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The author gave instructions for building a fractal surface in two dimensions which he called the snowflake curve. I had to draw one for myself to convince myself that such a beautiful curve could evolve from a simple series of nested equilateral triangles, a beauty is only hinted at by the four stages of drawing of the one in the book on page The snowflake curve is an infinite perimeter bounding an obviously finite area.
It reminds me of the small state of Rhode Island which claims to have miles of seashore. Seashores are fractals, rightly understood, and depending on how small you make your measurements, you can make the perimeter of a fractal area grow as large as you wish. The "butterfly effect" states that something as minute as the wind current from some butterfly's wings could trigger a sequence of events that could result in a cyclone half the world around.
I believe the author overstates the case when he refers to the impossibility of identifying one particular butterfly's wing movement as the cause of a particular storm. To my way of understanding the "butterfly effect", that is not a requirement, stated or unstated.
The idea is that the flapping of the wing of a butterfly can completely change the weather at a later date; a distant storm could be produced. The idea is not quite correct, however, as it is impossible to relate the flapping of a particular wing to the production of any particular effect such as a storm. Next Friedjung takes the reader through a review of my own favorite paradoxes of modern physics, the double-slit photo experiment and the Einstein-Poldosky-Rosen measurement paradox. Unfortunately his use of water waves instead of photons tends to obscure the intrinsic beauty of the double-slit experiment.
If you open a slit and allow one photon to pass through the slit, you will see a scintillation event on the screen corresponding to that one photon of light.
If you open a second slit off to the side of the first slit and repeat the experiment several times, you will see a photon blink behind the original slit sometimes and other times, you will see it blink behind the other slit. And you will not be able to predict which slit it will appear behind.
To understand what is happening, you need a little short course in QED , the mouthful of words created by Richard Feynman, Nobel laureate in physics, quantum electrodynamics. His basic rule is this, "A photon goes from place to place. But there is only one screen and his other rule tells us, "An electron emits or absorbs a photon.
Then the electron on the screen emits the photon and we see a scintilla of light with our eyes. Physics was based on the study of bodies which exist in space and time, only taking into account their spatial properties and their properties in time as measured by clocks, that is, those properties which can be described by the space-like aspects of time. In addition physical phenomena were studied to a greater and greater extent by instruments, thus bypassing direct human perception as much as possible.
Moreover, as the power of instruments was increased, it became more and more possible to study many phenomena which cannot be studied by other methods, such as those which occur on very small scales, which are generally believed by physicists to be fundamental. Therefore, what was studied was the interaction of the matter participating in a phenomenon with the matter associated with a measuring instrument.
This would be equivalent in my computer metaphor above of the computer believing that its instruments gave it the best view of the world which existed outside of its computer box, because after all, humans used computers to measure things accurately.
What humans used to measure the world has never been incorporated into the BS of physics and never will, because the very machines humans build lack the threefold human structure of body, soul, and spirit, each fold able to have direct experiences that no machine now or ever will have. With the loss of Newtonian and Laplacian predictability of the world, we have re-gained the possibility that there are "infinitely more things in heaven and earth than exists in our philosophies," as Shakespeare so aptly put it.
As a fan of science fiction from the age of seven, I was intrigued by the possibility of invisibility, particularly the "invisible man," which shows up in recent fiction as the invisibility cloak of Harry Potter. It was a shock to me recently to discover that to be invisible, means that no portion of one's body is visible, which means that all light passes unimpeded through the body. If one's body provides no resistance to light, then light passes unimpeded through one's retinas and therefore one is completely blind!
This illustrates the importance of the resistance provided by a measuring instrument -- no resistance, no measurement! It is this basic resistance which limits the accuracy of measurement, while the highest possible accuracy in measuring all the properties possessed by any physical object according to pre-twentieth century physics, would be needed to predict its future behavior and so to know everything about it. What all this discussion misses is a human being is the most sensitive instrument in the world, far surpassing any man-made instrument, and each of us owns one free and clear.
I recall the story about the man who returned his computer for another one because it was still under warranty. This is a consequence of the free will that each of us were provided with. No one forces us to use our human measuring and perceiving equipment in any way but the way we choose to use. An astronomer can look through the Hubble Telescope and see the very edge of our local universe, but Rudolf Steiner using his human capability was able to look to very edge of time in both directions to perceive and describe to us the beginning and ending of our Earth evolution in our local cosmos 3.
His measurements and perceptions cannot be confirmed by man-made instruments for the simple reason that no one has ever made an instrument as sensitive as the human being. And what Steiner did is a human capability available to every one of us, available for our use , if we choose to use it. The following is one of the points of lights shining at us from Friedjung's book, the metaphor of "happiness imprisoned in a constant of physics.
We would live in the world envisioned in the recent movie, "A. The world where this principle is important can be clearly pictured as being a world of cold resistance with happiness imprisoned inside a constant of physics, and can also be conceived of as a world of Ahriman.
Indeed, it was through such a picture that the author of this book was able to more clearly understand what Rudolf Steiner meant when he discussed the nature of Ahriman. In Danah Zohar's book, The Quantum Self , she lays out a theory of consciousness based on a new discovery in physics of correlated phase states in living tissue.
I wrote in my review of her book:. Previous to his discovery these were thought to exist only in superfluids and superconductors -- at very low temperatures. These correlated phase states in our cellular structures, Zohar suggests provide the physical basis for the phenomena we know as consciousness. Like a celestial choir of a myriad of voices each voice a cellular molecule - we have consciousness.
