Attending the Emergence of a New Science - Part I
Attending the Emergence of a New Science - Part I
Attending the Emergence of a New Science
A quiet revolution is occurring. There is something beginning in the fields of philosophy, mathematics, and the sciences, which holds the potential to transform the nature and function of science and mathematics-- and the very foundations of human inquiry and discovery, from physics and biology, to medicine and the social sciences. We are presently standing on the threshold of a truly profound and sweeping paradigm change, a real revolution in science whose implications are every bit as significant as the ancient discovery of fire. With the understanding of fire our civilization was born. With the understanding of life itself, civilization will take on a new dimension of completeness, ushered in with a new Renaissance in the sciences and humanities.
Mystic, Connecticut, an historic harbor town made famous as the starting point of many intrepid voyages, was the birthplace of TAI, a place where a global community of thinkers will soon embark on a new venture-- to give form to a new kind of science, the science of autognomics.
What is autognomics?
The term "autognomic" means "self-knowing"(Greek auto, self and gnosis, knowledge), referring to innate natural processes which allow living organisms to regulate and manage themselves. Autognomics is the study of the natural inherent principles organizing life itself, which involves the discovery of the natural logics within living systems. (A system is a composite unity-- that is, a collection of components integrated into mutual dependencies to function as one entity. Many non-living systems are simple systems such as our machines, that obey the laws of classical Newtonian physics. An automobile is an example of a simple non-living system. It is assembled from many parts, all of which have to function together.)
Living systems are natural systems-- that is, systems comprised of infinite functions and variables that cannot possibly be described or explained by the finite laws of Newtonian physics or Cartesian logic. Holistic fields form the living system (the organism, groups of organisms, and the ecosystem). The organizing field changes the "parts", such as the atoms. They are not the same in the system as they were before they became part of the system. Organisms and their communities, according to autognomic theory, are inter-connected, inter-dependent, yet autonomous, harmonic-holistic living systems. The term "logics" as it is used here refers to the organizational and structural patterning of a living system, in the sense that logistics applied to an organism would represent specifically the handling of the details of processes in that organism-- such as cycles, osmosis, mitosis, chromosome arrangement, etc.
Autognomic study recognizes a distinction between man-made logics and natural logics, and concerns itself mostly with describing the latter. The traditional domain of logic has been the expression of laws of deliberate, rationally controlled thought and conduct. Logic has been consigned specifically to the format of man-made reason, the necessary but artificial figurative cable or railing we hold onto as we navigate through our human existence and coexistence. But the guidance offered by conventional reason involves only a superficial layer of our experience and thought, and hence also of our actions. Reason-- and therefore traditional logic-- leaves out the irrational forces of fears and desires that compel us from beneath the surface level of the thinking we learn from our family and our society.
The new logics, and the new broader use of the term "logic", take on a meta-logical, or epi-logical dimension. That is to say, they consider courses and forms of thinking that are outside of the traditional course or track of rational thinking-- and even of human thought itself. "Logic" in its broader sense can now apply to the factors influencing "decisions" made by organisms never before considered intelligent enough to be evaluated in light of logic. Such newly considered logical decisions may even be made on a cellular level: a logic may be said to govern the processes of chromosome arrangement, for instance, or cell division.
At present, autognomics exists as a philosophy in the early stages of ushering in a new science-- the first science of natural logics. The emerging foundation for the coming science of autognomics lies in the natural laws and logics now being discovered in the working totalities of living systems. Individual scholars around the globe are working within several disciplines to create new models to illustrate the hidden dynamics in these natural processes in ways that will allow us to understand them. The goal at the Autognomics Institute is to synthesize those collective discoveries into one coherent theory-- a holistic theory of living systems and life itself. The science of autognomics will integrate new logics which will be foundational to the transformation of existing sciences and other disciplines, including fields in the humanities such as aesthetics and ethics. There will also be entirely new disciplines that will arise along the lines of the new logical foundation.
