wCHAP.16

(9/11/99)

CHAPTER XVI

CHAOS AND A SCIENCE OF RELIGION

Chaos theory presents the universe from a whole different perspective than the one most of us grew up with. Along with relativity and quantum theory, chaos theory gives us information necessary if we are to recognize that the model science has accepted since its inception is fatally flawed. Chaos theory proves that nothing is predictable in the sense classical science has implied. It makes clear that nothing can be predicted accurately "even by the perfect mind of God" when examined over sufficient time and space. However, there are different kinds of predictability.

Statistics has traditionally been used for making probability predictions. However, statistics and probability are phony mathematics. They look like mathematics and they give the illusion of being mathematical, but they have no firm mathematical foundation. Chaos theory handles those problems traditionally dealt with by probability, but it has a firm mathematical foundation and shows us what is really going on. Probability has provided a path that has led many good people astray. Any conclusion drawn from its use must be studied carefully to see if they are merited when analyzed by chaos theory. Chaos theory provides a way of looking at the complex events in the spirit of classical physics, but from a modern perspective. Chaos theory allows us to see the causal connections and at the same time see the total inability to make long term predictions.

CHAOS[1] describes the history of the development of the science of chaos. This book and this new science are of revolutionary significance. Although this book is of tremendous value, it is not my dream book on chaos theory. It gives an excellent historical account. But it does not provide a unified presentation and study of chaos theory. This approach based on the historical events that led to chaos theory is not the best one for understanding chaos theory itself. The presentation is of necessity fragmented and makes mastery of some ideas difficult. Nevertheless, it presents the key material in a readable and basically understandable format. And, it changes forever the way we must look at the world.

This book also provides us an example of what happens when the work of individual scientists goes beyond the wisdom of the day. Each of the "founders" of chaos science was initially ignored. Their efforts were belittled. And, their writings were either not accepted for publication in scientific journals, or only by obscure publications. This is a process that has happened over and over in the history of science. Perhaps, it must happen since thousands of theories and experiments are presented each year and many of them fail the critical examination of colleagues and the test of time. But it is disquieting to learn how difficult it is to get a hearing for new ideas. (See Volume I, Chapter Two, "New Ideas, Revolutionary Insights, and/or Unique Answers Institute" [2]under "Organizing for a Wise Community." This organization is suggested as one way to overcome current barriers to new ideas.)

Up to this point science's open-ended questioning and reliance on demonstration and repeatability have kept it from becoming trapped in an "orthodoxy." However, the advance of scientific thought on some occasions has more to do with the death of those in power than the rigorous pursuit of the goal of open-minded search for truth, or understanding. Considered against the full history of science the delay in recognizing chaos theory was minor, perhaps, a decade or less. Chaos theory did prevail because of the scientific community's commitment to truth and understanding. Slowly, chip by chip the dam was broken and the findings and ideas of chaos scientists were able to reach the larger reservoir of the scientific community.

CHAOS shows us that we live in a deterministic universe. But that determinism has been reduced to meaning cause and effect. Events follow definite laws and rules, even complex events that traditionally have been called random. However, in all cases our ability to predict is limited by the butterfly effect (sensitive dependence on initial conditions.)

I find value in chaos theory for an additional reason beyond that presented above. I feel it supports my model that Human Beings Are the Ultimate Reference System (HBAURS). Scientists have always thought of reality, the objective universe, as being the Ultimate Reference System that must be used to measure everything against. However, the foregoing approach produces assumptions that turn out to have serious negative consequences. Primarily it diverts recognition of what is of most fundamental value. Science has focused outward to Truth, rather than inward to knowledge. It has focused on Truth which is not achievable and away from knowledge which is achievable. It has focused resources on searching for Truth and then avoided focusing adequate resources to turn these discoveries into knowledge that helps improve the quality of human life.

Chaos theory, when joined with relativity and an improved understanding of quantum theory make it possible to realize that, in fact, Human Beings Are the Ultimate Reference System (HBAURS). They are the Ultimate Reference System (URS) not because their knowledge is Ultimate, and independent of reality. (Reality is indeed the Objective Reference System, the thing all observations must in the final analysis be tested against.) However, because all knowledge and understanding is tentative and depends on what is known or believed at a particular time. HBAURS forces us to realize that human beings have always provided the frame of reference to which outside data, events, objects, and phenomena have been referred. We are at this time in a position to realize that the human reference system is as close as we can get to an Ultimate Reference System. We must now explicitly recognize HBAURS.

