Op Art and More 

Under the menu item "Fatou", the formula (z3+c)/z showed Daphnia-like structures in the area with converging values enclosed by the Julia set, which is called filled-in Julia set here, which became visible by a mathematical distance calculation which is actually not allowed (see menu item "Fatou" - Fuzzy distance). The self-similarity of these "Daphnia" was the reason to investigate these structures in more detail.

In the following some videos are shown, which show the changeability of these structures. Since algorithmic art is a main focus of the website opartandmore, in a mixture of artistic freedom and scientific point of view, an attempt of interpretation is made for each video, through which a relation to our own world, which is perceived as real, could be established, even if it already seems quite surreal. The interpretations made are extremely speculative. They shall show here a way to make possible nonlinear fractal functions as an instrument for mapping the universe. If this text seems incomprehensible or boring to you, you can start the following videos from the video directory directly.

1. Space and time - a first approach

Since the calculation of the fractal function (z³+c)/z is based on the field of the complex number, the surfaces shown in the videos or photos do not represent an image of the conventional 3-dimensional world known to us and also not of the conventional 2-dimensional view. Instead, only the central axis from left to right exactly through the center represents our conventional known world in, however, only 1 dimension, i.e., actually, our descriptive 3-dimensional world is reduced here to only one space dimension, because already for the representation of complex number of the 1st dimension, a 2-dimensional plane is needed. All other pixels outside this central axis represent the imaginary area which results from the arithmetic operations of the complex number. To every real number (or Koordinate of our world perceived as real) on the central horizontal axis exist infinitely many imaginary number, which are arranged to it in the right angle according to their value as imaginary coordinates.

My interpretation of these imaginary values for our own world assumes assumes that the representation of the values, i.e. of the colors, on the the central horizontal axis represent a 1-dimensional image of our 3-dimensional world. Here the yellow and red mean unstable chaotic structures with values which strive towards infinite. They could be outside the expanding space of the universe. The areas with blue tones represent stable converging values, which lie within our expanding universe. See Figure 1.


Thus, the central horizontal line with its coloring could be regarded as the 1-dimensional map of our universe at a fixed point in time (without taking into account the effects of the properties of the speed of light), with an observer looking at the universe from the outside. The blue zones on the horizontal axis would then correspond to our universe with the physical laws known so far. Each left and right point on this line, which makes the boundary between stable zone and unstable zone, represents then the spatial boundary of the universe with the known physical laws, however without consideration of temporal or other spatial aspects. To the zone beyond the boundary of the map of the 1-dimensional universe no further statements can be made on the basis of this formula, because all values wander into the infinity; these areas of the world would then elude the physical laws known to us. Since our real universe expands and experiences a limitation by the speed of light in the form of an event horizon, also the real boundary of our observable universe from the earth cannot be made to coincide in contrast to the 2 boundary points of the 1-dimensional representation shown here. This means that the event horizon of the universe known to us measurable by us would be in the inner area of the blue area on the central axis.

Now the question arises, how can one interpret the colored lines parallel to the central axis with their imaginary values, which lie below and above the central horizontal axis and altogether result in an area picture, which probably opens up to our eye as an overall picture, whereby however its possible meaning does not become directly recognizable? Each parallel line seen from the central axis can be interpreted as a parallel world with identical time reference, as they are seen by the quantum physicist Hugh Everett as parallel worlds to our own world. A distance between 2 lines seems optically not to exist, but this is caused by the limitation of the pixel representation. Mathematically, between every 2 parallel lines there exist an infinite number of further parallel lines and thus also an infinite number of parallel worlds, which is shown in the videos in detail enlargements, where instead of one line a multitude of new lines with partly different details emerge. As the pictures and videos show, however, there are - apart from some chaotic structures - relationships between the parallel worlds, which show themselves to the eye as coherent two-dimensional formations. Thus at many places a natural order between the diverse parallel worlds results, caused by the formula (z³+c)/z, opposite to the central world line perceived by us as real.

