreover, I believe they are unwarranted, and that they often serve as dogmatic preconditions that confine knowledge to merely the empirical realm. As such, they seriously undermine the opportunity for dialogue and mutual understanding. Ultimately, they confine the range of human knowledge and deny the true richness and depth of the human experience. The second, and perhaps more significant, limitation to scientific truth, as I discuss in the body of my presentation, is that modern science and mathematics are increasingly confronted with fundamental paradoxes that cannot and will not be resolved. These conundrums point to the existence of a level of knowing that is inaccessible from within the physical and mathematical constructs of empirical science. The common feature of these paradoxes rests, in my opinion, on the inherent dualisms of consciousness and creation. Once the universe awakens to itself - which happens through the abstract forms of mathematics, the manifestations of the physical world and sentient consciousness - the reality of its incomprehensibility as a whole becomes manifest. The empirical ethos excludes from admissible reality a variety of things that are critical to human life and experience. These include the subjective reality of internal contemplation, self-awareness and the problem of qualia in philosophy. The mechanism of intention and choice, of free will, also does not sit well with the empirical tenets -- in spite of the evidence that these are inherent features of individuals, quantum particles and the universe as a whole. The hard problem of consciousness, the problem of the observer in quantum physics and the peculiarities of both infinity and recursive functions in mathematics remain unaddressed. Finally, love and the grand arena of feelings,

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affections and motivations, the very things that give meaning to our lives and to the universe as a whole, are largely disregarded as invisible. For these reasons, I suggest that adherence to an empirical standard for knowing reflects a faith that is misplaced. At it’s worst, such faith becomes an unquestioning and ideological dogma. But even in its more benign forms, the empirical standard limits unnecessarily the range of human knowing. Understanding these limits opens the door for a broader and deeper appreciation of the human experience; a potential range of knowing that can tap into the deep roots of our rich human heritage and our subjective and interpersonal experiences. Knowing is possible only through faith that reaches beyond the empirical to a spiritual knowing that aspires to the transcendent. 5. The Arrow of Time

The Moving Finger writes; and, having writ, Moves on: nor all your Piety nor Wit

Shall lure it back to cancel half a Line, Nor all your Tears wash out a Word of it.

The Rubaiyat of Omar Khayyam (tr. Fitzgerald) LXXI

This is one of the most famous quatrains in the Rubaiyat of Omar Khayyam, a work that captured my imagination as a teenager for its puzzles and riddles and the ironic tone it uses in dealing with deep philosophical issues. This quatrain addresses the directionality of time, one of the most challenging issues in modern physics, a challenge that was precipitated by Albert Einstein’s Theory of Special Relativity, published in 1905. Before Einstein’s paper, the prevailing Newtonian concept was that space was a fixed frame of reference for objects moving in time. This concept is consistent with our normal experience – objects appear and move within a fixed background reference frame. We can measure things with a yardstick and we can monitor their motion with a clock. But physicists at the time were dealing with phenomena operating well outside of normal experience. In the Michelson-Morley experiments (1887), for example, scientists expected to find that there was a difference in the speed of light for moving or stationary observations, consistent with Newtonian physics. Think of a train moving towards you - if you are stationary you will observe the train at one speed - but if you are moving toward the train, the train will appear to be moving faster, and the train whistle will sound higher in pitch - the Doppler effect we are all familiar with. The scientists knew that the earth was spinning and moving through space, so they cleverly measured the speed of light in the direction of motion and at the same time perpendicular to the motion. But they could detect no difference. This was a big problem! Einstein’s theory solved the problem in a remarkably elegant way by redefining the relationship of space and time – they do not provide a fixed frame of reference. In particular, objects and events in time and space will be perceived differently by two observers based on their relative position and motion! The only phenomenon that both will observe to be the same is the speed of light which is constant, and finite, in all directions and circumstances. For practical purposes, this revolution did not change our world – we live in a way that could be characterized as non-relativistic and largely local. We will never have the chance to travel at near the speed of light, so we will never experience the time dilation