Any attribute we assign to the universe comes out of a human attribute. The foregoing is obvious with concepts like: love, beauty, perfect, heavy, fast, bright, cold, huge, long, loud, etc. But it is equally true of words like: blue, rough, time, quark, gravity, vacuum, motion, force, entropy, mass, carbon, etc. The foregoing is not always understood. Because of this confusion some individuals find it difficult to recognize that human beings must in fact be seen as providing the Ultimate Reference System.

(p. 3) "Where chaos begins, classical science stops. For as long as the world has had physicists inquiring into the laws of nature, it has suffered a special ignorance about disorder in the atmosphere, in the turbulent sea, in the fluctuations of wildlife populations, in the oscillations of the heart and the brain. The irregular side of nature, the discontinuous and erratic side -- these have been puzzles to science, or worse, monstrosities."

RESPONSE: And, the above phenomena were largely swept under the carpet. They were seen as unimportant and to be ignored. As a result science was completely misrepresented not only to laypeople, but to scientists themselves. Scientists took individual linear equations as accurate statements about the universe. It was thought that these equations could be projected indefinitely into the future. The foregoing representation led to a total misunderstanding of what the universe is like.

In classical physics it was believed that we could know initial conditions well enough that anything/everything might be predicted. Yet, even where this is presented as being completely true, such as in the orbits of bodies in our solar system, we see that this is not the case. Beyond some point in the future it is not known what the orbits of the individual planets will be and even if current orbits are stable. (The foregoing doesn't even consider the potential of a visit by "rogue" stars or some other unknown factor.)

Past exaggerations and misrepresentation of science is to some degree understandable. Part of it is an honest mistake. This ability to predict seemed reasonable and possible in the initial stages of scientific discovery. It appeared natural that any problem areas could be conquered with more information. Equally important scientists required an abiding faith in this position. It was probably only possible to break the grasp of positions that were speculative and untestable by adopting a counter faith of similar power. At that time superstition and ignorance held all of society in its grip. The concepts of education (not indoctrination), knowledge (not Truth), understanding (not Faith), experimentation (not authority) needed single minded zealots in order to prevail against the entrenched power and suppression coming out of supernatural religion and authority.

Chaos theory shows us regularity and predictability, but of a totally different kind than we have been taught about in the past. Perhaps, without the faith in prediction that early interpretation provided it would not have been possible to develop the scientific community to the level where it could study and understand chaotic processes in the universe.

However, it is critical to understand that when chaos scientists talk about chaos theory supporting determinism they are talking about order without complete predictability.

(p. 4) "The new science [of chaos] has spawned its own language, an elegant shop talk of fractals and bifurcations, intermittencies and periodicities, folded-towel diffeomorphisms and smooth noodle maps. These are the new elements of motion...." Other key concepts in chaos: Lorenz attractor (butterfly curve/strange attractor); koch curve (snow flake); Mandelbrot set (wow!); sensitive dependence on initial conditions.

(p. 7-8) "The simplest systems are now seen to create extraordinarily difficult problems of predictability. Yet order arises spontaneously in those systems -- chaos and order together. Only a new kind of science could begin to cross the great gulf between knowledge of what one thing does -- one water molecule, one cell of heart tissue, one neuron -- and what millions of them do."

(p. 8) The key to chaos is "sensitive dependence on initial conditions."

"In weather, for example, this [sensitive dependence on initial conditions] translates into what is half-jokingly known as the Butterfly Effect -- the notion that a butterfly stirring the air today in Peking can transform storm systems next month in New York....For the young physicists and mathematicians leading the revolution, a starting point was the Butterfly Effect."

EDWARD LORENZ

(p. 11) Edward Lorenz was a research meteorologist at MIT. In 1960 he programmed a simple weather pattern into a computer. He believed, that, "Weather had a flavor that could not be expressed by talking about averages....The essence was the way patterns in the atmosphere changed over time...."

(p. 12) Lorenz adopted twelve equations [later reduced to 3, the minimum necessary to produce chaos] for aspects of weather he felt were important. "Thanks to the determinism of physical law, further intervention would be unnecessary....from present to future, the laws of motion provided the bridge of mathematical certainty. Understand the laws and you understand the universe. That was the philosophy behind modeling weather on a computer."

(p. 13-14) "Only a computer could cash in the Newtonian promise that the world unfolded along a deterministic path, rule-bound like the planets, predictable like eclipses and tides."

(p. 14) "There was always one small compromise....Measurements could never be perfect."

(p. 15) Scientists influenced by Newton, thought: "Given an approximate knowledge of a system's initial conditions and an understanding of natural law, one can calculate the approximate behavior of the system. This assumption lay at the philosophical heart of science."