The first video shows the connection between the parallel worlds also with variability as well as with section enlargements. The calculations are based, as far as not explicitly mentioned, all on application of 70 iteration steps on the formula at each single image point.
This world view with infinitely many parallel world lines to our own world line perceived as real could also describe the effects on some quantum physical processes as in the double slit experiment of Thomas Young or the probability of existence of an electron. The time-independent form of Erwin Schrödinger's wave equation , which describes the propagation of an electron as it travels through the double slit as a timeless wave, leads to a visible result when the electron is registered by an observer with the collapse of the wave. As a consequence of the Schrödinger equation, which is independent of the dimension of time and thus fits to the world map of parallel worlds with absolute time, the wave travels instantaneously through the whole real universe including the existing slits of the double slit experiment. However, since the universe does not only consist of the world line perceived by us as real, but also of all other uncountable many imaginary world lines which should also be covered by the wave equation, the wave also passes through all other world lines of the world map including all double slits existing in any worlds.

The world map of all (1-dimensional) parallel universes shows world lines which are very close to us and have a high similarity to our own world line, as can be seen from the optically connected structures of closely neighbouring world lines. In an extended double-slit experiment, it might therefore be possible to transfer a particle from our own worldline to a neighbouring worldline by an experimenter. In the neighbouring worldline, an only marginally different experimenter with an only marginally different experiment would also be engaged in transferring his particle to another worldline as well. So that the results of the experimenters do not neutralize themselves, a stochastic process would have to cause the control of the release of an electron gun with the emission of a single electron in each case several times in succession randomly as e.g. with the radioactive decay. If one finds that a triggered electron is lost and does not arrive at the projection plate of the double-slit experiment, then this is a clear indication that the electron may have arrived at the marginally different projection plate of a parallel world. And vice versa, it should be possible to determine that single electrons hit the projection plate of our own world line, caused by experimenters of other world lines, even if the electron gun of our own world line did not fire a shot. If this experiment should succeed, then this would be the proof of the real existence of parallel worlds as described by Hugh Everett.

I don't like to think at all about the philosophical consequences with regard to spirit, thoughts, consciousness or the being as such, which can result from the infinitely many parallel worlds. But what does reality mean here? Also the world perceived by us as real is based on the ideas in the consciousness of an I, which cannot be found itself and therefore proves to be an illusion. What therefore has to be proved is only that reality which results from the perceptible effect. There it is irrelevant whether effective things happen in the world perceived by us as real or in a parallel world.

Also the consequences for the quantum vacuum would have to be considered. Possible would be the existence of only one quantum vacuum, which takes all parallel worlds into itself and represents the projection surface for all appearances, to which then also time and space belong.

Moreover, a demarcation between the field of the complex number with their property of infinite number between two arbitrarily neighbouring number on the one hand and the Planck scale determined in physics with its finiteness on the other hand would still have to be examined. If the Planck scale is applicable also to parallel worlds, then there is a natural boundary below which no further parallel world exists. Between these directly adjacent parallel worlds, however, fluctuations and fuzziness should then be possible similar to our own physical world.

But the time is not ripe at the moment to make such considerations, as long as not further evidence for the reality of parallel worlds is to be recognized.

2. Time - another approach

Mutability as in the first video has something to do with the expiration of time, which, however, is not directly visible on the spatial world map of the parallel worlds with its one absolute point in time. As a dimension of time, the viewer of the video gets the perceived passage of time. The passage of time on the world map of parallel worlds is therefore correlated with the passage of time felt by the viewer through the sequence of video images. A progression of the time felt by the viewer is then also equivalent to a progression of the video sequence, i.e. to the progression of an absolute time uniform for all parallel worlds from one point of time to the next. For all parallel worlds the representation then gives the view of the viewer at each felt time to an absolute total world time (without consideration of the connections of relative space and relative time).