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effect, as Matthew McConaughey does in the movie Interstellar (2014). That story line is a version of the famous Twin Paradox that emerged from Einstein’s theory. Given the nature of relativity, if one of two identical twins sets off in a spaceship at near the speed of light, and then returns, the traveling twin will be much younger than the stay-at-home twin. The Twin Paradox is not the only puzzling feature of special relativity. Based on Einstein’s theory, physicists have reframed the conception of space and time as a four dimensional topological manifold referred to as Minkowski space. This four dimensional space has been characterized as a “loaf” of space-time. Any given slice of the loaf (or conic section to be precise) represents one observer’s frame of reference as a function of their location and motion. Different observers in different locations travelling at different speeds result in slicing the loaf quite differently. Considering the entire universe as a whole, there is an observer somewhere in the universe for whom our past is their present and, correspondingly, an observer for whom our future is their present. Past - present - and future are all there. This yields a peculiar form of observational determinism – the sense that our future has, in someone’s reference frame, already happened. Another remarkable features of the fundamental laws of physics, including Newton’s Laws of motion, Einstein’s Theories of relativity and gravity, Maxwell’s laws of electromagnetism and the Schrodinger equations of Quantum Physics, is that they are all symmetrical with respect to time. In other words, all of these laws are time invariant: They work equally well going forward in time as going backward. They do not require that time only move in one direction, and they do not explain time’s directionality, what many call “the arrow of time”. While this is remarkable, it is also inconsistent with one of the key regularities of the physical world we live in - that time only goes one way. It is perhaps not surprising, then, that physicists repeatedly tell us that our common sense understanding of time is an illusion. 6. Entropy and Complexity

What, without asking, hither hurried Whence? And, without asking, Whither hurried hence!

Oh, many a Cup of this forbidden Wine Must drown the memory of that insolence!

The Rubaiyat XXX The arrow of time can be found in another field of science, thermodynamics, the study of how energy behaves in dynamic systems. We are all, I suspect, familiar with the First Law of thermodynamics, the conservation of energy. In a closed system, energy cannot be created or destroyed. The Second Law of thermodynamics points to another feature of energetic behavior in closed systems: A system, whatever its initial configuration, always and inevitably progresses toward states of increasing homogeneity or “sameness”. Release gas into a closed box and it will eventually fill the box in an even distribution. The technical measure for this homogeneity is entropy, and the Second Law states that entropy always increases. A block of ice melts and becomes a puddle of water; an egg falls and breaks and, like Humpty-Dumpty, cannot be reassembled. The structure and morphology of the starting points of ice or egg have

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been lost, the end states of water and broken egg are all mixed up and the starting structures can never be reassembled. Entropy has increased. This indeed, is consistent with our perceptions and notions of the effects of time. We know perfectly well what time is in our lives – we remember the past, we experience the present, we anticipate the future, and we cannot go backwards. These are real experiences – they are not illusions. From this perspective, it seems that relativity and the time invariance of the physicists’ formulas have left something important out - and that is the real illusion. One additional puzzling aspect to the story of time is the fact that all of the interesting structures we see in the universe, including planetoids, stars and galaxies, crystals and fluid flow, life forms, human technology and creativity, seem to violate the Second Law. If time is the process of the universe “running down” by transitioning from the low entropy conditions of the Big Bang to states of increasing homogeneity and higher entropy, then where do the remarkable cosmological features of stars and galaxies, as well as the complex phenomena of chemistry and biology, come from? These phenomena all seem to reflect an increase in order, structure and variety quite at odds with the Second Law’s imperative for homogeneity from increasing entropy. This is, in fact, the case --- all of these phenomena are local violations of the Second Law. Local structure and order emerges by exporting entropy to the larger environment. The entire universe as a whole continues to run down, towards some icy and inevitable death state, but as it does, local pockets of increasing organization and structure emerge. An explanation for how this counter-entropic process operates to bring order, structure and growth can be found in the theory of non-linear dynamic systems pioneered by Ilya Prigione and others. This theory posits that in open dynamic systems where energy is in flux, stable structures tend to emerge in the otherwise chaotic flow. These structures succeed by dissipating the energy within the chaotic flow efficiently. For example, when we open the drain at the bottom of a sink the water molecules rush for the drain, bouncing and jostling in a disorganized and turbulent chaos - yet we can then see the swirl of a whirlpool – a stable and orderly structure – emerge. What we are watching is the transformation that the dynamic nonlinear system of flowing water is going through as it seeks out a state that maximizes the efficient local dissipation of energy. The result is a stable, persistent structure. Remarkably, all of the structures we see and study in the universe, from cosmological and geological to chemical and biological (indeed including all of life, ecology, even economics) are the result of dynamic systems that exhibit this behavior. Snowflakes form in the dynamic chaos of moisture-laden clouds and complex, beautiful and fragile crystalline forms of nearly infinite variety emerge. Turbulence in water results in swirling eddies, dancing waves and shimmering surfaces, all evidence of order and structure emerging from chaotic dynamic processes. The flocking of birds in a configuration known as a murmuration creates a dancing, spiraling pattern. The birds themselves follow simple, instinctive flight rules, but a form of intelligence and remarkable sophistication emerges from their simple behaviors, as it does in every bee and ant colony. The human immune system, consisting of many interlocking feedback loops acting in the complex soup of biochemistry and cellular dynamics, creates a powerful and purposeful functionality of human biology. Even the simplest of living structure