(p. 16) "One day in the winter of 1961, wanting to examine one sequence at greater length, Lorenz took a shortcut. Instead of starting the whole run over, he started midway through...."

"This new run should have exactly duplicated the old one...[But,] his weather diverged so rapidly from the pattern of the last run that, within a [short time] all resemblance had disappeared."

Lorenz had discovered sensitive dependence on initial conditions, chaos!

(p. 22) "...Lorenz saw more than randomness embedded in his weather model. He saw a fine geometrical structure, order masquerading as randomness."

RESPONSE: Lorenz and other chaos scientists have helped to demonstrate the truths about what random means. Random is a concept, an empirical description about effects not causes. Random is an adjective not a noun. There is no such thing as a "random." Random only provides us a way to generalize about complex situations with many (or at least three, nonlinear) causal factors. Random was a way of dealing with complex phenomena before chaos theory was discovered and described.

(p. 23) Lorenz found a simple way to produce chaotic behavior. He used three nonlinear equations.

(p. 29) Lorenz Attractors -- system never exactly repeats itself, the trajectory never intersects itself. It loops around and around forever. A double spiral (butterfly spiral).

(p. 168) Lorenz: "Does a climate exist?...is it possible that a system like the weather may never converge to an average?"

RESPONSE: Does anything converge to a true average? Would real coins and real cards ever produce the theoretical predictions?

(p. 38) Chaos theory demonstrated a truth about human behavior, "Shallow ideas can be assimilated; ideas that require people to reorganize their picture of the world provoke hostility."

RESPONSE: That does not bode well for a Science of Religion which questions every basic assumption of Western culture. It refocuses almost all assumptions that are not discarded outright. It requires every person to reorganize their picture of the world since even the clearest thinkers have utilized ideas that need to be significantly altered. What is the most productive way to deal with this hostility? Can chaos theory be used as a model of how to approach this issue?

(p. 38) But, "By the middle of the eighties a process of academic diffusion had brought chaos specialists into influential positions within university bureaucracies. Centers and institutes were founded to specialize in 'nonlinear dynamics' and 'complex systems.'" The scientific method had triumphed over scientific orthodoxy.

"Chaos has become not just theory but also method, not just a canon of beliefs but also a way of doing science. Chaos has created its own technique of using computers....To chaos researchers, mathematics has become an experimental science, with the computer replacing laboratories...."

RESPONSE: Because chaos theory had several inventors each of whom had their own area of power and prestige, they were able collectively to get a hearing and influence others by the strength of their information. This Science of Religion has none of those things so the path to success seems much less clear.

(p. 41) "Small nonlinearities [in scientific experiments] were easy to disregard. People who conduct experiments learn quickly that they live in an imperfect world. In the centuries since Galileo and Newton, the search for regularity in experiment has been fundamental. Any experimentalist looks for quantities that remain the same, or quantities that are zero. But that means disregarding bits of messiness that interfere with a neat picture."

RESPONSE: And, it is the above process that contributed to scientists' misperception of how the universe really works.

JAMES YORKE

(p. 65) James Yorke headed the Institute for Physical Science and Technology at the University of Maryland. He gave the science of chaos its name as a result of a paper, "Period Three Implies Chaos." He, "was a mathematician who liked to think of himself as a philosopher."

(p. 67) "Yorke felt that physicists had learned not to see chaos. In daily life, the Lorenzian quality of sensitive dependence on initial conditions lurks everywhere."

(p. 76) "...Yorke had offered more than a mathematical result. He had sent a message to physicists: Chaos is ubiquitous; it is stable; it is structured. He also gave reason to believe that complicated systems, traditionally modeled by hard continuous differential equations, could be understood in terms of easy discrete maps."

(p. 67) "It is no exaggeration to say that the vast business of calculus made possible most of the practical triumphs of post-medieval science; nor to say that it stands as one of the most ingenious creations of humans trying to model the changeable world around them. So by the time a scientist masters this way of thinking about nature, becoming comfortable with the theory and the hard, hard practice, they are likely to have lost sight of one fact. Most differential equations cannot be solved at all [those with chaos (non-linear parts)]."

RESPONSE: Gleick's discussion of the tremendous value of calculus provides an important point for those of us with a limited understanding of the true importance of mathematics. It is points like these that are essential if we are to really understand modern society. In addition the explanation above provides another great example of the fact that there are no unmixed blessings. No matter how useful something is it also has certain costs/negative effects. The more closely we look for these costs the better chance we have of reducing them.