From the mathematical point of view, the same is valid for the course of time as for the space, i.e. between every 2 points of time there are infinitely many further points of time which lie in between. This mathematical view does not consider here the limitations occurring in the real world with its physical laws like Planck time or Planck length, since the field of the real and complex number do not know such limitations. This can be also an indication that below the Planck scale other, up to now unknown physical laws are valid, as is assumed e.g. by the physicist Brian Greene (The Fabric of the Cosmos: Time, Space, and the Texture of reality).

The succession of time is caused in the formula (z³+c)/z used here for the Julia set by changing the term "c", in that this is no longer regarded as a constant, but is varied as a function of the time c(t), e.g. by simple addition of an increment at each individual video frame within a range of values at which representable results for the total picture of all parallel worlds arise. The temporal value range at which stable zones are created in the parallel worlds is limited. The sequence of the following 3 pictures shows as example for c the values c = -0.1E-66 RE, then c = 0 RE and in the 3rd picture c = +0.1E-66 RE (these are floating point number, where the number behind the E represents the number of shifts of the comma. Example: 0.1E-1 corresponds then to 0.01 and RE stands for the real part of the complex number). The lower picture with the time 0 RE leads because of the hyperbolic term in the formula to inadmissible zero division, why here except "infinite" or "undefined" no further statement can be made. But already the unimaginably small difference of 0.1E-66 with respect to 0, which seems to be smaller than the constant number part of the Planck scale, leads to the formation of stable structures (blue formations).


The variation of c as a temporal function c(t) can, as a consequence of the hyperbolic part (division by z) in the formula (z³+c)/z, result in time sequences where few changes can occur and then also in time sequences where extremely many changes occur within the smallest time differences, as in the example with frame sequence 2. Therefore, no constant change of time is made in the videos, but depending on the situation, a stretching or compression of time to the time measure of the videos with their 25 frames per second is carried out, i.e. for the observing viewer with his perceived uniformly running time, this results in time lapse or slow motion and, in the case of detail enlargements, also in time standstill.

This procedure is not unusual. Also with the representation of the development of the earth with its geological processes and the development of the life the time course of the drift of the continents is represented with fast time lapse, while on the other hand on this scale the extremely fast running development of humans is stretched opposite to it, so that a changeableness meaningful for the time feeling of humans results. The video 1 shows therefore the course of the time c(t) beginning from 0.1E-66 RE to approx. 0.1 RE in different time increments. The time "t" is changed in this video exclusively on the real axis. However, just as imaginary values can be made out as parallel world at the space axis, there is nothing against to use also imaginary values at the time axis, as it was done by the physicist Stephen W. Hawking (A Brief History of Time) to avoid singularities at black holes. One could do something similar here with the real value c(t) RE = 0, by setting then the imaginary value c(t) IM unequal 0. Then one could make statements about parallel worlds at the forbidden time 0 in the absolute real time. But more about this later. In video 1, starting from the time 0.1E-66 RE, the time up to the time ~0.1 RE was made in strong time lapse. There, time was stopped at ~0.1 RE to perform cropped enlargements of the Daphnia formations, revealing the first unstable zones (Fatou sets) within the stable Julia surface. This was followed by zooming back to an overall image. The time arrest was then resolved again. At time ~0.15 RE, the Julia surface began to dissolve into sub-surfaces, with increasingly unstable structures emerging. Into a spiral-shaped structure a zoom was then carried out once again. At the brief pause of the image there, time was again paused to allow the spiral structure to be examined. With the time stopped, the number of iteration was increased from 70 to 200, whereupon, due to the higher accuracy of the iterative calculation, it became apparent that apparently stable blue areas changed into an unstable state. After this, the iteration depth was returned to 70 for better comparability with the rest of the time course. After resuming the time course, almost all structures dissolved until at time ~550 RE the video recording was stopped.

The occurred changes in the spiral structure as a result of a changed number of iteration lead to the actually not admissible interpretation whether the number of iteration itself does not represent an own time dimension with "discrete time interval", which runs linearly independent of the conventional time axis. But more on this later.