The Autognomics Institute was founded by Norm and Skye Hirst, Jon Ray Hamann and Eugene Pendergraft in 1992 as a response to the Gulf War. When President Bush said he had sent a clear message to Saddam Hussein we knew there was something wrong. Understanding life it is clear that sending a clear message in impossible. For the President of the United States to claim to have done so indicated to us that even men in high places lack understanding of life and that is a dangerous condition.
Norman F. Hirst is an M.I.T. graduate in mathematics and physics who designed early autognomic programs at the University of Texas in Austin and holds several patents in artificial intelligence. Hirst's work on the theory of autognomics goes back to his taking a course on value theory with Robert Hartman, an internationally renowned philosopher visiting M.I.T. He realized that there was some systemic defect in our knowledge of the time that prevented our understanding values. Since the mid 1950s, Hirst has engaged in extensive studies of logic, philosophy (metaphysics), the foundations of scientific thinking and various sciences from physics to computer science. In addition he has been involved in many computer applications from calculating interplanetary transfer orbits to the field of computer language translation, developing programs at M.I.T. and the University of Texas.
Today, Hirst works at the Autognomics Institute, "a research and educational organization dedicated to the theory of living systems which, in addition , provides the logic for multi-enclave self-organizing computer systems." Using new computer simulations, Hirst and other pioneers of autognomic theory are taking closer looks at the seemingly random and "chaotic" changes in both the large-scale and the small-scale universe, from the micro-movements of quantum particles and fields, to the organization processes in living cells, and out to the formation patterns of billions of galaxies and star clusters, which on that newly surveyable grand scale bear striking resemblances to living tissue. Hirst invites scientists and other leading thinkers of all fields "to present their ideas and experience in an informal discussion process inviting exploration and inspiration."
"Human knowledge evolves through philosophy to science."
-- Robert Hartman
Dr. Robert Hartman, a professor of philosophy at M.I.T. during the 1950s, when Norm Hirst was a student there, presented a profoundly significant thesis. Philosophy, Hartman said, analyzed experience and in the course of time-- in the case of our history, more than two thousand years-- analysis yielded synthesis and scientific inquiry replaced philosophical inquiry. In a well-known incidence of this process, Isaac Newton turned the philosophy of motion into the science of motion. As a result, we live in a world transformed by Newton's laws of nature and his calculus. Now, Hartman believed, the time was right to turn the philosophy of value into a science of value.
The philosophy of autognomics
Autognomic theory in its present form is a holistic, "organicistic" philosophy of infinite dynamic process and natural meta-logic, inspired by the works of Charles Peirce, Alfred North Whitehead, and several other process philosophers, and carried forward into the present century by Norman Hirst and the scholars and scientists at the Autognomics Institute. The terms "holism" and "organicism" are for most purposes interchangeable. Holism, as it appears in autognomic theory, refers to a mode of organization found in natural, or living systems, in which parts are integrated into wholes, or totalities, which in turn relate to a greater whole (organisms, to eco-systems, ultimately to nature as a whole), and in which the properties and functions of any system cannot be reduced to or predicted by the smallest units in the system.
The idea of looking to the patterns found in nature for inspiration-- whether artistic or technological-- is not a new one. In fact, it's probably one of the oldest ideas out there, as the pictures on the walls of the Lascaux caves in France so vividly suggest. Process philosophy itself has a long history that began with Heraclitus in the sixth century B.C. (and perhaps earlier in China) and includes George Wilhelm Friedrich Hegel, William James, Charles Peirce, Henri Bergson, John Dewey, G.E. Moore, and Alfred North Whitehead, to name a few. The vigorous, roiling, revolutionary movement at the core of their thinking has never been well understood by the majority of any era in the past. Simpler, more static thinking has always dominated the inquiry and procedures in all fields of human endeavor. It is a matter of conjecture whether the true revolutionary mode of thinking in dynamic, holistic terms will catch on during our present century. But this time there is a very big difference in our looking to nature with an eye to change and the new. Today we have access to technology that is helping us dig beneath the surface of the very fabric of our universe itself.