(p. 68) "Physicists and mathematicians want to discover regularities. People say, what use is disorder. But people have to know about disorder if they are going to deal with it."

RESPONSE: By focusing on the things that appeared to be predictable and ignoring the things that were not (the bulk of things), scientists adopted a biased picture of the universe.

ROBERT MAY

(p. 70) Biologist Robert May of Australia taught at Princeton University. He studied a version of the logistic difference equation used to model how animal populations change over time. Through study of this equation he discovered bifurcation (period doubling) and chaos in a very simple, nonlinear equation.

(p. 80) May thought, "Chaos should be taught. It [is] time to recognize that the standard education of a scientist [gives] the wrong impression. No matter how elaborate linear mathematics [can] get...it inevitably misled scientists about their overwhelmingly nonlinear world."

"...simple nonlinear systems do not necessarily possess simple dynamical properties."

(p. 79) "...simple deterministic models could produce what looked like random behavior."

RESPONSE: And, what I take from chaos theory is that all randomness is similarly produced. There are deterministic, causal relationships, but effects are not predictable except in the way statistics has been used to tease out ranges of effects.

BENOIT MANDELBROT

(p. 86) Benoit Mandelbrot was a key contributor to chaos theory. He was a refugee born in Warsaw in 1924 to a Lithuanian Jewish family. He fled to France to find sanctuary from the Nazis. He fled France after surviving the war there to escape the dominance of Bourbaki[ism].

RESPONSE: Bourbaki[ism] was a powerful French "conspiracy" of mathematicians. It stressed the primacy of mathematics among sciences, and insisted upon a detachment from other sciences...[preaching that] it [mathematics] could not be valued in terms of the application to real physical phenomena. And above all, Bourbaki rejected the use of pictures. (p. 88)

And it is approaches such as Bourbakism that I preach against. Bourbakism is in fact a mystical religious position. The religion is mathematics. It was the search for TRUTH outside of human beings. They saw mathematics as the path to TRUTH. So instead of working to improve the quality of human life, thy ignored human well being and looked for a "higher purpose." This epitomizes the approach of many scientists. And from my perspective points out one of the prime errors of science because it lacked a foundation from which to draw direction (goals, focus).

Where Bourbakism saw understanding mathematics as a prime value a Science of Religion takes as one of its primary goals to generate a Religion of Wisdom focused on helping each person achieve a SFLIHM (a Sustainable Feeling that one's LIfe Has Meaning). Mathematics and science have value to the degree that they aid in this search. They are most useful in this effort as they cross-fertilize each other and help expand knowledge and understanding. The more knowledge and understanding we have the better we are able to help more persons achieve a SFLIHM.

(p. 86) Mandelbrot became an IBM mathematician and as part of his research studied cotton prices. "...when [he] sifted the cotton-price data through IBM's computers, he found the astonishing results he was seeking. The numbers that produced aberrations from the point of view of normal distribution[3] produced symmetry from the point of view of scaling. Each particular price change was random and unpredictable. But the sequence of changes was independent of scale: curves for daily price changes and monthly price changes matched perfectly. Incredibly, analyzed Mandelbrot's way, the degree of variation had remained constant over a tumultuous sixty-year period that saw two World Wars and a depression."

(p. 89) "Mathematicians could take pride in saying that their work explained nothing in the world or in science. Much good came from this attitude, and mathematicians treasured it....[It provided clarity.] And clarity...went hand in hand with the rigor of the axiomatic method....Rigor is what allows mathematicians to pick up a line of thought that extends over centuries and continue it, with a firm guarantee."

RESPONSE: I have no doubt that some good came out of this approach since I take it as a truism, that there are no unmixed blessings. However, for me this position is inherently wrong because it is placed on the wrong foundation. Knowledge is good and being able to build on the ideas of the past is good. But, it is only good because it helps people -- those who discover and those who use it. Knowledge achieves more and more value as it benefits more and more people to live a better life, to live at the highest level possible, to achieve a SFLIHM.

Mathematics is a powerful tool to help advance the human condition in many different ways. It is my belief that a mathematician (or anyone else) gains the most in their own life the more ways they utilize their interests and accomplishments to achieve a SFLIHM, and to help others do the same.

FRACTAL

Benoit Mandelbrot created the name fractal in 1975. "Above all fractal means self similar." (p. 103)

(p. 98) Fractal dimensions -- The degree of irregularity remains constant over different scales. Over and over again, the world displays a regular irregularity.

(p. 114) "The structure that provided the key to non-linear dynamics proved to be fractal."

(p. 97) What is the dimension of a ball of twine? Mandelbrot: "It depends on your point of view."