The video 1 also shows that in the further course of time within the stable zone in the parallel worlds as well as the 1-dimensional world represented as real, increasingly circular areas (red and yellow hues) with unstable values appear, which are not yet visible at the beginning of the video sequence, but which should already be present with sufficient detail enlargement with the Daphnia formations as a kind of crystallization points also directly at the beginning. An interpretation of these unstable formations could be that here singularities become indirectly visible like with black holes in our real universe.

First, however, the question arises, how does the temporal development of the parallel worlds run, if one changes the sign, i.e. the time's arrow, with the temporal increment, i.e. the time direction is mirrored? In the development state of our real world the change of the time direction is possible so far only in the trick film, by letting run a film backwards. Here, for example, one can produce an unbroken glass again from the fragments of a broken glass. Because of the empirical theorem of the increase of the entropy with progress of the time, the time reversal is not possible with the present state of development of our real universe, as Stephen W. Hawking has shown, although the physical laws actually allow a time reversal. Mathematically, however, one can change the time arrow in the world view of the parallel worlds set up here starting from the real time value of the present time 0 RE, by adding the time increments no more, but subtracting. Video 2 shows what happens then.

3. Past or Future

The playback of video 2 begins quite similarly to video 1, where one time increment was added at a time. Also with the subtraction of time increments made here beginning from -0.1E-66 RE again daphnia-shaped structures appear, which become visible with the first zoom, where the time was stopped. However, the structures with the "daphnia" are not completely identical to the first video (see image sequence 2). Noticeable are also symmetrical daphnia with respect to the shape, which are mirrored with respect to their color, i.e. their sign. The difference arises from changing signs in the fuzzy distance calculation. This type of symmetry is not present on the first video with positive increment at c(t). The representation as an overall view already shows clear differences in a comparison between video 2 and 1 (see image sequence 2 below).


Again, with negative increment at c(t), crystallization points appear which show up as circular unstable regions at higher magnification. Also, the double symmetry of the daphnia within an image between positive and negative distance values becomes apparent. Furthermore, the basic image structure is no longer invariant to the number of iteration. Image sequence 3 shows 3 different iteration steps: 50, 51 and 400.


In image sequence 3, the small point-like crystallization spots can also be seen, which form circular unstable regions as the process continues. These crystallization points are initially largely invariant with respect to space and internal structure compared to the iteration steps, which is clearly evident in both videos. The daphnia themselves dissolve with increasing iteration in video 2, while they remain stable in video 1. It is also apparent in video 2 that oscillations occur with 2 phases (rectangular oscillation) that correlate with the increase in iteration by 1 each, but the structure changes minimally at each iteration step. With further reduction of c in the real part, the stable regions increasingly dissolve at constant iteration and, moreover, also become increasingly unstable at deeper iteration, whereby it can be assumed that the increase of instability is due to a bifurcation of the Feigenbaum constant named by Henri Poincaré.

The sometimes voiced criticism that mathematical fractals are solely a result of the limitation of the number space existing in computers as a finite subset of the field of rational number compared to the over-countable field of real number as a result of rounding errors does not contradict the results of quantum physics. Quantum physics describes natural phenomena of smallest units, where a physical limitation occurs by the Planck scale, which is not known in mathematics to the field of the real and complex number, but which can be reproduced only by the special mathematics of quantum mechanics with its partial differential equations or by special wave equations (after Erwin Schrödinger) or also by the matrix mechanics developed by the physicists Werner Heisenberg, Max Born as well as Pascual Jordan. The results of arithmetic operations of nonlinear fractal functions by limited number sets in the computer can be called therefore as fuzzy as the observations of the fuzziness of smallest particles. The criticism expressed by some mathematicians would have the opposite consequence, however, that also our macroscopically perceptible and felt world must be regarded as not real; rather is valid then probably that the field of the real and complex number as well as mathematics must be regarded in their whole as not real, but exclusively as an indication for an approximation to the perceptible. But this is a philosophical and perhaps also a religious topic.