At present, autognomics exists as a philosophy in the early stages of ushering in a new science-- the first science of natural logics. The emerging foundation for the coming science of autognomics lies in the natural laws and logics now being discovered in the working totalities of living systems. Individual scholars around the globe are working within several disciplines to create new models to illustrate the hidden dynamics in these natural processes in ways that will allow us to understand them. The goal at the Autognomics Institute is to synthesize those collective discoveries into one coherent theory-- a holistic theory of living systems and life itself.
With the study of living systems, the process of synthesizing a new science from the emerging theories and logics now becoming available will be one of two ongoing endeavors at Autognomics Institute. Alongside of long-range research, existing autognomic theory is currently being applied by consultants at the Institute in the areas of business, education, medicine, economics, government, and other fields. The science of autonomics will integrate new logics which will be foundational to the transformation of existing sciences and other disciplines such as aesthetics and ethics. There will also be new disciplines that will arise along the lines of the new logical foundation. Applications of autonomic theory will change the way we look at life and the universe in the next century.
Here is the working hypothesis of Autognomics Institute in a nutshell (minus the technical equations), to paraphrase Norm Hirst:
A. When applied to life and living systems (including human) and other highly complex systems, our current scientific thinking and procedures, combined with the prevailing profit motive, are largely misguided, narrow, and dangerous. Much of today's science is not really true science at all, but more closely resembles ideological dogma and commercially driven propaganda. It is a science clogged with antiquated and primitive logic and obsolete notions, and with resistance to the spirit of change and open learning, which is above all else the true spirit of scientific inquiry and discovery. We can only understand and apply what we can think fully about, and 2500 years of traditional thinking combined with present day quick-fix approaches systematically prevent us from recognizing and respecting the dynamics-- and the wonders-- of any living system. Strong words, but not intended to be antagonistic; rather a tonic to a system in some need of rethinking.
B. We need, according to Hirst and his colleagues, a new process science of meta-logics, or epi-logics that can serve as a foundation and adjunct to other sciences. The new science will be a study of newly discovered patterns observed in the structures and processes within and around living systems of all kinds. It will be a science characterized and informed by an infinite dynamic systems perspective, and inquiry and experimentation will welcome change and paradox as vital, essential elements of learning and advances. The following are basic principles of the autognomic proto-science, broken down into seven axioms (again, minus the equations):
1. Organisms and groups of organisms-- including humans and our communities-- are infinitely complex dynamic systems of process-- living systems, complete and autonomous in themselves.
2. Being infinite and complete in itself, a living system is itself the only viable foundation for its study. No comprehensive standards exist outside of a living system which can aptly be applied to understanding the infinite dynamics of that specific system.
3. A living system is not a machine, and cannot be built by a mechanistic or reductionistic approach. The actual processes of organization, structure, building, and maintenance of a living system are paradoxical and cannot be understood from a Newtonian or Cartesian perspective. The "parts" of an organism or an ecosystem are given their design by the whole, or totality of the system.
4. Living systems are made up of processes that permit self-organization and self-building, recursiveness, self-knowing, and self-management (autonomy) by means of internal values. Living systems are driven by values-- a 'democratic' heterarchy of functions of living process. Values give order and direction to living systems.
5. Living systems constantly generate a coherence (holistic and harmonic), a rhythm, motion, and change that is growing, contracting, expanding, forming, maturing, and transforming.
6. The natural order and logic of living systems transcend traditional thinking and logic. The natural foundation of life and living systems will serve as a complete body of unfolding standards to which all of the sciences of the future will aspire.
7. Our understanding of the processes of life, living systems, and nature in general will increase dramatically as we begin to create versions of a scientific language and meta-logic of nature and living systems. This will be accomplished by letting go of obsolete (and in some cases to a large extent arbitrarily invented) symbols, syntaxes, and logics-- e.g., Aristotelian, Cartesian, Newtonian-- ultimately even Einsteinian and quantum-- and embracing worthy new perspectives and models discovered at the vanguard of all fields of science, notably biology as it will exist in the near future.