(p. 95) How long is a coast: 1) infinitely long. 2) Depends on the length of your ruler.

(p. 107) "How long is it? How long does it last? These are the most basic questions a scientist can ask about a thing. They are so basic to the way people conceptualize the world it is not easy to see that they imply a certain bias. They suggest that size and duration, qualities that depend on scale, are qualities with meaning, qualities that can help describe an object or classify it."

RESPONSE: And the meaning of size and duration comes completely out of the human reference system (HBAURS). "How long is it?" "How long does it last?" are totally meaningless except in terms of the human reference system. A meter has no meaning except as human beings have defined it. Whether it is defined in terms of its original meaning as one ten-millionth of the distance along a meridian from Earth's equator to the pole, or 1,650,763.73 times the wavelength of krypton 86, its meaning derives from human scale and human definition. A second whether defined as the period of time it takes to produce 9,192,631,770 vibrations of a cesium atom, or 1/86,400th of an average solar day (the average time it took for Earth to make one complete rotation on its axis in the year 1900), its meaning derives from human scale and human definition.

But, in spite of what fractals show us about the central importance of the human reference system, chaos scientists still think of "reality" as the Ultimate Reference System as do all other scientists. All scientists think they are studying "reality." Their goal is to impose themselves as little as possible into their observations/experiments in the hope of seeing things as they are objectively -- independent of the human observer. Although, the goal is admirable and worth maintaining, we must recognize that this is not what we are doing, what we cannot do. We cannot see things as they are. We can only perceive them as our senses, experiences, and perceptions allow us to.

We can only relate our observations to HBAURS and by a series of successive approximations gain a better and better picture/understanding of what the universe is like. This must be an infinite process and though we can get closer and closer to the goal we can never reach it. I call this goal TRUTH.

When scientists think they are observing the true nature of the universe their misunderstanding limits their movement toward TRUTH. The foregoing process whether applied to science or religion has the same result. An individual makes a giant step forward in understanding the nature of the universe. Because they think they are actually explaining the universe rather than expanding their understanding of it they spend the rest of their life protecting their insight from being superseded by the advancement of additional knowledge. Rather than being satisfied to know that they helped move human thought forward, their misunderstanding of the process leads them to believe they have taken the final step. Any new approaches become an attack on their position instead of another step forward toward TRUTH. Rather, they should realize that even the greatest achievement is only a longer step toward TRUTH. It cannot be the final step.

Scientists traditionally have failed to realize that all their studies are measured and collected in relationship to HBAURS. To other persons this seems so obvious they fail to understand that it lies at the core of everything else.

(p. 221) The Mandelbrot set (developed by Benoit Mandelbrot) is fractal in nature and is a kind of public emblem for chaos. "The Mandelbrot set is the most complex object in mathematics....It started appearing when Mandelbrot tried to find a way of generalizing about a class of shapes known as Julian sets. These were invented and studied during World War I by the French mathematicians Gaston Julia and Pierre Fatou...."

(p. 223) When Mandelbrot was developing his set he found much complexity. "And where the set intersected the real line, its successively smaller disks scaled with a geometric regularity that dynamicists now recognized: the Feigenbaum sequence of bifurcations."

RESPONSE: Nature (reality) is more subtle than any human being can ever know. But by diligent study and great mental effort, we can peel back layer after layer of that mystery and get closer, and closer to the core. However, the total comprehension of reality is a secondary goal, not a primary goal. Humanity's primary goal must be to help every person achieve a SFLIHM. Accepting the foregoing goal may only be possible after one recognizes that Truth can never be achieved.

However, expanding our understanding of reality is very closely intertwined with attaining a SFLIHM. Each advances the other. It wasn't until humanity achieved a critical level of understanding that it became possible to recognize that a SFLIHM is humanity's primary goal. No individual can achieve a SFLIHM until some additional advances are made in our understanding. The better understanding we have of reality the more people we can help achieve a SFLIHM. The more people who achieve a SFLIHM the more will humanity's understanding of the universe be advanced. This synergistic process will continue until every person achieves a SFLIHM.

And when this occurs Homo sapiens sapiens will have at last achieved the goal it has been struggling toward for the past 35-40,000 years since the evolution of the language instinct.

(p. 145) "The 3-body problem is most often impossible....long-term questions [predictions] about a 3-body system [like the solar system] cannot be answered."

(p. 134) "The strange attractor [named by David Ruelle and Floris Takens]...[has proven to be] one of the most powerful inventions of modern science.

(p. 152) Strange attractors showed that, "Nature was constrained. Disorder was channeled, it seemed, into patterns with some common underlying theme."