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such as a sunflower, a mindless and immobile plant, produces a beautifully ordered and structured flower. In minimizing the energy used in growing the flower, the plant follows the simple rules of the Fibonacci sequence and Golden Ratio, resulting in a structure with multiple interlocking spirals spinning both left and right. So, while time proceeds forward, marking the gradual build up of entropy throughout the universe, the dynamic nature of this forward progress leads to the emergence of increasing complexity and variability, to life itself and, ultimately, to human consciousness. From this perspective, it seems that the physicists’ proclamations that time is an illusion is quite unsupportable. The dynamics of movement through time is, indeed, the basis for all of the interesting stuff that happens in the universe. However, the interesting behaviors of these nonlinear dynamic systems, the structures that fill the universe, raise uncomfortable questions about causality and teleology. What is the cause of the order that emerges? How does a crystal structure itself? How does intelligence emerge from unintelligent creatures such as birds, cells or plants? The challenge is that emergent processes are counter-reductionist; they cannot be explained in terms of bottom-up causation. Moreover, the behaviors that emerge are purposeful and not random. How does one reconcile this with the unwarranted tenets of faith we discussed earlier? 7. Quantum Physics One of the very first things I learned in physics is the puzzle of Heisenberg’s Uncertainty Principle. In its simplest form, this principle recognizes that when scientists try to observe very, very small phenomena, the observations will necessarily change the phenomena. Classically, one can determine precisely the position of a particle, or its momentum (energy), but not both, since making the measurement of momentum changes the position, and vice versa. This actually makes sense! What does not make sense, however, is what happens in the double slit experiment of Thomas Young, first performed in 1801. In this experiment, a researcher fires photon particles from a light source towards an opaque surface with two slits. As the photons pass through the slits, they travel to a photosensitive screen that records where they land. From a Newtonian perspective, we would expect the photons to pass through one slit or the other and create two lines on the back screen. However, even when firing single photons as particles, one-at-a-time, through a double-slit device, the pattern displayed on the screen on the other side shows interference, with brighter and darker lines at various angles away from the straight line path the particles should have taken. The interference shown is consistent with the behavior of light acting as a wave. How can light be a wave and particles in the same experiment? How do the individual photons know where to land to create the interference pattern? Wave-particle duality is an example of a larger issue in QP known as indeterminacy. In the double-slit experiment, the precise location for any given light particle cannot be determined (it is indeterminate) until the particle strikes the screen. More broadly in QP, the characteristics of a particle (position, momentum, charge, spin, etc.) are not fixed, but subject to probability distributions. Only when the characteristic is measured in a given experiment (i.e. observed) does it reveal its characteristics.