C. The new science will emerge out of the now fully-mature autognomic process philosophy with the successful synthesis of a sufficient formal scientific language to describe and carry the emerging epi-logics now being matched with specific dynamics observed in natural systems. As new discoveries and innovations appear on the scientific horizon, autognomic theory will reorganize and revolutionize itself to match the ever-expanding and deepening picture of our universe as it reveals itself to us.
The purpose of science
Since we are considering the ushering-in of a new science, it might be helpful to ask the question, what is the purpose of science? Most scientists would probably agree that the purpose of science is to discover and create new ways to perceive and explain reality with ever-increasing clarity and in the context of ever-broadening and more complete perspective. Simply put, the purpose of science is to make more sense of more of the objects and activities that comprise our various environments and our universe (or universes) with the progression of time. In the physical sciences this means perceiving the shapes and colors and behaviors of objects and organisms and activities in the physical universe, and their relationships from an ever-broadening viewpoint. In the social sciences it means perceiving the patterns in personal, social, economic, and political systems and behaviors of people with the same ever-expanding perspective.
Given the static structure of our English language, that is probably the best we can do to suggest the element of constant change that true scientific inquiry involves.
The 'other half ' of the purpose of science, which is more easily obscured or dismissed in a reductionistic-mechanistic climate of procedure, is the responsibility that every scientist has-- whether or not he chooses to recognize it-- to carefully place his discovery in the context of his local and global community. From a living systems approach, Hirst emphasizes, this is a natural part of science. In an approach to science that relies entirely upon the whole organism or community functioning in a healthy living condition, a scientist puts on his respect, so to speak, when he puts on his glasses.
The world of tomorrow
What will our world look like a hundred years from now? If a growing minority of scientists have their way, the world will look as different then as the seventeenth century world looks to us today. We've already experienced one scientific revolution. Now another one is on the verge of beginning.
What will make the difference is not an extension of today's science, but rather an entirely new "paradigm"-- a new model of science. The old model served well for almost three hundred years, and brought us into a much different world than that of our Renaissance ancestors.
Out of science history
That old theoretical foundation was the seventeenth century reductionist, or mechanistic approach (the two terms being mostly interchangeable) inherited partly from the ancient Greek atomists and further developed and formalized by philosopher Rene Descartes and mathematician Isaac Newton. According to the reductionist/mechanistic view, a system is best understood by analyzing an assemblage of its basic parts, with the belief that, when we know how the smallest components are put together, we will know how the object (or organism or community) under study works. Physics, chemistry, and biology have used this approach for centuries. If you isolate the most fundamental particles they can be assembled into atoms. Atoms can be assembled into molecules. Molecules can then be assembled into cells. Cells can in turn be assembled into organs, and finally organs into organisms. Entire living systems can be put together in the same way that they were taken apart. It worked fine with machines. Today we know that it isn't that simple with organic systems. For Descartes and Newton, the material cosmos was a vast machine. Every object was a part in the machine, and every organism was a little machine within the larger one. But a number of unprecedented scientific findings abruptly burst the boundaries of the old model.
Everybody do the paradigm shift!
In the decades since philosopher and historian Thomas Kuhn published his theory of scientific revolutions, there has been a lot of talk in scientific circles about a new paradigm. "The word 'paradigm,' according to Hirst, refers to those scientific assumptions, both stated and unstated, which give meaning and validity to potential knowledge. For example, physicians are trained to view the body as a biochemical machine. Illness suggests that the machine is broken and someone has to fix it by known physical means, such as the addition of chemicals that alter the chemistry of the machine. Thus physicians turn to drugs. In contrast, the ancient Chinese and Indian models of energy flows carrying out the processes of self-creation and maintenance of the physical body may appear nonsensical to someone who believes in biochemical machines."