"...the recognition of strange attractors fed the revolution in chaos....[Scientists] looked for strange attractors everywhere, wherever nature seemed to be behaving randomly."

RESPONSE: Some day a new generation of physicists will look for strange attractors in the area of quantum phenomena, and lo! A new day will dawn. A new understanding will appear.

MITCHELL FEIGENBAUM: UNIVERSALITY

(p. 173) Mitchell Feigenbaum received his Ph.D. from M.I.T. in 1974. He worked at Los Alamos, NM in the '70s on turbulence which at that time posed a road block preventing understanding in many different fields of physics. He discovered universality, one of the most astonishing discoveries of chaos theory. It includes a universal scaling factor -- 4.6692016090...

(p. 175) "Feigenbaum's number let him predict when the period-doublings would occur. Now he discovered that he could also predict the precise values of each point on the ever-more-complicated attractor...."

(p. 180) Feigenbaum -- Universality: "Everyone knew that turbulence meant a continuous spectrum of different frequencies....Suddenly you could see the frequencies coming in sequentially....Feigenbaum's universality was not just qualitative, it was quantitative; not just structural, but metrical. It extended not just to patterns, but to precise numbers. To a physicist, that strained credulity."

"The notion of a scientific breakthrough so original and unexpected that it cannot be published seems a slightly tarnished myth." But, it happened to Feigenbaum -- for two years, 1976-1978.

"Feigenbaum had discovered universality and created a theory to explain it. That was the pivot on which the new science [of chaos] swung."

(p. 184) Feigenbaum: "Something dramatic happened in the twenties. For no good reason physicists stumbled upon an essentially correct description of the world around them -- because the theory of quantum mechanics is in some sense essentially correct...."

RESPONSE: The above expresses the basic failure of scientists and physicists in particular to understand the true nature of the universe: that is, that it can never be understood in such a way that it can be used as an Ultimate Reference System (URS). Quantum mechanics is certainly a more accurate description of the universe than that expressed by the Greek idea of four elements -- fire, water, earth, and air. And, I would agree that quantum mechanics is in some sense correct. But I disagree that it is essentially correct. It is my position, that in the final analysis it will be found to have flaws just like all past scientific (or, non-scientific) theories.

This is not a criticism of quantum mechanics. Quantum mechanics is a fantastic advance forward in grappling with the mysteries of this universe into which we have all been born without a road map, or a user's manual. However, once we realize HBAURS, we have a fundamental basis for assigning value. We then can easily see that the highest value any human being can achieve is a SFLIHM. Knowledge then becomes a tool to be used to achieve the foregoing end. It is the application of whatever knowledge we have to expanding the number of people who have achieved a SFLIHM that is most important. Whenever information is not used to achieve a SFLIHM we must realize that unnecessary suffering and despair will result.

However, Feigenbaum does end up moving beyond his initial statement presented above. He goes on to say, "...except at some level it [quantum mechanics] doesn't make good sense. Some part of the imagery is missing....Now maybe that's the way the world really is. But you don't really know that there isn't another way of assembling all this information that doesn't demand so radical a departure from the way in which you intuit things." And the foregoing is congruent with my own analysis of quantum mechanics.

(p. 163) Mitchell Feigenbaum: "You see some human transactions and you make deductions about them. Given the vast amount of information available to your senses, how does your decoding apparatus sort it out? Clearly -- or almost clearly -- the brain does not own any direct copies of stuff in the world. There is no library of forms and ideas against which to compare the images of perception. Information is stored in a plastic way, allowing fantastic juxtapositions and leaps of imagination. Some chaos exists out there, and the brain seems to have more flexibility than classical physics in finding the order in it."

RESPONSE: It seems very likely to me that our brain does have a library (not of direct copies of the world, but with programs developed over our evolutionary history) of our interpretation of reality plus those developed from our own individual experience. These stored forms must be used to compare outside stimuli against. Seeing order, even where it does not exist, is part of that library that is hardwired into our brain and nervous system. Seeing a bowl of pickled pig eye balls as a delicacy is programmed by our individual life experiences. I totally agree, that there are no copies of the "stuff of the world" in our heads. We only have an imprinted way to respond when something outside matches this stored "form" closely enough. However, the flexibility of the human brain and nervous system is a basic aspect of how we work. Most of the forms develop as a result of our experience. Once they get into our brain though, they are not easy to alter. And that will be a key challenge for a Science of Religion and even more so for a Religion of Wisdom.