Therefore I rather come back to possible interpretation attempts of the results at video 1 and video 2, which is based here on the principle of parallel world lines. Which relation exists between the increment or decrement related to the direction of the time arrow? And which meaning has the zero division at the time c = ( 0, 0 ) with regard to the world lines (see also lower picture in picture sequence 1)?

4. Interpretation - Emergence and Passing of the World

The increment of the time sequence as in video 1 shows stable structures over "long time", while in the decrement in video 2 very fast unstable and oscillating structures appear. Temporal evolution from a past into a future can be seen as a trajectory of points in a phase space under the increase of entropy starting from a state of smallest entropy into spaces of increasing dimensionality. In contrast, the observed past from a now point represents a definite line of past events. See Roger Penrose (Cycles of Time).

Based on this view of time, the video 1 with its increment in the real part of c(t RE , t IM ) with t RE increasing and t IM constant 0 represents a journey into the past, where the now time for t RE would be 0. The decrement of t in the real part would then be a journey into the future with its many unknown chaotic or oscillating states. Both far future and far past lead in this interpretation to the complete dissolution of stable states. With further increasing increment into the past or decrement into the future, in the form of a boundary value formation, more and more increasing mirror-like point symmetries result (see picture sequence 4), which could perhaps be interpreted as beginning and end of the time of our own world line by unification of past and future. This central point would then represent the situation to the big bang with smallest possible entropy from the view of the past, while mirrored to it from the view of the future timelessness with maximum entropy would be present. Roger Penrose describes in his conformal cyclic cosmology CCC how a new world cycle of the universe can finally form about a phase shift.


Now the state of time at c = ( 0 RE, 0 IM ) has to be interpreted at which a zero division takes place. This moment of time represents the situation at the punctiform moment of the present time and corresponds graphically to the lowest picture from picture sequence 1 with the black inner surface about which no statement can be made as a result of the zero division. The sounds contradictory, since to us as experiencing beings the present time seems to be present, while the future has not happened yet and the past always seems memory reproduction in the mind. Although all our perceptions incl. our thoughts happen on the basis of the now-time, however the now time is already past, if we look at it. Then there is nothing more, because the next future point of time at its perception in the now has already become the past. In Nagaruna's philosophy of the Madhyamaka of the 2nd century one can trace the discussion about the appearance of time that results from the sentence:



Khenpo Tsultrim Gyamtso Rinpoche explains in his work "The Sun of Wisdom" explains the interpretations of Nagarjuna from our modern point of view and leads the philosophical logical proof from the mere appearance of time.

5. Formation of Centers of Gravity

Another interpretation from the formation of the parallel world lines with their interconnected structures could be seen as analogous structures of our own universe. If one compares closely neighbouring world lines with each other large-scale, then the parallel lines are similar to each other, as is shown by the large-scale patterns. Therefore, starting from a 1-dimensional world line, one can infer a fundamentally similar structure in the 2nd and 3rd dimensions. The optical appearance of the 1-dimensional structure of the parallel worlds as an interconnected Julia surface would therefore also have a similarity with a 2-dimensional representation of our own world; it would be similar with the 3rd dimension. The 2-dimensional picture of the Julia surface with its intercalated structures present here would then correspond in its basic features also to the basic structure of our own universe.

The following picture No. 2 shows a section of this basic structure at c = (0.003 RE, 0 IM ) above and below the central world line. The appearing circular formations (embedded Fatou quantities with yellow and red tones) could be interpreted as singularities or black holes, which are the nuclei of the formation of early massive galaxies in the early time of the universe in the environment of mass centers (dark blue). Current research in the field of astrophysics provides evidence that quasars with their growing black holes were formed in the environment of massive regions in the early times of our Universe (10.1038/nature22358 of 24.05.2017).

Figures 3 and 4 below show a 3-dimensional section of the structure of our own real universe based on measurements for comparison.