In the latter part of the nineteenth century and the first few decades of the twentieth, a rapid series of discoveries and innovations occurred in the fields of human thought which, figuratively speaking, turned the known universe upside down-- and inside out. With the discovery of a number of paradoxes in mathematics and in the observed behavior of sub-atomic particles, it became evident that some of the theories and models basic to existing physical sciences-- especially physics-- and mathematics were obsolete. Those discoveries precipitated a crisis on a scale never known before. Suddenly, the sciences became disciplines shaken by revolution. The best minds in every field were not merely searching for isolated laws and classifications; now they were looking beyond small local structure and behaviors to discover larger, more inclusive patterns that could be part of a new foundation for understanding the deepest workings of the universe as a whole. Early notions of a science of systems appeared at the torn edge of physics, taking on several forms, all fragmentary but promising in terms of the evolution of science as a whole. Intriguing words have been attached to several tentative approaches to the awaited new science. Terms such as "chaos", "complexity", "systems approach", and "emergence" have been circulating energetically since the '60s and '70s, but although they represent fascinating and potentially valuable insights from beyond the cold dark "fringe" of the old paradigm of physics, they are all still homeless fragments of theory drifting in search of a solid foundation. That makes them no less exciting, and probably not a bit less useful in the search.
A new ground for biology
For centuries, physics has been the fundamental science, the parent science from which all others have derived their root principles and models. The chemical models of molecules, compounds, crystallization, and even biochemistry's early models of DNA and neuron synapses, were all based upon and informed by preceding models in physics. With the bedrock of physics theory as an unquestioned foundation-- after all, even in the twentieth century climate of radical change, what other foundation would replace the science of how things move and arrange themselves?-- the complex tower of chemistry and biochemistry in turn supported an even more complex figurative attic of biology, on top of whose roof the social sciences grew.
A century ago, this hierarchical arrangement made neat logical sense. But even today, physicists and mathematicians still stand looking into a yawning chasm that stretches between the macro-cosmic theory of Einsteinian space-time and the micro-cosmic sub-atomic quantum mechanics. Half a century ago it would have come as a surprise to many that the theoretical foundation for the next step in science would be found in an overview not of physics, but of biology, and such "soft" sciences as psychology-- not in the traditional foundation of science, but in its attic-- and even, perhaps, out on its roof! Now, for the first time in our history, biology stands on even ground with physics as a seminal theoretical science.
Promising variations on the holistic systems view popularized during the 1970s and '80s by Fritjof Capra, Ken Wilber and others have met with sporadic support, and remain largely in waiting for a formal system of language and logic to carry them into full scientific effectiveness. But like others working out on the frontiers of science, Hirst believes that our universe-- and our place in it-- are ultimately intelligible, though in a gradually unfolding course of discovery. We will never understand or intuit every aspect of those graduated enigmas, but our understanding of the various environments and activities and relationships that make up our universe and our existence in it will broaden and deepen, and in the process our collective human consciousness will evolve. The process, Hirst believes, is already underway. Like other important revolutions that have swept through our world since human time began-- the cultivation of fire, iron, the printing press, vaccines and antibiotics, and the current information revolution-- the movement in our consciousness that is showing itself now will increase in force and span as the new century gives up its new discoveries.
Upsides and downsides of paradigms
The positive side of any paradigm, or scientific model, is the practical guidance it provides. Scientists need a certain degree of structure before they can apply their thinking to any subject or problem practical intelligence and skill. The negative side of a paradigm shows itself when, in spite of a pressing need to let go of the old temporary model-- and all models in science must be treated as temporary-- we continue to rely upon it. To take the example of computer technology, if we had never replaced our old transistor circuit boards with microchip technology, our personal computers would require large areas of our houses and would cost hundreds of thousands of dollars, and supercomputers would be the size of small cities. In the case of medicine, where even the smallest differences can mean life or death for thousands or even millions of people, Louis Pasteur's demonstrations that microorganisms produce diseases (rather than "humors" or the even vaguer "bad blood" attributed as the cause of diseases by doctors of his time) saved many lives and laid a platform for further research in the new field of microbiology, which was carried into the twentieth century with the development of van Leeuwenhoek's microscope. If Pasteur hadn't abandoned old notions in the medicine theory of his day, who knows how long preventative sterilization and a lot of life-saving vaccines and antibiotics would have waited? Today, the search continues for cures for cancers, Aids, diabetes, and other serious diseases for which no effective vaccines or antibiotics yet exist. Perhaps the next breakthrough in viral disease research will come out of the work of someone who had a hunch and looked in a completely new direction for a solution. In spite of the fact that thousands of discoveries have burst the old scientific framework, there is still today a lingering adherence to antiquated procedure, following the lines of the traditional theoretical foundation, which has now been proved obsolete many times over.