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Let’s consider the case of a radioactive molecule that will, at some point in time, decay into two smaller molecules. That decay is subject to a probability - there is a 50% probability that it will decay within time X. If we set up multiple identical experiments and observe them after time X, then half will have decayed and half will not. However, we will not know which until we observe them all. Prior to the observations, the status of each individual experiment is indeterminate. This is not, as you might think, just a question of not knowing because we haven’t looked - the experiments confirm that it is the looking - the measurement or the observation - that causes the probability to go from “50%” to either one or zero. The peculiarity of this probabilistic feature of QP led physicists to develop an understanding known as the Copenhagen Interpretation (CI) of Quantum Physics. CI postulates that units of radiation remain suspended in the indeterminate wave-form as probability states or “super-positions” of the two alternate possibilities. These states (and the wave-form they are in) collapse into a single definite state, an outcome, when observed in an experiment. The indeterminate waveform probability state is a state of coherence, with both possibilities still in play, and the waveform collapse reflects what is called decoherence as one actuality is observed and the other lost. David Mermin characterized the CI derisively (in a quote often attributed to Richard Feynman, or Paul Dirac) as the “shut up and calculate” rule (Mermin, David 2004). Erwin Schrodinger developed a thought experiment known as Schrodinger’s Cat that demonstrates the illogical feature of the CI. In this experiment, a cat is kept in a cage in which the decay of a single radioactive atom will trigger a device to release poison, killing the cat inside. According to CI, before the box is opened and an observation made of the state of the radioactive atom, the atom is in a “superposition” and the cat, correspondingly, must be both dead and alive. Only when the box is opened and the status of the experiment observed does the wave-form collapse. At that point the cat is either alive or dead, but not both. No one ever seems to ask what the cat might think about all this. One line of thinking that seeks to respond to the confusion of CI has become widely popular. Known as the multiverse hypothesis, the idea is that for any wave-form superposition, alternate universes are created. That would mean there is one universe in which Schrodinger’s Cat is alive - and another in which the cat is dead. The observation we make at the end of the experiment just reveals which universe we are in: the one in which the cat is dead, or the other in which it is alive. Taken to its logical conclusion, the multiverse hypothesis applies to every waveform collapse that has ever taken place in the history of the universe, generating a seemingly infinite set of alternate universes, only one of which we have the opportunity to observe: the one we happen to be in. One might wonder what the appeal is of this theory that seems to stretch credulity to the limits. One answer is that it eliminates several sources of discomfort for physicists. For example, it is widely understood that the physical constants for the fundamental forces of physics appear to be very precisely specified - very minor deviations in any of them would have resulted in a universe in which the structure of stars and galaxies, the nature of chemistry and life itself would have been impossible. This is known as the “fine tuning” problem, or “why is our universe so special”? The multiverse theory offers a solution by suggesting that this is simply coincidental - we are in the one universe among countless universes that exhibits the particular fine-tuning constants that it does.

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Bottom-up causality and the absence of purpose can thus be sustained, in the face of the circumstantial evidence to the contrary which fine-tuning exhibits. Another set of problems in QP arises in the phenomenon known as entanglement, or paired particles. Entanglement occurs when two particles are created in an experiment that, by necessity, share specific attributes, such as spin, in order to preserve conservation laws. Two entangled, paired particles are created and then fly off in different directions. Being paired, they share the specific characteristics of spin, even though that characteristic is in the form of a probability distribution or waveform superposition. Until it is measured, the spin is indeterminate. Remarkably, when one of the paired particles is measured and the spin is determined, the other paired particle, no matter how far away, will prove to have the same spin. It is as if the first particle to be measured “chooses” and the other particle obeys instantaneously. One plausible explanation is that somehow the two particles communicate with each other. Some unseen, potentially massless messenger jumps to the second particle when the first is measured. However, if this were the case, the messenger would have to travel faster than the speed of light, violating Einstein’s relativity theory. Moreover, experiments have been conducted where each observation point would perceive the other to be in the future based on Einstein’s theory of relativity. Yet efforts to trick the paired particles into a contradiction always fail. One possible conclusion is that there is a form of “non-local” coordination that extends outside of space and time. Many physicists find the concept of non-locality troubling, as it introduces the idea that there can be “causes” outside of the physical constraints of space and time. An alternative conclusion is that when the particle measurement is taken, the outcome will, in effect, apply backwards in time to when the two particles were created. Once the measurement is made, it will be as if the particles had always been that way. This theory is called “retro-causality” and it has some significant implications (if true). While retro-causality does not require faster-than-light communication, and also moots the multiverse hypothesis, it does postulate a form of time travel. More significantly, retro-causality brings relevance to the concept of purpose or “ends”. The end-state of a quantum choice can influence past states and the resulting space-time trajectory. With retro-causality, evolution may be characterized as the future perfected state “coming into being”. While theologians are comfortable with this idea, physicists are not. As long as Newtonian and then Einsteinian physics held sway, physicists had no interest in teleology since the universe was perceived to behave deterministically. Now, however, in the case of entanglement, there is a potential mechanism being considered that brings teleology into consideration. End states in quantum physics may be found to play an instrumental role in evolutionary processes, serving as a “purpose”, which could solve some of the problems in evolutionary theory. Just as there is a need for “top down causation” in understanding emergent phenomena generally, there seems to be a need for a purposeful agency in evolution, and QP is pointing to that issue. As a final note, one of the central features of QP is the role of a conscious observer in establishing the conditions for quantum phenomena, e.g. collapse of the waveform superposition. In essence, there would be no physics if there were no observer. Some have speculated that, in some sense, the purpose of this universe has been to create