Between the structure picture No. 2 generated from the formula and the representation of the real measured situation with its 2-dimensional representation of the 3-dimensional space (picture 4) there are of course enormous differences, but nevertheless some rough similarities can be recognized. Provided that this interpretation is correct, then this would have the consequence that the structure of our own universe can be described by correspondingly more exactly adapted non-linear fractal functions. If one goes even further with this interpretation, then one could even say that the origin and the development of our universe happen out of itself on the basis of an inherent, fractal structure formation. But this can be interpreted of course from completely different.

If, however, the formula should give a hint to the structure of our universe, then one can also approach the limit at which a transition to stable structures occurs from the chaos of the situation of the big bang. Figure 5 shows an earlier time c = ( 0.148155 RE, 0 IM ) after 4000 iteration. The blue, apparently stable nuclei are still unstable here, as they again transition to unstable structures at further iteration. This is an indication that all the other stable structures that appear in this formula also become unstable when the iteration are bounded at infinity. Transferred to the real situation in our universe, this would mean that the space structures themselves would be unstable independent of the conventional dimension of time. Then not only space quantities in the range of the Planck scale would be unstable, but also all other space quantities. This would also have consequences for the constancy of our natural constants up to the 2nd law of thermodynamics.

With an interpretation as development of the universe, the picture 5 could represent the state of the universe shortly before the beginning of its transparency, which begins in the blue regions; but this is already very, very speculative.


The following video shows in a section the transition from unstable regions to apparently stable regions. For this purpose, first a time c = ( 0.16 RE , 0 IM ) is set via the term c and then zoomed into a selected region. Starting from this section, time is passed from the past toward the present via a decrement of 0.00001 RE until time 0.149. Thereafter, after reaching larger apparently stable structures, the time sequence is accelerated to 0.0004 RE until a state is reached which - as interpreted above under Fig. 2 - could correspond to the structure of centers of mass. The translational motion from left to right occurring thereby is not caused by changes in the coordinate system, but exclusively by the change of c(t). The image section remains unchanged in the whole video.

6. Imaginary Time

Stephen Hawking introduced the imaginary time to be able to deal better with singularities (black holes). The imaginary time results by assigning to each real time (c RE = t RE) an infinite number of imaginary times ( c IM = t' IM ) by the field of complex number. In the following video, for illustration purposes, the real part of c is set to 0 and instead only the imaginary part of c is ramped up with different increments from 0.1E-66 to 23000. The beginning of the imaginary time travel is quite similar to video 1 and 2. However, already after a short time clearly recognizable different structures appear, where then a zoom takes place. The then made change of the number of iteration shows a different oscillation compared to video 2.

With the imaginary time travel (parallel shift) in direction 23000 a similar basic form arises as also with the positive and negative time travels of our real world with c IM = 0 IM. The imaginary time course in the direction of very high values shows a form becoming more and more harmonious, which one could interpret in the infinity as phase of smallest entropy, provided that the entropic principle still has a validity here at all (compare also with picture sequence 4). It would correspond to the view on the world before the big bang or also as on the world after its complete dissolution and before the next world cycle (according to Roger Penrose; the problem to the entropy is solved by Roger Penrose by a change of scale with which the mass centers of the past universe continue to exist as crystallization centers for the galaxy formation in the new universe of the next world age).



Oscillations seem to occur with almost all time variants, with which the imaginary part is different from 0. Only with an imaginary part of 0 and a real part of the time in the area of the past as well as in very near surroundings of this no oscillations are to be found, as far as this was examined here. This behavior would correspond then to the course of the temporal development represented by Roger Penrose in a configuration space, in which the past is the only one unique.