As an example of the contrast between the traditional reductionistic-mechanistic logic and philosophy supporting past science and the new logics and philosophy now being matched to patterns observed in nature, organisms are systems that have traditionally been seen, as pointed out above, as being constructed like erector sets or automobiles out of trillions of parts, from atoms, to cells, to organs, to organisms. This view works for simple machines, but not for living systems, according to the new theories. Holistic, harmonic fields of electromagnetic energy and even consciousness form and inform organisms and the "parts" that make them up. The organizing field changes the "parts", such as the atoms, in accord with a higher-order design. The "parts" are not the same within the system as they were before becoming part of it.
Windows and handles on paradox
Jon Ray Hamann, a co-founder of Autognomics Institute, writes:
Humankind is poised for an imminent worldwide paradigmatic metamorpho- genesis in the very essence of scientific, technological, humanistic, cultural, social thought and actions... causing fundamental shifts which will reveal new logics, mathematics, even new sciences beyond our current scientific world view... moving us towards a wholeness that transcends a polarized, splintered separated, competitive and despairing existence.
What our newest windows of insight into the complex and mysterious corners of our universe are offering us, is a collection of small handles that we can use in order to gain some measure of grip on the paradoxes which we repeatedly encounter in this new universe that began unfolding before us a century ago. The "new paradigm" in the sciences seems to be comprised entirely of natural paradox, like one smooth, continuous, and impenetrable contoured surface that winds its mysterious way through everything. It is necessary to have some understanding of what natural paradox is about, in order to comprehend the kinds of logic that support and carry autognomic theory.
By definition, paradox is a condition of having contradictory characteristics. A paradox seems to be both true and not true simultaneously. Perhaps the most famous examples of paradox are Zeno's paradoxes of space and motion, which "prove" by logic that motion is impossible. Paradox of that kind points mostly, if not entirely, to the inherent incapacity of language and existing concepts to describe or explain a phenomenon or situation in its entirety. Paradox appears in nature whenever a pattern found in a natural system is too large or too complex to be perceived or measured in its entirety by a human observer. Quantum physics abounds with paradoxes, and each one of them has sent its own shocks through the physical sciences. Says Hirst, "Quantum physics, with its paradoxes, comes the closest of any phenomena we know to the paradoxes we find in living systems. Resolutions of these paradoxes requires a paradigm beyond what is currently imaginable. It appears that quantum physics and living systems may require the same new paradigm." Paradox, of the magnitude we find it in quantum physics is not something any scientist can just shake off. An example of paradoxical behavior in quantum physics that did not fall into existing standard atomic theory when it was discovered experimentally, is the single electron that, when fired at multiple targets acts like a wave and passes through all of the targets simultaneously. It would appear at first to be a contradiction for a physicist to assert that what he had isolated before all of the targets were simultaneously hit was in fact one electron. Surely, there must be some mistake, or some flaw in the equipment. Electrons are, after all, sub-atomic particles, and such particles take up small, definite volumes in space. Waves and fields had the capacity to spread out to multiple locations, but everyone knew that electrons were solid particles. --Or were they? Enter the notion of the quantum function of an electron. A paradoxical new model, or part of one. The quantum electron encountered by the early interpreters of quantum mechanics was neither fully particle nor fully wave or field, but could function as all three alternately. Physicists were left to argue whether those shifts were between actual functions of the nature of electrons or merely shifts in the perspective of human observers. That debate, along with others sparked by quantum discoveries, still continues.