(p. 164-65) Newton vs. Goethe re: color. Where Newton was reductionist, Goethe was holistic. (p. 165) "Goethe's ideas [on color] resemble a facile notion, popular among psychologists, that makes a distinction between hard physical reality and the variable subjective perception of it....It was the perception of color, to Goethe, that was universal and objective. What scientific evidence was there for a definable real-world quality of redness independent of our perception?"

RESPONSE: Here we see another aspect of the search for an Ultimate Reference System. I interpret Goethe above to be holding out for HBAURS. Hard physical reality has always seemed like an obvious Ultimate Reference System to most scientists. The human being has seemed too subjective and untrustworthy.

But, it is because human beings have sense organs that are sensitive to red wavelengths that red is given a special place as "hard physical reality." X-rays, gamma rays, and radio waves only became part of "hard physical reality" since human sense organs have been expanded by technology.

Perception as the crucial element about color is the essence of HBAURS. Whatever exists in the universe can only be scientifically demonstrated as a result of human perception. Since it is human perception that defines red, it is not possible to separate red, scientifically from our perceptions. Obviously, we can demonstrate that the electromagnetic frequency called red, or the pigment named red exist independent of our observations -- because we can set up experiments in which their redness effects something else which we can then analyze -- but until we observe that demonstration, we cannot prove anything.

Until there is a perception there is a "State of Non-Perception" (SONP). In the case of red a SONP exists when we are not viewing the red thing. Before science developed new transducers, X-rays, radio waves, etc. existed in a Permanent State of Non-Perception (PSONP).

(p. 185) Feigenbaum: "There's a fundamental presumption in physics that the way you understand the world is that you keep isolating its ingredients until you understand the stuff that you think is truly fundamental. Then you presume that the other things you don't understand are details."

RESPONSE: And when the foregoing process is properly followed, especially as shown by relativity and quantum mechanics, it becomes clear that a SFLIHM is fundamental and everything else is detail. Physicists might think this is a misapplication of their discoveries and efforts since meaning of human life is a philosophical/religious issue. But without the achievements of physicists we could not possibly have gotten to this truth. Philosophy and all traditional religions lead in other directions.

(p. 227) "...when a geometer iterates [uses result as input] an equation instead of solving it, the equation becomes a process instead of a description, dynamic instead of static."

ROBERT STETSON SHAW

(p. 243) Robert Stetson Shaw was a graduate physics student at the University of California at Santa Cruz. In 1977 he ran Lorenz's equations on an analog computer and became fascinated with the butterfly attractor in 1977. His efforts helped advance chaos theory.

(p. 255) "The most characteristically Santa Cruzian imprint on chaos research involved...information theory, invented in the late 1940s by...Claude Shannon."

Information was not, "facts, learning, wisdom, understanding, enlightenment....[but] bits [which] became the basic measure of information."

(p. 264) Shaw studied dripping faucets. "Shaw's model was exactly crude enough to be summed up in three differential equations, the minimum necessary for chaos, as Poincare and Lorenz had shown."

(p. 251) Norman Packard (UC Santa Cruz): "The phenomenon of chaos could have been discovered long, long ago. It wasn't in part because this huge body of work on the dynamics of regular motion didn't lead in that direction....It brought home the point that one should allow oneself to be guided by the physics, by observation, to see what kind of theoretical picture one could develop."

(p. 250) J. Doyne Farmer (UC Santa Cruz): "You're taught [in physics] that there are classical models where everything is determined by initial conditions, and there are quantum mechanical models where things are determined but you have to contend with a limit on how much initial information you can gather."

Farmer: "On a philosophical level, it [chaos theory] struck me as an operational way to define free will, in a way that allowed you to reconcile free will with determinism. The system is deterministic, but you can't say what it's going to do next."

RESPONSE: Here, again, we see the critical importance of defining terms. Farmer is using free will to mean unpredictable. He uses determinism to mean change that follows a rule. I want to clarify that when we talk about determinism in physics as in human behavior we are only talking about cause and effect. The element of prediction is more complex. We have to be careful to expunge all ideas that imply the ability to predict perfectly and forever. I think, we should adopt cause and effect as the basic concepts for discussing change of any part of the universe: turbulence, phase changes, quantum mechanics, human behavior, etc. Determinism, as it has traditionally been used, is a concept which focuses on reality as the Ultimate Reference System. Cause and effect, are concepts which more clearly take human beings as the Ultimate Reference System.