The influence of the number of iteration is immense for the determination of results with the computation of non-linear discontinuous functions. Further above it was already suggested whether a hidden linearly independent 2nd time axis could hide behind it, which we do not perceive in our natural world and also cannot prove up to now. In smallest scales hidden time dimensions would be conceivable in our real world in the 6-dimensional Calabi-Yau spaces discovered by the mathematicians Eugenio Calabi and Shing-Tung Yau. In the videos, not only chaotic processes become visible during iteration, but also largely stable forms appear with the singularities and differently oscillating rectangular oscillations with sometimes several phases become visible. These oscillations depend on the choice of the term c as a complex number. Thus the choice of the imaginary time has an influence on the oscillations caused by the iteration. Only when looking at the own world line in the direction of the past and also small imaginary time values (<~0.000045) there is apparently a zero oscillation; instead of oscillations then with increasing iteration the presenting forms become more precise.



Video 5 shows the limit range of stable and unstable formations at time with a fixed real value 0.0001 and variable imaginary imaginary values. At the beginning of the video c is ramped up from 0 IM to 0.000045 IM and then a section magnification is performed. There the iteration is increased from 50 to 250 in about 10 sec. and then in a shorter time back to 50. again in a shorter time. With constant iteration of 50 then the imaginary part of c is reduced to 0.00001. Translational movements in this phase result exclusively from the change of c; the selected section selected section remains unchanged in this phase. At c IM = 0.00001 IM, the number of iteration is once again increased within 10 seconds to 300 within 10 seconds and then reduced again in a shorter time to 50 in a shorter time. Finally, the magnification is reduced to an overview image. On the overview image again iteration to 125, so that the effect on the overview image can also be seen.



An interpretation of the iteration as 2nd time axis in the physical sense is difficult. At the moment the comparison with a clock pulse (clock) at electronic circuits (e.g. flip-flops or computers) or in the extreme case as a single clock the life span of our current universe comes to my mind most likely. Provided that at all a physical meaning of this kind can be assigned, this could mean that our world is formed about a clock pulse independent of our own time.

If it would be so, then the questions arise first, which clock pulse we experience just in our world perceived as real, what happens with a change of the clock pulse and how long does a clock pulse last, is there a zero point or a limit value? How do the fundamental physical or other conditions of our world change with respect to the next clock pulse?

But it remains completely open, how can such a linear independent 2nd time dimension with a clock pulse be integrated into a theory of a higher dimensional world (e.g. superstring theory)? Quite apart from the consequences for philosophy and religion.




Overall, however, the interpretations listed here should be considered artistic license.


 

Supplements as of Jun 29, 2019:

With regard to oscillations, however, there is a completely different explanation possibility within the framework of quantum physics. The quantum physicist H. Dieter Zeh (Physics without Reality: Profundity or Madness?) describes a quantum field theory where the field amplitudes at all places form the configuration space as coupled oscillators. A consequence of the decoherence concept also developed by him is then also the many-worlds interpretation of quantum mechanics seen by Hugh Everett.

7. Notes on Reality

The blue structures appearing in the videos and pictures and also the oscillations must be owed with a certain probability to the iteration procedure chosen here in connection with the limitation of the numerical model and the floating point operations performed in the processor. The computer scientists Jürg Nievergelt and Peter Schorn (Numerik des Chaos oder Chaos der Numerik) have already shown in 1993 how aspects of the image can change in recursive functions, whereby an actually non-existent chaotic behavior is feigned. This aside, however, the question of reality as a whole is paramount. For the parallel worlds postulated by Hugh Everett, H. Dieter Zeh sees a claim to reality despite the almost infinite splitting up of the world, whereby the individual worlds are considered to be decoupled from each other within the framework of the decoherence concept. According to this, only one world is subjectively perceived as real. But the observer himself is a member of the different partial worlds, even if he can perceive only one of these worlds, so that one has to assume a psycho-physical parallelism, which depends on the state of consciousness of the observer. According to Zeh, the occurring splittings of the observer's state are the actual motivation for the conceptual separation of the worlds. However, it remains open what consciousness actually is.

Interestingly, according to Tulku Urgyen Rinpoche, the Buddhist teachings of Dzogchen also describe an extreme parallelism of universes contained within an all-pervading Dharmakaya. With a nondual awareness practice, a direct perception of the Dharmakaya can occur by the observer in the moment of non-observation. However, since the observer has dissolved in the process, he is no longer able to observe or report anything. The true observing access to the parallel worlds but also to the own world therefore remains denied to him.