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the conscious observer that measures it. Others think that as consciousness is integral to QP, consciousness in some universal form has to exist prior to QP. Einstein once characterized quantum physics as “spooky action at a distance”. This is as much the case today as it was a century ago. While considerable experimental and intense theoretical efforts have been devoted to the resolution of these issues and the unification of quantum and classical physics, these efforts have failed. Increasingly, however, some theoreticians are calling into question the dogmas of a purposeless universe and causal determinism and raising speculations about there being non-physical attributes to our world. 8. Mathematics and Logic

For "Is" and "Is-not" though with Rule and Line And "UP-AND-DOWN" by Logic I define,

Of all that one should care to fathom, I was never deep in anything but--Wine.

The Rubaiyat LVI To an adherent of scientism, the seemingly intractable problems we discussed above are merely bumps in the road. We are making inevitable progress towards a universal empirical theory of everything, and when the next Einstein comes along, the current quandaries will be resolved. The optimists think we are very close citing superstring theory, Hawking’s M-theory, or Supersymmetry. This attitude is reminiscent of what A.A. Michelson said in 1903, just before relativity and quantum mechanics shook the foundations of physics: “The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote. ... our future discoveries must be looked for in the sixth place of decimals.” (Michelson, A.A. 1903, 23-4) Truthfully, science has made great advances, and some of the conundrums of today may be reconciled in the future. There is a class of these conundrums, however, that can never be reconciled. They involve the very foundation of thought itself. By its very nature, thought is a dualistic exercise - there is an observer (a thinker) and there is the object of thought. Moreover, one of the more interesting objects of thought is the thinker. This brings us to consider the implications of self-reflection in logic and math. Mathematical self-reflection, the property known as recursiveness, may not seem like a big deal, but major developments in the past century in set theory and symbolic logic have pointed to some unexpected and profound results. It might seem a little odd, but it is actually quite important to consider mathematical or logical statements that refer to themselves. Algebraic functions themselves often contain the dependent variable in the function, and set theory often deals with sets that may or may not be members of themselves. In logic, propositional statements often talk about themselves. For example, the sentence “This statement contains five words.” is understandable; and, it is also (TRUE). And the sentence “This sentence was written by hand.” is also understandable, even though it is (FALSE). Self-referential statements like these are quite common, useful and important. But knowing the meaning and truthfulness of a