Cause and effect require a point of view, a way of looking at the universe, a way of interpreting what is happening. It takes as fundamental that the Human Being is the Ultimate Reference System to which everything else must be referred. Human beings impose their interpretations on the universe. These interpretations are always wrong. The thrust of science is the correcting and perfecting of these erroneous interpretations. However, scientists have always thought reality was the coordinate system to use for measuring things. They all have a strong weakness for thinking they have arrived at the "correct" interpretation rather than recognizing that they have "only" moved in the right direction.

I start with Immanuel Kant's convention for thinking about cause and effect: "Everything that happens presupposes something which it follows according to a rule." We may through study understand the rule to varying degrees. But these rules do not guarantee predictions. Our ability to predict the future is limited by all the things chaos theory, quantum mechanics, and relativity show us.

(p. 275) Bernardo Huberman of Xerox Corporation's Palo Alto Research Center in 1986 presented a model for the erratic eye movement of schizophrenics based on chaos theory.

(p. 278) "The choice is always the same. You can make your model more complex and more faithful to reality, or you can make it simple and easier to handle. Only the most naive scientist believes that the perfect model is the one that perfectly represents reality. Such a model would have the same drawbacks as a map as large and detailed as the city it represents...."

RESPONSE: The map is not the territory, and the only thing human beings can have is a map of the universe. They cannot have the universe itself.

It is my opinion that persons err when they think they are seeing a reference system called "reality." Rather they are imposing a reference system called human beings on a complex, multi-dimensional, "unknowable" reality. When the foregoing is done it is easier to overlook the importance of ignorance. If we think we are seeing reality then, Where is there room for ignorance? If we know we are imposing our coordinate system on the "unknowable" then we are aware at every step that there is ignorance. We are more apt to remember that no matter what we say it will be wrong, but with luck it will lead in the right direction, toward TRUTH. But more important we will be forced to remember that our primary goal is a SFLIHM and this means using whatever knowledge we have to this end.

However, potentially a map can be bigger and more detailed than the territory it represents. But, of course only in the ways currently understood.

(p. 292) Arthur Winfree: "Dynamical things are generally counter intuitive, and the heart is no exception."

"...physiologists have...[begun] to see chaos as health. It has long been understood that non-linearity in feedback processes serves to regulate and control....[A] linear process, given a slight nudge, tends to remain slightly off track. A nonlinear process, given the same nudge, tends to return to its starting point."

(p. 293) "Mode locking [or entrainment] accounts for the ability of groups of oscillators, including biological oscillators, like heart cells and nerve cells, to work in synchronization."

"With all such control phenomena, a critical issue is robustness: how well can a system withstand small jolts. Equally critical in biological systems is flexibility: how well can a system function over a range of frequencies. A locking-in to a single mode can be enslavement, preventing a system from adapting to change. Organisms must respond to circumstances that vary rapidly and unpredictably; no heartbeat or respiratory rhythm can be locked into the strict periodicities of the simplest physical models, and the same is true of the subtler rhythms of the rest of the body."

(p. 303) "Two decades ago....most practicing scientists shared a set of beliefs about complexity....Only later did it become possible to say what these beliefs were and to bring them out for examination."

1). "Simple systems behave in simple ways."

2). "Complex behavior implies complex causes."

3). "Different systems behave differently."

"Now all that has changed. In the intervening twenty years, physicists, mathematicians, biologists and astronomers have created an alternative set of ideas. Simple systems give rise to complex behavior. Complex systems give rise to simple behavior. And most important, the laws of complexity hold universally...."

(p. 306) Roderick V. Jensen of Yale University is a theoretical physicist exploring the possibility of quantum chaos. ("Classical Chaos," AMERICAN SCIENTIST, April '87, p. 168-181) [I have studied this reference. It is interesting, but there is still much to be done on this approach -- that quantum mechanics deals with chaotic phenomena rather than random phenomena.]

(p. 307) "Chaos was the set of ideas persuading all these scientists that they were members of a shared enterprise. Physicist or biologist or mathematician, they believed that simple, deterministic systems could breed complexity...."

RESPONSE: One thing CHAOS shows very strongly is the negative effects of tight boundaries between the various specialties or fields of science. We see how this separation retards the advancement of each specialty. Each area of science is working on its particular path toward TRUTH. Each has something important to say to the others. Without cross communication all advancement is retarded.

This lack of communication makes it easier for scientists to miss the point that it is not the mastery and advancement of one's field that is of primary importance, but the application of that knowledge to the improvement of the human condition, the achievement of a SFLIHM by more and more people.

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1. CHAOS: The Making of a New Science, James Gleick, Penguin Books, New York, 1987.

3. Economists expected prices to follow the bell shaped curve -- Gaussian distribution, normal distribution -- characterization of randomness. They didn't.

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