With the decoherence concept H. Dieter Zeh has eliminated the inadequacies of the Copenhagen interpretation with his interpretation of quantum physics and has assigned a prominent role to consciousness. The quantum physicist Amit Goswami (The SelfAware Universe) goes one step further with an interpretation of quantum physics which is to be regarded as complete, by considering consciousness as the only remaining element of being. The up to now materialistic views are replaced thereby by purely spiritual working. Matter represents then only a form of consciousness. Thus he transfers the interpretation of quantum physics directly into the mind-only doctrine of the Tibetan Buddhism Chittamatra of the Yogacarins, whose contents and conclusions arise from the Lankavatara Sutra of the 4th century. The short formula of this new interpretation of quantum physics is then:

The short formula of the Chittamatra is practically identical:


The Madhyamaka philosophy of Nagarjuna, however, goes a small step further. According to this, the world, all things, space, time, movement, the ego and even the mind exist only in appearance. The mind and also consciousness are considered as non-existent, but at the same time also as non-existent, neither existent nor non-existent and also not as its opposite. Only consciousness can be experienced. The short formula of the Madhyamaka is therefore:


Between the followers of the Madhyamaka and the Cittamatra there were extensive disputes about the correctness of the respective philosophy commented by Vasubandhu and Shtiramati, which were translated from Sanskrit into English by Th. Stcherbatsky (Madhyanta-Vibhanga Discourse on Discrimination between Middle and Extremes). Contemporary Tibetan Buddhism, according to the Dalai Lama (The World of Tibetan Buddhism), invokes a special interpretation, the Prasangika-Madhyamaka, which reads in short form:



Only with this special interpretation of the Dalai Lama alone, which is incomplete in my personal opinion, one would make a not necessary restriction against the pure Madhyamaka of Nagarjuna and also the interpretation of other Buddhist teachers as for example Khenpo Tsultrim Gyamtso or Chögyam Trungpa. Also this short interpretation of this Tibetan Buddhist teaching by the Dalai Lama seems to contradict the measuring results of quantum physics with regard to non-locality and coincidence. H. Dieter Zeh however describes in his interpretation of quantum mechanics in a quantum field theory superpositions (superpositions of states) in a single quantum world which also includes all parallel worlds. This quantum field theory with its superpositions sees this one quantum world with its parallel worlds as a basis, in which the observations like to the non-locality or to the coincidence are valid only the result of the limitedness of the local observer in this one from all other parallel worlds separated, but experienced world. Even if herewith the view of the Tibetan Buddhism with the Madhyamaka and even with the Chittamatra can be brought together again with the interpretations to quantum physics by H. Dieter Zeh and Amit Goswami, nevertheless, in the end it remains open which of the 3 here mentioned philosophies of Buddhism, beside still existing further views, represent the reality in the best possible way. That lies then probably also in the freedom of decision of the examining consciousness of the individual.

A complete quantum field theory, which still goes beyond the view developed by Zeh, was developed by Burkard Heim and Walter Dröscher, in which the material world, the quantum mechanics and also the spiritual world are described together unified in a 12-dimensional mathematical tensor model. In this tensor model possibly even the above mentioned clock pulse could be described in the sense of a linearly independent time component, however, the difficulty would still be to recognize the mode of action of a clock pulse in the world perceptible by us.

For the individual, the path of cognition remains the nondual awareness practice (As It Is) taught by the Dzogchen teacher Tulku Urgyen Rinpoche, in which all questions dissolve at the moment of cognition. This is also symbolized by the 8th ox image in Zen, where man and mind are "lost" in emptiness. This symbolic picture of emptiness coincidentally shows a great similarity with the fractal function considered in this essay in its 0-state, which corresponds with the interpretation made here to the apparent moment of the present time (compare last picture of the picture sequence 1).