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sentence becomes more difficult when you say, “This statement is false.” If true, the statement contradicts itself. If false, it curls back and bites its own tail. This curious linguistic sample is known as the liar’s paradox, and while it may seem no more than a parlor trick, among mathematicians since Frege and Russell, it has led to no end of difficulties. Bertrand Russell coined his own version in set theory by postulating a special Set, the Set that contains all of the Sets that do not contain themselves as members. If that Set does include itself as a member, then it must be excluded. If excluded, then it must be a member of the Set! The definitive statement about the significance of these difficulties came some eighty years ago, when renowned logician Kurt Gödel proved his incompleteness theorems. The proofs address two key characteristics we require in any formal system of logic, the qualities of consistency and completeness. Among the many systems of logic we are concerned with here is the very helpful and ubiquitous mathematical system of arithmetic. Consistency means that in our system of logic we can prove things that are true, and that we cannot prove things that are false. Completeness means that we can determine in our system of logic whether any particular statement is true or false. So consistency deals with the trustworthiness of the logical system: knowing that we cannot prove a lie. Completeness deals with the usefulness of the system; Undecidable statements, ones which we cannot prove as being true or false, are, after all, a significant nuisance, if our goal is to know the truth. Gödel’s theorems prove that it is impossible to achieve both consistency and completeness in any but trivial logical systems. If we demand consistency, then there will be statements that are true but unprovable. Moreover, if you design a logical system that is provably complete and therefore has no indeterminate statements, then it will necessarily be inconsistent, which means, effectively, you can prove anything. To put it simply, there is a serious blind spot in logic itself, and the implications to mathematics and all the fields of science that depend on it are philosophically significant. Many thinkers, over the millennia, have vested mathematics with an absolute and inviolable perfection that in some cases rises to the level of mysticism or religion. But now we know that our very best logic has blind spots. The most we can hope for in terms of proving truths is consistency, but not completeness. Some true logical conjectures can never be proved. In these cases, ascertaining truth requires stepping outside of the specifications of that logical system. By analogy, a logical system is like being in a box with some truths written on the outside of the box. These can only be verified from the outside. There are additional challenges to mathematical knowledge relating to complexity and computability. For example, consider the simple challenge known as the traveling salesman problem (“TSP”). As a salesman, or a tourist, if you want to plan an optimal route through a few cities, you can make a few calculations of how the mileages all add up between the locations, and pick the route that minimizes the miles. However, as you add to the number of cities, the complexity of the required calculations goes up incredibly fast! It quickly becomes exceedingly difficult to calculate all of the route options in order to be certain that you select the correct answer. Remarkably, in the case of just 100 cities, there are more route options than there are atoms in the known universe. Such calculations are not just difficult – they are impossible.

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The TSP is an example of a broad class of hard problems, some of which show up in fields such as logistics, the manufacture of microchips and DNA-sequencing, to name just a few. These problems are referred to in mathematics as “NP” (Non Polynomial, or technically, NP-complete), in contrast with the more congenial class of problems known as “P” (Polynomial). P problems may be very complex, but they can, at least in theory, be solved in a reasonable amount of time. There is always the hope, however, that someone can find a shortcut to any particular NP-complete problem that would reduce it to a P problem. Quite surprisingly, there is a proof that if one such shortcut exists, then all NP-complete problems have shortcuts and the world immediately gets much simpler. The stakes for solving this problem are very high, and a Clay Prize of $1M is being offered for anyone that can solve it. Most experts believe a P shortcut does not exist for any NP-complete problem, but if it did, the challenges of complexity would be reduced from impossible to merely very hard. Alan Turing, another brilliant 20th century logician, tackled the very practical concern of constructing a universal computing machine (technically a computational algorithm) to solve math problems. Turing proved the feasibility of a universal computing machine. As we know, computers are now ubiquitous in the 21st century world we live in. All math and logic can be coded in machine language. Any such problem can be put through machine algorithms for a solution. However, Turing was also concerned with how long a given algorithm might take to solve a problem. Would the algorithm ever halt? This is the so-called halting problem. Turing was able to prove that the halting problem does not have a finite solution. Therefore, for some algorithms (including the halting algorithm) we are unable to determine if they will complete their task in a finite amount of time. Do you remember the scene in The Imitation Game (2014) when Alan Turing was staring at his computing machine as the dials were spinning and the gears cranking away late into the night as it sought to solve the Enigma Code? That was a lovely metaphor for the halting problem. There are other continuing challenges in the field of mathematics, including the very nature and interrelationship between the concepts of zero and infinity. Suffice it to say that in logic and mathematics we are eyeball to eyeball with the truth - and it slides from our comprehension. Mathematics may be the ultimate tool, but it denies us the ultimate truth. 9. Revising the Empirical Tenets of Faith I hope you are convinced that the empiricist worldview is premised upon certain articles of faith that are forever unprovable. You may also agree that the articles of faith that underlay the empiricist worldview remain largely unexamined. When this faith becomes rigid dogma, as it has among many practitioners and believers and, to an extent, in the mainstream culture, it destroys constructive inquiry and undermines the quest for knowledge. Empirical knowledge is limited, and developments in mathematics and science over the last hundred years have laid bare a variety of inconsistencies and gaps that can only be addressed by engaging in different forms of knowledge acquisition. When we entered the 20th century, the Newtonian metaphor of a predictable and mechanical world was also accompanied by a buoyant empirical optimism. Just think of the crowds at the Paris World’s Fair in 1900, celebrating the rapid advancements of science and technology and the certainty they brought with them. Remember the quote