A few other equally mysterious behaviors displayed by the electron were observed in the orbit shells around atoms. Physicist Max Planck's term "quantum" referred to specific quantifiable amounts of energy that determined which orbit an electron positioned itself in. The orbit shell closest to the nucleus of an atom-- orbit shell S-- was comprised of two electrons in field state-- two quanta. These two electrons were said to be in orbit separately as two distinct particles, yet together they formed one field, called the orbit shell. Werner Heisenberg, one of the international team of physicists and mathematicians who worked during the first three decades of the twentieth century to solve the quantum puzzle, presented the statement that at the microscopic, or quantum level, it is not possible to determine the momentum or position of a sub-atomic particle with absolute precision. Strange, but it gets stranger. Each electron within a given orbit shell S, P, or K was found theoretically to be vibrating at a specific frequency and with a specific level of energy, which together determined which of the three orbit shells the electron belonged in. Electrons with higher energy (and proportionately higher frequencies of radiation) were positioned in outer orbits, according to a precise architectural design that all atoms seemed to go by. Whenever an electron receives extra energy or loses energy, it no longer belongs in its current orbit shell and must jump to the closest neighboring shell-- farther away from the nucleus if it gained energy, or closer to the nucleus if it lost energy. But here is where it gets very mysterious. At the moment when the electron leaves a shell bound for another one, it completely vanishes from detection. It seems to cease to exist. And then, just as mysteriously, it reappears in a new and proper position around the nucleus, with a new precise level of energy and an exactly proportionate frequency. What was happening in that space between the two orbits? Where did the electron go in between orbits? Was it travelling through a wormhole in subspace? Or was the new electron even the same one that left the old shell? Did it cease to exist upon leaving the first shell, and was a new electron spontaneously created in the next shell-- and at what might have been the exact same moment? If so, where and what did the old electron disappear into, and what was the invisible matrix it was created out of?
For a future science
There were no conclusive answers found for these questions in the first thirty years of quantum interpretation, and as it stands today, the same questions are just as puzzling. A few theoretical predictions have been verified with the development of certain pieces of equipment for measuring and observing objects and activities on microscopic levels. For example, our newest electron microscopes are capable of such extreme magnification that we can now view individual atoms and even actual quantum fields, which appear like crests and ripples on a liquid surface. Are we perhaps getting close to being capable of viewing something beyond our present sub-atomic model-- perhaps even an undiscovered energetic foundation with a shape so paradoxical that we presently have no visual frame of reference to imagine it? One thing remains as certain now as it was a century ago: neither Newtonian physics nor Cartesian binary logic (which insists that an electron is either a particle or not a particle, and exists or does not exist) can touch the new electron. Real understanding of the quantum particle/wave/field entity belongs to a future science. In 1900 there were already a number of examples of phenomena which that future science would have to explain, but even as another century turned, no new foundation had yet been discovered in which to arrange all of those pieces of the cosmic puzzle together in a way that makes sense.
When paradox and complexity hit mathematics
At the same time as physicists were attempting to make sense of the quantum discoveries, a crisis was erupting in the field of mathematics. One example of the baffling problems that greeted mathematicians of the new century was the "three body" problem, stated by Henri Poincare in 1890. When calculating the gravitational effects of one heavenly body on another-- the moon on the earth, for instance-- the force of gravitational attraction between the two bodies could be calculated with practical accuracy using Newtonian equations. But when a third body-- say, the sun-- was introduced into consideration, the entire operation exploded into infinite complexity. As soon as the gravitational influence of the sun was factored in, a staggering difficulty arose. The pull of the moon on the earth caused disturbances in the orbit of the earth around the sun, which in turn altered the moon's prior orbit around the earth. That variation affected the moon's pull on the earth, which in turn caused yet another disturbance in the earth's orbit around the sun. The "three body" problem would prove in the twentieth century to be just one of many problems mathematicians would encounter which would involve very real infinite regression and would call for an entirely new calculus-- and a new foundation for mathematics as a whole. The "new paradigm" mathematics would need to be compatible with activities of infinite complexity, a challenge which both our technology and our logic would have to rise to.
Continue: Attending the Emergence of a New Science - Part II