Our very thought exists as the chords sung by this multitudinous choral array. It is possible to state the aims of this book in another way. The well known twentieth century philosopher Karl R. The first is the physical world or world of physical states. The second is the world of mental states, while the third world is that of ideas in an objective sense, which can be possible objects of thought.
When we examine the worlds of inner experience we find that when they are considered by themselves they also have a threefold character, so that three different aspects can readily be distinguished. These laws, as now understood, are not the mechanical laws of nineteenth century physics, so materialism is no longer mechanical. Some scientific colleagues are adherents of spiritual movements; they often appear to me to have split their activities and perhaps their personalities in two, without much connection existing between the two halves. Certain new substances are much used in contemporary medicine. In Danah Zohar's book, The Quantum Self , she lays out a theory of consciousness based on a new discovery in physics of correlated phase states in living tissue. This technology has very much influenced the daily lives of people. The snowflake curve is an infinite perimeter bounding an obviously finite area.
This indicates that the second world is that of subjective experience, while the third world is that of pure ideas, which show themselves in human culture. Each human being must then possess his or her own second world, which will be different from that of any other human. This means that there will not be one second world in this framework, but rather a very large number of second worlds.
According to Popper, the first two worlds can directly interact with each other, while the last two can also do so in a similar way. The mind provides an indirect link between the first and third worlds; the ideas of the third world can be made material through technology. Popper states that the third world is a product of human activity.
If we try to understand present-day science in the framework of Popper's ideas, we might say that it is a science of the first world obeying the mathematical laws of the third world. This science then eliminates the second world. However for him the third world is the eternal world of "Platonic" ideas, which is independent of human beings and includes the unchangeable concepts of mathematics. According to Penrose, the Platonic world gives rise to the physical world, because nature is describable in a mathematical way.
The latter gives rise to the mental world, which in turn again gives rise to the Platonic world. His scheme is like that of a serpent chasing its own tail. Roger Penrose is more open-minded than most contemporary scientists and his reputation is not always good in official circles for that reason. In particular he believes that human thinking cannot be reproduced by the kind of computers constructed up to now.
However he runs into a barrier, as he still appears to consider reasoning based on the world of physics as fundamental. Apparently he is not able to completely abandon the basic assumptions of present-day science. He emphasizes in his book that inner experience cannot be explained by physics. It is very easy to see that the three worlds correspond to the traditional idea of body, soul and spirit. This threefold scheme was forgotten, if not suppressed, in western culture, in which the dualism of body and soul was taught for a long time, until the soul was then also eliminated by materialism.
However the reality of the threefold nature of experience has forced its reappearance in contemporary thought. In this book I endeavor to show that the soul, or second world, is basic; it is present in certain ways also in the two other worlds. It is only when this is taken into account that a fundamentally different kind of science can arise. It is not sufficient to produce some sort of unorthodox physics, as is often done by people trying to prove that something "spiritual" exists, if soul and spirit are left out.
The universe has, in fact, a threefold trinitarian nature, revealing itself in several different ways. Such ways of thinking about the Universe will be discussed in this book. In order to progress in the kind of work this book is concerned with, we must be very precise.
It is not sufficient to talk vaguely about the soul if we wish to be scientific about it and attempt to lay the foundations of a new science. We must therefore clarify the nature of the world or rather worlds of inner experience, or soul, which I shall consider to belong to many sorts of conscious beings. My approach to this question has been inspired to a great extent by Rudolf Steiner, the Austrian philosopher and spiritual teacher, already mentioned in the preface to this book. When we examine the worlds of inner experience we find that when they are considered by themselves they also have a threefold character, so that three different aspects can readily be distinguished.
Both perceptions and concepts are experienced in the inner world. Other quite different ways of arriving at knowledge are conceivable however. These three aspects can be related to thinking, feeling and willing. The idea that the human soul possesses these three abilities is relatively new. He defines in this connection the will as the ability to be active, excluding the abilities of representing things making mental images of them and thinking. This book is the result of thinking for many years about the apparent contradictions between what is accepted as scientific knowledge and various forms of spiritual teaching.
These include the "anthroposophy" of Rudolf Steiner, to which I shall refer fairly frequently in the book. These contradictions have preoccupied me since late childhood. Some scientific colleagues are adherents of spiritual movements; they often appear to me to have split their activities and perhaps their personalities in two, without much connection existing between the two halves.
The problem is that modern science is based on materialistic assumptions; it supposes that the whole Universe is, in the last instance, explainable by the laws of physics. Such laws are "blind", not requiring any conscious participation. Human beings are then considered to be only very complicated machines. On the other hand, many kinds of spiritual teachings exist.
Most religions speak about God or about gods who rule over the world. The existence of non-material components of the Universe like souls, spirits and non-material places that humans can inhabit after death is emphasized in spiritual conceptions, and spiritual development through meditation is sometimes recommended.
Usually only the results of materialistic science based on apparently rigorous methods are considered in the present-day world to be "true", although they seem in many ways to be inhuman, while spiritual ideas, often taught in a dogmatic way, are thought to be mere superstition. Indeed one can argue that differences in religion and religious dogma have in many situations been good excuses for violence and massacres. It should be emphasized that among spiritual teachers Rudolf Steiner in particular spoke of paths of human development leading to the ability to obtain rigorous scientific knowledge of spiritual truths including, for example, those concerning the spiritual evolution of the Universe and of human beings.
This characteristic is certainly a good reason for paying special attention to him.