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from A.A. Michelson in 1903: “The more important fundamental laws and facts of physical science have all been discovered.” There was also the movement in the 1920’s known as Logical Positivism - premised on the goal of codifying all knowledge in propositional logic. Despite the ravages of two world wars, economic and technological progress continued to accelerate during the 20th century. Yet, at the same time, the certainty and predictability inherent in the Newtonian worldview was being eroded. In the latter half of the 20th century, the notions of uncertainty, indeterminacy and relativity had seeped into the popular culture. Chaos theory and black holes became common metaphors. Relativism, the idea that there is no absolute truth and that truth is only subjective and relative, became commonplace. These cultural memes and the anxiety and existential queasiness that accompany them are, in large measure, the consequence of the wave of continuing revolutionary scientific discoveries. Certainly, while our standard of living has risen, the world has become a more unsettled place. Confidence has been lost. With this context in mind, let us examine again the empirical tenets of faith introduced earlier, and consider how, in light of the findings here, we might consider revising them. 1. The regularities we observe in the physical world are reliable, consistent and enduring.

1. (Restated): The regularities we observe in the physical world are reliable, consistent and enduring.

2. These regularities are rational and comprehensible.

2. (Restated): These regularities are rational and comprehensible, however our ability to comprehend them is fundamentally limited.

3. Mathematics is the language by which we can best explore and describe these regularities.

3. (Restated): Mathematics is a useful language to explore and describe these regularities; however there are aspects of knowing that extend beyond logic and mathematics.

4. The world is fundamentally random - there is no purposeful intentionality or agency involved in its functioning.

4. (Restated): The world seems to be both random and purposeful - we need explore these questions and invest faith in the explanations that provide the deepest understanding.

5. The world is causally determined, from small to large, from past to future -- reductionism is methodologically exclusive.

5. (Restated): The world functions causally, probabilistically and intentionally - we need to explore these questions and invest faith in the explanations that provide the deepest understanding.

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6. The physical world is all there is - there are no non-physical causes, no miracles and no mystery.

6. (Restated): The physical world is immediately accessible to our physical beings; however there are also realms of experience beyond the physical and these are the wellspring of love, creativity, and mystery.

In summary, there are levels of knowing that are inaccessible from within the physical and mathematical constructs of empirical science. The universe has awakened to itself. Evidence of this awakening and self-awareness can be found in the abstract forms of mathematics as well as in the manifestations of complexity, emergence and quantum theory in the physical world. At the pinnacle of this awakening is our human consciousness. We are reflective observers of the world and self, and our consciousness is, in some sense an anchor for quantum physics and a purposeful end-state of evolutionary complexity. The empirical standard for knowing is faith misplaced. Understanding the limits of empirical knowing opens the door for a broader and deeper inquiry into the human experience through alternative ways of knowing that draw from our rich human heritage and build on our subjective and interpersonal experiences. We come full circle to the roots of our humanity and our quest for knowing and to the origins of this mystery we call life.

Figure 3. Yin Yang Balance Symbol (Pixabay.com 145874), downloaded 10-4-16. 10. Conclusion We began this paper with an image of The Goblet Illusion. Based on the themes discussed in this paper, it is appropriate to end with an image that captures the concepts with more subtlety, the Yin Yang Symbol shown above in Figure 3.

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Perhaps this is a fruitful way of thinking about science and religion. The two disciplines are intertwined. Both seek knowledge about the same totality in which we live. At the heart of science is ineffable mystery. At the heart of religious transcendence is the mystery of our physical embodiment in the empirical world. We can also look at this as a picture of the reflective, conscious self dancing with the outside world, which is the entirety of the other, or non-self. At the heart of our subjective self, we find the deep relationships we have with the world, through which the self is created, nurtured and shaped. At the core of the world is the fact that it needs to be observed and our subjective self is the observer. We may also consider the image as showing creation in its totality. Creation requires both mathematics, the pure form within which creation unfolds, and movement, the action and change that constitutes its becoming. At the core of both is the ineffable, infinite mystery by which they are united. Yet, as in the cases above, they comprise a unitary whole. ____________________________________________________________________

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